From ea64f11a2c48affac89dd2b61980443ce42fd995 Mon Sep 17 00:00:00 2001 From: Daniel Kotik Date: Sat, 22 Feb 2020 14:35:16 +0100 Subject: [PATCH 001/145] Change version number to 1.5-beta --- Airy_2d/Airy2d.py | 4 ++-- Gauss_2d/Gauss2d.py | 4 ++-- Laguerre_Gauss_3d/LaguerreGauss3d.py | 4 ++-- 3 files changed, 6 insertions(+), 6 deletions(-) diff --git a/Airy_2d/Airy2d.py b/Airy_2d/Airy2d.py index a058211..da232eb 100644 --- a/Airy_2d/Airy2d.py +++ b/Airy_2d/Airy2d.py @@ -5,8 +5,8 @@ brief: Python configuration input file for the FDTD solver Meep simulating the scattering of an incomplete Airy beam at a planar dielectric interface author: Daniel Kotik -version: 1.4.2 -release date: 27.02.2020 +version: 1.5-beta +release date: xx.xx.2020 creation date: 30.11.2019 diff --git a/Gauss_2d/Gauss2d.py b/Gauss_2d/Gauss2d.py index a1407a7..5d1a0f7 100644 --- a/Gauss_2d/Gauss2d.py +++ b/Gauss_2d/Gauss2d.py @@ -5,8 +5,8 @@ brief: Python configuration input file for the FDTD solver Meep simulating the scattering of a Gaussian beam at planar and curved dielectric interfaces author: Daniel Kotik -version: 1.4.2 -release date: 27.02.2020 +version: 1.5-beta +release date: xx.xx.2020 creation date: 17.12.2019 diff --git a/Laguerre_Gauss_3d/LaguerreGauss3d.py b/Laguerre_Gauss_3d/LaguerreGauss3d.py index a98dfde..2bedb5d 100644 --- a/Laguerre_Gauss_3d/LaguerreGauss3d.py +++ b/Laguerre_Gauss_3d/LaguerreGauss3d.py @@ -6,8 +6,8 @@ scattering of a polarised Laguerre-Gaussian beam at a planar dielectric interface (3d) author: Daniel Kotik -version: 1.4.2 -release date: 27.02.2020 +version: 1.5-beta +release date: xx.xx.2020 creation date: 10.01.2020 From 6a557d97b57b3e5aace94e66b9495d8fd0f9a241 Mon Sep 17 00:00:00 2001 From: Daniel Kotik Date: Sat, 22 Feb 2020 14:38:43 +0100 Subject: [PATCH 002/145] Add files beamprofile.py, beamprofiles.pxd --- Laguerre_Gauss_3d/beamprofile.pxd | 9 +++++++++ Laguerre_Gauss_3d/beamprofile.py | 9 +++++++++ 2 files changed, 18 insertions(+) create mode 100644 Laguerre_Gauss_3d/beamprofile.pxd create mode 100644 Laguerre_Gauss_3d/beamprofile.py diff --git a/Laguerre_Gauss_3d/beamprofile.pxd b/Laguerre_Gauss_3d/beamprofile.pxd new file mode 100644 index 0000000..78818e2 --- /dev/null +++ b/Laguerre_Gauss_3d/beamprofile.pxd @@ -0,0 +1,9 @@ +# -*- coding: utf-8 -*- +""" +file: beamprofile.pxd +brief: ... +author: Daniel Kotik +version: 1.5-beta +release date: xx.xx.2020 +creation date: 22.02.2020 +""" \ No newline at end of file diff --git a/Laguerre_Gauss_3d/beamprofile.py b/Laguerre_Gauss_3d/beamprofile.py new file mode 100644 index 0000000..a122e63 --- /dev/null +++ b/Laguerre_Gauss_3d/beamprofile.py @@ -0,0 +1,9 @@ +# -*- coding: utf-8 -*- +""" +file: beamprofile.py +brief: ... +author: Daniel Kotik +version: 1.5-beta +release date: xx.xx.2020 +creation date: 22.02.2020 +""" \ No newline at end of file From d90f17c2a8b70368841039bfc222371bf3551eff Mon Sep 17 00:00:00 2001 From: Daniel Kotik Date: Sat, 22 Feb 2020 15:41:24 +0100 Subject: [PATCH 003/145] Refactor code: Put psi_spherical and all subroutines to external file beamprofile.py. This file will then be modified by cython decorators and be compiled by cython to speedup calculation of psi_spherical. --- Laguerre_Gauss_3d/LaguerreGauss3d.py | 54 +------------------------ Laguerre_Gauss_3d/beamprofile.py | 60 +++++++++++++++++++++++++++- 2 files changed, 61 insertions(+), 53 deletions(-) diff --git a/Laguerre_Gauss_3d/LaguerreGauss3d.py b/Laguerre_Gauss_3d/LaguerreGauss3d.py index 2bedb5d..bcb8920 100644 --- a/Laguerre_Gauss_3d/LaguerreGauss3d.py +++ b/Laguerre_Gauss_3d/LaguerreGauss3d.py @@ -55,26 +55,13 @@ import sys from datetime import datetime -from scipy.integrate import dblquad +from beamprofile import psi_spherical +from beamprofile import complex_dblquad print("Meep version:", mp.__version__) -def complex_dblquad(func, a, b, gfun, hfun, **kwargs): - """Integrate real and imaginary part of the given function.""" - def real_func(x, y): - return func(x, y).real - - def imag_func(x, y): - return func(x, y).imag - - real, real_tol = dblquad(real_func, a, b, gfun, hfun, **kwargs) - imag, imag_tol = dblquad(imag_func, a, b, gfun, hfun, **kwargs) - - return real + 1j*imag, real_tol, imag_tol - - def Critical(n1, n2): """Calculate critical angle in degrees.""" assert n1 > n2, "\nWarning: Critical angle is not defined, since n1 <= n2!" @@ -313,43 +300,6 @@ def phase(k_y, k_z, x, y, z): return result - def psi_spherical(r, x, params): - """Field amplitude function. - - Integration in spherical coordinates. - """ - k, m = params['k'], params['m'] - - try: - getattr(psi_spherical, "called") - except AttributeError: - psi_spherical.called = True - print("Calculating inital field configuration. " - "This will take some time...") - - def phase(theta, phi, x, y, z): - """Phase function.""" - sin_theta, sin_phi = math.sin(theta), math.sin(phi) - cos_theta, cos_phi = math.cos(theta), math.cos(phi) - - return k*(sin_theta*(y*sin_phi - z*cos_phi) + cos_theta*x) - - f = (f_Gauss_spherical if m == 0 else f_Laguerre_Gauss_spherical) - - try: - (result, - real_tol, - imag_tol) = complex_dblquad(lambda theta, phi: - math.sin(theta) * math.cos(theta) * - f(math.sin(theta), theta, phi, params) * - cmath.exp(1j*phase(theta, phi, x, r.y, r.z)), - 0, 2*math.pi, 0, math.pi/2) - except Exception as e: - print(type(e).__name__ + ":", e) - sys.exit() - - return k**2 * result - # -------------------------------------------------------------------------- # some test outputs (uncomment if needed) # -------------------------------------------------------------------------- diff --git a/Laguerre_Gauss_3d/beamprofile.py b/Laguerre_Gauss_3d/beamprofile.py index a122e63..cb5ca61 100644 --- a/Laguerre_Gauss_3d/beamprofile.py +++ b/Laguerre_Gauss_3d/beamprofile.py @@ -6,4 +6,62 @@ version: 1.5-beta release date: xx.xx.2020 creation date: 22.02.2020 -""" \ No newline at end of file +""" +import math +import numpy as np +import sys + +from scipy.integrate import dblquad + +def complex_dblquad(func, a, b, gfun, hfun, **kwargs): + """Integrate real and imaginary part of the given function.""" + def real_func(x, y): + return np.real(func(x, y)) + + def imag_func(x, y): + return np.imag(func(x, y)) + + def real_integral(): + return dblquad(real_func, a, b, gfun, hfun, **kwargs) + + def imag_integral(): + return dblquad(imag_func, a, b, gfun, hfun, **kwargs) + + result = real_integral()[0] + 1j * imag_integral()[0] + real_tol = real_integral()[1] + imag_tol = imag_integral()[1] + + return result, real_tol, imag_tol + +def psi_spherical(r, f, x, k): + """Field amplitude function. + + Integration in spherical coordinates. + """ + try: + getattr(psi_spherical, "called") + except AttributeError: + psi_spherical.called = True + print("Calculating inital field configuration. " + "This will take some time...") + + def phase(theta, phi, x, y, z): + """Phase function.""" + sin_theta, sin_phi = math.sin(theta), math.sin(phi) + cos_theta, cos_phi = math.cos(theta), math.cos(phi) + + return k*(sin_theta*(y*sin_phi - z*cos_phi) + cos_theta*x) + + try: + (result, + real_tol, + imag_tol) = complex_dblquad(lambda theta, phi: + math.sin(theta) * math.cos(theta) * \ + f(math.sin(theta), theta, phi) * \ + np.exp(1j*phase(theta, phi, x, r.y, r.z)), + 0, 2*math.pi, 0, math.pi/2) + except Exception as e: + print(type(e).__name__ + ":", e) + sys.exit() + + return k**2 * result From 5eb0af7de08455269ef605be3f536062ce268917 Mon Sep 17 00:00:00 2001 From: Daniel Kotik Date: Sat, 22 Feb 2020 18:12:28 +0100 Subject: [PATCH 004/145] Move spectral amplitudes (spherical) to beamprofile.py --- Laguerre_Gauss_3d/LaguerreGauss3d.py | 24 ++++-------------------- Laguerre_Gauss_3d/beamprofile.py | 17 ++++++++++++++++- 2 files changed, 20 insertions(+), 21 deletions(-) diff --git a/Laguerre_Gauss_3d/LaguerreGauss3d.py b/Laguerre_Gauss_3d/LaguerreGauss3d.py index bcb8920..a6120c6 100644 --- a/Laguerre_Gauss_3d/LaguerreGauss3d.py +++ b/Laguerre_Gauss_3d/LaguerreGauss3d.py @@ -55,7 +55,8 @@ import sys from datetime import datetime -from beamprofile import psi_spherical + +from beamprofile import psi_spherical, f_Gauss_spherical, f_Laguerre_Gauss_spherical from beamprofile import complex_dblquad @@ -224,24 +225,7 @@ def f_Laguerre_Gauss_cartesian(k_y, k_z, params): cmath.exp(1j*m*phi(k_y, k_z)) * theta(k_y, k_z, k)**abs(m) # spherical coordinates -------------------------------------------- - def f_Gauss_spherical(sin_theta, theta, phi, params): - """2d-Gaussian spectrum amplitude. - - Impementation for spherical coordinates. - """ - W_y, k = params['W_y'], params['k'] - - return math.exp(-(k*W_y*sin_theta/2)**2) - - def f_Laguerre_Gauss_spherical(sin_theta, theta, phi, params): - """Laguerre-Gaussian spectrum amplitude. - - Impementation for spherical coordinates. - """ - m = params['m'] - return f_Gauss_spherical(sin_theta, theta, phi, params) * theta**abs(m) * \ - cmath.exp(1j*m*phi) # -------------------------------------------------------------------------- # some test outputs @@ -313,8 +297,8 @@ def phase(k_y, k_z, x, y, z): print("psi (cartesian):", psi_cartesian(r, f_Laguerre_Gauss_cartesian, x, params)) print("psi (spherical):", - psi_spherical(r, f_Laguerre_Gauss_spherical, x, params)) - print("psi (origin, simple):", Gauss(r, params)) + psi_spherical(r, lambda st, t, p: f_Laguerre_Gauss_spherical(st, t, p, W_y=w_0, m=m_charge, k=k1), x, k1)) + print("psi (origin, simple):", Gauss(r)) sys.exit() # -------------------------------------------------------------------------- diff --git a/Laguerre_Gauss_3d/beamprofile.py b/Laguerre_Gauss_3d/beamprofile.py index cb5ca61..8ed61fa 100644 --- a/Laguerre_Gauss_3d/beamprofile.py +++ b/Laguerre_Gauss_3d/beamprofile.py @@ -33,6 +33,21 @@ def imag_integral(): return result, real_tol, imag_tol +def f_Gauss_spherical(sin_theta, theta, phi, W_y, k): + """2d-Gaussian spectrum amplitude. + + Impementation for spherical coordinates. + """ + return math.exp(-(k*W_y*sin_theta/2)**2) + +def f_Laguerre_Gauss_spherical(sin_theta, theta, phi, W_y, m, k): + """Laguerre-Gaussian spectrum amplitude. + + Impementation for spherical coordinates. + """ + return f_Gauss_spherical(sin_theta, theta, phi, W_y, k) * theta**abs(m) * \ + np.exp(1j*m*phi) + def psi_spherical(r, f, x, k): """Field amplitude function. @@ -64,4 +79,4 @@ def phase(theta, phi, x, y, z): print(type(e).__name__ + ":", e) sys.exit() - return k**2 * result + return k**2 * result \ No newline at end of file From 4ca8473ee813949ac7c81488ae1624cdf02123b3 Mon Sep 17 00:00:00 2001 From: Daniel Kotik Date: Sat, 22 Feb 2020 18:24:30 +0100 Subject: [PATCH 005/145] Add test section to main(): By using the Ipython interpreter with ``` %load beamprofile.py %timeit psi() ``` the evaluation time of psi can be measured. --- Laguerre_Gauss_3d/beamprofile.py | 20 +++++++++++++++++++- 1 file changed, 19 insertions(+), 1 deletion(-) diff --git a/Laguerre_Gauss_3d/beamprofile.py b/Laguerre_Gauss_3d/beamprofile.py index 8ed61fa..24d58de 100644 --- a/Laguerre_Gauss_3d/beamprofile.py +++ b/Laguerre_Gauss_3d/beamprofile.py @@ -79,4 +79,22 @@ def phase(theta, phi, x, y, z): print(type(e).__name__ + ":", e) sys.exit() - return k**2 * result \ No newline at end of file + return k**2 * result + + +if __name__ == '__main__': + k_y, k_z = 1.0, 5.2 + x, y, z = -2.15, 0.3, 0.5 + import meep as mp + r = mp.Vector3(0, y, z) + + k1 = 31.41592653589793 + w_0 = 0.25464790894703254 + m_charge = 2 + + f_ = lambda sin_theta, theta, phi: f_Laguerre_Gauss_spherical(sin_theta, theta, phi, W_y=w_0, m=m_charge, k=k1) + + psi = lambda: psi_spherical(r, f_, x, k1) + + print("psi (spherical):", psi()) + From 2775b282e502c3281587d142f2c564c8c480de84 Mon Sep 17 00:00:00 2001 From: Daniel Kotik Date: Sun, 23 Feb 2020 14:56:57 +0100 Subject: [PATCH 006/145] Add Cython stuff to .gitignore --- .gitignore | 4 ++++ 1 file changed, 4 insertions(+) diff --git a/.gitignore b/.gitignore index ff388aa..212c7d5 100644 --- a/.gitignore +++ b/.gitignore @@ -8,6 +8,10 @@ Gauss_2d/convex/* .ipynb_checkpoints */.ipynb_checkpoints/* +### Cython ### +Laguerre_Gauss_3d/beamprofile.c +Laguerre_Gauss_3d/beamprofile.html + ### Python ### # Byte-compiled / optimized / DLL files __pycache__/ From 4be15e542256ae29bba68ad20ef773e1bc68659e Mon Sep 17 00:00:00 2001 From: Daniel Kotik Date: Sun, 23 Feb 2020 15:07:28 +0100 Subject: [PATCH 007/145] Add main() function: Move everything below __name__ == '__main__' to main() function. This enables to run main() in Ipython and get direct access to psi_spherical as return value of main(). --- Laguerre_Gauss_3d/beamprofile.py | 13 ++++++++----- 1 file changed, 8 insertions(+), 5 deletions(-) diff --git a/Laguerre_Gauss_3d/beamprofile.py b/Laguerre_Gauss_3d/beamprofile.py index 24d58de..98235b1 100644 --- a/Laguerre_Gauss_3d/beamprofile.py +++ b/Laguerre_Gauss_3d/beamprofile.py @@ -81,20 +81,23 @@ def phase(theta, phi, x, y, z): return k**2 * result +def main(): + + import meep as mp -if __name__ == '__main__': k_y, k_z = 1.0, 5.2 x, y, z = -2.15, 0.3, 0.5 - import meep as mp r = mp.Vector3(0, y, z) k1 = 31.41592653589793 w_0 = 0.25464790894703254 m_charge = 2 - f_ = lambda sin_theta, theta, phi: f_Laguerre_Gauss_spherical(sin_theta, theta, phi, W_y=w_0, m=m_charge, k=k1) + f = lambda sin_theta, theta, phi: f_Laguerre_Gauss_spherical(sin_theta, theta, phi, W_y=w_0, m=m_charge, k=k1) + + return lambda: psi_spherical(r, f, x, k1) - psi = lambda: psi_spherical(r, f_, x, k1) - print("psi (spherical):", psi()) +if __name__ == '__main__': + main() From 072a02efe2ea2d7adf082daadac169c7c484fae9 Mon Sep 17 00:00:00 2001 From: Daniel Kotik Date: Sun, 23 Feb 2020 18:22:09 +0100 Subject: [PATCH 008/145] Add function declarations --- Laguerre_Gauss_3d/beamprofile.pxd | 12 +++++++++++- 1 file changed, 11 insertions(+), 1 deletion(-) diff --git a/Laguerre_Gauss_3d/beamprofile.pxd b/Laguerre_Gauss_3d/beamprofile.pxd index 78818e2..2730382 100644 --- a/Laguerre_Gauss_3d/beamprofile.pxd +++ b/Laguerre_Gauss_3d/beamprofile.pxd @@ -6,4 +6,14 @@ author: Daniel Kotik version: 1.5-beta release date: xx.xx.2020 creation date: 22.02.2020 -""" \ No newline at end of file +""" +import cython + + +cdef double f_Gauss_spherical(double sin_theta, double theta, double phi, + double W_y, double k) + +cdef double complex f_Laguerre_Gauss_spherical(double sin_theta, double theta, + double phi, double W_y, int m, + double k) + From 52f3367e61c66cd62ae473eafa6506c3fed6fe2b Mon Sep 17 00:00:00 2001 From: Daniel Kotik Date: Sun, 23 Feb 2020 18:23:53 +0100 Subject: [PATCH 009/145] Add some Cython magic --- Laguerre_Gauss_3d/beamprofile.py | 9 +++++++++ 1 file changed, 9 insertions(+) diff --git a/Laguerre_Gauss_3d/beamprofile.py b/Laguerre_Gauss_3d/beamprofile.py index 98235b1..f05e241 100644 --- a/Laguerre_Gauss_3d/beamprofile.py +++ b/Laguerre_Gauss_3d/beamprofile.py @@ -7,12 +7,17 @@ release date: xx.xx.2020 creation date: 22.02.2020 """ +import cython import math import numpy as np import sys from scipy.integrate import dblquad +if not cython.compiled: + print("Please consider compiling `beamprofile.py` via Cython:\n\n" + " `$ cythonize -3 -i beamprofile.py`") + def complex_dblquad(func, a, b, gfun, hfun, **kwargs): """Integrate real and imaginary part of the given function.""" def real_func(x, y): @@ -60,6 +65,10 @@ def psi_spherical(r, f, x, k): print("Calculating inital field configuration. " "This will take some time...") + #@cython.cfunc + #@cython.returns(cython.double) + #@cython.locals(x=cython.double, y=cython.double, z=cython.double, + # theta=cython.double, phi=cython.double) def phase(theta, phi, x, y, z): """Phase function.""" sin_theta, sin_phi = math.sin(theta), math.sin(phi) From 16d57f637be2bafa4627b850089dca356db3d055 Mon Sep 17 00:00:00 2001 From: Daniel Kotik Date: Mon, 24 Feb 2020 18:56:04 +0100 Subject: [PATCH 010/145] Add spectrum function prototype --- Laguerre_Gauss_3d/beamprofile.pxd | 5 +++++ 1 file changed, 5 insertions(+) diff --git a/Laguerre_Gauss_3d/beamprofile.pxd b/Laguerre_Gauss_3d/beamprofile.pxd index 2730382..1af1253 100644 --- a/Laguerre_Gauss_3d/beamprofile.pxd +++ b/Laguerre_Gauss_3d/beamprofile.pxd @@ -9,6 +9,10 @@ creation date: 22.02.2020 """ import cython +# function type declaration for spectrum amplitudes +ctypedef double complex (*f_spectrum_type)(double theta, double phi) + +#def (double complex, double, double) complex_dblquad(f_spectrum_type func, double a, double b, double gfun, double hfun) cdef double f_Gauss_spherical(double sin_theta, double theta, double phi, double W_y, double k) @@ -17,3 +21,4 @@ cdef double complex f_Laguerre_Gauss_spherical(double sin_theta, double theta, double phi, double W_y, int m, double k) +#cpdef double complex psi_spherical(r, f_spectrum_type f, x, k) From 2796a7fb8ddd7f8c205b0179514402ba06f24009 Mon Sep 17 00:00:00 2001 From: Daniel Kotik Date: Mon, 24 Feb 2020 19:21:23 +0100 Subject: [PATCH 011/145] Remove **kwargs: Unpacking a dictionary is not supported by Cython. --- Laguerre_Gauss_3d/beamprofile.py | 6 +++--- 1 file changed, 3 insertions(+), 3 deletions(-) diff --git a/Laguerre_Gauss_3d/beamprofile.py b/Laguerre_Gauss_3d/beamprofile.py index f05e241..9b24c7e 100644 --- a/Laguerre_Gauss_3d/beamprofile.py +++ b/Laguerre_Gauss_3d/beamprofile.py @@ -18,7 +18,7 @@ print("Please consider compiling `beamprofile.py` via Cython:\n\n" " `$ cythonize -3 -i beamprofile.py`") -def complex_dblquad(func, a, b, gfun, hfun, **kwargs): +def complex_dblquad(func, a, b, gfun, hfun): """Integrate real and imaginary part of the given function.""" def real_func(x, y): return np.real(func(x, y)) @@ -27,10 +27,10 @@ def imag_func(x, y): return np.imag(func(x, y)) def real_integral(): - return dblquad(real_func, a, b, gfun, hfun, **kwargs) + return dblquad(real_func, a, b, gfun, hfun) def imag_integral(): - return dblquad(imag_func, a, b, gfun, hfun, **kwargs) + return dblquad(imag_func, a, b, gfun, hfun) result = real_integral()[0] + 1j * imag_integral()[0] real_tol = real_integral()[1] From b74c2e184a3c5314071b692a09fd4555f4829b72 Mon Sep 17 00:00:00 2001 From: Daniel Kotik Date: Mon, 24 Feb 2020 20:04:48 +0100 Subject: [PATCH 012/145] Make integrand function explicit: The integrand function should become a pure C function, however lambda functions are phytonic and not converted by Cython. --- Laguerre_Gauss_3d/beamprofile.py | 12 +++++++----- 1 file changed, 7 insertions(+), 5 deletions(-) diff --git a/Laguerre_Gauss_3d/beamprofile.py b/Laguerre_Gauss_3d/beamprofile.py index 9b24c7e..031e614 100644 --- a/Laguerre_Gauss_3d/beamprofile.py +++ b/Laguerre_Gauss_3d/beamprofile.py @@ -75,15 +75,17 @@ def phase(theta, phi, x, y, z): cos_theta, cos_phi = math.cos(theta), math.cos(phi) return k*(sin_theta*(y*sin_phi - z*cos_phi) + cos_theta*x) + + def integrand(theta, phi): + """...""" + return math.sin(theta) * math.cos(theta) * \ + f(math.sin(theta), theta, phi) * \ + np.exp(1j*phase(theta, phi, x, r.y, r.z)) try: (result, real_tol, - imag_tol) = complex_dblquad(lambda theta, phi: - math.sin(theta) * math.cos(theta) * \ - f(math.sin(theta), theta, phi) * \ - np.exp(1j*phase(theta, phi, x, r.y, r.z)), - 0, 2*math.pi, 0, math.pi/2) + imag_tol) = complex_dblquad(integrand, 0, 2*math.pi, 0, math.pi/2) except Exception as e: print(type(e).__name__ + ":", e) sys.exit() From 7dc498f67d91da407fda398b22e80f1ead567ce8 Mon Sep 17 00:00:00 2001 From: Daniel Kotik Date: Mon, 24 Feb 2020 20:27:19 +0100 Subject: [PATCH 013/145] Speed up of complex double integration: Avoid a redundant call of dblquad for the real and imaginary part. This reduces enormously the Python function call overhead. --- Laguerre_Gauss_3d/beamprofile.py | 15 ++++----------- 1 file changed, 4 insertions(+), 11 deletions(-) diff --git a/Laguerre_Gauss_3d/beamprofile.py b/Laguerre_Gauss_3d/beamprofile.py index 031e614..8126fb0 100644 --- a/Laguerre_Gauss_3d/beamprofile.py +++ b/Laguerre_Gauss_3d/beamprofile.py @@ -25,18 +25,11 @@ def real_func(x, y): def imag_func(x, y): return np.imag(func(x, y)) + + real, real_tol = dblquad(real_func, a, b, gfun, hfun) + imag, imag_tol = dblquad(imag_func, a, b, gfun, hfun) - def real_integral(): - return dblquad(real_func, a, b, gfun, hfun) - - def imag_integral(): - return dblquad(imag_func, a, b, gfun, hfun) - - result = real_integral()[0] + 1j * imag_integral()[0] - real_tol = real_integral()[1] - imag_tol = imag_integral()[1] - - return result, real_tol, imag_tol + return real + 1j*imag, real_tol, imag_tol def f_Gauss_spherical(sin_theta, theta, phi, W_y, k): """2d-Gaussian spectrum amplitude. From 0856cb3ae14fa30ac9d13304ae3611c3735317aa Mon Sep 17 00:00:00 2001 From: Daniel Kotik Date: Tue, 25 Feb 2020 15:27:18 +0100 Subject: [PATCH 014/145] Replace numpy calls with cmath calls: This leads to faster code execution (speedup ~2.4). --- Laguerre_Gauss_3d/beamprofile.py | 10 +++++----- 1 file changed, 5 insertions(+), 5 deletions(-) diff --git a/Laguerre_Gauss_3d/beamprofile.py b/Laguerre_Gauss_3d/beamprofile.py index 8126fb0..9fd7c02 100644 --- a/Laguerre_Gauss_3d/beamprofile.py +++ b/Laguerre_Gauss_3d/beamprofile.py @@ -7,9 +7,9 @@ release date: xx.xx.2020 creation date: 22.02.2020 """ +import cmath import cython import math -import numpy as np import sys from scipy.integrate import dblquad @@ -21,10 +21,10 @@ def complex_dblquad(func, a, b, gfun, hfun): """Integrate real and imaginary part of the given function.""" def real_func(x, y): - return np.real(func(x, y)) + return func(x, y).real def imag_func(x, y): - return np.imag(func(x, y)) + return func(x, y).imag real, real_tol = dblquad(real_func, a, b, gfun, hfun) imag, imag_tol = dblquad(imag_func, a, b, gfun, hfun) @@ -44,7 +44,7 @@ def f_Laguerre_Gauss_spherical(sin_theta, theta, phi, W_y, m, k): Impementation for spherical coordinates. """ return f_Gauss_spherical(sin_theta, theta, phi, W_y, k) * theta**abs(m) * \ - np.exp(1j*m*phi) + cmath.exp(1j*m*phi) def psi_spherical(r, f, x, k): """Field amplitude function. @@ -73,7 +73,7 @@ def integrand(theta, phi): """...""" return math.sin(theta) * math.cos(theta) * \ f(math.sin(theta), theta, phi) * \ - np.exp(1j*phase(theta, phi, x, r.y, r.z)) + cmath.exp(1j*phase(theta, phi, x, r.y, r.z)) try: (result, From ca22777bd25c970d91f2bce47b749129ac80616b Mon Sep 17 00:00:00 2001 From: Daniel Kotik Date: Tue, 25 Feb 2020 16:50:45 +0100 Subject: [PATCH 015/145] Define real_func and imag_func as pure C functions --- Laguerre_Gauss_3d/beamprofile.pxd | 6 +++++- Laguerre_Gauss_3d/beamprofile.py | 20 +++++++++----------- 2 files changed, 14 insertions(+), 12 deletions(-) diff --git a/Laguerre_Gauss_3d/beamprofile.pxd b/Laguerre_Gauss_3d/beamprofile.pxd index 1af1253..8c1c5ea 100644 --- a/Laguerre_Gauss_3d/beamprofile.pxd +++ b/Laguerre_Gauss_3d/beamprofile.pxd @@ -12,7 +12,11 @@ import cython # function type declaration for spectrum amplitudes ctypedef double complex (*f_spectrum_type)(double theta, double phi) -#def (double complex, double, double) complex_dblquad(f_spectrum_type func, double a, double b, double gfun, double hfun) +# function prototypes +cdef double real_func(double x, double y, func) +cdef double imag_func(double x, double y, func) + +cdef (double complex, double, double) complex_dblquad(func, double a, double b, double gfun, double hfun) cdef double f_Gauss_spherical(double sin_theta, double theta, double phi, double W_y, double k) diff --git a/Laguerre_Gauss_3d/beamprofile.py b/Laguerre_Gauss_3d/beamprofile.py index 9fd7c02..d782282 100644 --- a/Laguerre_Gauss_3d/beamprofile.py +++ b/Laguerre_Gauss_3d/beamprofile.py @@ -18,16 +18,18 @@ print("Please consider compiling `beamprofile.py` via Cython:\n\n" " `$ cythonize -3 -i beamprofile.py`") + +def real_func(x, y, func): + return func(x, y).real + +def imag_func(x, y, func): + return func(x, y).imag + def complex_dblquad(func, a, b, gfun, hfun): """Integrate real and imaginary part of the given function.""" - def real_func(x, y): - return func(x, y).real - - def imag_func(x, y): - return func(x, y).imag - real, real_tol = dblquad(real_func, a, b, gfun, hfun) - imag, imag_tol = dblquad(imag_func, a, b, gfun, hfun) + real, real_tol = dblquad(real_func, a, b, gfun, hfun, (func,)) + imag, imag_tol = dblquad(imag_func, a, b, gfun, hfun, (func,)) return real + 1j*imag, real_tol, imag_tol @@ -58,10 +60,6 @@ def psi_spherical(r, f, x, k): print("Calculating inital field configuration. " "This will take some time...") - #@cython.cfunc - #@cython.returns(cython.double) - #@cython.locals(x=cython.double, y=cython.double, z=cython.double, - # theta=cython.double, phi=cython.double) def phase(theta, phi, x, y, z): """Phase function.""" sin_theta, sin_phi = math.sin(theta), math.sin(phi) From 188630ab5d7db4c3dd1bfe5a84c07ca4966873b4 Mon Sep 17 00:00:00 2001 From: Daniel Kotik Date: Thu, 27 Feb 2020 16:25:53 +0100 Subject: [PATCH 016/145] Fix formatting issues --- Laguerre_Gauss_3d/beamprofile.py | 97 +++++++++++++++++--------------- 1 file changed, 51 insertions(+), 46 deletions(-) diff --git a/Laguerre_Gauss_3d/beamprofile.py b/Laguerre_Gauss_3d/beamprofile.py index d782282..9e54883 100644 --- a/Laguerre_Gauss_3d/beamprofile.py +++ b/Laguerre_Gauss_3d/beamprofile.py @@ -20,19 +20,23 @@ def real_func(x, y, func): + """Return real part of function.""" return func(x, y).real - + + def imag_func(x, y, func): - return func(x, y).imag + """Return imag part of function.""" + return func(x, y).imag + def complex_dblquad(func, a, b, gfun, hfun): """Integrate real and imaginary part of the given function.""" - real, real_tol = dblquad(real_func, a, b, gfun, hfun, (func,)) imag, imag_tol = dblquad(imag_func, a, b, gfun, hfun, (func,)) return real + 1j*imag, real_tol, imag_tol + def f_Gauss_spherical(sin_theta, theta, phi, W_y, k): """2d-Gaussian spectrum amplitude. @@ -40,6 +44,7 @@ def f_Gauss_spherical(sin_theta, theta, phi, W_y, k): """ return math.exp(-(k*W_y*sin_theta/2)**2) + def f_Laguerre_Gauss_spherical(sin_theta, theta, phi, W_y, m, k): """Laguerre-Gaussian spectrum amplitude. @@ -48,58 +53,58 @@ def f_Laguerre_Gauss_spherical(sin_theta, theta, phi, W_y, m, k): return f_Gauss_spherical(sin_theta, theta, phi, W_y, k) * theta**abs(m) * \ cmath.exp(1j*m*phi) + def psi_spherical(r, f, x, k): - """Field amplitude function. - - Integration in spherical coordinates. - """ - try: - getattr(psi_spherical, "called") - except AttributeError: - psi_spherical.called = True - print("Calculating inital field configuration. " - "This will take some time...") - - def phase(theta, phi, x, y, z): - """Phase function.""" - sin_theta, sin_phi = math.sin(theta), math.sin(phi) - cos_theta, cos_phi = math.cos(theta), math.cos(phi) - - return k*(sin_theta*(y*sin_phi - z*cos_phi) + cos_theta*x) - - def integrand(theta, phi): - """...""" - return math.sin(theta) * math.cos(theta) * \ - f(math.sin(theta), theta, phi) * \ - cmath.exp(1j*phase(theta, phi, x, r.y, r.z)) - - try: - (result, - real_tol, - imag_tol) = complex_dblquad(integrand, 0, 2*math.pi, 0, math.pi/2) - except Exception as e: - print(type(e).__name__ + ":", e) - sys.exit() - - return k**2 * result - + """Field amplitude function. + + Integration in spherical coordinates. + """ + try: + getattr(psi_spherical, "called") + except AttributeError: + psi_spherical.called = True + print("Calculating inital field configuration. " + "This will take some time...") + + def phase(theta, phi, x, y, z): + """Phase function.""" + sin_theta, sin_phi = math.sin(theta), math.sin(phi) + cos_theta, cos_phi = math.cos(theta), math.cos(phi) + + return k*(sin_theta*(y*sin_phi - z*cos_phi) + cos_theta*x) + + def integrand(theta, phi): + """...""" + return math.sin(theta) * math.cos(theta) * \ + f(math.sin(theta), theta, phi) * \ + cmath.exp(1j*phase(theta, phi, x, r.y, r.z)) + + try: + (result, + real_tol, + imag_tol) = complex_dblquad(integrand, 0, 2*math.pi, 0, math.pi/2) + except Exception as e: + print(type(e).__name__ + ":", e) + sys.exit() + + return k**2 * result + + def main(): - + import meep as mp - - k_y, k_z = 1.0, 5.2 + x, y, z = -2.15, 0.3, 0.5 r = mp.Vector3(0, y, z) - + k1 = 31.41592653589793 w_0 = 0.25464790894703254 m_charge = 2 - + f = lambda sin_theta, theta, phi: f_Laguerre_Gauss_spherical(sin_theta, theta, phi, W_y=w_0, m=m_charge, k=k1) - + return lambda: psi_spherical(r, f, x, k1) - - + + if __name__ == '__main__': main() - From 50e48ee43cfc35ccbddd8eb004b6141653b47804 Mon Sep 17 00:00:00 2001 From: Daniel Kotik Date: Thu, 27 Feb 2020 18:44:42 +0100 Subject: [PATCH 017/145] Cython optimisation --- Laguerre_Gauss_3d/beamprofile.pxd | 23 +++++++++++++++------ Laguerre_Gauss_3d/beamprofile.py | 34 +++++++++++++++++++++---------- 2 files changed, 40 insertions(+), 17 deletions(-) diff --git a/Laguerre_Gauss_3d/beamprofile.pxd b/Laguerre_Gauss_3d/beamprofile.pxd index 8c1c5ea..ee35612 100644 --- a/Laguerre_Gauss_3d/beamprofile.pxd +++ b/Laguerre_Gauss_3d/beamprofile.pxd @@ -9,6 +9,15 @@ creation date: 22.02.2020 """ import cython +# declare a C function as "cpdef" to export it to the module +cdef extern from "math.h": + cpdef double sin(double x) + cpdef double cos(double x) + cpdef double exp(double x) + +#cdef extern from "complex.h": +# cpdef double complex exp(double complex) + # function type declaration for spectrum amplitudes ctypedef double complex (*f_spectrum_type)(double theta, double phi) @@ -16,13 +25,15 @@ ctypedef double complex (*f_spectrum_type)(double theta, double phi) cdef double real_func(double x, double y, func) cdef double imag_func(double x, double y, func) +@cython.locals(real=cython.double, imag=cython.double, real_tol=cython.double, imag_tol=cython.double) cdef (double complex, double, double) complex_dblquad(func, double a, double b, double gfun, double hfun) -cdef double f_Gauss_spherical(double sin_theta, double theta, double phi, - double W_y, double k) +@cython.locals(W_y=cython.double, k=cython.double) +cdef double complex f_Gauss_spherical(double sin_theta, double theta, double phi, + dict params) -cdef double complex f_Laguerre_Gauss_spherical(double sin_theta, double theta, - double phi, double W_y, int m, - double k) +@cython.locals(m=cython.int) +cdef double complex f_Laguerre_Gauss_spherical(double sin_theta, double theta, + double phi, dict params) -#cpdef double complex psi_spherical(r, f_spectrum_type f, x, k) +#cpdef double complex psi_spherical(r, double x, dict params) diff --git a/Laguerre_Gauss_3d/beamprofile.py b/Laguerre_Gauss_3d/beamprofile.py index 9e54883..fc502ed 100644 --- a/Laguerre_Gauss_3d/beamprofile.py +++ b/Laguerre_Gauss_3d/beamprofile.py @@ -15,6 +15,7 @@ from scipy.integrate import dblquad if not cython.compiled: + from math import sin, cos, exp print("Please consider compiling `beamprofile.py` via Cython:\n\n" " `$ cythonize -3 -i beamprofile.py`") @@ -37,28 +38,39 @@ def complex_dblquad(func, a, b, gfun, hfun): return real + 1j*imag, real_tol, imag_tol -def f_Gauss_spherical(sin_theta, theta, phi, W_y, k): +def f_Gauss_spherical(sin_theta, theta, phi, params): """2d-Gaussian spectrum amplitude. Impementation for spherical coordinates. """ - return math.exp(-(k*W_y*sin_theta/2)**2) + W_y, k = params['W_y'], params['k'] + return exp(-(k*W_y*sin_theta/2)**2) -def f_Laguerre_Gauss_spherical(sin_theta, theta, phi, W_y, m, k): + +def f_Laguerre_Gauss_spherical(sin_theta, theta, phi, params): """Laguerre-Gaussian spectrum amplitude. Impementation for spherical coordinates. """ - return f_Gauss_spherical(sin_theta, theta, phi, W_y, k) * theta**abs(m) * \ + m = params['m'] + + return f_Gauss_spherical(sin_theta, theta, phi, params) * theta**abs(m) * \ cmath.exp(1j*m*phi) -def psi_spherical(r, f, x, k): +def psi_spherical(r, x, params): """Field amplitude function. Integration in spherical coordinates. """ + k, m = params['k'], params['m'] + + if m == 0: + f = f_Gauss_spherical + else: + f = f_Laguerre_Gauss_spherical + try: getattr(psi_spherical, "called") except AttributeError: @@ -68,15 +80,15 @@ def psi_spherical(r, f, x, k): def phase(theta, phi, x, y, z): """Phase function.""" - sin_theta, sin_phi = math.sin(theta), math.sin(phi) - cos_theta, cos_phi = math.cos(theta), math.cos(phi) + sin_theta, sin_phi = sin(theta), sin(phi) + cos_theta, cos_phi = cos(theta), cos(phi) return k*(sin_theta*(y*sin_phi - z*cos_phi) + cos_theta*x) def integrand(theta, phi): """...""" - return math.sin(theta) * math.cos(theta) * \ - f(math.sin(theta), theta, phi) * \ + return sin(theta) * cos(theta) * \ + f(sin(theta), theta, phi, params) * \ cmath.exp(1j*phase(theta, phi, x, r.y, r.z)) try: @@ -101,9 +113,9 @@ def main(): w_0 = 0.25464790894703254 m_charge = 2 - f = lambda sin_theta, theta, phi: f_Laguerre_Gauss_spherical(sin_theta, theta, phi, W_y=w_0, m=m_charge, k=k1) + params = dict(W_y=w_0, m=m_charge, k=k1) - return lambda: psi_spherical(r, f, x, k1) + return lambda: psi_spherical(r, x, params) if __name__ == '__main__': From 4dd272ae83bc3b8ab969831162808f35673e1d07 Mon Sep 17 00:00:00 2001 From: Daniel Kotik Date: Fri, 28 Feb 2020 14:40:38 +0100 Subject: [PATCH 018/145] Call C functions: Combine C function coercion with a conditional importfor sin, cos, exp, abs and cexp. --- Laguerre_Gauss_3d/beamprofile.pxd | 9 ++++++--- Laguerre_Gauss_3d/beamprofile.py | 6 +++--- 2 files changed, 9 insertions(+), 6 deletions(-) diff --git a/Laguerre_Gauss_3d/beamprofile.pxd b/Laguerre_Gauss_3d/beamprofile.pxd index ee35612..ea942d0 100644 --- a/Laguerre_Gauss_3d/beamprofile.pxd +++ b/Laguerre_Gauss_3d/beamprofile.pxd @@ -9,14 +9,17 @@ creation date: 22.02.2020 """ import cython -# declare a C function as "cpdef" to export it to the module +# declare C functions as "cpdef" to export them to the module +cdef extern from "stdlib.h": + cpdef int abs (int n) + cdef extern from "math.h": cpdef double sin(double x) cpdef double cos(double x) cpdef double exp(double x) -#cdef extern from "complex.h": -# cpdef double complex exp(double complex) +cdef extern from "complex.h": + cpdef double complex cexp(double complex z) # function type declaration for spectrum amplitudes ctypedef double complex (*f_spectrum_type)(double theta, double phi) diff --git a/Laguerre_Gauss_3d/beamprofile.py b/Laguerre_Gauss_3d/beamprofile.py index fc502ed..763f83a 100644 --- a/Laguerre_Gauss_3d/beamprofile.py +++ b/Laguerre_Gauss_3d/beamprofile.py @@ -7,7 +7,6 @@ release date: xx.xx.2020 creation date: 22.02.2020 """ -import cmath import cython import math import sys @@ -16,6 +15,7 @@ if not cython.compiled: from math import sin, cos, exp + from cmath import exp as cexp print("Please consider compiling `beamprofile.py` via Cython:\n\n" " `$ cythonize -3 -i beamprofile.py`") @@ -56,7 +56,7 @@ def f_Laguerre_Gauss_spherical(sin_theta, theta, phi, params): m = params['m'] return f_Gauss_spherical(sin_theta, theta, phi, params) * theta**abs(m) * \ - cmath.exp(1j*m*phi) + cexp(1j*m*phi) def psi_spherical(r, x, params): @@ -89,7 +89,7 @@ def integrand(theta, phi): """...""" return sin(theta) * cos(theta) * \ f(sin(theta), theta, phi, params) * \ - cmath.exp(1j*phase(theta, phi, x, r.y, r.z)) + cexp(1j*phase(theta, phi, x, r.y, r.z)) try: (result, From 8c520c6685e9c650ee3e3f382d0c130d5ff9e7e7 Mon Sep 17 00:00:00 2001 From: Daniel Kotik Date: Fri, 28 Feb 2020 17:37:56 +0100 Subject: [PATCH 019/145] Rewrite psi_spherical as a class: A Python class can then be converted to a Cython extension module and methods therein can then become pure C functions. --- Laguerre_Gauss_3d/beamprofile.py | 11 ++++++++--- 1 file changed, 8 insertions(+), 3 deletions(-) diff --git a/Laguerre_Gauss_3d/beamprofile.py b/Laguerre_Gauss_3d/beamprofile.py index 763f83a..4b72c5f 100644 --- a/Laguerre_Gauss_3d/beamprofile.py +++ b/Laguerre_Gauss_3d/beamprofile.py @@ -59,12 +59,17 @@ def f_Laguerre_Gauss_spherical(sin_theta, theta, phi, params): cexp(1j*m*phi) -def psi_spherical(r, x, params): - """Field amplitude function. +class PsiSpherical: + """Field amplitude class. Integration in spherical coordinates. """ - k, m = params['k'], params['m'] + + def __init__(self, r, x, params): + self.r = r + self.x = x + self.k = params['k'] + self.m = params['m'] if m == 0: f = f_Gauss_spherical From d582855f9ed5172c33b041807beda86040f697c5 Mon Sep 17 00:00:00 2001 From: Daniel Kotik Date: Sat, 29 Feb 2020 15:51:00 +0100 Subject: [PATCH 020/145] Change class: Objects of PsiSpherical class are now a callable instance (functors). --- Laguerre_Gauss_3d/beamprofile.py | 35 ++++++++++++++++++++------------ 1 file changed, 22 insertions(+), 13 deletions(-) diff --git a/Laguerre_Gauss_3d/beamprofile.py b/Laguerre_Gauss_3d/beamprofile.py index 4b72c5f..0e31cb9 100644 --- a/Laguerre_Gauss_3d/beamprofile.py +++ b/Laguerre_Gauss_3d/beamprofile.py @@ -63,25 +63,32 @@ class PsiSpherical: """Field amplitude class. Integration in spherical coordinates. + + Usage: + psi_spherical = PsiSpherical(x=shift, params=params) + psi_spherical(r) """ - def __init__(self, r, x, params): - self.r = r + def __init__(self, x, params): self.x = x self.k = params['k'] self.m = params['m'] - if m == 0: - f = f_Gauss_spherical - else: - f = f_Laguerre_Gauss_spherical + if self.m == 0: + self.f = f_Gauss_spherical + else: + self.f = f_Laguerre_Gauss_spherical + + def __call__(self, r): + pass - try: - getattr(psi_spherical, "called") - except AttributeError: - psi_spherical.called = True - print("Calculating inital field configuration. " - "This will take some time...") + + #try: + # getattr(psi_spherical, "called") + #except AttributeError: + # psi_spherical.called = True + # print("Calculating inital field configuration. " + # "This will take some time...") def phase(theta, phi, x, y, z): """Phase function.""" @@ -120,7 +127,9 @@ def main(): params = dict(W_y=w_0, m=m_charge, k=k1) - return lambda: psi_spherical(r, x, params) + psi_spherical = PsiSpherical(x=x, params=params) + + return lambda: psi_spherical(r) if __name__ == '__main__': From 5e3e128d725a7c12de752542c6c29a1b931eb706 Mon Sep 17 00:00:00 2001 From: Daniel Kotik Date: Sat, 29 Feb 2020 16:24:37 +0100 Subject: [PATCH 021/145] Fix class issues --- Laguerre_Gauss_3d/beamprofile.py | 63 ++++++++++++++++---------------- 1 file changed, 32 insertions(+), 31 deletions(-) diff --git a/Laguerre_Gauss_3d/beamprofile.py b/Laguerre_Gauss_3d/beamprofile.py index 0e31cb9..31a6d02 100644 --- a/Laguerre_Gauss_3d/beamprofile.py +++ b/Laguerre_Gauss_3d/beamprofile.py @@ -20,20 +20,20 @@ " `$ cythonize -3 -i beamprofile.py`") -def real_func(x, y, func): +def real_func(x, y, func, r): """Return real part of function.""" - return func(x, y).real + return func(x, y, r).real -def imag_func(x, y, func): +def imag_func(x, y, func, r): """Return imag part of function.""" - return func(x, y).imag + return func(x, y, r).imag -def complex_dblquad(func, a, b, gfun, hfun): +def complex_dblquad(func, a, b, gfun, hfun, r): """Integrate real and imaginary part of the given function.""" - real, real_tol = dblquad(real_func, a, b, gfun, hfun, (func,)) - imag, imag_tol = dblquad(imag_func, a, b, gfun, hfun, (func,)) + real, real_tol = dblquad(real_func, a, b, gfun, hfun, (func, r)) + imag, imag_tol = dblquad(imag_func, a, b, gfun, hfun, (func, r)) return real + 1j*imag, real_tol, imag_tol @@ -70,7 +70,9 @@ class PsiSpherical: """ def __init__(self, x, params): + """...""" self.x = x + self.params = params self.k = params['k'] self.m = params['m'] @@ -80,8 +82,30 @@ def __init__(self, x, params): self.f = f_Laguerre_Gauss_spherical def __call__(self, r): - pass + """...""" + try: + (result, + real_tol, + imag_tol) = complex_dblquad(self.integrand, + 0, 2*math.pi, 0, math.pi/2, r) + except Exception as e: + print(type(e).__name__ + ":", e) + sys.exit() + + return self.k**2 * result + + def phase(self, theta, phi, x, y, z): + """Phase function.""" + sin_theta, sin_phi = sin(theta), sin(phi) + cos_theta, cos_phi = cos(theta), cos(phi) + + return self.k*(sin_theta*(y*sin_phi - z*cos_phi) + cos_theta*x) + def integrand(self, theta, phi, r): + """...""" + return sin(theta) * cos(theta) * \ + self.f(sin(theta), theta, phi, self.params) * \ + cexp(1j*self.phase(theta, phi, self.x, r.y, r.z)) #try: # getattr(psi_spherical, "called") @@ -90,29 +114,6 @@ def __call__(self, r): # print("Calculating inital field configuration. " # "This will take some time...") - def phase(theta, phi, x, y, z): - """Phase function.""" - sin_theta, sin_phi = sin(theta), sin(phi) - cos_theta, cos_phi = cos(theta), cos(phi) - - return k*(sin_theta*(y*sin_phi - z*cos_phi) + cos_theta*x) - - def integrand(theta, phi): - """...""" - return sin(theta) * cos(theta) * \ - f(sin(theta), theta, phi, params) * \ - cexp(1j*phase(theta, phi, x, r.y, r.z)) - - try: - (result, - real_tol, - imag_tol) = complex_dblquad(integrand, 0, 2*math.pi, 0, math.pi/2) - except Exception as e: - print(type(e).__name__ + ":", e) - sys.exit() - - return k**2 * result - def main(): From 1c0c5705633ab2c4410f6b092a8547ab41b3f849 Mon Sep 17 00:00:00 2001 From: Daniel Kotik Date: Sat, 29 Feb 2020 20:04:49 +0100 Subject: [PATCH 022/145] Pass r.y and r.z instead of r: Now the C type can be given in the function prototypes. --- Laguerre_Gauss_3d/beamprofile.py | 21 +++++++++++---------- 1 file changed, 11 insertions(+), 10 deletions(-) diff --git a/Laguerre_Gauss_3d/beamprofile.py b/Laguerre_Gauss_3d/beamprofile.py index 31a6d02..53ef6ac 100644 --- a/Laguerre_Gauss_3d/beamprofile.py +++ b/Laguerre_Gauss_3d/beamprofile.py @@ -20,20 +20,20 @@ " `$ cythonize -3 -i beamprofile.py`") -def real_func(x, y, func, r): +def real_func(x, y, func, ry, rz): """Return real part of function.""" - return func(x, y, r).real + return func(x, y, ry, rz).real -def imag_func(x, y, func, r): +def imag_func(x, y, func, ry, rz): """Return imag part of function.""" - return func(x, y, r).imag + return func(x, y, ry, rz).imag -def complex_dblquad(func, a, b, gfun, hfun, r): +def complex_dblquad(func, a, b, gfun, hfun, ry, rz): """Integrate real and imaginary part of the given function.""" - real, real_tol = dblquad(real_func, a, b, gfun, hfun, (func, r)) - imag, imag_tol = dblquad(imag_func, a, b, gfun, hfun, (func, r)) + real, real_tol = dblquad(real_func, a, b, gfun, hfun, (func, ry, rz)) + imag, imag_tol = dblquad(imag_func, a, b, gfun, hfun, (func, ry, rz)) return real + 1j*imag, real_tol, imag_tol @@ -87,7 +87,8 @@ def __call__(self, r): (result, real_tol, imag_tol) = complex_dblquad(self.integrand, - 0, 2*math.pi, 0, math.pi/2, r) + 0, 2*math.pi, 0, math.pi/2, + r.y, r.z) except Exception as e: print(type(e).__name__ + ":", e) sys.exit() @@ -101,11 +102,11 @@ def phase(self, theta, phi, x, y, z): return self.k*(sin_theta*(y*sin_phi - z*cos_phi) + cos_theta*x) - def integrand(self, theta, phi, r): + def integrand(self, theta, phi, ry, rz): """...""" return sin(theta) * cos(theta) * \ self.f(sin(theta), theta, phi, self.params) * \ - cexp(1j*self.phase(theta, phi, self.x, r.y, r.z)) + cexp(1j*self.phase(theta, phi, self.x, ry, rz)) #try: # getattr(psi_spherical, "called") From 2bf2afb82fc0a9032c40de9b8702a0d14be20413 Mon Sep 17 00:00:00 2001 From: Daniel Kotik Date: Sat, 29 Feb 2020 20:06:09 +0100 Subject: [PATCH 023/145] Define cdef class --- Laguerre_Gauss_3d/beamprofile.pxd | 17 ++++++++++++----- 1 file changed, 12 insertions(+), 5 deletions(-) diff --git a/Laguerre_Gauss_3d/beamprofile.pxd b/Laguerre_Gauss_3d/beamprofile.pxd index ea942d0..5aa7383 100644 --- a/Laguerre_Gauss_3d/beamprofile.pxd +++ b/Laguerre_Gauss_3d/beamprofile.pxd @@ -22,14 +22,14 @@ cdef extern from "complex.h": cpdef double complex cexp(double complex z) # function type declaration for spectrum amplitudes -ctypedef double complex (*f_spectrum_type)(double theta, double phi) +ctypedef double complex (*f_spectrum_type)(double sin_theta, double theta, double phi, dict params) # function prototypes -cdef double real_func(double x, double y, func) -cdef double imag_func(double x, double y, func) +cdef double real_func(double x, double y, func, double ry, double rz) +cdef double imag_func(double x, double y, func, double ry, double rz) @cython.locals(real=cython.double, imag=cython.double, real_tol=cython.double, imag_tol=cython.double) -cdef (double complex, double, double) complex_dblquad(func, double a, double b, double gfun, double hfun) +cdef (double complex, double, double) complex_dblquad(func, double a, double b, double gfun, double hfun, double ry, double rz) @cython.locals(W_y=cython.double, k=cython.double) cdef double complex f_Gauss_spherical(double sin_theta, double theta, double phi, @@ -39,4 +39,11 @@ cdef double complex f_Gauss_spherical(double sin_theta, double theta, double phi cdef double complex f_Laguerre_Gauss_spherical(double sin_theta, double theta, double phi, dict params) -#cpdef double complex psi_spherical(r, double x, dict params) +cdef class PsiSpherical: + cdef public int m + cdef public double x, k + cdef public dict params + cdef f_spectrum_type f + + cdef double phase(self, double theta, double phi, double x, double y, double z) + cpdef integrand(self, double theta, double phi, double ry, double rz) From bbf332cdd86eb9f58b0e8452c634023910c1283e Mon Sep 17 00:00:00 2001 From: Daniel Kotik Date: Sun, 1 Mar 2020 17:59:56 +0100 Subject: [PATCH 024/145] Add integrand type declaration --- Laguerre_Gauss_3d/beamprofile.pxd | 3 ++- 1 file changed, 2 insertions(+), 1 deletion(-) diff --git a/Laguerre_Gauss_3d/beamprofile.pxd b/Laguerre_Gauss_3d/beamprofile.pxd index 5aa7383..173bf1a 100644 --- a/Laguerre_Gauss_3d/beamprofile.pxd +++ b/Laguerre_Gauss_3d/beamprofile.pxd @@ -23,6 +23,7 @@ cdef extern from "complex.h": # function type declaration for spectrum amplitudes ctypedef double complex (*f_spectrum_type)(double sin_theta, double theta, double phi, dict params) +ctypedef double complex (*integrand_type)(double theta, double phi, double ry, double rz) # function prototypes cdef double real_func(double x, double y, func, double ry, double rz) @@ -46,4 +47,4 @@ cdef class PsiSpherical: cdef f_spectrum_type f cdef double phase(self, double theta, double phi, double x, double y, double z) - cpdef integrand(self, double theta, double phi, double ry, double rz) + cpdef double complex integrand(self, double theta, double phi, double ry, double rz) From 8518a737f89338c45e33e92eb97aabbd0585c51f Mon Sep 17 00:00:00 2001 From: Daniel Kotik Date: Tue, 10 Mar 2020 22:37:55 +0100 Subject: [PATCH 025/145] Initialise ry and rz with __call__ method --- Laguerre_Gauss_3d/beamprofile.pxd | 15 ++++++++------- Laguerre_Gauss_3d/beamprofile.py | 25 +++++++++++++------------ 2 files changed, 21 insertions(+), 19 deletions(-) diff --git a/Laguerre_Gauss_3d/beamprofile.pxd b/Laguerre_Gauss_3d/beamprofile.pxd index 173bf1a..27d1c3d 100644 --- a/Laguerre_Gauss_3d/beamprofile.pxd +++ b/Laguerre_Gauss_3d/beamprofile.pxd @@ -23,18 +23,18 @@ cdef extern from "complex.h": # function type declaration for spectrum amplitudes ctypedef double complex (*f_spectrum_type)(double sin_theta, double theta, double phi, dict params) -ctypedef double complex (*integrand_type)(double theta, double phi, double ry, double rz) +ctypedef double complex (*integrand_type)(double theta, double phi) # function prototypes -cdef double real_func(double x, double y, func, double ry, double rz) -cdef double imag_func(double x, double y, func, double ry, double rz) +cdef double real_func(double x, double y, func) +cdef double imag_func(double x, double y, func) @cython.locals(real=cython.double, imag=cython.double, real_tol=cython.double, imag_tol=cython.double) -cdef (double complex, double, double) complex_dblquad(func, double a, double b, double gfun, double hfun, double ry, double rz) +cdef (double complex, double, double) complex_dblquad(func, double a, double b, double gfun, double hfun) @cython.locals(W_y=cython.double, k=cython.double) cdef double complex f_Gauss_spherical(double sin_theta, double theta, double phi, - dict params) + dict params) @cython.locals(m=cython.int) cdef double complex f_Laguerre_Gauss_spherical(double sin_theta, double theta, @@ -45,6 +45,7 @@ cdef class PsiSpherical: cdef public double x, k cdef public dict params cdef f_spectrum_type f - + cdef double ry, rz + cdef double phase(self, double theta, double phi, double x, double y, double z) - cpdef double complex integrand(self, double theta, double phi, double ry, double rz) + cpdef double complex integrand(self, double theta, double phi) diff --git a/Laguerre_Gauss_3d/beamprofile.py b/Laguerre_Gauss_3d/beamprofile.py index 53ef6ac..2323365 100644 --- a/Laguerre_Gauss_3d/beamprofile.py +++ b/Laguerre_Gauss_3d/beamprofile.py @@ -20,20 +20,20 @@ " `$ cythonize -3 -i beamprofile.py`") -def real_func(x, y, func, ry, rz): +def real_func(x, y, func): """Return real part of function.""" - return func(x, y, ry, rz).real + return func(x, y).real -def imag_func(x, y, func, ry, rz): +def imag_func(x, y, func): """Return imag part of function.""" - return func(x, y, ry, rz).imag + return func(x, y).imag -def complex_dblquad(func, a, b, gfun, hfun, ry, rz): +def complex_dblquad(func, a, b, gfun, hfun): """Integrate real and imaginary part of the given function.""" - real, real_tol = dblquad(real_func, a, b, gfun, hfun, (func, ry, rz)) - imag, imag_tol = dblquad(imag_func, a, b, gfun, hfun, (func, ry, rz)) + real, real_tol = dblquad(real_func, a, b, gfun, hfun, (func,)) + imag, imag_tol = dblquad(imag_func, a, b, gfun, hfun, (func,)) return real + 1j*imag, real_tol, imag_tol @@ -83,12 +83,13 @@ def __init__(self, x, params): def __call__(self, r): """...""" + self.ry = r.y + self.rz = r.z + try: (result, real_tol, - imag_tol) = complex_dblquad(self.integrand, - 0, 2*math.pi, 0, math.pi/2, - r.y, r.z) + imag_tol) = complex_dblquad(self.integrand, 0, 2*math.pi, 0, math.pi/2) except Exception as e: print(type(e).__name__ + ":", e) sys.exit() @@ -102,11 +103,11 @@ def phase(self, theta, phi, x, y, z): return self.k*(sin_theta*(y*sin_phi - z*cos_phi) + cos_theta*x) - def integrand(self, theta, phi, ry, rz): + def integrand(self, theta, phi): """...""" return sin(theta) * cos(theta) * \ self.f(sin(theta), theta, phi, self.params) * \ - cexp(1j*self.phase(theta, phi, self.x, ry, rz)) + cexp(1j*self.phase(theta, phi, self.x, self.ry, self.rz)) #try: # getattr(psi_spherical, "called") From 077405f00f8b6040c3f062b022438cb073f248b6 Mon Sep 17 00:00:00 2001 From: Daniel Kotik Date: Tue, 10 Mar 2020 22:38:44 +0100 Subject: [PATCH 026/145] Fix typo --- Laguerre_Gauss_3d/beamprofile.py | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/Laguerre_Gauss_3d/beamprofile.py b/Laguerre_Gauss_3d/beamprofile.py index 2323365..0b5c903 100644 --- a/Laguerre_Gauss_3d/beamprofile.py +++ b/Laguerre_Gauss_3d/beamprofile.py @@ -41,7 +41,7 @@ def complex_dblquad(func, a, b, gfun, hfun): def f_Gauss_spherical(sin_theta, theta, phi, params): """2d-Gaussian spectrum amplitude. - Impementation for spherical coordinates. + Implementation for spherical coordinates. """ W_y, k = params['W_y'], params['k'] @@ -51,7 +51,7 @@ def f_Gauss_spherical(sin_theta, theta, phi, params): def f_Laguerre_Gauss_spherical(sin_theta, theta, phi, params): """Laguerre-Gaussian spectrum amplitude. - Impementation for spherical coordinates. + Implementation for spherical coordinates. """ m = params['m'] From 20db4522916e956615e2772d856a25c0c2d07de6 Mon Sep 17 00:00:00 2001 From: Daniel Kotik Date: Tue, 10 Mar 2020 22:38:53 +0100 Subject: [PATCH 027/145] Add leading underscore: This indicates functions imag_func, real_func and complex_dblquad for internal use only. --- Laguerre_Gauss_3d/beamprofile.pxd | 6 +++--- Laguerre_Gauss_3d/beamprofile.py | 12 ++++++------ 2 files changed, 9 insertions(+), 9 deletions(-) diff --git a/Laguerre_Gauss_3d/beamprofile.pxd b/Laguerre_Gauss_3d/beamprofile.pxd index 27d1c3d..638e3d1 100644 --- a/Laguerre_Gauss_3d/beamprofile.pxd +++ b/Laguerre_Gauss_3d/beamprofile.pxd @@ -26,11 +26,11 @@ ctypedef double complex (*f_spectrum_type)(double sin_theta, double theta, doubl ctypedef double complex (*integrand_type)(double theta, double phi) # function prototypes -cdef double real_func(double x, double y, func) -cdef double imag_func(double x, double y, func) +cdef double _real_func(double x, double y, func) +cdef double _imag_func(double x, double y, func) @cython.locals(real=cython.double, imag=cython.double, real_tol=cython.double, imag_tol=cython.double) -cdef (double complex, double, double) complex_dblquad(func, double a, double b, double gfun, double hfun) +cdef (double complex, double, double) _complex_dblquad(func, double a, double b, double gfun, double hfun) @cython.locals(W_y=cython.double, k=cython.double) cdef double complex f_Gauss_spherical(double sin_theta, double theta, double phi, diff --git a/Laguerre_Gauss_3d/beamprofile.py b/Laguerre_Gauss_3d/beamprofile.py index 0b5c903..2512477 100644 --- a/Laguerre_Gauss_3d/beamprofile.py +++ b/Laguerre_Gauss_3d/beamprofile.py @@ -20,20 +20,20 @@ " `$ cythonize -3 -i beamprofile.py`") -def real_func(x, y, func): +def _real_func(x, y, func): """Return real part of function.""" return func(x, y).real -def imag_func(x, y, func): +def _imag_func(x, y, func): """Return imag part of function.""" return func(x, y).imag -def complex_dblquad(func, a, b, gfun, hfun): +def _complex_dblquad(func, a, b, gfun, hfun): """Integrate real and imaginary part of the given function.""" - real, real_tol = dblquad(real_func, a, b, gfun, hfun, (func,)) - imag, imag_tol = dblquad(imag_func, a, b, gfun, hfun, (func,)) + real, real_tol = dblquad(_real_func, a, b, gfun, hfun, (func,)) + imag, imag_tol = dblquad(_imag_func, a, b, gfun, hfun, (func,)) return real + 1j*imag, real_tol, imag_tol @@ -89,7 +89,7 @@ def __call__(self, r): try: (result, real_tol, - imag_tol) = complex_dblquad(self.integrand, 0, 2*math.pi, 0, math.pi/2) + imag_tol) = _complex_dblquad(self.integrand, 0, 2*math.pi, 0, math.pi/2) except Exception as e: print(type(e).__name__ + ":", e) sys.exit() From 13db1db74d40c6754d83d91a5be642e87395fcd2 Mon Sep 17 00:00:00 2001 From: Daniel Kotik Date: Wed, 11 Mar 2020 13:37:12 +0100 Subject: [PATCH 028/145] Update docstring --- Laguerre_Gauss_3d/beamprofile.py | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/Laguerre_Gauss_3d/beamprofile.py b/Laguerre_Gauss_3d/beamprofile.py index 2512477..947ceff 100644 --- a/Laguerre_Gauss_3d/beamprofile.py +++ b/Laguerre_Gauss_3d/beamprofile.py @@ -104,7 +104,7 @@ def phase(self, theta, phi, x, y, z): return self.k*(sin_theta*(y*sin_phi - z*cos_phi) + cos_theta*x) def integrand(self, theta, phi): - """...""" + """Integrand function.""" return sin(theta) * cos(theta) * \ self.f(sin(theta), theta, phi, self.params) * \ cexp(1j*self.phase(theta, phi, self.x, self.ry, self.rz)) From 6cc43adb415e4ba4dc04bb6f198c708bf023a27c Mon Sep 17 00:00:00 2001 From: Daniel Kotik Date: Wed, 11 Mar 2020 18:16:11 +0100 Subject: [PATCH 029/145] Reduce integration overhead with LowLevelCallable: Implement real_func and imag_func as C functions with integrand function as void* parameter. --- Laguerre_Gauss_3d/beamprofile.pxd | 4 +++- Laguerre_Gauss_3d/beamprofile.py | 35 +++++++++++++++++++++++++++++-- 2 files changed, 36 insertions(+), 3 deletions(-) diff --git a/Laguerre_Gauss_3d/beamprofile.pxd b/Laguerre_Gauss_3d/beamprofile.pxd index 638e3d1..f59c3ec 100644 --- a/Laguerre_Gauss_3d/beamprofile.pxd +++ b/Laguerre_Gauss_3d/beamprofile.pxd @@ -7,7 +7,8 @@ version: 1.5-beta release date: xx.xx.2020 creation date: 22.02.2020 """ -import cython +cimport cython +from cpython.pycapsule cimport PyCapsule_New # declare C functions as "cpdef" to export them to the module cdef extern from "stdlib.h": @@ -28,6 +29,7 @@ ctypedef double complex (*integrand_type)(double theta, double phi) # function prototypes cdef double _real_func(double x, double y, func) cdef double _imag_func(double x, double y, func) +cdef double __imag_func(double x, double y, void *func_ptr) @cython.locals(real=cython.double, imag=cython.double, real_tol=cython.double, imag_tol=cython.double) cdef (double complex, double, double) _complex_dblquad(func, double a, double b, double gfun, double hfun) diff --git a/Laguerre_Gauss_3d/beamprofile.py b/Laguerre_Gauss_3d/beamprofile.py index 947ceff..8a01e8f 100644 --- a/Laguerre_Gauss_3d/beamprofile.py +++ b/Laguerre_Gauss_3d/beamprofile.py @@ -13,11 +13,14 @@ from scipy.integrate import dblquad + if not cython.compiled: from math import sin, cos, exp from cmath import exp as cexp print("Please consider compiling `beamprofile.py` via Cython:\n\n" " `$ cythonize -3 -i beamprofile.py`") +else: + from scipy import LowLevelCallable def _real_func(x, y, func): @@ -30,10 +33,38 @@ def _imag_func(x, y, func): return func(x, y).imag +#cdef double _imag_func(double x, double y, void *func_ptr): +# """Return imag part of function.""" +# return (func_ptr)(x, y).imag + +def __imag_func(x, y, func_ptr): + """Return imag part of function.""" + func = cython.cast(object, func_ptr) + return func(x, y).imag + + def _complex_dblquad(func, a, b, gfun, hfun): """Integrate real and imaginary part of the given function.""" - real, real_tol = dblquad(_real_func, a, b, gfun, hfun, (func,)) - imag, imag_tol = dblquad(_imag_func, a, b, gfun, hfun, (func,)) + + if cython.compiled: + # pure python formulation of: cdef void *f_ptr = func + f_ptr = cython.declare(cython.p_void, cython.cast(cython.p_void, func)) + + func_capsule = PyCapsule_New(f_ptr, cython.NULL, cython.NULL) + + current_module = sys.modules[__name__] + + #ll_real_func = LowLevelCallable.from_cython(current_module, '_real_func', func_capsule) + ll_imag_func = LowLevelCallable.from_cython(current_module, '__imag_func', func_capsule) + + #real, real_tol = dblquad(ll_real_func, a, b, gfun, hfun) + #imag, imag_tol = dblquad(ll_imag_func, a, b, gfun, hfun) + + real, real_tol = dblquad(_real_func, a, b, gfun, hfun, (func,)) + imag, imag_tol = dblquad(_imag_func, a, b, gfun, hfun, (func,)) + else: + real, real_tol = dblquad(_real_func, a, b, gfun, hfun, (func,)) + imag, imag_tol = dblquad(_imag_func, a, b, gfun, hfun, (func,)) return real + 1j*imag, real_tol, imag_tol From 8633f26455b58b61460d7508a6cac86b53000a5f Mon Sep 17 00:00:00 2001 From: Daniel Kotik Date: Wed, 11 Mar 2020 19:12:42 +0100 Subject: [PATCH 030/145] Rewrite function signatures --- Laguerre_Gauss_3d/beamprofile.pxd | 3 ++- Laguerre_Gauss_3d/beamprofile.py | 25 +++++++++++++++++-------- 2 files changed, 19 insertions(+), 9 deletions(-) diff --git a/Laguerre_Gauss_3d/beamprofile.pxd b/Laguerre_Gauss_3d/beamprofile.pxd index f59c3ec..3556b6e 100644 --- a/Laguerre_Gauss_3d/beamprofile.pxd +++ b/Laguerre_Gauss_3d/beamprofile.pxd @@ -29,7 +29,8 @@ ctypedef double complex (*integrand_type)(double theta, double phi) # function prototypes cdef double _real_func(double x, double y, func) cdef double _imag_func(double x, double y, func) -cdef double __imag_func(double x, double y, void *func_ptr) +cdef double __imag_func(int n, double *arr, void *func_ptr) +cdef double __real_func(int n, double *arr, void *func_ptr) @cython.locals(real=cython.double, imag=cython.double, real_tol=cython.double, imag_tol=cython.double) cdef (double complex, double, double) _complex_dblquad(func, double a, double b, double gfun, double hfun) diff --git a/Laguerre_Gauss_3d/beamprofile.py b/Laguerre_Gauss_3d/beamprofile.py index 8a01e8f..03c12ef 100644 --- a/Laguerre_Gauss_3d/beamprofile.py +++ b/Laguerre_Gauss_3d/beamprofile.py @@ -11,7 +11,7 @@ import math import sys -from scipy.integrate import dblquad +from scipy.integrate import dblquad, nquad, quad if not cython.compiled: @@ -37,10 +37,16 @@ def _imag_func(x, y, func): # """Return imag part of function.""" # return (func_ptr)(x, y).imag -def __imag_func(x, y, func_ptr): +def __imag_func(n, arr, func_ptr): """Return imag part of function.""" func = cython.cast(object, func_ptr) - return func(x, y).imag + return func(arr[0], arr[1]).imag + + +def __real_func(n, arr, func_ptr): + """Return imag part of function.""" + func = cython.cast(object, func_ptr) + return func(arr[0], arr[1]).real def _complex_dblquad(func, a, b, gfun, hfun): @@ -54,17 +60,20 @@ def _complex_dblquad(func, a, b, gfun, hfun): current_module = sys.modules[__name__] - #ll_real_func = LowLevelCallable.from_cython(current_module, '_real_func', func_capsule) + ll_real_func = LowLevelCallable.from_cython(current_module, '__real_func', func_capsule) ll_imag_func = LowLevelCallable.from_cython(current_module, '__imag_func', func_capsule) - #real, real_tol = dblquad(ll_real_func, a, b, gfun, hfun) - #imag, imag_tol = dblquad(ll_imag_func, a, b, gfun, hfun) + real, real_tol = dblquad(ll_real_func, a, b, gfun, hfun) + imag, imag_tol = dblquad(ll_imag_func, a, b, gfun, hfun) + + #real, real_tol = dblquad(_real_func, a, b, gfun, hfun, (func,)) + #imag, imag_tol = dblquad(_imag_func, a, b, gfun, hfun, (func,)) + #imag, imag_tol = 0,0 - real, real_tol = dblquad(_real_func, a, b, gfun, hfun, (func,)) - imag, imag_tol = dblquad(_imag_func, a, b, gfun, hfun, (func,)) else: real, real_tol = dblquad(_real_func, a, b, gfun, hfun, (func,)) imag, imag_tol = dblquad(_imag_func, a, b, gfun, hfun, (func,)) + #imag, imag_tol = 0,0 return real + 1j*imag, real_tol, imag_tol From 9cb2533bc4d25978075798aad86872e8df260ea1 Mon Sep 17 00:00:00 2001 From: Daniel Kotik Date: Fri, 13 Mar 2020 23:52:56 +0100 Subject: [PATCH 031/145] Clean up code --- Laguerre_Gauss_3d/beamprofile.py | 28 ++++++++++------------------ 1 file changed, 10 insertions(+), 18 deletions(-) diff --git a/Laguerre_Gauss_3d/beamprofile.py b/Laguerre_Gauss_3d/beamprofile.py index 03c12ef..298056d 100644 --- a/Laguerre_Gauss_3d/beamprofile.py +++ b/Laguerre_Gauss_3d/beamprofile.py @@ -33,20 +33,16 @@ def _imag_func(x, y, func): return func(x, y).imag -#cdef double _imag_func(double x, double y, void *func_ptr): -# """Return imag part of function.""" -# return (func_ptr)(x, y).imag - def __imag_func(n, arr, func_ptr): """Return imag part of function.""" - func = cython.cast(object, func_ptr) - return func(arr[0], arr[1]).imag + #return (func_ptr)(arr[0], arr[1]).imag + return cython.cast(object, func_ptr)(arr[0], arr[1]).imag def __real_func(n, arr, func_ptr): - """Return imag part of function.""" - func = cython.cast(object, func_ptr) - return func(arr[0], arr[1]).real + """Return real part of function.""" + #return (func_ptr)(arr[0], arr[1]).real + return cython.cast(object, func_ptr)(arr[0], arr[1]).real def _complex_dblquad(func, a, b, gfun, hfun): @@ -60,20 +56,16 @@ def _complex_dblquad(func, a, b, gfun, hfun): current_module = sys.modules[__name__] - ll_real_func = LowLevelCallable.from_cython(current_module, '__real_func', func_capsule) - ll_imag_func = LowLevelCallable.from_cython(current_module, '__imag_func', func_capsule) + ll_real_func = LowLevelCallable.from_cython(current_module, + '__real_func', func_capsule) + ll_imag_func = LowLevelCallable.from_cython(current_module, + '__imag_func', func_capsule) real, real_tol = dblquad(ll_real_func, a, b, gfun, hfun) - imag, imag_tol = dblquad(ll_imag_func, a, b, gfun, hfun) - - #real, real_tol = dblquad(_real_func, a, b, gfun, hfun, (func,)) - #imag, imag_tol = dblquad(_imag_func, a, b, gfun, hfun, (func,)) - #imag, imag_tol = 0,0 - + imag, imag_tol = dblquad(ll_imag_func, a, b, gfun, hfun) else: real, real_tol = dblquad(_real_func, a, b, gfun, hfun, (func,)) imag, imag_tol = dblquad(_imag_func, a, b, gfun, hfun, (func,)) - #imag, imag_tol = 0,0 return real + 1j*imag, real_tol, imag_tol From 38aa0f40996ab44a918cd29decb3ddb838e5d6d8 Mon Sep 17 00:00:00 2001 From: Daniel Kotik Date: Fri, 13 Mar 2020 23:53:09 +0100 Subject: [PATCH 032/145] Declare func_ptr of type PsiSpherical: This change makes the actual integrand fucntions fully C functions without any Python overhead! --- Laguerre_Gauss_3d/beamprofile.pxd | 14 +++++++------- Laguerre_Gauss_3d/beamprofile.py | 11 +++++++---- 2 files changed, 14 insertions(+), 11 deletions(-) diff --git a/Laguerre_Gauss_3d/beamprofile.pxd b/Laguerre_Gauss_3d/beamprofile.pxd index 3556b6e..e206c05 100644 --- a/Laguerre_Gauss_3d/beamprofile.pxd +++ b/Laguerre_Gauss_3d/beamprofile.pxd @@ -12,15 +12,15 @@ from cpython.pycapsule cimport PyCapsule_New # declare C functions as "cpdef" to export them to the module cdef extern from "stdlib.h": - cpdef int abs (int n) + cpdef int abs (int n) nogil cdef extern from "math.h": - cpdef double sin(double x) - cpdef double cos(double x) - cpdef double exp(double x) + cpdef double sin(double x) nogil + cpdef double cos(double x) nogil + cpdef double exp(double x) nogil cdef extern from "complex.h": - cpdef double complex cexp(double complex z) + cpdef double complex cexp(double complex z) nogil # function type declaration for spectrum amplitudes ctypedef double complex (*f_spectrum_type)(double sin_theta, double theta, double phi, dict params) @@ -33,7 +33,7 @@ cdef double __imag_func(int n, double *arr, void *func_ptr) cdef double __real_func(int n, double *arr, void *func_ptr) @cython.locals(real=cython.double, imag=cython.double, real_tol=cython.double, imag_tol=cython.double) -cdef (double complex, double, double) _complex_dblquad(func, double a, double b, double gfun, double hfun) +cdef (double complex, double, double) _complex_dblquad(PsiSpherical func, double a, double b, double gfun, double hfun) @cython.locals(W_y=cython.double, k=cython.double) cdef double complex f_Gauss_spherical(double sin_theta, double theta, double phi, @@ -50,5 +50,5 @@ cdef class PsiSpherical: cdef f_spectrum_type f cdef double ry, rz - cdef double phase(self, double theta, double phi, double x, double y, double z) + cdef double phase(self, double theta, double phi, double x, double y, double z) nogil cpdef double complex integrand(self, double theta, double phi) diff --git a/Laguerre_Gauss_3d/beamprofile.py b/Laguerre_Gauss_3d/beamprofile.py index 298056d..91edcfe 100644 --- a/Laguerre_Gauss_3d/beamprofile.py +++ b/Laguerre_Gauss_3d/beamprofile.py @@ -36,13 +36,16 @@ def _imag_func(x, y, func): def __imag_func(n, arr, func_ptr): """Return imag part of function.""" #return (func_ptr)(arr[0], arr[1]).imag - return cython.cast(object, func_ptr)(arr[0], arr[1]).imag + #return cython.cast(object, func_ptr)(arr[0], arr[1]).imag + return cython.cast(PsiSpherical, func_ptr).integrand(arr[0], arr[1]).imag + def __real_func(n, arr, func_ptr): """Return real part of function.""" #return (func_ptr)(arr[0], arr[1]).real - return cython.cast(object, func_ptr)(arr[0], arr[1]).real + #return cython.cast(object, func_ptr)(arr[0], arr[1]).real + return cython.cast(PsiSpherical, func_ptr).integrand(arr[0], arr[1]).real def _complex_dblquad(func, a, b, gfun, hfun): @@ -60,7 +63,6 @@ def _complex_dblquad(func, a, b, gfun, hfun): '__real_func', func_capsule) ll_imag_func = LowLevelCallable.from_cython(current_module, '__imag_func', func_capsule) - real, real_tol = dblquad(ll_real_func, a, b, gfun, hfun) imag, imag_tol = dblquad(ll_imag_func, a, b, gfun, hfun) else: @@ -121,7 +123,8 @@ def __call__(self, r): try: (result, real_tol, - imag_tol) = _complex_dblquad(self.integrand, 0, 2*math.pi, 0, math.pi/2) + imag_tol) = _complex_dblquad(self if cython.compiled else self.integrand, + 0, 2*math.pi, 0, math.pi/2) except Exception as e: print(type(e).__name__ + ":", e) sys.exit() From 4f117b49b94a0cab847b3d58afcac787a41ac0a6 Mon Sep 17 00:00:00 2001 From: Daniel Kotik Date: Fri, 13 Mar 2020 23:53:11 +0100 Subject: [PATCH 033/145] Remove double calculation of trig functions --- Laguerre_Gauss_3d/beamprofile.py | 19 +++++++++++-------- 1 file changed, 11 insertions(+), 8 deletions(-) diff --git a/Laguerre_Gauss_3d/beamprofile.py b/Laguerre_Gauss_3d/beamprofile.py index 91edcfe..a43b13d 100644 --- a/Laguerre_Gauss_3d/beamprofile.py +++ b/Laguerre_Gauss_3d/beamprofile.py @@ -11,7 +11,7 @@ import math import sys -from scipy.integrate import dblquad, nquad, quad +from scipy.integrate import dblquad if not cython.compiled: @@ -124,25 +124,28 @@ def __call__(self, r): (result, real_tol, imag_tol) = _complex_dblquad(self if cython.compiled else self.integrand, - 0, 2*math.pi, 0, math.pi/2) + 0, 2*math.pi, 0, math.pi/2) except Exception as e: print(type(e).__name__ + ":", e) sys.exit() return self.k**2 * result - def phase(self, theta, phi, x, y, z): + def phase(self, sin_theta, cos_theta, phi, x, y, z): """Phase function.""" - sin_theta, sin_phi = sin(theta), sin(phi) - cos_theta, cos_phi = cos(theta), cos(phi) + sin_phi = sin(phi) + cos_phi = cos(phi) return self.k*(sin_theta*(y*sin_phi - z*cos_phi) + cos_theta*x) def integrand(self, theta, phi): """Integrand function.""" - return sin(theta) * cos(theta) * \ - self.f(sin(theta), theta, phi, self.params) * \ - cexp(1j*self.phase(theta, phi, self.x, self.ry, self.rz)) + sin_theta = sin(theta) + cos_theta = cos(theta) + + return sin_theta * cos_theta * \ + self.f(sin_theta, theta, phi, self.params) * \ + cexp(1j*self.phase(sin_theta, cos_theta, phi, self.x, self.ry, self.rz)) #try: # getattr(psi_spherical, "called") From c529d75fc0bb3367970245b9ef8667ac1d5eccdb Mon Sep 17 00:00:00 2001 From: Daniel Kotik Date: Fri, 13 Mar 2020 23:53:15 +0100 Subject: [PATCH 034/145] Align code to 80 characters per line --- Laguerre_Gauss_3d/beamprofile.pxd | 13 +++++++++---- Laguerre_Gauss_3d/beamprofile.py | 1 - 2 files changed, 9 insertions(+), 5 deletions(-) diff --git a/Laguerre_Gauss_3d/beamprofile.pxd b/Laguerre_Gauss_3d/beamprofile.pxd index e206c05..35661c1 100644 --- a/Laguerre_Gauss_3d/beamprofile.pxd +++ b/Laguerre_Gauss_3d/beamprofile.pxd @@ -23,7 +23,8 @@ cdef extern from "complex.h": cpdef double complex cexp(double complex z) nogil # function type declaration for spectrum amplitudes -ctypedef double complex (*f_spectrum_type)(double sin_theta, double theta, double phi, dict params) +ctypedef double complex (*f_spectrum_type)(double sin_theta, double theta, + double phi, dict params) ctypedef double complex (*integrand_type)(double theta, double phi) # function prototypes @@ -32,8 +33,11 @@ cdef double _imag_func(double x, double y, func) cdef double __imag_func(int n, double *arr, void *func_ptr) cdef double __real_func(int n, double *arr, void *func_ptr) -@cython.locals(real=cython.double, imag=cython.double, real_tol=cython.double, imag_tol=cython.double) -cdef (double complex, double, double) _complex_dblquad(PsiSpherical func, double a, double b, double gfun, double hfun) +@cython.locals(real=cython.double, imag=cython.double, real_tol=cython.double, + imag_tol=cython.double) +cdef (double complex, double, double) _complex_dblquad(PsiSpherical func, + double a, double b, + double gfun, double hfun) @cython.locals(W_y=cython.double, k=cython.double) cdef double complex f_Gauss_spherical(double sin_theta, double theta, double phi, @@ -50,5 +54,6 @@ cdef class PsiSpherical: cdef f_spectrum_type f cdef double ry, rz - cdef double phase(self, double theta, double phi, double x, double y, double z) nogil + cdef double phase(self, double sin_theta, double cos_theta, double phi, + double x, double y, double z) nogil cpdef double complex integrand(self, double theta, double phi) diff --git a/Laguerre_Gauss_3d/beamprofile.py b/Laguerre_Gauss_3d/beamprofile.py index a43b13d..6d43a99 100644 --- a/Laguerre_Gauss_3d/beamprofile.py +++ b/Laguerre_Gauss_3d/beamprofile.py @@ -40,7 +40,6 @@ def __imag_func(n, arr, func_ptr): return cython.cast(PsiSpherical, func_ptr).integrand(arr[0], arr[1]).imag - def __real_func(n, arr, func_ptr): """Return real part of function.""" #return (func_ptr)(arr[0], arr[1]).real From dde2079e5bee7528cc915ec4466d61fb7f4413dc Mon Sep 17 00:00:00 2001 From: Daniel Kotik Date: Sat, 14 Mar 2020 10:42:03 +0100 Subject: [PATCH 035/145] Update comments --- Laguerre_Gauss_3d/beamprofile.py | 9 ++++----- 1 file changed, 4 insertions(+), 5 deletions(-) diff --git a/Laguerre_Gauss_3d/beamprofile.py b/Laguerre_Gauss_3d/beamprofile.py index 6d43a99..82785cf 100644 --- a/Laguerre_Gauss_3d/beamprofile.py +++ b/Laguerre_Gauss_3d/beamprofile.py @@ -35,21 +35,20 @@ def _imag_func(x, y, func): def __imag_func(n, arr, func_ptr): """Return imag part of function.""" - #return (func_ptr)(arr[0], arr[1]).imag - #return cython.cast(object, func_ptr)(arr[0], arr[1]).imag + # pure python formulation of: + # return (func_ptr)(arr[0], arr[1]).imag return cython.cast(PsiSpherical, func_ptr).integrand(arr[0], arr[1]).imag def __real_func(n, arr, func_ptr): """Return real part of function.""" - #return (func_ptr)(arr[0], arr[1]).real - #return cython.cast(object, func_ptr)(arr[0], arr[1]).real + # pure python formulation of: + # return (func_ptr)(arr[0], arr[1]).real return cython.cast(PsiSpherical, func_ptr).integrand(arr[0], arr[1]).real def _complex_dblquad(func, a, b, gfun, hfun): """Integrate real and imaginary part of the given function.""" - if cython.compiled: # pure python formulation of: cdef void *f_ptr = func f_ptr = cython.declare(cython.p_void, cython.cast(cython.p_void, func)) From 9990f75ec2449bbb24ca8a857d04262a98db69c0 Mon Sep 17 00:00:00 2001 From: Daniel Kotik Date: Sat, 14 Mar 2020 11:06:47 +0100 Subject: [PATCH 036/145] Code improvements: - rename self.f to self.f_spectrum for clarity - change atrubute modifiers (public to ptivate and readonly) - make integrand fucntion cdef --- Laguerre_Gauss_3d/beamprofile.pxd | 10 +++++----- Laguerre_Gauss_3d/beamprofile.py | 6 +++--- 2 files changed, 8 insertions(+), 8 deletions(-) diff --git a/Laguerre_Gauss_3d/beamprofile.pxd b/Laguerre_Gauss_3d/beamprofile.pxd index 35661c1..4b34522 100644 --- a/Laguerre_Gauss_3d/beamprofile.pxd +++ b/Laguerre_Gauss_3d/beamprofile.pxd @@ -48,12 +48,12 @@ cdef double complex f_Laguerre_Gauss_spherical(double sin_theta, double theta, double phi, dict params) cdef class PsiSpherical: - cdef public int m - cdef public double x, k - cdef public dict params - cdef f_spectrum_type f + cdef int m + cdef double x, k + cdef readonly dict params + cdef f_spectrum_type f_spectrum cdef double ry, rz cdef double phase(self, double sin_theta, double cos_theta, double phi, double x, double y, double z) nogil - cpdef double complex integrand(self, double theta, double phi) + cdef double complex integrand(self, double theta, double phi) diff --git a/Laguerre_Gauss_3d/beamprofile.py b/Laguerre_Gauss_3d/beamprofile.py index 82785cf..6834b7b 100644 --- a/Laguerre_Gauss_3d/beamprofile.py +++ b/Laguerre_Gauss_3d/beamprofile.py @@ -109,9 +109,9 @@ def __init__(self, x, params): self.m = params['m'] if self.m == 0: - self.f = f_Gauss_spherical + self.f_spectrum = f_Gauss_spherical else: - self.f = f_Laguerre_Gauss_spherical + self.f_spectrum = f_Laguerre_Gauss_spherical def __call__(self, r): """...""" @@ -142,7 +142,7 @@ def integrand(self, theta, phi): cos_theta = cos(theta) return sin_theta * cos_theta * \ - self.f(sin_theta, theta, phi, self.params) * \ + self.f_spectrum(sin_theta, theta, phi, self.params) * \ cexp(1j*self.phase(sin_theta, cos_theta, phi, self.x, self.ry, self.rz)) #try: From a23ab2db65362feeca4cbee76569fd1cc1e7ee63 Mon Sep 17 00:00:00 2001 From: Daniel Kotik Date: Sat, 14 Mar 2020 11:45:02 +0100 Subject: [PATCH 037/145] Avoid sin, cos etc showing up in module space --- Laguerre_Gauss_3d/beamprofile.pxd | 10 +++++----- Laguerre_Gauss_3d/beamprofile.py | 23 +++++++++++++---------- 2 files changed, 18 insertions(+), 15 deletions(-) diff --git a/Laguerre_Gauss_3d/beamprofile.pxd b/Laguerre_Gauss_3d/beamprofile.pxd index 4b34522..0725717 100644 --- a/Laguerre_Gauss_3d/beamprofile.pxd +++ b/Laguerre_Gauss_3d/beamprofile.pxd @@ -12,15 +12,15 @@ from cpython.pycapsule cimport PyCapsule_New # declare C functions as "cpdef" to export them to the module cdef extern from "stdlib.h": - cpdef int abs (int n) nogil + cpdef int _abs "abs" (int n) nogil cdef extern from "math.h": - cpdef double sin(double x) nogil - cpdef double cos(double x) nogil - cpdef double exp(double x) nogil + cpdef double _sin "sin" (double x) nogil + cpdef double _cos "cos" (double x) nogil + cpdef double _exp "exp" (double x) nogil cdef extern from "complex.h": - cpdef double complex cexp(double complex z) nogil + cpdef double complex _cexp "cexp" (double complex z) nogil # function type declaration for spectrum amplitudes ctypedef double complex (*f_spectrum_type)(double sin_theta, double theta, diff --git a/Laguerre_Gauss_3d/beamprofile.py b/Laguerre_Gauss_3d/beamprofile.py index 6834b7b..487f8e5 100644 --- a/Laguerre_Gauss_3d/beamprofile.py +++ b/Laguerre_Gauss_3d/beamprofile.py @@ -15,8 +15,11 @@ if not cython.compiled: - from math import sin, cos, exp - from cmath import exp as cexp + from math import (sin as _sin, + cos as _cos, + exp as _exp) + from cmath import exp as _cexp + from builtins import abs as _abs print("Please consider compiling `beamprofile.py` via Cython:\n\n" " `$ cythonize -3 -i beamprofile.py`") else: @@ -77,7 +80,7 @@ def f_Gauss_spherical(sin_theta, theta, phi, params): """ W_y, k = params['W_y'], params['k'] - return exp(-(k*W_y*sin_theta/2)**2) + return _exp(-(k*W_y*sin_theta/2)**2) def f_Laguerre_Gauss_spherical(sin_theta, theta, phi, params): @@ -87,8 +90,8 @@ def f_Laguerre_Gauss_spherical(sin_theta, theta, phi, params): """ m = params['m'] - return f_Gauss_spherical(sin_theta, theta, phi, params) * theta**abs(m) * \ - cexp(1j*m*phi) + return f_Gauss_spherical(sin_theta, theta, phi, params) * theta**_abs(m) * \ + _cexp(1j*m*phi) class PsiSpherical: @@ -131,19 +134,19 @@ def __call__(self, r): def phase(self, sin_theta, cos_theta, phi, x, y, z): """Phase function.""" - sin_phi = sin(phi) - cos_phi = cos(phi) + sin_phi = _sin(phi) + cos_phi = _cos(phi) return self.k*(sin_theta*(y*sin_phi - z*cos_phi) + cos_theta*x) def integrand(self, theta, phi): """Integrand function.""" - sin_theta = sin(theta) - cos_theta = cos(theta) + sin_theta = _sin(theta) + cos_theta = _cos(theta) return sin_theta * cos_theta * \ self.f_spectrum(sin_theta, theta, phi, self.params) * \ - cexp(1j*self.phase(sin_theta, cos_theta, phi, self.x, self.ry, self.rz)) + _cexp(1j*self.phase(sin_theta, cos_theta, phi, self.x, self.ry, self.rz)) #try: # getattr(psi_spherical, "called") From e3e5b8ca67b3287882af986e86e971cb1b636c3e Mon Sep 17 00:00:00 2001 From: Daniel Kotik Date: Mon, 16 Mar 2020 17:33:01 +0100 Subject: [PATCH 038/145] Remove params from spectrum functions signature: The signature should only constist of paramter that are acutually used in the function body. --- Laguerre_Gauss_3d/beamprofile.pxd | 12 ++++-------- Laguerre_Gauss_3d/beamprofile.py | 32 +++++++++++++++---------------- 2 files changed, 20 insertions(+), 24 deletions(-) diff --git a/Laguerre_Gauss_3d/beamprofile.pxd b/Laguerre_Gauss_3d/beamprofile.pxd index 0725717..e86ca36 100644 --- a/Laguerre_Gauss_3d/beamprofile.pxd +++ b/Laguerre_Gauss_3d/beamprofile.pxd @@ -23,8 +23,6 @@ cdef extern from "complex.h": cpdef double complex _cexp "cexp" (double complex z) nogil # function type declaration for spectrum amplitudes -ctypedef double complex (*f_spectrum_type)(double sin_theta, double theta, - double phi, dict params) ctypedef double complex (*integrand_type)(double theta, double phi) # function prototypes @@ -40,20 +38,18 @@ cdef (double complex, double, double) _complex_dblquad(PsiSpherical func, double gfun, double hfun) @cython.locals(W_y=cython.double, k=cython.double) -cdef double complex f_Gauss_spherical(double sin_theta, double theta, double phi, - dict params) +cdef double complex f_Gauss_spherical(double sin_theta, double W_y, double k) nogil @cython.locals(m=cython.int) cdef double complex f_Laguerre_Gauss_spherical(double sin_theta, double theta, - double phi, dict params) + double phi, double W_y, double k, int m) nogil cdef class PsiSpherical: cdef int m - cdef double x, k - cdef readonly dict params - cdef f_spectrum_type f_spectrum + cdef double x, k, W_y cdef double ry, rz cdef double phase(self, double sin_theta, double cos_theta, double phi, double x, double y, double z) nogil cdef double complex integrand(self, double theta, double phi) + cdef double complex f_spectrum(self, double sin_theta, double theta, double phi) nogil \ No newline at end of file diff --git a/Laguerre_Gauss_3d/beamprofile.py b/Laguerre_Gauss_3d/beamprofile.py index 487f8e5..e71571e 100644 --- a/Laguerre_Gauss_3d/beamprofile.py +++ b/Laguerre_Gauss_3d/beamprofile.py @@ -73,24 +73,20 @@ def _complex_dblquad(func, a, b, gfun, hfun): return real + 1j*imag, real_tol, imag_tol -def f_Gauss_spherical(sin_theta, theta, phi, params): +def f_Gauss_spherical(sin_theta, W_y, k): """2d-Gaussian spectrum amplitude. Implementation for spherical coordinates. """ - W_y, k = params['W_y'], params['k'] - return _exp(-(k*W_y*sin_theta/2)**2) -def f_Laguerre_Gauss_spherical(sin_theta, theta, phi, params): +def f_Laguerre_Gauss_spherical(sin_theta, theta, phi, W_y, k, m): """Laguerre-Gaussian spectrum amplitude. Implementation for spherical coordinates. """ - m = params['m'] - - return f_Gauss_spherical(sin_theta, theta, phi, params) * theta**_abs(m) * \ + return f_Gauss_spherical(sin_theta, W_y, k) * theta**_abs(m) * \ _cexp(1j*m*phi) @@ -107,14 +103,10 @@ class PsiSpherical: def __init__(self, x, params): """...""" self.x = x - self.params = params + self.W_y = params['W_y'] self.k = params['k'] self.m = params['m'] - - if self.m == 0: - self.f_spectrum = f_Gauss_spherical - else: - self.f_spectrum = f_Laguerre_Gauss_spherical + def __call__(self, r): """...""" @@ -138,14 +130,22 @@ def phase(self, sin_theta, cos_theta, phi, x, y, z): cos_phi = _cos(phi) return self.k*(sin_theta*(y*sin_phi - z*cos_phi) + cos_theta*x) + + + def f_spectrum(self, sin_theta, theta, phi): + """Spectrum amplitude function.""" + if self.m == 0: + return f_Gauss_spherical(sin_theta, self.W_y, self.k) + else: + return f_Laguerre_Gauss_spherical(sin_theta, theta, phi, + self.W_y, self.k, self.m) def integrand(self, theta, phi): """Integrand function.""" sin_theta = _sin(theta) cos_theta = _cos(theta) - - return sin_theta * cos_theta * \ - self.f_spectrum(sin_theta, theta, phi, self.params) * \ + + return sin_theta * cos_theta * self.f_spectrum(sin_theta, theta, phi) * \ _cexp(1j*self.phase(sin_theta, cos_theta, phi, self.x, self.ry, self.rz)) #try: From f4b3fe5da16afc84e28eec5ce445b6d27c98a30b Mon Sep 17 00:00:00 2001 From: Daniel Kotik Date: Tue, 17 Mar 2020 11:00:30 +0100 Subject: [PATCH 039/145] Add called paramter: Signals when Functor gets called the first time. --- Laguerre_Gauss_3d/beamprofile.pxd | 2 ++ Laguerre_Gauss_3d/beamprofile.py | 16 ++++++++-------- 2 files changed, 10 insertions(+), 8 deletions(-) diff --git a/Laguerre_Gauss_3d/beamprofile.pxd b/Laguerre_Gauss_3d/beamprofile.pxd index e86ca36..877efd9 100644 --- a/Laguerre_Gauss_3d/beamprofile.pxd +++ b/Laguerre_Gauss_3d/beamprofile.pxd @@ -9,6 +9,7 @@ creation date: 22.02.2020 """ cimport cython from cpython.pycapsule cimport PyCapsule_New +from cpython cimport bool # declare C functions as "cpdef" to export them to the module cdef extern from "stdlib.h": @@ -48,6 +49,7 @@ cdef class PsiSpherical: cdef int m cdef double x, k, W_y cdef double ry, rz + cdef bool called cdef double phase(self, double sin_theta, double cos_theta, double phi, double x, double y, double z) nogil diff --git a/Laguerre_Gauss_3d/beamprofile.py b/Laguerre_Gauss_3d/beamprofile.py index e71571e..ef1d8be 100644 --- a/Laguerre_Gauss_3d/beamprofile.py +++ b/Laguerre_Gauss_3d/beamprofile.py @@ -100,19 +100,25 @@ class PsiSpherical: psi_spherical(r) """ - def __init__(self, x, params): + def __init__(self, x, params, called=False): """...""" self.x = x self.W_y = params['W_y'] self.k = params['k'] self.m = params['m'] + self.called = called def __call__(self, r): """...""" self.ry = r.y self.rz = r.z - + + if not self.called: + print("Calculating inital field configuration. " + "This will take some time...") + self.called = True + try: (result, real_tol, @@ -148,12 +154,6 @@ def integrand(self, theta, phi): return sin_theta * cos_theta * self.f_spectrum(sin_theta, theta, phi) * \ _cexp(1j*self.phase(sin_theta, cos_theta, phi, self.x, self.ry, self.rz)) - #try: - # getattr(psi_spherical, "called") - #except AttributeError: - # psi_spherical.called = True - # print("Calculating inital field configuration. " - # "This will take some time...") def main(): From 56ee48d0b02caa26f84254d6896633fd271e3ac6 Mon Sep 17 00:00:00 2001 From: Daniel Kotik Date: Tue, 17 Mar 2020 13:03:36 +0100 Subject: [PATCH 040/145] Replace fixed module name with __name__ in text string --- Laguerre_Gauss_3d/beamprofile.py | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/Laguerre_Gauss_3d/beamprofile.py b/Laguerre_Gauss_3d/beamprofile.py index ef1d8be..92fd52c 100644 --- a/Laguerre_Gauss_3d/beamprofile.py +++ b/Laguerre_Gauss_3d/beamprofile.py @@ -20,8 +20,8 @@ exp as _exp) from cmath import exp as _cexp from builtins import abs as _abs - print("Please consider compiling `beamprofile.py` via Cython:\n\n" - " `$ cythonize -3 -i beamprofile.py`") + print("Please consider compiling `%s.py` via Cython:\n\n" + " `$ cythonize -3 -i %s.py`" % (__name__, __name__)) else: from scipy import LowLevelCallable From 5166a01587115e08b455ed8c99f810a1dfea1ce5 Mon Sep 17 00:00:00 2001 From: Daniel Kotik Date: Tue, 17 Mar 2020 14:58:04 +0100 Subject: [PATCH 041/145] Change line spacing --- Laguerre_Gauss_3d/beamprofile.py | 5 +++-- 1 file changed, 3 insertions(+), 2 deletions(-) diff --git a/Laguerre_Gauss_3d/beamprofile.py b/Laguerre_Gauss_3d/beamprofile.py index 92fd52c..9fb7eac 100644 --- a/Laguerre_Gauss_3d/beamprofile.py +++ b/Laguerre_Gauss_3d/beamprofile.py @@ -20,8 +20,8 @@ exp as _exp) from cmath import exp as _cexp from builtins import abs as _abs - print("Please consider compiling `%s.py` via Cython:\n\n" - " `$ cythonize -3 -i %s.py`" % (__name__, __name__)) + print("\nPlease consider compiling `%s.py` via Cython: " + "`$ cythonize -3 -i %s.py`\n" % (__name__, __name__)) else: from scipy import LowLevelCallable @@ -130,6 +130,7 @@ def __call__(self, r): return self.k**2 * result + def phase(self, sin_theta, cos_theta, phi, x, y, z): """Phase function.""" sin_phi = _sin(phi) From d4a3e1145dc72436e8bc4148467e21e72412c326 Mon Sep 17 00:00:00 2001 From: Daniel Kotik Date: Tue, 17 Mar 2020 15:06:51 +0100 Subject: [PATCH 042/145] Use PsiSpherical class --- Laguerre_Gauss_3d/LaguerreGauss3d.py | 14 ++++++++++---- 1 file changed, 10 insertions(+), 4 deletions(-) diff --git a/Laguerre_Gauss_3d/LaguerreGauss3d.py b/Laguerre_Gauss_3d/LaguerreGauss3d.py index a6120c6..19c6716 100644 --- a/Laguerre_Gauss_3d/LaguerreGauss3d.py +++ b/Laguerre_Gauss_3d/LaguerreGauss3d.py @@ -56,8 +56,9 @@ from datetime import datetime -from beamprofile import psi_spherical, f_Gauss_spherical, f_Laguerre_Gauss_spherical -from beamprofile import complex_dblquad +#from beamprofile import psi_spherical, f_Gauss_spherical, f_Laguerre_Gauss_spherical +#from beamprofile import complex_dblquad +from beamprofile import PsiSpherical print("Meep version:", mp.__version__) @@ -353,6 +354,9 @@ def phase(k_y, k_z, x, y, z): eps_averaging = True # default: True sources = [] + + # define beam profile function + psi_spherical = PsiSpherical(x=shift, params=params) if e_z != 0: source_Ez = mp.Source(src=mp.ContinuousSource(frequency=freq, width=0.5), @@ -362,7 +366,8 @@ def phase(k_y, k_z, x, y, z): center=mp.Vector3(source_shift, 0, 0), #amp_func=lambda r: Gauss(r, params) #amp_func=lambda r: psi_cartesian(r, shift, params) - amp_func=lambda r: psi_spherical(r, shift, params) + #amp_func=lambda r: psi_spherical(r)#, shift, params) + amp_func=psi_spherical ) sources.append(source_Ez) @@ -374,7 +379,8 @@ def phase(k_y, k_z, x, y, z): center=mp.Vector3(source_shift, 0, 0), #amp_func=lambda r: Gauss(r, params) #amp_func=lambda r: psi_cartesian(r, shift, params) - amp_func=lambda r: psi_spherical(r, shift, params) + #amp_func=lambda r: psi_spherical(r)#, shift, params) + amp_func=psi_spherical ) sources.append(source_Ey) From 05a00395cdc33d6617e2b318d1928f2d805227e5 Mon Sep 17 00:00:00 2001 From: Daniel Kotik Date: Tue, 17 Mar 2020 18:37:58 +0100 Subject: [PATCH 043/145] Code polishing --- Laguerre_Gauss_3d/beamprofile.pxd | 9 +++++---- 1 file changed, 5 insertions(+), 4 deletions(-) diff --git a/Laguerre_Gauss_3d/beamprofile.pxd b/Laguerre_Gauss_3d/beamprofile.pxd index 877efd9..18d4a9c 100644 --- a/Laguerre_Gauss_3d/beamprofile.pxd +++ b/Laguerre_Gauss_3d/beamprofile.pxd @@ -46,10 +46,11 @@ cdef double complex f_Laguerre_Gauss_spherical(double sin_theta, double theta, double phi, double W_y, double k, int m) nogil cdef class PsiSpherical: - cdef int m - cdef double x, k, W_y - cdef double ry, rz - cdef bool called + cdef: + int m + double x, k, W_y + double ry, rz + bool called cdef double phase(self, double sin_theta, double cos_theta, double phi, double x, double y, double z) nogil From 59a583664b03b5795f216fba722669156c168fba Mon Sep 17 00:00:00 2001 From: Daniel Kotik Date: Wed, 18 Mar 2020 14:02:59 +0100 Subject: [PATCH 044/145] Add empty line --- Laguerre_Gauss_3d/beamprofile.py | 1 + 1 file changed, 1 insertion(+) diff --git a/Laguerre_Gauss_3d/beamprofile.py b/Laguerre_Gauss_3d/beamprofile.py index 9fb7eac..4b98538 100644 --- a/Laguerre_Gauss_3d/beamprofile.py +++ b/Laguerre_Gauss_3d/beamprofile.py @@ -64,6 +64,7 @@ def _complex_dblquad(func, a, b, gfun, hfun): '__real_func', func_capsule) ll_imag_func = LowLevelCallable.from_cython(current_module, '__imag_func', func_capsule) + real, real_tol = dblquad(ll_real_func, a, b, gfun, hfun) imag, imag_tol = dblquad(ll_imag_func, a, b, gfun, hfun) else: From 5dd5c3e57aa3941a51898bedddb304cf58c54080 Mon Sep 17 00:00:00 2001 From: Daniel Kotik Date: Thu, 19 Mar 2020 18:36:30 +0100 Subject: [PATCH 045/145] Name real and imag part func appropriately: Remove unused declaration real_func and imag func. Rename real and imag functions in such a way, that it is clear they are ment for use with two dimensional functions and to discriminate the Python from the Cython versions. --- Laguerre_Gauss_3d/beamprofile.pxd | 6 ++--- Laguerre_Gauss_3d/beamprofile.py | 38 ++++++++++++++++++------------- 2 files changed, 24 insertions(+), 20 deletions(-) diff --git a/Laguerre_Gauss_3d/beamprofile.pxd b/Laguerre_Gauss_3d/beamprofile.pxd index 18d4a9c..05ffe1f 100644 --- a/Laguerre_Gauss_3d/beamprofile.pxd +++ b/Laguerre_Gauss_3d/beamprofile.pxd @@ -27,10 +27,8 @@ cdef extern from "complex.h": ctypedef double complex (*integrand_type)(double theta, double phi) # function prototypes -cdef double _real_func(double x, double y, func) -cdef double _imag_func(double x, double y, func) -cdef double __imag_func(int n, double *arr, void *func_ptr) -cdef double __real_func(int n, double *arr, void *func_ptr) +cdef double _imag_2d_func_c(int n, double *arr, void *func_ptr) +cdef double _real_2d_func_c(int n, double *arr, void *func_ptr) @cython.locals(real=cython.double, imag=cython.double, real_tol=cython.double, imag_tol=cython.double) diff --git a/Laguerre_Gauss_3d/beamprofile.py b/Laguerre_Gauss_3d/beamprofile.py index 4b98538..0dd8cf6 100644 --- a/Laguerre_Gauss_3d/beamprofile.py +++ b/Laguerre_Gauss_3d/beamprofile.py @@ -26,25 +26,31 @@ from scipy import LowLevelCallable -def _real_func(x, y, func): - """Return real part of function.""" +def _real_2d_func(x, y, func): + """Return real part of 2d function.""" return func(x, y).real -def _imag_func(x, y, func): - """Return imag part of function.""" +def _imag_2d_func(x, y, func): + """Return imag part of 2d function.""" return func(x, y).imag -def __imag_func(n, arr, func_ptr): - """Return imag part of function.""" +def _imag_2d_func_c(n, arr, func_ptr): + """Return imag part of 2d function. + + Cython implementation. + """ # pure python formulation of: # return (func_ptr)(arr[0], arr[1]).imag return cython.cast(PsiSpherical, func_ptr).integrand(arr[0], arr[1]).imag -def __real_func(n, arr, func_ptr): - """Return real part of function.""" +def _real_2d_func_c(n, arr, func_ptr): + """Return real part of 2d function. + + Cython implementation. + """ # pure python formulation of: # return (func_ptr)(arr[0], arr[1]).real return cython.cast(PsiSpherical, func_ptr).integrand(arr[0], arr[1]).real @@ -60,16 +66,16 @@ def _complex_dblquad(func, a, b, gfun, hfun): current_module = sys.modules[__name__] - ll_real_func = LowLevelCallable.from_cython(current_module, - '__real_func', func_capsule) - ll_imag_func = LowLevelCallable.from_cython(current_module, - '__imag_func', func_capsule) + ll_real_2d_func_c = LowLevelCallable.from_cython(current_module, + '_real_2d_func_c', func_capsule) + ll_imag_2d_func_c = LowLevelCallable.from_cython(current_module, + '_imag_2d_func_c', func_capsule) - real, real_tol = dblquad(ll_real_func, a, b, gfun, hfun) - imag, imag_tol = dblquad(ll_imag_func, a, b, gfun, hfun) + real, real_tol = dblquad(ll_real_2d_func_c, a, b, gfun, hfun) + imag, imag_tol = dblquad(ll_imag_2d_func_c, a, b, gfun, hfun) else: - real, real_tol = dblquad(_real_func, a, b, gfun, hfun, (func,)) - imag, imag_tol = dblquad(_imag_func, a, b, gfun, hfun, (func,)) + real, real_tol = dblquad(_real_2d_func, a, b, gfun, hfun, (func,)) + imag, imag_tol = dblquad(_imag_2d_func, a, b, gfun, hfun, (func,)) return real + 1j*imag, real_tol, imag_tol From 414d72a467e224bb4488d63f52bdde4a204ecb61 Mon Sep 17 00:00:00 2001 From: Daniel Kotik Date: Fri, 20 Mar 2020 14:33:22 +0100 Subject: [PATCH 046/145] Remove whitespace characters etc. --- Laguerre_Gauss_3d/beamprofile.pxd | 16 +++++----- Laguerre_Gauss_3d/beamprofile.py | 49 +++++++++++++++---------------- 2 files changed, 30 insertions(+), 35 deletions(-) diff --git a/Laguerre_Gauss_3d/beamprofile.pxd b/Laguerre_Gauss_3d/beamprofile.pxd index 05ffe1f..2fa088e 100644 --- a/Laguerre_Gauss_3d/beamprofile.pxd +++ b/Laguerre_Gauss_3d/beamprofile.pxd @@ -23,17 +23,15 @@ cdef extern from "math.h": cdef extern from "complex.h": cpdef double complex _cexp "cexp" (double complex z) nogil -# function type declaration for spectrum amplitudes -ctypedef double complex (*integrand_type)(double theta, double phi) # function prototypes cdef double _imag_2d_func_c(int n, double *arr, void *func_ptr) cdef double _real_2d_func_c(int n, double *arr, void *func_ptr) -@cython.locals(real=cython.double, imag=cython.double, real_tol=cython.double, +@cython.locals(real=cython.double, imag=cython.double, real_tol=cython.double, imag_tol=cython.double) -cdef (double complex, double, double) _complex_dblquad(PsiSpherical func, - double a, double b, +cdef (double complex, double, double) _complex_dblquad(PsiSpherical func, + double a, double b, double gfun, double hfun) @cython.locals(W_y=cython.double, k=cython.double) @@ -49,8 +47,8 @@ cdef class PsiSpherical: double x, k, W_y double ry, rz bool called - - cdef double phase(self, double sin_theta, double cos_theta, double phi, + + cdef double phase(self, double sin_theta, double cos_theta, double phi, double x, double y, double z) nogil - cdef double complex integrand(self, double theta, double phi) - cdef double complex f_spectrum(self, double sin_theta, double theta, double phi) nogil \ No newline at end of file + cdef double complex integrand(self, double theta, double phi) nogil + cdef double complex f_spectrum(self, double sin_theta, double theta, double phi) nogil diff --git a/Laguerre_Gauss_3d/beamprofile.py b/Laguerre_Gauss_3d/beamprofile.py index 0dd8cf6..f9a94c0 100644 --- a/Laguerre_Gauss_3d/beamprofile.py +++ b/Laguerre_Gauss_3d/beamprofile.py @@ -27,31 +27,31 @@ def _real_2d_func(x, y, func): - """Return real part of 2d function.""" + """Return real part of a 2d function.""" return func(x, y).real def _imag_2d_func(x, y, func): - """Return imag part of 2d function.""" + """Return imag part of a 2d function.""" return func(x, y).imag def _imag_2d_func_c(n, arr, func_ptr): - """Return imag part of 2d function. - + """Return imag part of a 2d function. + Cython implementation. - """ - # pure python formulation of: + """ + # pure python formulation of: # return (func_ptr)(arr[0], arr[1]).imag return cython.cast(PsiSpherical, func_ptr).integrand(arr[0], arr[1]).imag def _real_2d_func_c(n, arr, func_ptr): - """Return real part of 2d function. - + """Return real part of a 2d function. + Cython implementation. """ - # pure python formulation of: + # pure python formulation of: # return (func_ptr)(arr[0], arr[1]).real return cython.cast(PsiSpherical, func_ptr).integrand(arr[0], arr[1]).real @@ -61,18 +61,19 @@ def _complex_dblquad(func, a, b, gfun, hfun): if cython.compiled: # pure python formulation of: cdef void *f_ptr = func f_ptr = cython.declare(cython.p_void, cython.cast(cython.p_void, func)) - + func_capsule = PyCapsule_New(f_ptr, cython.NULL, cython.NULL) - + current_module = sys.modules[__name__] - ll_real_2d_func_c = LowLevelCallable.from_cython(current_module, - '_real_2d_func_c', func_capsule) - ll_imag_2d_func_c = LowLevelCallable.from_cython(current_module, - '_imag_2d_func_c', func_capsule) - + ll_real_2d_func_c = LowLevelCallable.from_cython(current_module, + '_real_2d_func_c', + func_capsule) + ll_imag_2d_func_c = LowLevelCallable.from_cython(current_module, + '_imag_2d_func_c', + func_capsule) real, real_tol = dblquad(ll_real_2d_func_c, a, b, gfun, hfun) - imag, imag_tol = dblquad(ll_imag_2d_func_c, a, b, gfun, hfun) + imag, imag_tol = dblquad(ll_imag_2d_func_c, a, b, gfun, hfun) else: real, real_tol = dblquad(_real_2d_func, a, b, gfun, hfun, (func,)) imag, imag_tol = dblquad(_imag_2d_func, a, b, gfun, hfun, (func,)) @@ -114,22 +115,21 @@ def __init__(self, x, params, called=False): self.k = params['k'] self.m = params['m'] self.called = called - def __call__(self, r): """...""" self.ry = r.y self.rz = r.z - + if not self.called: print("Calculating inital field configuration. " "This will take some time...") self.called = True - + try: (result, real_tol, - imag_tol) = _complex_dblquad(self if cython.compiled else self.integrand, + imag_tol) = _complex_dblquad(self if cython.compiled else self.integrand, 0, 2*math.pi, 0, math.pi/2) except Exception as e: print(type(e).__name__ + ":", e) @@ -137,21 +137,19 @@ def __call__(self, r): return self.k**2 * result - def phase(self, sin_theta, cos_theta, phi, x, y, z): """Phase function.""" sin_phi = _sin(phi) cos_phi = _cos(phi) return self.k*(sin_theta*(y*sin_phi - z*cos_phi) + cos_theta*x) - - + def f_spectrum(self, sin_theta, theta, phi): """Spectrum amplitude function.""" if self.m == 0: return f_Gauss_spherical(sin_theta, self.W_y, self.k) else: - return f_Laguerre_Gauss_spherical(sin_theta, theta, phi, + return f_Laguerre_Gauss_spherical(sin_theta, theta, phi, self.W_y, self.k, self.m) def integrand(self, theta, phi): @@ -163,7 +161,6 @@ def integrand(self, theta, phi): _cexp(1j*self.phase(sin_theta, cos_theta, phi, self.x, self.ry, self.rz)) - def main(): import meep as mp From 81e7b97295e99c5d3143e0cb9877362262aef291 Mon Sep 17 00:00:00 2001 From: Daniel Kotik Date: Fri, 20 Mar 2020 14:46:05 +0100 Subject: [PATCH 047/145] Update docstring --- Laguerre_Gauss_3d/beamprofile.py | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/Laguerre_Gauss_3d/beamprofile.py b/Laguerre_Gauss_3d/beamprofile.py index f9a94c0..faefe88 100644 --- a/Laguerre_Gauss_3d/beamprofile.py +++ b/Laguerre_Gauss_3d/beamprofile.py @@ -105,7 +105,7 @@ class PsiSpherical: Usage: psi_spherical = PsiSpherical(x=shift, params=params) - psi_spherical(r) + psi_spherical(r) # r...vector-like object with scalar y and z attributes """ def __init__(self, x, params, called=False): From c67998e4b5fffa6dd0244d7b4fa9f3078642500c Mon Sep 17 00:00:00 2001 From: Daniel Kotik Date: Fri, 20 Mar 2020 15:51:25 +0100 Subject: [PATCH 048/145] Rename beamprofile.p* to optbeam.* --- Laguerre_Gauss_3d/LaguerreGauss3d.py | 4 ++-- Laguerre_Gauss_3d/{beamprofile.pxd => optbeam.pxd} | 2 +- Laguerre_Gauss_3d/{beamprofile.py => optbeam.py} | 2 +- 3 files changed, 4 insertions(+), 4 deletions(-) rename Laguerre_Gauss_3d/{beamprofile.pxd => optbeam.pxd} (98%) rename Laguerre_Gauss_3d/{beamprofile.py => optbeam.py} (99%) diff --git a/Laguerre_Gauss_3d/LaguerreGauss3d.py b/Laguerre_Gauss_3d/LaguerreGauss3d.py index 19c6716..7eb8aec 100644 --- a/Laguerre_Gauss_3d/LaguerreGauss3d.py +++ b/Laguerre_Gauss_3d/LaguerreGauss3d.py @@ -58,7 +58,7 @@ #from beamprofile import psi_spherical, f_Gauss_spherical, f_Laguerre_Gauss_spherical #from beamprofile import complex_dblquad -from beamprofile import PsiSpherical +from optbeam import PsiSpherical print("Meep version:", mp.__version__) @@ -354,7 +354,7 @@ def phase(k_y, k_z, x, y, z): eps_averaging = True # default: True sources = [] - + # define beam profile function psi_spherical = PsiSpherical(x=shift, params=params) diff --git a/Laguerre_Gauss_3d/beamprofile.pxd b/Laguerre_Gauss_3d/optbeam.pxd similarity index 98% rename from Laguerre_Gauss_3d/beamprofile.pxd rename to Laguerre_Gauss_3d/optbeam.pxd index 2fa088e..d696391 100644 --- a/Laguerre_Gauss_3d/beamprofile.pxd +++ b/Laguerre_Gauss_3d/optbeam.pxd @@ -1,6 +1,6 @@ # -*- coding: utf-8 -*- """ -file: beamprofile.pxd +file: optbeam.pxd brief: ... author: Daniel Kotik version: 1.5-beta diff --git a/Laguerre_Gauss_3d/beamprofile.py b/Laguerre_Gauss_3d/optbeam.py similarity index 99% rename from Laguerre_Gauss_3d/beamprofile.py rename to Laguerre_Gauss_3d/optbeam.py index faefe88..5e82e4c 100644 --- a/Laguerre_Gauss_3d/beamprofile.py +++ b/Laguerre_Gauss_3d/optbeam.py @@ -1,6 +1,6 @@ # -*- coding: utf-8 -*- """ -file: beamprofile.py +file: optbeam.py brief: ... author: Daniel Kotik version: 1.5-beta From 7a00307d4eea85870aeaf5d6606170d86b6a12b5 Mon Sep 17 00:00:00 2001 From: Daniel Kotik Date: Fri, 20 Mar 2020 16:56:25 +0100 Subject: [PATCH 049/145] Adapt .gitignore --- .gitignore | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/.gitignore b/.gitignore index 212c7d5..d151ebf 100644 --- a/.gitignore +++ b/.gitignore @@ -9,8 +9,8 @@ Gauss_2d/convex/* */.ipynb_checkpoints/* ### Cython ### -Laguerre_Gauss_3d/beamprofile.c -Laguerre_Gauss_3d/beamprofile.html +Laguerre_Gauss_3d/optbeam.c +Laguerre_Gauss_3d/optbeam.html ### Python ### # Byte-compiled / optimized / DLL files From d59ba03e6d69c0ed5a65ec953687a4a2c6ba2d2a Mon Sep 17 00:00:00 2001 From: Daniel Kotik Date: Mon, 23 Mar 2020 00:18:05 +0100 Subject: [PATCH 050/145] Add params attribute as readonly --- Laguerre_Gauss_3d/optbeam.pxd | 1 + Laguerre_Gauss_3d/optbeam.py | 1 + 2 files changed, 2 insertions(+) diff --git a/Laguerre_Gauss_3d/optbeam.pxd b/Laguerre_Gauss_3d/optbeam.pxd index d696391..04aebb6 100644 --- a/Laguerre_Gauss_3d/optbeam.pxd +++ b/Laguerre_Gauss_3d/optbeam.pxd @@ -43,6 +43,7 @@ cdef double complex f_Laguerre_Gauss_spherical(double sin_theta, double theta, cdef class PsiSpherical: cdef: + readonly dict params int m double x, k, W_y double ry, rz diff --git a/Laguerre_Gauss_3d/optbeam.py b/Laguerre_Gauss_3d/optbeam.py index 5e82e4c..072add0 100644 --- a/Laguerre_Gauss_3d/optbeam.py +++ b/Laguerre_Gauss_3d/optbeam.py @@ -111,6 +111,7 @@ class PsiSpherical: def __init__(self, x, params, called=False): """...""" self.x = x + self.params = params self.W_y = params['W_y'] self.k = params['k'] self.m = params['m'] From 896e8f6924c50babc0eac2510b7a75be971348ed Mon Sep 17 00:00:00 2001 From: Daniel Kotik Date: Mon, 23 Mar 2020 00:20:17 +0100 Subject: [PATCH 051/145] Add docstring --- Laguerre_Gauss_3d/optbeam.py | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/Laguerre_Gauss_3d/optbeam.py b/Laguerre_Gauss_3d/optbeam.py index 072add0..e4c5d18 100644 --- a/Laguerre_Gauss_3d/optbeam.py +++ b/Laguerre_Gauss_3d/optbeam.py @@ -118,7 +118,7 @@ def __init__(self, x, params, called=False): self.called = called def __call__(self, r): - """...""" + """Beam profile function.""" self.ry = r.y self.rz = r.z From 05f6d51ee7fffef00fe82e6d09c5a5933ec9f551 Mon Sep 17 00:00:00 2001 From: Daniel Kotik Date: Fri, 20 Mar 2020 18:01:43 +0100 Subject: [PATCH 052/145] Clarify imports; add TODOs --- Laguerre_Gauss_3d/LaguerreGauss3d.py | 5 +++-- 1 file changed, 3 insertions(+), 2 deletions(-) diff --git a/Laguerre_Gauss_3d/LaguerreGauss3d.py b/Laguerre_Gauss_3d/LaguerreGauss3d.py index 7eb8aec..80c55fe 100644 --- a/Laguerre_Gauss_3d/LaguerreGauss3d.py +++ b/Laguerre_Gauss_3d/LaguerreGauss3d.py @@ -56,9 +56,9 @@ from datetime import datetime -#from beamprofile import psi_spherical, f_Gauss_spherical, f_Laguerre_Gauss_spherical -#from beamprofile import complex_dblquad from optbeam import PsiSpherical +from optbeam2 import PsiCartesian +# TODO: change in future versions to PsiLaguerreGauss, PsiAiry etc. print("Meep version:", mp.__version__) @@ -357,6 +357,7 @@ def phase(k_y, k_z, x, y, z): # define beam profile function psi_spherical = PsiSpherical(x=shift, params=params) + # TODO: change to psi_LaguerreGauss = PsiLaguerreGauss(...) in future versions if e_z != 0: source_Ez = mp.Source(src=mp.ContinuousSource(frequency=freq, width=0.5), From 504d60f018ce4665642fd4c6873e480358462834 Mon Sep 17 00:00:00 2001 From: Daniel Kotik Date: Fri, 20 Mar 2020 18:15:47 +0100 Subject: [PATCH 053/145] Add optbeam2.p* for cartesian integration --- Laguerre_Gauss_3d/LaguerreGauss3d.py | 36 +---- Laguerre_Gauss_3d/optbeam2.pxd | 0 Laguerre_Gauss_3d/optbeam2.py | 219 +++++++++++++++++++++++++++ 3 files changed, 222 insertions(+), 33 deletions(-) create mode 100644 Laguerre_Gauss_3d/optbeam2.pxd create mode 100644 Laguerre_Gauss_3d/optbeam2.py diff --git a/Laguerre_Gauss_3d/LaguerreGauss3d.py b/Laguerre_Gauss_3d/LaguerreGauss3d.py index 80c55fe..fc610df 100644 --- a/Laguerre_Gauss_3d/LaguerreGauss3d.py +++ b/Laguerre_Gauss_3d/LaguerreGauss3d.py @@ -58,7 +58,7 @@ from optbeam import PsiSpherical from optbeam2 import PsiCartesian -# TODO: change in future versions to PsiLaguerreGauss, PsiAiry etc. +# TODO: change in future versions to LaguerreGauss3d, Airy3d etc. print("Meep version:", mp.__version__) @@ -192,38 +192,7 @@ def Gauss(r, params): # -------------------------------------------------------------------------- # cartesian coordinates (not recommmended) ------------------------- - def phi(k_y, k_z): - """Azimuthal angle. - Part of coordinate transformation from k-space to (theta, phi)-space. - """ - return math.atan2(k_y, -k_z) - - def theta(k_y, k_z, k): - """Polar angle. - - Part of coordinate transformation from k-space to (theta, phi)-space. - """ - return math.acos(cmath.sqrt(k**2 - k_y**2 - k_z**2).real / k) - - def f_Gauss_cartesian(k_y, k_z, params): - """2d-Gaussian spectrum amplitude. - - Impementation for Cartesian coordinates. - """ - W_y = params['W_y'] - - return math.exp(-W_y**2 * (k_y**2 + k_z**2)/4) - - def f_Laguerre_Gauss_cartesian(k_y, k_z, params): - """Laguerre-Gaussian spectrum amplitude. - - Impementation for Cartesian coordinates. - """ - m, k = params['m'], params['k'] - - return f_Gauss_cartesian(k_y, k_z, params) * \ - cmath.exp(1j*m*phi(k_y, k_z)) * theta(k_y, k_z, k)**abs(m) # spherical coordinates -------------------------------------------- @@ -357,7 +326,8 @@ def phase(k_y, k_z, x, y, z): # define beam profile function psi_spherical = PsiSpherical(x=shift, params=params) - # TODO: change to psi_LaguerreGauss = PsiLaguerreGauss(...) in future versions + # TODO: change to psi_LaguerreGauss = LaguerreGauss3d.psi(...) in future versions + # f_Laguerre_Gauss = LaguerreGauss3d.f_spectrum(...) if e_z != 0: source_Ez = mp.Source(src=mp.ContinuousSource(frequency=freq, width=0.5), diff --git a/Laguerre_Gauss_3d/optbeam2.pxd b/Laguerre_Gauss_3d/optbeam2.pxd new file mode 100644 index 0000000..e69de29 diff --git a/Laguerre_Gauss_3d/optbeam2.py b/Laguerre_Gauss_3d/optbeam2.py new file mode 100644 index 0000000..ad8f7a3 --- /dev/null +++ b/Laguerre_Gauss_3d/optbeam2.py @@ -0,0 +1,219 @@ +# -*- coding: utf-8 -*- +""" +file: optbeam2.py +brief: ... +author: Daniel Kotik +version: 1.5-beta +release date: xx.xx.2020 +creation date: 20.03.2020 +""" +import cython +import math +import sys + +from scipy.integrate import dblquad + + +if not cython.compiled: + from math import (sin as _sin, + cos as _cos, + exp as _exp, + acos as _acos, + atan2 as _atan2) + from cmath import (exp as _cexp, + sqrt as _csqrt) + from builtins import abs as _abs + print("\nPlease consider compiling `%s.py` via Cython: " + "`$ cythonize -3 -i %s.py`\n" % (__name__, __name__)) +else: + from scipy import LowLevelCallable + + +def _real_2d_func(x, y, func): + """Return real part of a 2d function.""" + return func(x, y).real + + +def _imag_2d_func(x, y, func): + """Return imag part of a 2d function.""" + return func(x, y).imag + + +def _imag_2d_func_c(n, arr, func_ptr): + """Return imag part of a 2d function. + + Cython implementation. + """ + # pure python formulation of: + # return (func_ptr)(arr[0], arr[1]).imag + return cython.cast(PsiCartesian, func_ptr).integrand(arr[0], arr[1]).imag + + +def _real_2d_func_c(n, arr, func_ptr): + """Return real part of a 2d function. + + Cython implementation. + """ + # pure python formulation of: + # return (func_ptr)(arr[0], arr[1]).real + return cython.cast(PsiCartesian, func_ptr).integrand(arr[0], arr[1]).real + + +def _complex_dblquad(func, a, b, gfun, hfun): + """Integrate real and imaginary part of the given function.""" + if cython.compiled: + # pure python formulation of: cdef void *f_ptr = func + f_ptr = cython.declare(cython.p_void, cython.cast(cython.p_void, func)) + + func_capsule = PyCapsule_New(f_ptr, cython.NULL, cython.NULL) + + current_module = sys.modules[__name__] + + ll_real_2d_func_c = LowLevelCallable.from_cython(current_module, + '_real_2d_func_c', + func_capsule) + ll_imag_2d_func_c = LowLevelCallable.from_cython(current_module, + '_imag_2d_func_c', + func_capsule) + real, real_tol = dblquad(ll_real_2d_func_c, a, b, gfun, hfun) + imag, imag_tol = dblquad(ll_imag_2d_func_c, a, b, gfun, hfun) + else: + real, real_tol = dblquad(_real_2d_func, a, b, gfun, hfun, (func,)) + imag, imag_tol = dblquad(_imag_2d_func, a, b, gfun, hfun, (func,)) + + return real + 1j*imag, real_tol, imag_tol + + +def f_Gauss_spherical(sin_theta, W_y, k): + """2d-Gaussian spectrum amplitude. + + Implementation for spherical coordinates. + """ + return _exp(-(k*W_y*sin_theta/2)**2) + + +def f_Laguerre_Gauss_spherical(sin_theta, theta, phi, W_y, k, m): + """Laguerre-Gaussian spectrum amplitude. + + Implementation for spherical coordinates. + """ + return f_Gauss_spherical(sin_theta, W_y, k) * theta**_abs(m) * \ + _cexp(1j*m*phi) + + +def _phi(k_y, k_z): + """Azimuthal angle. + + Part of coordinate transformation from k-space to (theta, phi)-space. + """ + return _atan2(k_y, -k_z) + + +def _theta(k_y, k_z, k): + """Polar angle. + + Part of coordinate transformation from k-space to (theta, phi)-space. + """ + return _acos(_csqrt(k**2 - k_y**2 - k_z**2).real / k) + + +def f_Gauss_cartesian(k_y, k_z, W_y): + """2d-Gaussian spectrum amplitude. + + Impementation for Cartesian coordinates. + """ + return _exp(-W_y**2 * (k_y**2 + k_z**2)/4) + + +def f_Laguerre_Gauss_cartesian(k_y, k_z, W_y, k, m): + """Laguerre-Gaussian spectrum amplitude. + + Impementation for Cartesian coordinates. + """ + return f_Gauss_cartesian(k_y, k_z, W_y) * \ + _cexp(1j*m*_phi(k_y, k_z)) * _theta(k_y, k_z, k)**_abs(m) + + +class PsiCartesian: + """Field amplitude class. + + Integration in cartesian coordinates. + + Usage: + psi_cartesian = PsiCartesian(x=shift, params=params) + psi_cartesian(r) # r...vector-like object with scalar y and z attributes + """ + + def __init__(self, x, params, called=False): + """...""" + self.x = x + self.W_y = params['W_y'] + self.k = params['k'] + self.m = params['m'] + self.called = called + + def __call__(self, r): + """...""" + self.ry = r.y + self.rz = r.z + + if not self.called: + print("Calculating inital field configuration. " + "This will take some time...") + self.called = True + + try: + (result, + real_tol, + imag_tol) = _complex_dblquad(self if cython.compiled else self.integrand, + 0, 2*math.pi, 0, math.pi/2) + except Exception as e: + print(type(e).__name__ + ":", e) + sys.exit() + + return self.k**2 * result + + def phase(self, sin_theta, cos_theta, phi, x, y, z): + """Phase function.""" + sin_phi = _sin(phi) + cos_phi = _cos(phi) + + return self.k*(sin_theta*(y*sin_phi - z*cos_phi) + cos_theta*x) + + def f_spectrum(self, sin_theta, theta, phi): + """Spectrum amplitude function.""" + if self.m == 0: + return f_Gauss_spherical(sin_theta, self.W_y, self.k) + else: + return f_Laguerre_Gauss_spherical(sin_theta, theta, phi, + self.W_y, self.k, self.m) + + def integrand(self, theta, phi): + """Integrand function.""" + sin_theta = _sin(theta) + cos_theta = _cos(theta) + + return sin_theta * cos_theta * self.f_spectrum(sin_theta, theta, phi) * \ + _cexp(1j*self.phase(sin_theta, cos_theta, phi, self.x, self.ry, self.rz)) + + +def main(): + + import meep as mp + + x, y, z = -2.15, 0.3, 0.5 + r = mp.Vector3(0, y, z) + + k1 = 31.41592653589793 + w_0 = 0.25464790894703254 + m_charge = 2 + + params = dict(W_y=w_0, m=m_charge, k=k1) + + psi_cartesian = PsiCartesian(x=x, params=params) + + return lambda: psi_cartesian(r) + + +if __name__ == '__main__': + main() From b80cfe7125496ff304065ea4fdb88334940d3783 Mon Sep 17 00:00:00 2001 From: Daniel Kotik Date: Sun, 22 Mar 2020 15:31:12 +0100 Subject: [PATCH 054/145] Replace phase function (spherical to cartesian) --- Laguerre_Gauss_3d/optbeam2.py | 24 ++---------------------- 1 file changed, 2 insertions(+), 22 deletions(-) diff --git a/Laguerre_Gauss_3d/optbeam2.py b/Laguerre_Gauss_3d/optbeam2.py index ad8f7a3..a1ff114 100644 --- a/Laguerre_Gauss_3d/optbeam2.py +++ b/Laguerre_Gauss_3d/optbeam2.py @@ -84,23 +84,6 @@ def _complex_dblquad(func, a, b, gfun, hfun): return real + 1j*imag, real_tol, imag_tol -def f_Gauss_spherical(sin_theta, W_y, k): - """2d-Gaussian spectrum amplitude. - - Implementation for spherical coordinates. - """ - return _exp(-(k*W_y*sin_theta/2)**2) - - -def f_Laguerre_Gauss_spherical(sin_theta, theta, phi, W_y, k, m): - """Laguerre-Gaussian spectrum amplitude. - - Implementation for spherical coordinates. - """ - return f_Gauss_spherical(sin_theta, W_y, k) * theta**_abs(m) * \ - _cexp(1j*m*phi) - - def _phi(k_y, k_z): """Azimuthal angle. @@ -173,12 +156,9 @@ def __call__(self, r): return self.k**2 * result - def phase(self, sin_theta, cos_theta, phi, x, y, z): + def phase(k, k_y, k_z, x, y, z): """Phase function.""" - sin_phi = _sin(phi) - cos_phi = _cos(phi) - - return self.k*(sin_theta*(y*sin_phi - z*cos_phi) + cos_theta*x) + return x*_csqrt(k**2 - k_y**2 - k_z**2).real + y*k_y + z*k_z def f_spectrum(self, sin_theta, theta, phi): """Spectrum amplitude function.""" From 9722b200a8bae1e7dfaf9c44454517ed0e33f743 Mon Sep 17 00:00:00 2001 From: Daniel Kotik Date: Mon, 23 Mar 2020 16:48:58 +0100 Subject: [PATCH 055/145] Finalize class PsiCartesian --- Laguerre_Gauss_3d/optbeam2.py | 27 ++++++++++++--------------- 1 file changed, 12 insertions(+), 15 deletions(-) diff --git a/Laguerre_Gauss_3d/optbeam2.py b/Laguerre_Gauss_3d/optbeam2.py index a1ff114..3475e4f 100644 --- a/Laguerre_Gauss_3d/optbeam2.py +++ b/Laguerre_Gauss_3d/optbeam2.py @@ -130,13 +130,14 @@ class PsiCartesian: def __init__(self, x, params, called=False): """...""" self.x = x + self.params = params self.W_y = params['W_y'] self.k = params['k'] self.m = params['m'] self.called = called def __call__(self, r): - """...""" + """Beam profile function.""" self.ry = r.y self.rz = r.z @@ -149,32 +150,28 @@ def __call__(self, r): (result, real_tol, imag_tol) = _complex_dblquad(self if cython.compiled else self.integrand, - 0, 2*math.pi, 0, math.pi/2) + -self.k, self.k, -self.k, self.k) except Exception as e: print(type(e).__name__ + ":", e) sys.exit() - return self.k**2 * result + return result - def phase(k, k_y, k_z, x, y, z): + def phase(self, k_y, k_z, x, y, z): """Phase function.""" - return x*_csqrt(k**2 - k_y**2 - k_z**2).real + y*k_y + z*k_z + return x*_csqrt(self.k**2 - k_y**2 - k_z**2).real + y*k_y + z*k_z - def f_spectrum(self, sin_theta, theta, phi): + def f_spectrum(self, k_y, k_z): """Spectrum amplitude function.""" if self.m == 0: - return f_Gauss_spherical(sin_theta, self.W_y, self.k) + return f_Gauss_cartesian(k_y, k_z, self.W_y, self.k) else: - return f_Laguerre_Gauss_spherical(sin_theta, theta, phi, - self.W_y, self.k, self.m) + return f_Laguerre_Gauss_cartesian(k_y, k_z, self.W_y, self.k, self.m) - def integrand(self, theta, phi): + def integrand(self, k_y, k_z): """Integrand function.""" - sin_theta = _sin(theta) - cos_theta = _cos(theta) - - return sin_theta * cos_theta * self.f_spectrum(sin_theta, theta, phi) * \ - _cexp(1j*self.phase(sin_theta, cos_theta, phi, self.x, self.ry, self.rz)) + return self.f_spectrum(k_y, k_z) * \ + _cexp(1j*self.phase(k_y, k_z, self.x, self.ry, self.rz)) def main(): From b9d1720eeb9f5d54c7797680e04b5990a98db38b Mon Sep 17 00:00:00 2001 From: Daniel Kotik Date: Mon, 23 Mar 2020 17:03:53 +0100 Subject: [PATCH 056/145] Remove obsolete code --- Laguerre_Gauss_3d/LaguerreGauss3d.py | 31 ---------------------------- 1 file changed, 31 deletions(-) diff --git a/Laguerre_Gauss_3d/LaguerreGauss3d.py b/Laguerre_Gauss_3d/LaguerreGauss3d.py index fc610df..a6a8b02 100644 --- a/Laguerre_Gauss_3d/LaguerreGauss3d.py +++ b/Laguerre_Gauss_3d/LaguerreGauss3d.py @@ -221,38 +221,7 @@ def Gauss(r, params): # (purpose: calculate field amplitude at light source position if not # coinciding with beam waist) # -------------------------------------------------------------------------- - def psi_cartesian(r, x, params): - """Field amplitude function. - Integration in Cartesian coordinates. - """ - k, m = params['k'], params['m'] - - try: - getattr(psi_cartesian, "called") - except AttributeError: - psi_cartesian.called = True - print("Calculating inital field configuration. " - "This will take some time...") - - def phase(k_y, k_z, x, y, z): - """Phase function.""" - return x*cmath.sqrt(k**2 - k_y**2 - k_z**2).real + y*k_y + z*k_z - - f = (f_Gauss_cartesian if m == 0 else f_Laguerre_Gauss_cartesian) - - try: - (result, - real_tol, - imag_tol) = complex_dblquad(lambda k_y, k_z: - f(k_y, k_z, params) * - cmath.exp(1j*phase(k_y, k_z, x, r.y, r.z)), - -k, k, -k, k) - except Exception as e: - print(type(e).__name__ + ":", e) - sys.exit() - - return result # -------------------------------------------------------------------------- # some test outputs (uncomment if needed) From e1e54210a2bdaf6bd04691227d47f61f106cc1f2 Mon Sep 17 00:00:00 2001 From: Daniel Kotik Date: Mon, 23 Mar 2020 18:47:56 +0100 Subject: [PATCH 057/145] Add Cython declarations to pxd file --- Laguerre_Gauss_3d/optbeam2.pxd | 60 ++++++++++++++++++++++++++++++++++ Laguerre_Gauss_3d/optbeam2.py | 2 +- 2 files changed, 61 insertions(+), 1 deletion(-) diff --git a/Laguerre_Gauss_3d/optbeam2.pxd b/Laguerre_Gauss_3d/optbeam2.pxd index e69de29..6f5383d 100644 --- a/Laguerre_Gauss_3d/optbeam2.pxd +++ b/Laguerre_Gauss_3d/optbeam2.pxd @@ -0,0 +1,60 @@ +# -*- coding: utf-8 -*- +""" +file: optbeam2.pxd +brief: ... +author: Daniel Kotik +version: 1.5-beta +release date: xx.xx.2020 +creation date: 23.02.2020 +""" +cimport cython +from cpython.pycapsule cimport PyCapsule_New +from cpython cimport bool + +# declare C functions as "cpdef" to export them to the module +cdef extern from "stdlib.h": + cpdef int _abs "abs" (int n) nogil + +cdef extern from "math.h": + cpdef double _sin "sin" (double x) nogil + cpdef double _cos "cos" (double x) nogil + cpdef double _exp "exp" (double x) nogil + cpdef double _acos "acos" (double x) nogil + cpdef double _atan2 "atan2" (double y, double x) nogil + +cdef extern from "complex.h": + cpdef double complex _cexp "cexp" (double complex z) nogil + cpdef double complex _csqrt "csqrt" (double complex z) nogil + + +# function prototypes +cdef double _imag_2d_func_c(int n, double *arr, void *func_ptr) +cdef double _real_2d_func_c(int n, double *arr, void *func_ptr) + +@cython.locals(real=cython.double, imag=cython.double, real_tol=cython.double, + imag_tol=cython.double) +cdef (double complex, double, double) _complex_dblquad(PsiCartesian func, + double a, double b, + double gfun, double hfun) + +cdef double _phi(double k_y, double k_z) nogil +cdef double _theta(double k_y, double k_z, double k) nogil + +@cython.locals(W_y=cython.double) +cdef double complex f_Gauss_cartesian(double k_y, double k_z, double W_y) nogil + +@cython.locals(m=cython.int) +cdef double complex f_Laguerre_Gauss_cartesian(double k_y, double k_z, + double W_y, double k, int m) nogil + +cdef class PsiCartesian: + cdef: + readonly dict params + int m + double x, k, W_y + double ry, rz + bool called + + cdef double phase(self, double k_y, double k_z, double x, double y, double z) nogil + cdef double complex integrand(self, double k_y, double k_z) nogil + cdef double complex f_spectrum(self, double k_y, double k_z) nogil diff --git a/Laguerre_Gauss_3d/optbeam2.py b/Laguerre_Gauss_3d/optbeam2.py index 3475e4f..b2d2897 100644 --- a/Laguerre_Gauss_3d/optbeam2.py +++ b/Laguerre_Gauss_3d/optbeam2.py @@ -164,7 +164,7 @@ def phase(self, k_y, k_z, x, y, z): def f_spectrum(self, k_y, k_z): """Spectrum amplitude function.""" if self.m == 0: - return f_Gauss_cartesian(k_y, k_z, self.W_y, self.k) + return f_Gauss_cartesian(k_y, k_z, self.W_y) else: return f_Laguerre_Gauss_cartesian(k_y, k_z, self.W_y, self.k, self.m) From 088a11294d9cf901e8b87d840b02d52d8d84bd0a Mon Sep 17 00:00:00 2001 From: Daniel Kotik Date: Tue, 24 Mar 2020 00:24:01 +0100 Subject: [PATCH 058/145] Add abstract base class Beam3d --- Laguerre_Gauss_3d/optbeam.pxd | 13 ++++++++++--- Laguerre_Gauss_3d/optbeam.py | 21 ++++++++++++++++----- 2 files changed, 26 insertions(+), 8 deletions(-) diff --git a/Laguerre_Gauss_3d/optbeam.pxd b/Laguerre_Gauss_3d/optbeam.pxd index 04aebb6..a2458f5 100644 --- a/Laguerre_Gauss_3d/optbeam.pxd +++ b/Laguerre_Gauss_3d/optbeam.pxd @@ -24,13 +24,13 @@ cdef extern from "complex.h": cpdef double complex _cexp "cexp" (double complex z) nogil -# function prototypes +# function declarations cdef double _imag_2d_func_c(int n, double *arr, void *func_ptr) cdef double _real_2d_func_c(int n, double *arr, void *func_ptr) @cython.locals(real=cython.double, imag=cython.double, real_tol=cython.double, imag_tol=cython.double) -cdef (double complex, double, double) _complex_dblquad(PsiSpherical func, +cdef (double complex, double, double) _complex_dblquad(Beam3d func, double a, double b, double gfun, double hfun) @@ -41,7 +41,14 @@ cdef double complex f_Gauss_spherical(double sin_theta, double W_y, double k) no cdef double complex f_Laguerre_Gauss_spherical(double sin_theta, double theta, double phi, double W_y, double k, int m) nogil -cdef class PsiSpherical: +# class declarations +cdef class Beam3d: + cdef double phase(self, double sin_theta, double cos_theta, double phi, + double x, double y, double z) nogil + cdef double complex integrand(self, double theta, double phi) nogil + cdef double complex f_spectrum(self, double sin_theta, double theta, double phi) nogil + +cdef class PsiSpherical(Beam3d): cdef: readonly dict params int m diff --git a/Laguerre_Gauss_3d/optbeam.py b/Laguerre_Gauss_3d/optbeam.py index e4c5d18..8fa6da1 100644 --- a/Laguerre_Gauss_3d/optbeam.py +++ b/Laguerre_Gauss_3d/optbeam.py @@ -42,8 +42,8 @@ def _imag_2d_func_c(n, arr, func_ptr): Cython implementation. """ # pure python formulation of: - # return (func_ptr)(arr[0], arr[1]).imag - return cython.cast(PsiSpherical, func_ptr).integrand(arr[0], arr[1]).imag + # return (func_ptr)(arr[0], arr[1]).imag + return cython.cast(Beam3d, func_ptr).integrand(arr[0], arr[1]).imag def _real_2d_func_c(n, arr, func_ptr): @@ -52,8 +52,8 @@ def _real_2d_func_c(n, arr, func_ptr): Cython implementation. """ # pure python formulation of: - # return (func_ptr)(arr[0], arr[1]).real - return cython.cast(PsiSpherical, func_ptr).integrand(arr[0], arr[1]).real + # return (func_ptr)(arr[0], arr[1]).real + return cython.cast(Beam3d, func_ptr).integrand(arr[0], arr[1]).real def _complex_dblquad(func, a, b, gfun, hfun): @@ -98,7 +98,18 @@ def f_Laguerre_Gauss_spherical(sin_theta, theta, phi, W_y, k, m): _cexp(1j*m*phi) -class PsiSpherical: +class Beam3d: + def phase(self, sin_theta, cos_theta, phi, x, y, z): + pass + + def f_spectrum(self, sin_theta, theta, phi): + pass + + def integrand(self, theta, phi): + pass + + +class PsiSpherical(Beam3d): """Field amplitude class. Integration in spherical coordinates. From 660c9597865bbb2a872d2e88d06dd810d0d04188 Mon Sep 17 00:00:00 2001 From: Daniel Kotik Date: Tue, 24 Mar 2020 22:36:23 +0100 Subject: [PATCH 059/145] Reduce number of essential methods in base class --- Laguerre_Gauss_3d/optbeam.pxd | 5 +---- Laguerre_Gauss_3d/optbeam.py | 8 +------- 2 files changed, 2 insertions(+), 11 deletions(-) diff --git a/Laguerre_Gauss_3d/optbeam.pxd b/Laguerre_Gauss_3d/optbeam.pxd index a2458f5..0227142 100644 --- a/Laguerre_Gauss_3d/optbeam.pxd +++ b/Laguerre_Gauss_3d/optbeam.pxd @@ -43,10 +43,7 @@ cdef double complex f_Laguerre_Gauss_spherical(double sin_theta, double theta, # class declarations cdef class Beam3d: - cdef double phase(self, double sin_theta, double cos_theta, double phi, - double x, double y, double z) nogil - cdef double complex integrand(self, double theta, double phi) nogil - cdef double complex f_spectrum(self, double sin_theta, double theta, double phi) nogil + cdef double complex integrand(self, double x, double y) nogil cdef class PsiSpherical(Beam3d): cdef: diff --git a/Laguerre_Gauss_3d/optbeam.py b/Laguerre_Gauss_3d/optbeam.py index 8fa6da1..620c6de 100644 --- a/Laguerre_Gauss_3d/optbeam.py +++ b/Laguerre_Gauss_3d/optbeam.py @@ -99,13 +99,7 @@ def f_Laguerre_Gauss_spherical(sin_theta, theta, phi, W_y, k, m): class Beam3d: - def phase(self, sin_theta, cos_theta, phi, x, y, z): - pass - - def f_spectrum(self, sin_theta, theta, phi): - pass - - def integrand(self, theta, phi): + def integrand(self, x, y): pass From 5d9d7fe02a6f240539bfe8ecd7d55e9761a8a719 Mon Sep 17 00:00:00 2001 From: Daniel Kotik Date: Tue, 24 Mar 2020 22:48:50 +0100 Subject: [PATCH 060/145] Add TODOs --- Laguerre_Gauss_3d/optbeam.py | 3 +++ 1 file changed, 3 insertions(+) diff --git a/Laguerre_Gauss_3d/optbeam.py b/Laguerre_Gauss_3d/optbeam.py index 620c6de..bcc16be 100644 --- a/Laguerre_Gauss_3d/optbeam.py +++ b/Laguerre_Gauss_3d/optbeam.py @@ -115,6 +115,7 @@ class PsiSpherical(Beam3d): def __init__(self, x, params, called=False): """...""" + # TODO: rename x to x_shift self.x = x self.params = params self.W_y = params['W_y'] @@ -124,6 +125,7 @@ def __init__(self, x, params, called=False): def __call__(self, r): """Beam profile function.""" + # TODO: rename __call__(self, r) to profile(self, r) self.ry = r.y self.rz = r.z @@ -170,6 +172,7 @@ def integrand(self, theta, phi): def main(): import meep as mp + # TODO: remove meep dependency x, y, z = -2.15, 0.3, 0.5 r = mp.Vector3(0, y, z) From 2ad2d465aedba52d1fec9453445a100b20025753 Mon Sep 17 00:00:00 2001 From: Daniel Kotik Date: Tue, 24 Mar 2020 22:50:37 +0100 Subject: [PATCH 061/145] Remove main function --- Laguerre_Gauss_3d/optbeam.py | 9 +-------- 1 file changed, 1 insertion(+), 8 deletions(-) diff --git a/Laguerre_Gauss_3d/optbeam.py b/Laguerre_Gauss_3d/optbeam.py index bcc16be..078d8f2 100644 --- a/Laguerre_Gauss_3d/optbeam.py +++ b/Laguerre_Gauss_3d/optbeam.py @@ -169,8 +169,7 @@ def integrand(self, theta, phi): _cexp(1j*self.phase(sin_theta, cos_theta, phi, self.x, self.ry, self.rz)) -def main(): - +if __name__ == '__main__': import meep as mp # TODO: remove meep dependency @@ -184,9 +183,3 @@ def main(): params = dict(W_y=w_0, m=m_charge, k=k1) psi_spherical = PsiSpherical(x=x, params=params) - - return lambda: psi_spherical(r) - - -if __name__ == '__main__': - main() From 3df04a2d1aefe71fc8e33c269851b312ea733241 Mon Sep 17 00:00:00 2001 From: Daniel Kotik Date: Tue, 24 Mar 2020 23:04:47 +0100 Subject: [PATCH 062/145] Add Cartesian implementation --- Laguerre_Gauss_3d/optbeam.py | 98 +++++++++++++++++++++++++++++++++++- 1 file changed, 96 insertions(+), 2 deletions(-) diff --git a/Laguerre_Gauss_3d/optbeam.py b/Laguerre_Gauss_3d/optbeam.py index 078d8f2..7de2600 100644 --- a/Laguerre_Gauss_3d/optbeam.py +++ b/Laguerre_Gauss_3d/optbeam.py @@ -17,8 +17,11 @@ if not cython.compiled: from math import (sin as _sin, cos as _cos, - exp as _exp) - from cmath import exp as _cexp + exp as _exp, + acos as _acos, + atan2 as _atan2) + from cmath import (exp as _cexp, + sqrt as _csqrt) from builtins import abs as _abs print("\nPlease consider compiling `%s.py` via Cython: " "`$ cythonize -3 -i %s.py`\n" % (__name__, __name__)) @@ -169,6 +172,96 @@ def integrand(self, theta, phi): _cexp(1j*self.phase(sin_theta, cos_theta, phi, self.x, self.ry, self.rz)) +def _phi(k_y, k_z): + """Azimuthal angle. + + Part of coordinate transformation from k-space to (theta, phi)-space. + """ + return _atan2(k_y, -k_z) + + +def _theta(k_y, k_z, k): + """Polar angle. + + Part of coordinate transformation from k-space to (theta, phi)-space. + """ + return _acos(_csqrt(k**2 - k_y**2 - k_z**2).real / k) + + +def f_Gauss_cartesian(k_y, k_z, W_y): + """2d-Gaussian spectrum amplitude. + + Impementation for Cartesian coordinates. + """ + return _exp(-W_y**2 * (k_y**2 + k_z**2)/4) + + +def f_Laguerre_Gauss_cartesian(k_y, k_z, W_y, k, m): + """Laguerre-Gaussian spectrum amplitude. + + Impementation for Cartesian coordinates. + """ + return f_Gauss_cartesian(k_y, k_z, W_y) * \ + _cexp(1j*m*_phi(k_y, k_z)) * _theta(k_y, k_z, k)**_abs(m) + + +class PsiCartesian: + """Field amplitude class. + + Integration in cartesian coordinates. + + Usage: + psi_cartesian = PsiCartesian(x=shift, params=params) + psi_cartesian(r) # r...vector-like object with scalar y and z attributes + """ + + def __init__(self, x, params, called=False): + """...""" + self.x = x + self.params = params + self.W_y = params['W_y'] + self.k = params['k'] + self.m = params['m'] + self.called = called + + def __call__(self, r): + """Beam profile function.""" + self.ry = r.y + self.rz = r.z + + if not self.called: + print("Calculating inital field configuration. " + "This will take some time...") + self.called = True + + try: + (result, + real_tol, + imag_tol) = _complex_dblquad(self if cython.compiled else self.integrand, + -self.k, self.k, -self.k, self.k) + except Exception as e: + print(type(e).__name__ + ":", e) + sys.exit() + + return result + + def phase(self, k_y, k_z, x, y, z): + """Phase function.""" + return x*_csqrt(self.k**2 - k_y**2 - k_z**2).real + y*k_y + z*k_z + + def f_spectrum(self, k_y, k_z): + """Spectrum amplitude function.""" + if self.m == 0: + return f_Gauss_cartesian(k_y, k_z, self.W_y) + else: + return f_Laguerre_Gauss_cartesian(k_y, k_z, self.W_y, self.k, self.m) + + def integrand(self, k_y, k_z): + """Integrand function.""" + return self.f_spectrum(k_y, k_z) * \ + _cexp(1j*self.phase(k_y, k_z, self.x, self.ry, self.rz)) + + if __name__ == '__main__': import meep as mp # TODO: remove meep dependency @@ -183,3 +276,4 @@ def integrand(self, theta, phi): params = dict(W_y=w_0, m=m_charge, k=k1) psi_spherical = PsiSpherical(x=x, params=params) + psi_cartesian = PsiCartesian(x=x, params=params) From bc1f3b53f45f41483e42ff99e531fadb6051c47c Mon Sep 17 00:00:00 2001 From: Daniel Kotik Date: Wed, 25 Mar 2020 16:34:42 +0100 Subject: [PATCH 063/145] Replace meep dependency with a simple vector class --- Laguerre_Gauss_3d/optbeam.py | 12 +++++++++--- 1 file changed, 9 insertions(+), 3 deletions(-) diff --git a/Laguerre_Gauss_3d/optbeam.py b/Laguerre_Gauss_3d/optbeam.py index 7de2600..b11935d 100644 --- a/Laguerre_Gauss_3d/optbeam.py +++ b/Laguerre_Gauss_3d/optbeam.py @@ -263,11 +263,17 @@ def integrand(self, k_y, k_z): if __name__ == '__main__': - import meep as mp - # TODO: remove meep dependency + class Vector3: + """Simple vector class.""" + + def __init__(self, x, y, z): + self.x = x + self.y = y + self.z = z x, y, z = -2.15, 0.3, 0.5 - r = mp.Vector3(0, y, z) + # import meep; r = meep.Vector3(0, y, z) + r = Vector3(0, y, z) k1 = 31.41592653589793 w_0 = 0.25464790894703254 From e279b4c005ac743677b017045f273be63344368d Mon Sep 17 00:00:00 2001 From: Daniel Kotik Date: Wed, 25 Mar 2020 16:51:43 +0100 Subject: [PATCH 064/145] Fall back to main using main function --- Laguerre_Gauss_3d/optbeam.py | 9 ++++++++- 1 file changed, 8 insertions(+), 1 deletion(-) diff --git a/Laguerre_Gauss_3d/optbeam.py b/Laguerre_Gauss_3d/optbeam.py index b11935d..b1ea10c 100644 --- a/Laguerre_Gauss_3d/optbeam.py +++ b/Laguerre_Gauss_3d/optbeam.py @@ -262,7 +262,7 @@ def integrand(self, k_y, k_z): _cexp(1j*self.phase(k_y, k_z, self.x, self.ry, self.rz)) -if __name__ == '__main__': +def main(): class Vector3: """Simple vector class.""" @@ -272,6 +272,7 @@ def __init__(self, x, y, z): self.z = z x, y, z = -2.15, 0.3, 0.5 + # import meep; r = meep.Vector3(0, y, z) r = Vector3(0, y, z) @@ -283,3 +284,9 @@ def __init__(self, x, y, z): psi_spherical = PsiSpherical(x=x, params=params) psi_cartesian = PsiCartesian(x=x, params=params) + + return (psi_spherical, psi_cartesian, r) + + +if __name__ == '__main__': + main() From 47174e8a903b7ee3ce4968b73a86ef1cdc3c6b83 Mon Sep 17 00:00:00 2001 From: Daniel Kotik Date: Wed, 25 Mar 2020 17:21:55 +0100 Subject: [PATCH 065/145] Merge declarations form optbeam2.pxd into optbeam.pxd --- Laguerre_Gauss_3d/optbeam.pxd | 27 +++++++++++++++++++++++---- 1 file changed, 23 insertions(+), 4 deletions(-) diff --git a/Laguerre_Gauss_3d/optbeam.pxd b/Laguerre_Gauss_3d/optbeam.pxd index 0227142..2820c41 100644 --- a/Laguerre_Gauss_3d/optbeam.pxd +++ b/Laguerre_Gauss_3d/optbeam.pxd @@ -19,9 +19,12 @@ cdef extern from "math.h": cpdef double _sin "sin" (double x) nogil cpdef double _cos "cos" (double x) nogil cpdef double _exp "exp" (double x) nogil + cpdef double _acos "acos" (double x) nogil + cpdef double _atan2 "atan2" (double y, double x) nogil cdef extern from "complex.h": cpdef double complex _cexp "cexp" (double complex z) nogil + cpdef double complex _csqrt "csqrt" (double complex z) nogil # function declarations @@ -34,12 +37,16 @@ cdef (double complex, double, double) _complex_dblquad(Beam3d func, double a, double b, double gfun, double hfun) -@cython.locals(W_y=cython.double, k=cython.double) +cdef double _phi(double k_y, double k_z) nogil +cdef double _theta(double k_y, double k_z, double k) nogil # TODO: allow cdivison + cdef double complex f_Gauss_spherical(double sin_theta, double W_y, double k) nogil +cdef double complex f_Gauss_cartesian(double k_y, double k_z, double W_y) nogil -@cython.locals(m=cython.int) -cdef double complex f_Laguerre_Gauss_spherical(double sin_theta, double theta, - double phi, double W_y, double k, int m) nogil +cdef double complex f_Laguerre_Gauss_spherical(double sin_theta, double theta, double phi, + double W_y, double k, int m) nogil +cdef double complex f_Laguerre_Gauss_cartesian(double k_y, double k_z, + double W_y, double k, int m) nogil # class declarations cdef class Beam3d: @@ -57,3 +64,15 @@ cdef class PsiSpherical(Beam3d): double x, double y, double z) nogil cdef double complex integrand(self, double theta, double phi) nogil cdef double complex f_spectrum(self, double sin_theta, double theta, double phi) nogil + +cdef class PsiCartesian(Beam3d): + cdef: + readonly dict params + int m + double x, k, W_y + double ry, rz + bool called + + cdef double phase(self, double k_y, double k_z, double x, double y, double z) nogil + cdef double complex integrand(self, double k_y, double k_z) nogil + cdef double complex f_spectrum(self, double k_y, double k_z) nogil From 587f6c443e6832086c00903ab733f9da7506c12a Mon Sep 17 00:00:00 2001 From: Daniel Kotik Date: Wed, 25 Mar 2020 17:27:16 +0100 Subject: [PATCH 066/145] Delete optbeam2.p*: Established class hierachy makes separation of PsiSpherical and PsiCartesian into separate extension modules obsolete. --- Laguerre_Gauss_3d/optbeam2.pxd | 60 ---------- Laguerre_Gauss_3d/optbeam2.py | 196 --------------------------------- 2 files changed, 256 deletions(-) delete mode 100644 Laguerre_Gauss_3d/optbeam2.pxd delete mode 100644 Laguerre_Gauss_3d/optbeam2.py diff --git a/Laguerre_Gauss_3d/optbeam2.pxd b/Laguerre_Gauss_3d/optbeam2.pxd deleted file mode 100644 index 6f5383d..0000000 --- a/Laguerre_Gauss_3d/optbeam2.pxd +++ /dev/null @@ -1,60 +0,0 @@ -# -*- coding: utf-8 -*- -""" -file: optbeam2.pxd -brief: ... -author: Daniel Kotik -version: 1.5-beta -release date: xx.xx.2020 -creation date: 23.02.2020 -""" -cimport cython -from cpython.pycapsule cimport PyCapsule_New -from cpython cimport bool - -# declare C functions as "cpdef" to export them to the module -cdef extern from "stdlib.h": - cpdef int _abs "abs" (int n) nogil - -cdef extern from "math.h": - cpdef double _sin "sin" (double x) nogil - cpdef double _cos "cos" (double x) nogil - cpdef double _exp "exp" (double x) nogil - cpdef double _acos "acos" (double x) nogil - cpdef double _atan2 "atan2" (double y, double x) nogil - -cdef extern from "complex.h": - cpdef double complex _cexp "cexp" (double complex z) nogil - cpdef double complex _csqrt "csqrt" (double complex z) nogil - - -# function prototypes -cdef double _imag_2d_func_c(int n, double *arr, void *func_ptr) -cdef double _real_2d_func_c(int n, double *arr, void *func_ptr) - -@cython.locals(real=cython.double, imag=cython.double, real_tol=cython.double, - imag_tol=cython.double) -cdef (double complex, double, double) _complex_dblquad(PsiCartesian func, - double a, double b, - double gfun, double hfun) - -cdef double _phi(double k_y, double k_z) nogil -cdef double _theta(double k_y, double k_z, double k) nogil - -@cython.locals(W_y=cython.double) -cdef double complex f_Gauss_cartesian(double k_y, double k_z, double W_y) nogil - -@cython.locals(m=cython.int) -cdef double complex f_Laguerre_Gauss_cartesian(double k_y, double k_z, - double W_y, double k, int m) nogil - -cdef class PsiCartesian: - cdef: - readonly dict params - int m - double x, k, W_y - double ry, rz - bool called - - cdef double phase(self, double k_y, double k_z, double x, double y, double z) nogil - cdef double complex integrand(self, double k_y, double k_z) nogil - cdef double complex f_spectrum(self, double k_y, double k_z) nogil diff --git a/Laguerre_Gauss_3d/optbeam2.py b/Laguerre_Gauss_3d/optbeam2.py deleted file mode 100644 index b2d2897..0000000 --- a/Laguerre_Gauss_3d/optbeam2.py +++ /dev/null @@ -1,196 +0,0 @@ -# -*- coding: utf-8 -*- -""" -file: optbeam2.py -brief: ... -author: Daniel Kotik -version: 1.5-beta -release date: xx.xx.2020 -creation date: 20.03.2020 -""" -import cython -import math -import sys - -from scipy.integrate import dblquad - - -if not cython.compiled: - from math import (sin as _sin, - cos as _cos, - exp as _exp, - acos as _acos, - atan2 as _atan2) - from cmath import (exp as _cexp, - sqrt as _csqrt) - from builtins import abs as _abs - print("\nPlease consider compiling `%s.py` via Cython: " - "`$ cythonize -3 -i %s.py`\n" % (__name__, __name__)) -else: - from scipy import LowLevelCallable - - -def _real_2d_func(x, y, func): - """Return real part of a 2d function.""" - return func(x, y).real - - -def _imag_2d_func(x, y, func): - """Return imag part of a 2d function.""" - return func(x, y).imag - - -def _imag_2d_func_c(n, arr, func_ptr): - """Return imag part of a 2d function. - - Cython implementation. - """ - # pure python formulation of: - # return (func_ptr)(arr[0], arr[1]).imag - return cython.cast(PsiCartesian, func_ptr).integrand(arr[0], arr[1]).imag - - -def _real_2d_func_c(n, arr, func_ptr): - """Return real part of a 2d function. - - Cython implementation. - """ - # pure python formulation of: - # return (func_ptr)(arr[0], arr[1]).real - return cython.cast(PsiCartesian, func_ptr).integrand(arr[0], arr[1]).real - - -def _complex_dblquad(func, a, b, gfun, hfun): - """Integrate real and imaginary part of the given function.""" - if cython.compiled: - # pure python formulation of: cdef void *f_ptr = func - f_ptr = cython.declare(cython.p_void, cython.cast(cython.p_void, func)) - - func_capsule = PyCapsule_New(f_ptr, cython.NULL, cython.NULL) - - current_module = sys.modules[__name__] - - ll_real_2d_func_c = LowLevelCallable.from_cython(current_module, - '_real_2d_func_c', - func_capsule) - ll_imag_2d_func_c = LowLevelCallable.from_cython(current_module, - '_imag_2d_func_c', - func_capsule) - real, real_tol = dblquad(ll_real_2d_func_c, a, b, gfun, hfun) - imag, imag_tol = dblquad(ll_imag_2d_func_c, a, b, gfun, hfun) - else: - real, real_tol = dblquad(_real_2d_func, a, b, gfun, hfun, (func,)) - imag, imag_tol = dblquad(_imag_2d_func, a, b, gfun, hfun, (func,)) - - return real + 1j*imag, real_tol, imag_tol - - -def _phi(k_y, k_z): - """Azimuthal angle. - - Part of coordinate transformation from k-space to (theta, phi)-space. - """ - return _atan2(k_y, -k_z) - - -def _theta(k_y, k_z, k): - """Polar angle. - - Part of coordinate transformation from k-space to (theta, phi)-space. - """ - return _acos(_csqrt(k**2 - k_y**2 - k_z**2).real / k) - - -def f_Gauss_cartesian(k_y, k_z, W_y): - """2d-Gaussian spectrum amplitude. - - Impementation for Cartesian coordinates. - """ - return _exp(-W_y**2 * (k_y**2 + k_z**2)/4) - - -def f_Laguerre_Gauss_cartesian(k_y, k_z, W_y, k, m): - """Laguerre-Gaussian spectrum amplitude. - - Impementation for Cartesian coordinates. - """ - return f_Gauss_cartesian(k_y, k_z, W_y) * \ - _cexp(1j*m*_phi(k_y, k_z)) * _theta(k_y, k_z, k)**_abs(m) - - -class PsiCartesian: - """Field amplitude class. - - Integration in cartesian coordinates. - - Usage: - psi_cartesian = PsiCartesian(x=shift, params=params) - psi_cartesian(r) # r...vector-like object with scalar y and z attributes - """ - - def __init__(self, x, params, called=False): - """...""" - self.x = x - self.params = params - self.W_y = params['W_y'] - self.k = params['k'] - self.m = params['m'] - self.called = called - - def __call__(self, r): - """Beam profile function.""" - self.ry = r.y - self.rz = r.z - - if not self.called: - print("Calculating inital field configuration. " - "This will take some time...") - self.called = True - - try: - (result, - real_tol, - imag_tol) = _complex_dblquad(self if cython.compiled else self.integrand, - -self.k, self.k, -self.k, self.k) - except Exception as e: - print(type(e).__name__ + ":", e) - sys.exit() - - return result - - def phase(self, k_y, k_z, x, y, z): - """Phase function.""" - return x*_csqrt(self.k**2 - k_y**2 - k_z**2).real + y*k_y + z*k_z - - def f_spectrum(self, k_y, k_z): - """Spectrum amplitude function.""" - if self.m == 0: - return f_Gauss_cartesian(k_y, k_z, self.W_y) - else: - return f_Laguerre_Gauss_cartesian(k_y, k_z, self.W_y, self.k, self.m) - - def integrand(self, k_y, k_z): - """Integrand function.""" - return self.f_spectrum(k_y, k_z) * \ - _cexp(1j*self.phase(k_y, k_z, self.x, self.ry, self.rz)) - - -def main(): - - import meep as mp - - x, y, z = -2.15, 0.3, 0.5 - r = mp.Vector3(0, y, z) - - k1 = 31.41592653589793 - w_0 = 0.25464790894703254 - m_charge = 2 - - params = dict(W_y=w_0, m=m_charge, k=k1) - - psi_cartesian = PsiCartesian(x=x, params=params) - - return lambda: psi_cartesian(r) - - -if __name__ == '__main__': - main() From ee11ce50fbac1b377a80a1e45856729b31d8c630 Mon Sep 17 00:00:00 2001 From: Daniel Kotik Date: Thu, 26 Mar 2020 19:27:26 +0100 Subject: [PATCH 067/145] Modify __init__function of subclasses --- Laguerre_Gauss_3d/optbeam.py | 16 +++++++++------- 1 file changed, 9 insertions(+), 7 deletions(-) diff --git a/Laguerre_Gauss_3d/optbeam.py b/Laguerre_Gauss_3d/optbeam.py index b1ea10c..f445d68 100644 --- a/Laguerre_Gauss_3d/optbeam.py +++ b/Laguerre_Gauss_3d/optbeam.py @@ -102,6 +102,13 @@ def f_Laguerre_Gauss_spherical(sin_theta, theta, phi, W_y, k, m): class Beam3d: + """Abstract base class.""" + + def __init__(self, x, params, called=False): + self.x = x # TODO: rename x to x_shift + self.params = params + self.called = called + def integrand(self, x, y): pass @@ -118,13 +125,10 @@ class PsiSpherical(Beam3d): def __init__(self, x, params, called=False): """...""" - # TODO: rename x to x_shift - self.x = x - self.params = params + super().__init__(x, params, called) self.W_y = params['W_y'] self.k = params['k'] self.m = params['m'] - self.called = called def __call__(self, r): """Beam profile function.""" @@ -217,12 +221,10 @@ class PsiCartesian: def __init__(self, x, params, called=False): """...""" - self.x = x - self.params = params + super().__init__(x, params, called) self.W_y = params['W_y'] self.k = params['k'] self.m = params['m'] - self.called = called def __call__(self, r): """Beam profile function.""" From 72eac44974c716a0f3317edd17d4725c97300d9c Mon Sep 17 00:00:00 2001 From: Daniel Kotik Date: Fri, 27 Mar 2020 16:07:51 +0100 Subject: [PATCH 068/145] Add TODO --- Laguerre_Gauss_3d/optbeam.py | 1 + 1 file changed, 1 insertion(+) diff --git a/Laguerre_Gauss_3d/optbeam.py b/Laguerre_Gauss_3d/optbeam.py index f445d68..62b56c3 100644 --- a/Laguerre_Gauss_3d/optbeam.py +++ b/Laguerre_Gauss_3d/optbeam.py @@ -132,6 +132,7 @@ def __init__(self, x, params, called=False): def __call__(self, r): """Beam profile function.""" + # TODO: Consider calling simple Gauss for special case x=0 # TODO: rename __call__(self, r) to profile(self, r) self.ry = r.y self.rz = r.z From 9e1f3dc79476cf608bb1ef4144cf2afb69edc05b Mon Sep 17 00:00:00 2001 From: Daniel Kotik Date: Fri, 27 Mar 2020 18:23:38 +0100 Subject: [PATCH 069/145] Fix inheritance: PsiCartesian needs to inherit from Beam3d, at least for the cythonized version, where the integrand function is casted to a Beam3d type. --- Laguerre_Gauss_3d/optbeam.py | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/Laguerre_Gauss_3d/optbeam.py b/Laguerre_Gauss_3d/optbeam.py index 62b56c3..925737c 100644 --- a/Laguerre_Gauss_3d/optbeam.py +++ b/Laguerre_Gauss_3d/optbeam.py @@ -210,7 +210,7 @@ def f_Laguerre_Gauss_cartesian(k_y, k_z, W_y, k, m): _cexp(1j*m*_phi(k_y, k_z)) * _theta(k_y, k_z, k)**_abs(m) -class PsiCartesian: +class PsiCartesian(Beam3d): """Field amplitude class. Integration in cartesian coordinates. From 3b716ca0b98d51f4c1dfba22db6669668a11d0c2 Mon Sep 17 00:00:00 2001 From: Daniel Kotik Date: Fri, 27 Mar 2020 18:24:39 +0100 Subject: [PATCH 070/145] Adjust declaration file to align with the implementation. --- Laguerre_Gauss_3d/optbeam.pxd | 13 +++++++------ 1 file changed, 7 insertions(+), 6 deletions(-) diff --git a/Laguerre_Gauss_3d/optbeam.pxd b/Laguerre_Gauss_3d/optbeam.pxd index 2820c41..505a249 100644 --- a/Laguerre_Gauss_3d/optbeam.pxd +++ b/Laguerre_Gauss_3d/optbeam.pxd @@ -50,15 +50,18 @@ cdef double complex f_Laguerre_Gauss_cartesian(double k_y, double k_z, # class declarations cdef class Beam3d: + cdef: + readonly dict params + double x + bool called + cdef double complex integrand(self, double x, double y) nogil cdef class PsiSpherical(Beam3d): cdef: - readonly dict params int m - double x, k, W_y + double k, W_y double ry, rz - bool called cdef double phase(self, double sin_theta, double cos_theta, double phi, double x, double y, double z) nogil @@ -67,11 +70,9 @@ cdef class PsiSpherical(Beam3d): cdef class PsiCartesian(Beam3d): cdef: - readonly dict params int m - double x, k, W_y + double k, W_y double ry, rz - bool called cdef double phase(self, double k_y, double k_z, double x, double y, double z) nogil cdef double complex integrand(self, double k_y, double k_z) nogil From 6852f4c0c37201e4f3659f7c6ad1669482bfd609 Mon Sep 17 00:00:00 2001 From: Daniel Kotik Date: Sun, 29 Mar 2020 14:18:37 +0200 Subject: [PATCH 071/145] Add Beam3dSpherical and LaguerreGauss3d specialised classes --- Laguerre_Gauss_3d/optbeam.py | 120 ++++++++++++++++++++++++++++------- 1 file changed, 97 insertions(+), 23 deletions(-) diff --git a/Laguerre_Gauss_3d/optbeam.py b/Laguerre_Gauss_3d/optbeam.py index 925737c..97b09de 100644 --- a/Laguerre_Gauss_3d/optbeam.py +++ b/Laguerre_Gauss_3d/optbeam.py @@ -84,35 +84,107 @@ def _complex_dblquad(func, a, b, gfun, hfun): return real + 1j*imag, real_tol, imag_tol -def f_Gauss_spherical(sin_theta, W_y, k): - """2d-Gaussian spectrum amplitude. - - Implementation for spherical coordinates. - """ - return _exp(-(k*W_y*sin_theta/2)**2) - - -def f_Laguerre_Gauss_spherical(sin_theta, theta, phi, W_y, k, m): - """Laguerre-Gaussian spectrum amplitude. - - Implementation for spherical coordinates. - """ - return f_Gauss_spherical(sin_theta, W_y, k) * theta**_abs(m) * \ - _cexp(1j*m*phi) - - class Beam3d: """Abstract base class.""" def __init__(self, x, params, called=False): self.x = x # TODO: rename x to x_shift + self.k = params['k'] self.params = params self.called = called def integrand(self, x, y): + """Integrand function over two coordinates x and y.""" pass +class Beam3dSpherical(Beam3d): + """Implementaion of a 3d beam in spherical coordinates.""" + + def profile(self, r): + """Beam profile function, psi.""" + # TODO: Consider calling simple Gauss for special case x=0 + # TODO: rename __call__(self, r) to profile(self, r) + self.ry = r.y + self.rz = r.z + + if not self.called: + print("Calculating inital field configuration. " + "This will take some time...") + self.called = True + + try: + (result, + real_tol, + imag_tol) = _complex_dblquad(self if cython.compiled else self.integrand, + 0, 2*math.pi, 0, math.pi/2) + except Exception as e: + print(type(e).__name__ + ":", e) + sys.exit() + + return self.k**2 * result + + def phase(self, sin_theta, cos_theta, phi, x, y, z): + """Phase function.""" + sin_phi = _sin(phi) + cos_phi = _cos(phi) + + return self.k*(sin_theta*(y*sin_phi - z*cos_phi) + cos_theta*x) + + def spectrum(self, sin_theta, theta, phi): + """Spectrum amplitude function, f.""" + pass + + def integrand(self, theta, phi): + """Integrand function.""" + sin_theta = _sin(theta) + cos_theta = _cos(theta) + + return sin_theta * cos_theta * self.spectrum(sin_theta, theta, phi) * \ + _cexp(1j*self.phase(sin_theta, cos_theta, phi, self.x, self.ry, self.rz)) + + +class LaguerreGauss3d(Beam3dSpherical): + """3d Laguerre-Gauss beam. + + Usage: + LGbeam = LaguerreGauss3d(x=x, params=params) + LGbeam.profile(r) + LGbeam.spectrum(sin_theta, theta, phi) + """ + + def __init__(self, x, params, called=False): + """Specific paramters for Laguerre-Gauss beam.""" + super().__init__(x, params, called) + self.W_y = params['W_y'] + self.m = params['m'] + + @classmethod + def _f_Gauss_spherical(cls, sin_theta, W_y, k): + """2d-Gaussian spectrum amplitude. + + Implementation for spherical coordinates. + """ + return _exp(-(k*W_y*sin_theta/2)**2) + + @classmethod + def _f_Laguerre_Gauss_spherical(cls, sin_theta, theta, phi, W_y, k, m): + """Laguerre-Gaussian spectrum amplitude. + + Implementation for spherical coordinates. + """ + return cls._f_Gauss_spherical(sin_theta, W_y, k) * theta**_abs(m) * \ + _cexp(1j*m*phi) + + def spectrum(self, sin_theta, theta, phi): + """Spectrum amplitude function, f.""" + if self.m == 0: + return type(self)._f_Gauss_spherical(sin_theta, self.W_y, self.k) + else: + return type(self)._f_Laguerre_Gauss_spherical(sin_theta, theta, phi, + self.W_y, self.k, self.m) + +''' class PsiSpherical(Beam3d): """Field amplitude class. @@ -127,7 +199,6 @@ def __init__(self, x, params, called=False): """...""" super().__init__(x, params, called) self.W_y = params['W_y'] - self.k = params['k'] self.m = params['m'] def __call__(self, r): @@ -224,7 +295,6 @@ def __init__(self, x, params, called=False): """...""" super().__init__(x, params, called) self.W_y = params['W_y'] - self.k = params['k'] self.m = params['m'] def __call__(self, r): @@ -264,7 +334,7 @@ def integrand(self, k_y, k_z): return self.f_spectrum(k_y, k_z) * \ _cexp(1j*self.phase(k_y, k_z, self.x, self.ry, self.rz)) - +''' def main(): class Vector3: """Simple vector class.""" @@ -285,10 +355,14 @@ def __init__(self, x, y, z): params = dict(W_y=w_0, m=m_charge, k=k1) - psi_spherical = PsiSpherical(x=x, params=params) - psi_cartesian = PsiCartesian(x=x, params=params) + #psi_spherical = PsiSpherical(x=x, params=params) + #psi_cartesian = PsiCartesian(x=x, params=params) + + #return (psi_spherical, psi_cartesian, r) + + LGbeam = LaguerreGauss3d(x=x, params=params) - return (psi_spherical, psi_cartesian, r) + return (LGbeam, r) if __name__ == '__main__': From 112b14052b6c1592378b2b3013ab6cb134201175 Mon Sep 17 00:00:00 2001 From: Daniel Kotik Date: Sun, 29 Mar 2020 15:18:01 +0200 Subject: [PATCH 072/145] Replace pass with NotImplemented Error --- Laguerre_Gauss_3d/optbeam.py | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/Laguerre_Gauss_3d/optbeam.py b/Laguerre_Gauss_3d/optbeam.py index 97b09de..b1d0433 100644 --- a/Laguerre_Gauss_3d/optbeam.py +++ b/Laguerre_Gauss_3d/optbeam.py @@ -95,7 +95,7 @@ def __init__(self, x, params, called=False): def integrand(self, x, y): """Integrand function over two coordinates x and y.""" - pass + raise NotImplementedError class Beam3dSpherical(Beam3d): @@ -133,7 +133,7 @@ def phase(self, sin_theta, cos_theta, phi, x, y, z): def spectrum(self, sin_theta, theta, phi): """Spectrum amplitude function, f.""" - pass + raise NotImplementedError def integrand(self, theta, phi): """Integrand function.""" From 31c2d9e9fd4fed52b6aaf44ee239a4dbe759057c Mon Sep 17 00:00:00 2001 From: Daniel Kotik Date: Sun, 29 Mar 2020 15:18:22 +0200 Subject: [PATCH 073/145] Remove TODO --- Laguerre_Gauss_3d/optbeam.py | 1 - 1 file changed, 1 deletion(-) diff --git a/Laguerre_Gauss_3d/optbeam.py b/Laguerre_Gauss_3d/optbeam.py index b1d0433..39cc225 100644 --- a/Laguerre_Gauss_3d/optbeam.py +++ b/Laguerre_Gauss_3d/optbeam.py @@ -104,7 +104,6 @@ class Beam3dSpherical(Beam3d): def profile(self, r): """Beam profile function, psi.""" # TODO: Consider calling simple Gauss for special case x=0 - # TODO: rename __call__(self, r) to profile(self, r) self.ry = r.y self.rz = r.z From 6e8127cb5d30503848c0de8bdc45886fd6d4df4c Mon Sep 17 00:00:00 2001 From: Daniel Kotik Date: Sun, 29 Mar 2020 15:21:22 +0200 Subject: [PATCH 074/145] Add Beam3dSpherical class --- Laguerre_Gauss_3d/optbeam.pxd | 29 ++++++++++++++++++++--------- 1 file changed, 20 insertions(+), 9 deletions(-) diff --git a/Laguerre_Gauss_3d/optbeam.pxd b/Laguerre_Gauss_3d/optbeam.pxd index 505a249..efaf10b 100644 --- a/Laguerre_Gauss_3d/optbeam.pxd +++ b/Laguerre_Gauss_3d/optbeam.pxd @@ -37,26 +37,36 @@ cdef (double complex, double, double) _complex_dblquad(Beam3d func, double a, double b, double gfun, double hfun) -cdef double _phi(double k_y, double k_z) nogil -cdef double _theta(double k_y, double k_z, double k) nogil # TODO: allow cdivison +#cdef double _phi(double k_y, double k_z) nogil +#cdef double _theta(double k_y, double k_z, double k) nogil # TODO: allow cdivison -cdef double complex f_Gauss_spherical(double sin_theta, double W_y, double k) nogil -cdef double complex f_Gauss_cartesian(double k_y, double k_z, double W_y) nogil +#cdef double complex f_Gauss_spherical(double sin_theta, double W_y, double k) nogil +#cdef double complex f_Gauss_cartesian(double k_y, double k_z, double W_y) nogil -cdef double complex f_Laguerre_Gauss_spherical(double sin_theta, double theta, double phi, - double W_y, double k, int m) nogil -cdef double complex f_Laguerre_Gauss_cartesian(double k_y, double k_z, - double W_y, double k, int m) nogil +#cdef double complex f_Laguerre_Gauss_spherical(double sin_theta, double theta, double phi, +# double W_y, double k, int m) nogil +#cdef double complex f_Laguerre_Gauss_cartesian(double k_y, double k_z, +# double W_y, double k, int m) nogil # class declarations cdef class Beam3d: cdef: readonly dict params - double x + double x, k bool called cdef double complex integrand(self, double x, double y) nogil +cdef class Beam3dSpherical(Beam3d): + cdef: + double ry, rz + + cdef double phase(self, double sin_theta, double cos_theta, double phi, + double x, double y, double z) nogil + cdef double complex spectrum(self, double sin_theta, double theta, double phi) nogil + cdef double complex integrand(self, double theta, double phi) nogil + +""" cdef class PsiSpherical(Beam3d): cdef: int m @@ -77,3 +87,4 @@ cdef class PsiCartesian(Beam3d): cdef double phase(self, double k_y, double k_z, double x, double y, double z) nogil cdef double complex integrand(self, double k_y, double k_z) nogil cdef double complex f_spectrum(self, double k_y, double k_z) nogil +""" From 5438b9541e0893b574505ef10d2c367917c218cf Mon Sep 17 00:00:00 2001 From: Daniel Kotik Date: Sun, 29 Mar 2020 17:33:48 +0200 Subject: [PATCH 075/145] Reorder functions, improve docstrings, avoid classmethods (for now) --- Laguerre_Gauss_3d/optbeam.py | 28 +++++++++++++++------------- 1 file changed, 15 insertions(+), 13 deletions(-) diff --git a/Laguerre_Gauss_3d/optbeam.py b/Laguerre_Gauss_3d/optbeam.py index 39cc225..adced59 100644 --- a/Laguerre_Gauss_3d/optbeam.py +++ b/Laguerre_Gauss_3d/optbeam.py @@ -123,6 +123,10 @@ def profile(self, r): return self.k**2 * result + def spectrum(self, sin_theta, theta, phi): + """Spectrum amplitude function, f.""" + raise NotImplementedError + def phase(self, sin_theta, cos_theta, phi, x, y, z): """Phase function.""" sin_phi = _sin(phi) @@ -130,10 +134,6 @@ def phase(self, sin_theta, cos_theta, phi, x, y, z): return self.k*(sin_theta*(y*sin_phi - z*cos_phi) + cos_theta*x) - def spectrum(self, sin_theta, theta, phi): - """Spectrum amplitude function, f.""" - raise NotImplementedError - def integrand(self, theta, phi): """Integrand function.""" sin_theta = _sin(theta) @@ -153,35 +153,37 @@ class LaguerreGauss3d(Beam3dSpherical): """ def __init__(self, x, params, called=False): - """Specific paramters for Laguerre-Gauss beam.""" + """Laguerre-Gauss beam specifc parameters.""" super().__init__(x, params, called) self.W_y = params['W_y'] self.m = params['m'] - @classmethod - def _f_Gauss_spherical(cls, sin_theta, W_y, k): + #@classmethod + #@cython.binding(True) + def _f_Gauss_spherical(self, sin_theta, W_y, k): """2d-Gaussian spectrum amplitude. Implementation for spherical coordinates. """ return _exp(-(k*W_y*sin_theta/2)**2) - @classmethod - def _f_Laguerre_Gauss_spherical(cls, sin_theta, theta, phi, W_y, k, m): + #@classmethod + #@cython.binding(True) + def _f_Laguerre_Gauss_spherical(self, sin_theta, theta, phi, W_y, k, m): """Laguerre-Gaussian spectrum amplitude. Implementation for spherical coordinates. """ - return cls._f_Gauss_spherical(sin_theta, W_y, k) * theta**_abs(m) * \ + return self._f_Gauss_spherical(sin_theta, W_y, k) * theta**_abs(m) * \ _cexp(1j*m*phi) def spectrum(self, sin_theta, theta, phi): """Spectrum amplitude function, f.""" if self.m == 0: - return type(self)._f_Gauss_spherical(sin_theta, self.W_y, self.k) + return self._f_Gauss_spherical(sin_theta, self.W_y, self.k) else: - return type(self)._f_Laguerre_Gauss_spherical(sin_theta, theta, phi, - self.W_y, self.k, self.m) + return self._f_Laguerre_Gauss_spherical(sin_theta, theta, phi, + self.W_y, self.k, self.m) ''' class PsiSpherical(Beam3d): From d3d241a227e2e2f61359159681b60a5601385625 Mon Sep 17 00:00:00 2001 From: Daniel Kotik Date: Sun, 29 Mar 2020 17:34:34 +0200 Subject: [PATCH 076/145] Add declaration for LaguerreGauss3d class --- Laguerre_Gauss_3d/optbeam.pxd | 15 +++++++++++++++ 1 file changed, 15 insertions(+) diff --git a/Laguerre_Gauss_3d/optbeam.pxd b/Laguerre_Gauss_3d/optbeam.pxd index efaf10b..b102303 100644 --- a/Laguerre_Gauss_3d/optbeam.pxd +++ b/Laguerre_Gauss_3d/optbeam.pxd @@ -66,6 +66,21 @@ cdef class Beam3dSpherical(Beam3d): cdef double complex spectrum(self, double sin_theta, double theta, double phi) nogil cdef double complex integrand(self, double theta, double phi) nogil +cdef class LaguerreGauss3d(Beam3dSpherical): + cdef: + int m + double W_y + + #@classmethod + #@cython.binding(True) + cdef double complex _f_Gauss_spherical(self, double sin_theta, double W_y, double k) nogil + cdef double complex _f_Laguerre_Gauss_spherical(self, double sin_theta, double theta, double phi, + double W_y, double k, int m) nogil + cdef double complex spectrum(self, double sin_theta, double theta, double phi) nogil + + + + """ cdef class PsiSpherical(Beam3d): cdef: From 71c57ef5316e0c97f38abc86c9e3be8c4709f814 Mon Sep 17 00:00:00 2001 From: Daniel Kotik Date: Sun, 29 Mar 2020 18:22:13 +0200 Subject: [PATCH 077/145] Add LaguerreGauss3d_ class: This is bases on the Cartesian reference implementation and serves only as an example bz now. --- Laguerre_Gauss_3d/optbeam.py | 225 +++++++++++++---------------------- 1 file changed, 81 insertions(+), 144 deletions(-) diff --git a/Laguerre_Gauss_3d/optbeam.py b/Laguerre_Gauss_3d/optbeam.py index adced59..2c622ae 100644 --- a/Laguerre_Gauss_3d/optbeam.py +++ b/Laguerre_Gauss_3d/optbeam.py @@ -99,7 +99,7 @@ def integrand(self, x, y): class Beam3dSpherical(Beam3d): - """Implementaion of a 3d beam in spherical coordinates.""" + """Reference implementaion of a 3d beam in spherical coordinates.""" def profile(self, r): """Beam profile function, psi.""" @@ -143,69 +143,11 @@ def integrand(self, theta, phi): _cexp(1j*self.phase(sin_theta, cos_theta, phi, self.x, self.ry, self.rz)) -class LaguerreGauss3d(Beam3dSpherical): - """3d Laguerre-Gauss beam. - - Usage: - LGbeam = LaguerreGauss3d(x=x, params=params) - LGbeam.profile(r) - LGbeam.spectrum(sin_theta, theta, phi) - """ - - def __init__(self, x, params, called=False): - """Laguerre-Gauss beam specifc parameters.""" - super().__init__(x, params, called) - self.W_y = params['W_y'] - self.m = params['m'] - - #@classmethod - #@cython.binding(True) - def _f_Gauss_spherical(self, sin_theta, W_y, k): - """2d-Gaussian spectrum amplitude. +class Beam3dCartesian(Beam3d): + """Reference implementaion of a 3d beam in Cartesian coordinates.""" - Implementation for spherical coordinates. - """ - return _exp(-(k*W_y*sin_theta/2)**2) - - #@classmethod - #@cython.binding(True) - def _f_Laguerre_Gauss_spherical(self, sin_theta, theta, phi, W_y, k, m): - """Laguerre-Gaussian spectrum amplitude. - - Implementation for spherical coordinates. - """ - return self._f_Gauss_spherical(sin_theta, W_y, k) * theta**_abs(m) * \ - _cexp(1j*m*phi) - - def spectrum(self, sin_theta, theta, phi): - """Spectrum amplitude function, f.""" - if self.m == 0: - return self._f_Gauss_spherical(sin_theta, self.W_y, self.k) - else: - return self._f_Laguerre_Gauss_spherical(sin_theta, theta, phi, - self.W_y, self.k, self.m) - -''' -class PsiSpherical(Beam3d): - """Field amplitude class. - - Integration in spherical coordinates. - - Usage: - psi_spherical = PsiSpherical(x=shift, params=params) - psi_spherical(r) # r...vector-like object with scalar y and z attributes - """ - - def __init__(self, x, params, called=False): - """...""" - super().__init__(x, params, called) - self.W_y = params['W_y'] - self.m = params['m'] - - def __call__(self, r): - """Beam profile function.""" - # TODO: Consider calling simple Gauss for special case x=0 - # TODO: rename __call__(self, r) to profile(self, r) + def profile(self, r): + """Beam profile function, psi.""" self.ry = r.y self.rz = r.z @@ -218,124 +160,118 @@ def __call__(self, r): (result, real_tol, imag_tol) = _complex_dblquad(self if cython.compiled else self.integrand, - 0, 2*math.pi, 0, math.pi/2) + -self.k, self.k, -self.k, self.k) except Exception as e: print(type(e).__name__ + ":", e) sys.exit() - return self.k**2 * result - - def phase(self, sin_theta, cos_theta, phi, x, y, z): - """Phase function.""" - sin_phi = _sin(phi) - cos_phi = _cos(phi) + return result - return self.k*(sin_theta*(y*sin_phi - z*cos_phi) + cos_theta*x) + def spectrum(self, sin_theta, theta, phi): + """Spectrum amplitude function, f.""" + raise NotImplementedError - def f_spectrum(self, sin_theta, theta, phi): - """Spectrum amplitude function.""" - if self.m == 0: - return f_Gauss_spherical(sin_theta, self.W_y, self.k) - else: - return f_Laguerre_Gauss_spherical(sin_theta, theta, phi, - self.W_y, self.k, self.m) + def phase(self, k_y, k_z, x, y, z): + """Phase function.""" + return x*_csqrt(self.k**2 - k_y**2 - k_z**2).real + y*k_y + z*k_z - def integrand(self, theta, phi): + def integrand(self, k_y, k_z): """Integrand function.""" - sin_theta = _sin(theta) - cos_theta = _cos(theta) - - return sin_theta * cos_theta * self.f_spectrum(sin_theta, theta, phi) * \ - _cexp(1j*self.phase(sin_theta, cos_theta, phi, self.x, self.ry, self.rz)) - + return self.spectrum(k_y, k_z) * \ + _cexp(1j*self.phase(k_y, k_z, self.x, self.ry, self.rz)) -def _phi(k_y, k_z): - """Azimuthal angle. - Part of coordinate transformation from k-space to (theta, phi)-space. +class LaguerreGauss3d_(Beam3dCartesian): + """This class serves only as an example for a Cartesian implementaions and + will be removed in future versions. """ - return _atan2(k_y, -k_z) + def __init__(self, x, params, called=False): + """Laguerre-Gauss beam specifc parameters.""" + super().__init__(x, params, called) + self.W_y = params['W_y'] + self.m = params['m'] -def _theta(k_y, k_z, k): - """Polar angle. + def spectrum(self, k_y, k_z): + """Spectrum amplitude function, f.""" + if self.m == 0: + return self._f_Gauss_cartesian(k_y, k_z, self.W_y) + else: + return self._f_Laguerre_Gauss_cartesian(k_y, k_z, self.W_y, self.k, self.m) - Part of coordinate transformation from k-space to (theta, phi)-space. - """ - return _acos(_csqrt(k**2 - k_y**2 - k_z**2).real / k) + def _phi(self, k_y, k_z): + """Azimuthal angle. + Part of coordinate transformation from k-space to (theta, phi)-space. + """ + return _atan2(k_y, -k_z) -def f_Gauss_cartesian(k_y, k_z, W_y): - """2d-Gaussian spectrum amplitude. + def _theta(self, k_y, k_z, k): + """Polar angle. - Impementation for Cartesian coordinates. - """ - return _exp(-W_y**2 * (k_y**2 + k_z**2)/4) + Part of coordinate transformation from k-space to (theta, phi)-space. + """ + return _acos(_csqrt(k**2 - k_y**2 - k_z**2).real / k) + def _f_Gauss_cartesian(self, k_y, k_z, W_y): + """2d-Gaussian spectrum amplitude. -def f_Laguerre_Gauss_cartesian(k_y, k_z, W_y, k, m): - """Laguerre-Gaussian spectrum amplitude. + Impementation for Cartesian coordinates. + """ + return _exp(-W_y**2 * (k_y**2 + k_z**2)/4) - Impementation for Cartesian coordinates. - """ - return f_Gauss_cartesian(k_y, k_z, W_y) * \ - _cexp(1j*m*_phi(k_y, k_z)) * _theta(k_y, k_z, k)**_abs(m) + def _f_Laguerre_Gauss_cartesian(self, k_y, k_z, W_y, k, m): + """Laguerre-Gaussian spectrum amplitude. + Impementation for Cartesian coordinates. + """ + return self._f_Gauss_cartesian(k_y, k_z, W_y) * \ + _cexp(1j*m*self._phi(k_y, k_z)) * self._theta(k_y, k_z, k)**_abs(m) -class PsiCartesian(Beam3d): - """Field amplitude class. - Integration in cartesian coordinates. +class LaguerreGauss3d(Beam3dSpherical): + """3d Laguerre-Gauss beam. Usage: - psi_cartesian = PsiCartesian(x=shift, params=params) - psi_cartesian(r) # r...vector-like object with scalar y and z attributes + LGbeam = LaguerreGauss3d(x=x, params=params) + LGbeam.profile(r) + LGbeam.spectrum(sin_theta, theta, phi) """ def __init__(self, x, params, called=False): - """...""" + """Laguerre-Gauss beam specifc parameters.""" super().__init__(x, params, called) self.W_y = params['W_y'] self.m = params['m'] - def __call__(self, r): - """Beam profile function.""" - self.ry = r.y - self.rz = r.z - - if not self.called: - print("Calculating inital field configuration. " - "This will take some time...") - self.called = True + def spectrum(self, sin_theta, theta, phi): + """Spectrum amplitude function, f.""" + if self.m == 0: + return self._f_Gauss_spherical(sin_theta, self.W_y, self.k) + else: + return self._f_Laguerre_Gauss_spherical(sin_theta, theta, phi, + self.W_y, self.k, self.m) - try: - (result, - real_tol, - imag_tol) = _complex_dblquad(self if cython.compiled else self.integrand, - -self.k, self.k, -self.k, self.k) - except Exception as e: - print(type(e).__name__ + ":", e) - sys.exit() + #@classmethod + #@cython.binding(True) + def _f_Gauss_spherical(self, sin_theta, W_y, k): + """2d-Gaussian spectrum amplitude. - return result + Implementation for spherical coordinates. + """ + return _exp(-(k*W_y*sin_theta/2)**2) - def phase(self, k_y, k_z, x, y, z): - """Phase function.""" - return x*_csqrt(self.k**2 - k_y**2 - k_z**2).real + y*k_y + z*k_z + #@classmethod + #@cython.binding(True) + def _f_Laguerre_Gauss_spherical(self, sin_theta, theta, phi, W_y, k, m): + """Laguerre-Gaussian spectrum amplitude. - def f_spectrum(self, k_y, k_z): - """Spectrum amplitude function.""" - if self.m == 0: - return f_Gauss_cartesian(k_y, k_z, self.W_y) - else: - return f_Laguerre_Gauss_cartesian(k_y, k_z, self.W_y, self.k, self.m) + Implementation for spherical coordinates. + """ + return self._f_Gauss_spherical(sin_theta, W_y, k) * theta**_abs(m) * \ + _cexp(1j*m*phi) - def integrand(self, k_y, k_z): - """Integrand function.""" - return self.f_spectrum(k_y, k_z) * \ - _cexp(1j*self.phase(k_y, k_z, self.x, self.ry, self.rz)) -''' def main(): class Vector3: """Simple vector class.""" @@ -362,8 +298,9 @@ def __init__(self, x, y, z): #return (psi_spherical, psi_cartesian, r) LGbeam = LaguerreGauss3d(x=x, params=params) + LGbeam_ = LaguerreGauss3d_(x=x, params=params) - return (LGbeam, r) + return (LGbeam, LGbeam_, r) if __name__ == '__main__': From c930a2266a973869d80b94c533b574693e8afd1b Mon Sep 17 00:00:00 2001 From: Daniel Kotik Date: Sun, 29 Mar 2020 19:15:13 +0200 Subject: [PATCH 078/145] Override profile function for special case x=0 --- Laguerre_Gauss_3d/optbeam.py | 21 ++++++++++++++++++--- 1 file changed, 18 insertions(+), 3 deletions(-) diff --git a/Laguerre_Gauss_3d/optbeam.py b/Laguerre_Gauss_3d/optbeam.py index 2c622ae..c0f88f4 100644 --- a/Laguerre_Gauss_3d/optbeam.py +++ b/Laguerre_Gauss_3d/optbeam.py @@ -103,7 +103,6 @@ class Beam3dSpherical(Beam3d): def profile(self, r): """Beam profile function, psi.""" - # TODO: Consider calling simple Gauss for special case x=0 self.ry = r.y self.rz = r.z @@ -167,7 +166,7 @@ def profile(self, r): return result - def spectrum(self, sin_theta, theta, phi): + def spectrum(self, k_y, k_z): """Spectrum amplitude function, f.""" raise NotImplementedError @@ -182,7 +181,7 @@ def integrand(self, k_y, k_z): class LaguerreGauss3d_(Beam3dCartesian): - """This class serves only as an example for a Cartesian implementaions and + """This class serves only as an example for a Cartesian implementaion and will be removed in future versions. """ @@ -192,6 +191,14 @@ def __init__(self, x, params, called=False): self.W_y = params['W_y'] self.m = params['m'] + def profile(self, r): + """...""" + if self.x == 0: + # TODO: Consider calling simple Gauss for special case x=0 + return NotImplemented + else: + return super().profile(r) + def spectrum(self, k_y, k_z): """Spectrum amplitude function, f.""" if self.m == 0: @@ -244,6 +251,14 @@ def __init__(self, x, params, called=False): self.W_y = params['W_y'] self.m = params['m'] + def profile(self, r): + """...""" + if self.x == 0: + # TODO: Consider calling simple Gauss for special case x=0 + return NotImplemented + else: + return super().profile(r) + def spectrum(self, sin_theta, theta, phi): """Spectrum amplitude function, f.""" if self.m == 0: From b684256579649574c82812d4ad4e35953c79a28c Mon Sep 17 00:00:00 2001 From: Daniel Kotik Date: Sun, 29 Mar 2020 19:15:56 +0200 Subject: [PATCH 079/145] Add class declaration LaguerreGauss3d_ --- Laguerre_Gauss_3d/optbeam.pxd | 51 ++++++++++++----------------------- 1 file changed, 17 insertions(+), 34 deletions(-) diff --git a/Laguerre_Gauss_3d/optbeam.pxd b/Laguerre_Gauss_3d/optbeam.pxd index b102303..149d78a 100644 --- a/Laguerre_Gauss_3d/optbeam.pxd +++ b/Laguerre_Gauss_3d/optbeam.pxd @@ -37,17 +37,6 @@ cdef (double complex, double, double) _complex_dblquad(Beam3d func, double a, double b, double gfun, double hfun) -#cdef double _phi(double k_y, double k_z) nogil -#cdef double _theta(double k_y, double k_z, double k) nogil # TODO: allow cdivison - -#cdef double complex f_Gauss_spherical(double sin_theta, double W_y, double k) nogil -#cdef double complex f_Gauss_cartesian(double k_y, double k_z, double W_y) nogil - -#cdef double complex f_Laguerre_Gauss_spherical(double sin_theta, double theta, double phi, -# double W_y, double k, int m) nogil -#cdef double complex f_Laguerre_Gauss_cartesian(double k_y, double k_z, -# double W_y, double k, int m) nogil - # class declarations cdef class Beam3d: cdef: @@ -66,6 +55,14 @@ cdef class Beam3dSpherical(Beam3d): cdef double complex spectrum(self, double sin_theta, double theta, double phi) nogil cdef double complex integrand(self, double theta, double phi) nogil +cdef class Beam3dCartesian(Beam3d): + cdef: + double ry, rz + + cdef double phase(self, double k_y, double k_z, double x, double y, double z) nogil + cdef double complex spectrum(self, double k_y, double k_z) nogil + cdef double complex integrand(self, double k_y, double k_z) nogil + cdef class LaguerreGauss3d(Beam3dSpherical): cdef: int m @@ -78,28 +75,14 @@ cdef class LaguerreGauss3d(Beam3dSpherical): double W_y, double k, int m) nogil cdef double complex spectrum(self, double sin_theta, double theta, double phi) nogil - - - -""" -cdef class PsiSpherical(Beam3d): +cdef class LaguerreGauss3d_(Beam3dCartesian): cdef: - int m - double k, W_y - double ry, rz - - cdef double phase(self, double sin_theta, double cos_theta, double phi, - double x, double y, double z) nogil - cdef double complex integrand(self, double theta, double phi) nogil - cdef double complex f_spectrum(self, double sin_theta, double theta, double phi) nogil - -cdef class PsiCartesian(Beam3d): - cdef: - int m - double k, W_y - double ry, rz + int m + double W_y - cdef double phase(self, double k_y, double k_z, double x, double y, double z) nogil - cdef double complex integrand(self, double k_y, double k_z) nogil - cdef double complex f_spectrum(self, double k_y, double k_z) nogil -""" + cdef double _phi(self, double k_y, double k_z) nogil + cdef double _theta(self, double k_y, double k_z, double k) nogil + cdef double complex _f_Gauss_cartesian(self, double k_y, double k_z, double W_y) nogil + cdef double complex _f_Laguerre_Gauss_cartesian(self, double k_y, double k_z, + double W_y, double k, int m) nogil + cdef double complex spectrum(self, double k_y, double k_z) nogil From 6e804557b626d2e2913e8f69187687c8317c3164 Mon Sep 17 00:00:00 2001 From: Daniel Kotik Date: Tue, 31 Mar 2020 18:32:14 +0200 Subject: [PATCH 080/145] Fix over indentation --- Laguerre_Gauss_3d/optbeam.py | 8 ++++---- 1 file changed, 4 insertions(+), 4 deletions(-) diff --git a/Laguerre_Gauss_3d/optbeam.py b/Laguerre_Gauss_3d/optbeam.py index c0f88f4..e1a6ffc 100644 --- a/Laguerre_Gauss_3d/optbeam.py +++ b/Laguerre_Gauss_3d/optbeam.py @@ -123,8 +123,8 @@ def profile(self, r): return self.k**2 * result def spectrum(self, sin_theta, theta, phi): - """Spectrum amplitude function, f.""" - raise NotImplementedError + """Spectrum amplitude function, f.""" + raise NotImplementedError def phase(self, sin_theta, cos_theta, phi, x, y, z): """Phase function.""" @@ -167,8 +167,8 @@ def profile(self, r): return result def spectrum(self, k_y, k_z): - """Spectrum amplitude function, f.""" - raise NotImplementedError + """Spectrum amplitude function, f.""" + raise NotImplementedError def phase(self, k_y, k_z, x, y, z): """Phase function.""" From 4e9ad7e2ee3ce5d774f36aa44b136920479f42a6 Mon Sep 17 00:00:00 2001 From: Daniel Kotik Date: Tue, 31 Mar 2020 18:32:29 +0200 Subject: [PATCH 081/145] Make integrand method private --- Laguerre_Gauss_3d/optbeam.pxd | 6 +++--- Laguerre_Gauss_3d/optbeam.py | 14 +++++++------- 2 files changed, 10 insertions(+), 10 deletions(-) diff --git a/Laguerre_Gauss_3d/optbeam.pxd b/Laguerre_Gauss_3d/optbeam.pxd index 149d78a..79281f4 100644 --- a/Laguerre_Gauss_3d/optbeam.pxd +++ b/Laguerre_Gauss_3d/optbeam.pxd @@ -44,7 +44,7 @@ cdef class Beam3d: double x, k bool called - cdef double complex integrand(self, double x, double y) nogil + cdef double complex _integrand(self, double x, double y) nogil cdef class Beam3dSpherical(Beam3d): cdef: @@ -53,7 +53,7 @@ cdef class Beam3dSpherical(Beam3d): cdef double phase(self, double sin_theta, double cos_theta, double phi, double x, double y, double z) nogil cdef double complex spectrum(self, double sin_theta, double theta, double phi) nogil - cdef double complex integrand(self, double theta, double phi) nogil + cdef double complex _integrand(self, double theta, double phi) nogil cdef class Beam3dCartesian(Beam3d): cdef: @@ -61,7 +61,7 @@ cdef class Beam3dCartesian(Beam3d): cdef double phase(self, double k_y, double k_z, double x, double y, double z) nogil cdef double complex spectrum(self, double k_y, double k_z) nogil - cdef double complex integrand(self, double k_y, double k_z) nogil + cdef double complex _integrand(self, double k_y, double k_z) nogil cdef class LaguerreGauss3d(Beam3dSpherical): cdef: diff --git a/Laguerre_Gauss_3d/optbeam.py b/Laguerre_Gauss_3d/optbeam.py index e1a6ffc..2aedf94 100644 --- a/Laguerre_Gauss_3d/optbeam.py +++ b/Laguerre_Gauss_3d/optbeam.py @@ -46,7 +46,7 @@ def _imag_2d_func_c(n, arr, func_ptr): """ # pure python formulation of: # return (func_ptr)(arr[0], arr[1]).imag - return cython.cast(Beam3d, func_ptr).integrand(arr[0], arr[1]).imag + return cython.cast(Beam3d, func_ptr)._integrand(arr[0], arr[1]).imag def _real_2d_func_c(n, arr, func_ptr): @@ -56,7 +56,7 @@ def _real_2d_func_c(n, arr, func_ptr): """ # pure python formulation of: # return (func_ptr)(arr[0], arr[1]).real - return cython.cast(Beam3d, func_ptr).integrand(arr[0], arr[1]).real + return cython.cast(Beam3d, func_ptr)._integrand(arr[0], arr[1]).real def _complex_dblquad(func, a, b, gfun, hfun): @@ -93,7 +93,7 @@ def __init__(self, x, params, called=False): self.params = params self.called = called - def integrand(self, x, y): + def _integrand(self, x, y): """Integrand function over two coordinates x and y.""" raise NotImplementedError @@ -114,7 +114,7 @@ def profile(self, r): try: (result, real_tol, - imag_tol) = _complex_dblquad(self if cython.compiled else self.integrand, + imag_tol) = _complex_dblquad(self if cython.compiled else self._integrand, 0, 2*math.pi, 0, math.pi/2) except Exception as e: print(type(e).__name__ + ":", e) @@ -133,7 +133,7 @@ def phase(self, sin_theta, cos_theta, phi, x, y, z): return self.k*(sin_theta*(y*sin_phi - z*cos_phi) + cos_theta*x) - def integrand(self, theta, phi): + def _integrand(self, theta, phi): """Integrand function.""" sin_theta = _sin(theta) cos_theta = _cos(theta) @@ -158,7 +158,7 @@ def profile(self, r): try: (result, real_tol, - imag_tol) = _complex_dblquad(self if cython.compiled else self.integrand, + imag_tol) = _complex_dblquad(self if cython.compiled else self._integrand, -self.k, self.k, -self.k, self.k) except Exception as e: print(type(e).__name__ + ":", e) @@ -174,7 +174,7 @@ def phase(self, k_y, k_z, x, y, z): """Phase function.""" return x*_csqrt(self.k**2 - k_y**2 - k_z**2).real + y*k_y + z*k_z - def integrand(self, k_y, k_z): + def _integrand(self, k_y, k_z): """Integrand function.""" return self.spectrum(k_y, k_z) * \ _cexp(1j*self.phase(k_y, k_z, self.x, self.ry, self.rz)) From 12fba0ab0a9aab5f29d78735fee85ee262c463fa Mon Sep 17 00:00:00 2001 From: Daniel Kotik Date: Tue, 31 Mar 2020 18:32:32 +0200 Subject: [PATCH 082/145] Make phase method private --- Laguerre_Gauss_3d/optbeam.pxd | 4 ++-- Laguerre_Gauss_3d/optbeam.py | 8 ++++---- 2 files changed, 6 insertions(+), 6 deletions(-) diff --git a/Laguerre_Gauss_3d/optbeam.pxd b/Laguerre_Gauss_3d/optbeam.pxd index 79281f4..5bd7e2d 100644 --- a/Laguerre_Gauss_3d/optbeam.pxd +++ b/Laguerre_Gauss_3d/optbeam.pxd @@ -50,7 +50,7 @@ cdef class Beam3dSpherical(Beam3d): cdef: double ry, rz - cdef double phase(self, double sin_theta, double cos_theta, double phi, + cdef double _phase(self, double sin_theta, double cos_theta, double phi, double x, double y, double z) nogil cdef double complex spectrum(self, double sin_theta, double theta, double phi) nogil cdef double complex _integrand(self, double theta, double phi) nogil @@ -59,7 +59,7 @@ cdef class Beam3dCartesian(Beam3d): cdef: double ry, rz - cdef double phase(self, double k_y, double k_z, double x, double y, double z) nogil + cdef double _phase(self, double k_y, double k_z, double x, double y, double z) nogil cdef double complex spectrum(self, double k_y, double k_z) nogil cdef double complex _integrand(self, double k_y, double k_z) nogil diff --git a/Laguerre_Gauss_3d/optbeam.py b/Laguerre_Gauss_3d/optbeam.py index 2aedf94..b861339 100644 --- a/Laguerre_Gauss_3d/optbeam.py +++ b/Laguerre_Gauss_3d/optbeam.py @@ -126,7 +126,7 @@ def spectrum(self, sin_theta, theta, phi): """Spectrum amplitude function, f.""" raise NotImplementedError - def phase(self, sin_theta, cos_theta, phi, x, y, z): + def _phase(self, sin_theta, cos_theta, phi, x, y, z): """Phase function.""" sin_phi = _sin(phi) cos_phi = _cos(phi) @@ -139,7 +139,7 @@ def _integrand(self, theta, phi): cos_theta = _cos(theta) return sin_theta * cos_theta * self.spectrum(sin_theta, theta, phi) * \ - _cexp(1j*self.phase(sin_theta, cos_theta, phi, self.x, self.ry, self.rz)) + _cexp(1j*self._phase(sin_theta, cos_theta, phi, self.x, self.ry, self.rz)) class Beam3dCartesian(Beam3d): @@ -170,14 +170,14 @@ def spectrum(self, k_y, k_z): """Spectrum amplitude function, f.""" raise NotImplementedError - def phase(self, k_y, k_z, x, y, z): + def _phase(self, k_y, k_z, x, y, z): """Phase function.""" return x*_csqrt(self.k**2 - k_y**2 - k_z**2).real + y*k_y + z*k_z def _integrand(self, k_y, k_z): """Integrand function.""" return self.spectrum(k_y, k_z) * \ - _cexp(1j*self.phase(k_y, k_z, self.x, self.ry, self.rz)) + _cexp(1j*self._phase(k_y, k_z, self.x, self.ry, self.rz)) class LaguerreGauss3d_(Beam3dCartesian): From d56f380b1381f774907b075465d5c2930ab2c4de Mon Sep 17 00:00:00 2001 From: Daniel Kotik Date: Wed, 1 Apr 2020 14:57:53 +0200 Subject: [PATCH 083/145] Implement special case x=0, m=0 --- Laguerre_Gauss_3d/optbeam.py | 14 ++++---------- 1 file changed, 4 insertions(+), 10 deletions(-) diff --git a/Laguerre_Gauss_3d/optbeam.py b/Laguerre_Gauss_3d/optbeam.py index b861339..43a7fd5 100644 --- a/Laguerre_Gauss_3d/optbeam.py +++ b/Laguerre_Gauss_3d/optbeam.py @@ -193,9 +193,8 @@ def __init__(self, x, params, called=False): def profile(self, r): """...""" - if self.x == 0: - # TODO: Consider calling simple Gauss for special case x=0 - return NotImplemented + if self.x == 0 and self.m == 0: + return _exp(-((r.y**2 + r.z**2) / self.W_y**2)) * (2*math.pi*self.k) else: return super().profile(r) @@ -253,9 +252,8 @@ def __init__(self, x, params, called=False): def profile(self, r): """...""" - if self.x == 0: - # TODO: Consider calling simple Gauss for special case x=0 - return NotImplemented + if self.x == 0 and self.m == 0: + return _exp(-((r.y**2 + r.z**2) / self.W_y**2)) * (2*math.pi*self.k) else: return super().profile(r) @@ -267,8 +265,6 @@ def spectrum(self, sin_theta, theta, phi): return self._f_Laguerre_Gauss_spherical(sin_theta, theta, phi, self.W_y, self.k, self.m) - #@classmethod - #@cython.binding(True) def _f_Gauss_spherical(self, sin_theta, W_y, k): """2d-Gaussian spectrum amplitude. @@ -276,8 +272,6 @@ def _f_Gauss_spherical(self, sin_theta, W_y, k): """ return _exp(-(k*W_y*sin_theta/2)**2) - #@classmethod - #@cython.binding(True) def _f_Laguerre_Gauss_spherical(self, sin_theta, theta, phi, W_y, k, m): """Laguerre-Gaussian spectrum amplitude. From 046e482417ef20616bf43b49b0fc0c33091ade68 Mon Sep 17 00:00:00 2001 From: Daniel Kotik Date: Wed, 1 Apr 2020 17:17:17 +0200 Subject: [PATCH 084/145] Make ry and rz private member variables --- Laguerre_Gauss_3d/optbeam.pxd | 6 +++--- Laguerre_Gauss_3d/optbeam.py | 12 ++++++------ 2 files changed, 9 insertions(+), 9 deletions(-) diff --git a/Laguerre_Gauss_3d/optbeam.pxd b/Laguerre_Gauss_3d/optbeam.pxd index 5bd7e2d..d1c25a0 100644 --- a/Laguerre_Gauss_3d/optbeam.pxd +++ b/Laguerre_Gauss_3d/optbeam.pxd @@ -42,13 +42,13 @@ cdef class Beam3d: cdef: readonly dict params double x, k - bool called + public bool called cdef double complex _integrand(self, double x, double y) nogil cdef class Beam3dSpherical(Beam3d): cdef: - double ry, rz + double _ry, _rz cdef double _phase(self, double sin_theta, double cos_theta, double phi, double x, double y, double z) nogil @@ -57,7 +57,7 @@ cdef class Beam3dSpherical(Beam3d): cdef class Beam3dCartesian(Beam3d): cdef: - double ry, rz + double _ry, _rz cdef double _phase(self, double k_y, double k_z, double x, double y, double z) nogil cdef double complex spectrum(self, double k_y, double k_z) nogil diff --git a/Laguerre_Gauss_3d/optbeam.py b/Laguerre_Gauss_3d/optbeam.py index 43a7fd5..b1d1289 100644 --- a/Laguerre_Gauss_3d/optbeam.py +++ b/Laguerre_Gauss_3d/optbeam.py @@ -103,8 +103,8 @@ class Beam3dSpherical(Beam3d): def profile(self, r): """Beam profile function, psi.""" - self.ry = r.y - self.rz = r.z + self._ry = r.y + self._rz = r.z if not self.called: print("Calculating inital field configuration. " @@ -139,7 +139,7 @@ def _integrand(self, theta, phi): cos_theta = _cos(theta) return sin_theta * cos_theta * self.spectrum(sin_theta, theta, phi) * \ - _cexp(1j*self._phase(sin_theta, cos_theta, phi, self.x, self.ry, self.rz)) + _cexp(1j*self._phase(sin_theta, cos_theta, phi, self.x, self._ry, self._rz)) class Beam3dCartesian(Beam3d): @@ -147,8 +147,8 @@ class Beam3dCartesian(Beam3d): def profile(self, r): """Beam profile function, psi.""" - self.ry = r.y - self.rz = r.z + self._ry = r.y + self._rz = r.z if not self.called: print("Calculating inital field configuration. " @@ -177,7 +177,7 @@ def _phase(self, k_y, k_z, x, y, z): def _integrand(self, k_y, k_z): """Integrand function.""" return self.spectrum(k_y, k_z) * \ - _cexp(1j*self._phase(k_y, k_z, self.x, self.ry, self.rz)) + _cexp(1j*self._phase(k_y, k_z, self.x, self._ry, self._rz)) class LaguerreGauss3d_(Beam3dCartesian): From 9aef15c82d6b3400d3c537ed3590f25e8821732e Mon Sep 17 00:00:00 2001 From: Daniel Kotik Date: Wed, 1 Apr 2020 18:25:50 +0200 Subject: [PATCH 085/145] Fix format issues, add comments --- Laguerre_Gauss_3d/optbeam.pxd | 11 +++++++---- Laguerre_Gauss_3d/optbeam.py | 32 ++++++++++++++++++-------------- 2 files changed, 25 insertions(+), 18 deletions(-) diff --git a/Laguerre_Gauss_3d/optbeam.pxd b/Laguerre_Gauss_3d/optbeam.pxd index d1c25a0..15660bb 100644 --- a/Laguerre_Gauss_3d/optbeam.pxd +++ b/Laguerre_Gauss_3d/optbeam.pxd @@ -11,7 +11,9 @@ cimport cython from cpython.pycapsule cimport PyCapsule_New from cpython cimport bool +# ----------------------------------------------------------------------------- # declare C functions as "cpdef" to export them to the module +# ----------------------------------------------------------------------------- cdef extern from "stdlib.h": cpdef int _abs "abs" (int n) nogil @@ -26,8 +28,9 @@ cdef extern from "complex.h": cpdef double complex _cexp "cexp" (double complex z) nogil cpdef double complex _csqrt "csqrt" (double complex z) nogil - +# ----------------------------------------------------------------------------- # function declarations +# ----------------------------------------------------------------------------- cdef double _imag_2d_func_c(int n, double *arr, void *func_ptr) cdef double _real_2d_func_c(int n, double *arr, void *func_ptr) @@ -37,7 +40,9 @@ cdef (double complex, double, double) _complex_dblquad(Beam3d func, double a, double b, double gfun, double hfun) +# ----------------------------------------------------------------------------- # class declarations +# ----------------------------------------------------------------------------- cdef class Beam3d: cdef: readonly dict params @@ -68,14 +73,12 @@ cdef class LaguerreGauss3d(Beam3dSpherical): int m double W_y - #@classmethod - #@cython.binding(True) cdef double complex _f_Gauss_spherical(self, double sin_theta, double W_y, double k) nogil cdef double complex _f_Laguerre_Gauss_spherical(self, double sin_theta, double theta, double phi, double W_y, double k, int m) nogil cdef double complex spectrum(self, double sin_theta, double theta, double phi) nogil -cdef class LaguerreGauss3d_(Beam3dCartesian): +cdef class LaguerreGauss3dCartesian(Beam3dCartesian): cdef: int m double W_y diff --git a/Laguerre_Gauss_3d/optbeam.py b/Laguerre_Gauss_3d/optbeam.py index b1d1289..dd60982 100644 --- a/Laguerre_Gauss_3d/optbeam.py +++ b/Laguerre_Gauss_3d/optbeam.py @@ -88,6 +88,7 @@ class Beam3d: """Abstract base class.""" def __init__(self, x, params, called=False): + """...""" self.x = x # TODO: rename x to x_shift self.k = params['k'] self.params = params @@ -180,9 +181,15 @@ def _integrand(self, k_y, k_z): _cexp(1j*self._phase(k_y, k_z, self.x, self._ry, self._rz)) -class LaguerreGauss3d_(Beam3dCartesian): - """This class serves only as an example for a Cartesian implementaion and - will be removed in future versions. +# ----------------------------------------------------------------------------- +# specific beam implementations based on Beam3dSpherical or Beam3dCartesian +# base classes depending on the choice of a suitable coordinate system +# ----------------------------------------------------------------------------- +class LaguerreGauss3dCartesian(Beam3dCartesian): + """Cartesian implementaion of a 3d Laguerre-Gauss beam. + + This class serves only as an example for a will be removed in future + versions. """ def __init__(self, x, params, called=False): @@ -194,7 +201,7 @@ def __init__(self, x, params, called=False): def profile(self, r): """...""" if self.x == 0 and self.m == 0: - return _exp(-((r.y**2 + r.z**2) / self.W_y**2)) * (2*math.pi*self.k) + return _exp(-((r.y**2 + r.z**2) / self.W_y**2)) * 2*math.pi*self.k else: return super().profile(r) @@ -203,7 +210,8 @@ def spectrum(self, k_y, k_z): if self.m == 0: return self._f_Gauss_cartesian(k_y, k_z, self.W_y) else: - return self._f_Laguerre_Gauss_cartesian(k_y, k_z, self.W_y, self.k, self.m) + return self._f_Laguerre_Gauss_cartesian(k_y, k_z, + self.W_y, self.k, self.m) def _phi(self, k_y, k_z): """Azimuthal angle. @@ -253,7 +261,7 @@ def __init__(self, x, params, called=False): def profile(self, r): """...""" if self.x == 0 and self.m == 0: - return _exp(-((r.y**2 + r.z**2) / self.W_y**2)) * (2*math.pi*self.k) + return _exp(-((r.y**2 + r.z**2) / self.W_y**2)) * 2*math.pi*self.k else: return super().profile(r) @@ -292,8 +300,9 @@ def __init__(self, x, y, z): x, y, z = -2.15, 0.3, 0.5 - # import meep; r = meep.Vector3(0, y, z) r = Vector3(0, y, z) + # alternative: + # import meep; r = meep.Vector3(0, y, z) k1 = 31.41592653589793 w_0 = 0.25464790894703254 @@ -301,15 +310,10 @@ def __init__(self, x, y, z): params = dict(W_y=w_0, m=m_charge, k=k1) - #psi_spherical = PsiSpherical(x=x, params=params) - #psi_cartesian = PsiCartesian(x=x, params=params) - - #return (psi_spherical, psi_cartesian, r) - LGbeam = LaguerreGauss3d(x=x, params=params) - LGbeam_ = LaguerreGauss3d_(x=x, params=params) + LGbeamCartesian = LaguerreGauss3dCartesian(x=x, params=params) - return (LGbeam, LGbeam_, r) + return (LGbeam, LGbeamCartesian, r) if __name__ == '__main__': From 466e066c9d255fb9de78fa3ad99545db4ec0d67e Mon Sep 17 00:00:00 2001 From: Daniel Kotik Date: Wed, 1 Apr 2020 21:42:16 +0200 Subject: [PATCH 086/145] Make m member variable private --- Laguerre_Gauss_3d/optbeam.pxd | 8 ++++---- Laguerre_Gauss_3d/optbeam.py | 16 ++++++++-------- 2 files changed, 12 insertions(+), 12 deletions(-) diff --git a/Laguerre_Gauss_3d/optbeam.pxd b/Laguerre_Gauss_3d/optbeam.pxd index 15660bb..765ae94 100644 --- a/Laguerre_Gauss_3d/optbeam.pxd +++ b/Laguerre_Gauss_3d/optbeam.pxd @@ -70,22 +70,22 @@ cdef class Beam3dCartesian(Beam3d): cdef class LaguerreGauss3d(Beam3dSpherical): cdef: - int m + int _m double W_y cdef double complex _f_Gauss_spherical(self, double sin_theta, double W_y, double k) nogil cdef double complex _f_Laguerre_Gauss_spherical(self, double sin_theta, double theta, double phi, - double W_y, double k, int m) nogil + double W_y, double k, int _m) nogil cdef double complex spectrum(self, double sin_theta, double theta, double phi) nogil cdef class LaguerreGauss3dCartesian(Beam3dCartesian): cdef: - int m + int _m double W_y cdef double _phi(self, double k_y, double k_z) nogil cdef double _theta(self, double k_y, double k_z, double k) nogil cdef double complex _f_Gauss_cartesian(self, double k_y, double k_z, double W_y) nogil cdef double complex _f_Laguerre_Gauss_cartesian(self, double k_y, double k_z, - double W_y, double k, int m) nogil + double W_y, double k, int _m) nogil cdef double complex spectrum(self, double k_y, double k_z) nogil diff --git a/Laguerre_Gauss_3d/optbeam.py b/Laguerre_Gauss_3d/optbeam.py index dd60982..e63f26f 100644 --- a/Laguerre_Gauss_3d/optbeam.py +++ b/Laguerre_Gauss_3d/optbeam.py @@ -196,22 +196,22 @@ def __init__(self, x, params, called=False): """Laguerre-Gauss beam specifc parameters.""" super().__init__(x, params, called) self.W_y = params['W_y'] - self.m = params['m'] + self._m = params['m'] def profile(self, r): """...""" - if self.x == 0 and self.m == 0: + if self.x == 0 and self._m == 0: return _exp(-((r.y**2 + r.z**2) / self.W_y**2)) * 2*math.pi*self.k else: return super().profile(r) def spectrum(self, k_y, k_z): """Spectrum amplitude function, f.""" - if self.m == 0: + if self._m == 0: return self._f_Gauss_cartesian(k_y, k_z, self.W_y) else: return self._f_Laguerre_Gauss_cartesian(k_y, k_z, - self.W_y, self.k, self.m) + self.W_y, self.k, self._m) def _phi(self, k_y, k_z): """Azimuthal angle. @@ -256,22 +256,22 @@ def __init__(self, x, params, called=False): """Laguerre-Gauss beam specifc parameters.""" super().__init__(x, params, called) self.W_y = params['W_y'] - self.m = params['m'] + self._m = params['m'] def profile(self, r): """...""" - if self.x == 0 and self.m == 0: + if self.x == 0 and self._m == 0: return _exp(-((r.y**2 + r.z**2) / self.W_y**2)) * 2*math.pi*self.k else: return super().profile(r) def spectrum(self, sin_theta, theta, phi): """Spectrum amplitude function, f.""" - if self.m == 0: + if self._m == 0: return self._f_Gauss_spherical(sin_theta, self.W_y, self.k) else: return self._f_Laguerre_Gauss_spherical(sin_theta, theta, phi, - self.W_y, self.k, self.m) + self.W_y, self.k, self._m) def _f_Gauss_spherical(self, sin_theta, W_y, k): """2d-Gaussian spectrum amplitude. From 2f2da463f404612c6d7228797992c0cb8a259375 Mon Sep 17 00:00:00 2001 From: Daniel Kotik Date: Wed, 1 Apr 2020 21:45:58 +0200 Subject: [PATCH 087/145] Make W_y member variable private --- Laguerre_Gauss_3d/optbeam.pxd | 12 ++++++------ Laguerre_Gauss_3d/optbeam.py | 16 ++++++++-------- 2 files changed, 14 insertions(+), 14 deletions(-) diff --git a/Laguerre_Gauss_3d/optbeam.pxd b/Laguerre_Gauss_3d/optbeam.pxd index 765ae94..5395494 100644 --- a/Laguerre_Gauss_3d/optbeam.pxd +++ b/Laguerre_Gauss_3d/optbeam.pxd @@ -71,21 +71,21 @@ cdef class Beam3dCartesian(Beam3d): cdef class LaguerreGauss3d(Beam3dSpherical): cdef: int _m - double W_y + double _W_y - cdef double complex _f_Gauss_spherical(self, double sin_theta, double W_y, double k) nogil + cdef double complex _f_Gauss_spherical(self, double sin_theta, double _W_y, double k) nogil cdef double complex _f_Laguerre_Gauss_spherical(self, double sin_theta, double theta, double phi, - double W_y, double k, int _m) nogil + double _W_y, double k, int _m) nogil cdef double complex spectrum(self, double sin_theta, double theta, double phi) nogil cdef class LaguerreGauss3dCartesian(Beam3dCartesian): cdef: int _m - double W_y + double _W_y cdef double _phi(self, double k_y, double k_z) nogil cdef double _theta(self, double k_y, double k_z, double k) nogil - cdef double complex _f_Gauss_cartesian(self, double k_y, double k_z, double W_y) nogil + cdef double complex _f_Gauss_cartesian(self, double k_y, double k_z, double _W_y) nogil cdef double complex _f_Laguerre_Gauss_cartesian(self, double k_y, double k_z, - double W_y, double k, int _m) nogil + double _W_y, double k, int _m) nogil cdef double complex spectrum(self, double k_y, double k_z) nogil diff --git a/Laguerre_Gauss_3d/optbeam.py b/Laguerre_Gauss_3d/optbeam.py index e63f26f..94bc399 100644 --- a/Laguerre_Gauss_3d/optbeam.py +++ b/Laguerre_Gauss_3d/optbeam.py @@ -195,23 +195,23 @@ class LaguerreGauss3dCartesian(Beam3dCartesian): def __init__(self, x, params, called=False): """Laguerre-Gauss beam specifc parameters.""" super().__init__(x, params, called) - self.W_y = params['W_y'] + self._W_y = params['W_y'] self._m = params['m'] def profile(self, r): """...""" if self.x == 0 and self._m == 0: - return _exp(-((r.y**2 + r.z**2) / self.W_y**2)) * 2*math.pi*self.k + return _exp(-((r.y**2 + r.z**2) / self._W_y**2)) * 2*math.pi*self.k else: return super().profile(r) def spectrum(self, k_y, k_z): """Spectrum amplitude function, f.""" if self._m == 0: - return self._f_Gauss_cartesian(k_y, k_z, self.W_y) + return self._f_Gauss_cartesian(k_y, k_z, self._W_y) else: return self._f_Laguerre_Gauss_cartesian(k_y, k_z, - self.W_y, self.k, self._m) + self._W_y, self.k, self._m) def _phi(self, k_y, k_z): """Azimuthal angle. @@ -255,23 +255,23 @@ class LaguerreGauss3d(Beam3dSpherical): def __init__(self, x, params, called=False): """Laguerre-Gauss beam specifc parameters.""" super().__init__(x, params, called) - self.W_y = params['W_y'] + self._W_y = params['W_y'] self._m = params['m'] def profile(self, r): """...""" if self.x == 0 and self._m == 0: - return _exp(-((r.y**2 + r.z**2) / self.W_y**2)) * 2*math.pi*self.k + return _exp(-((r.y**2 + r.z**2) / self._W_y**2)) * 2*math.pi*self.k else: return super().profile(r) def spectrum(self, sin_theta, theta, phi): """Spectrum amplitude function, f.""" if self._m == 0: - return self._f_Gauss_spherical(sin_theta, self.W_y, self.k) + return self._f_Gauss_spherical(sin_theta, self._W_y, self.k) else: return self._f_Laguerre_Gauss_spherical(sin_theta, theta, phi, - self.W_y, self.k, self._m) + self._W_y, self.k, self._m) def _f_Gauss_spherical(self, sin_theta, W_y, k): """2d-Gaussian spectrum amplitude. From 3fba21edbcd6e3910befbf848216a20935add186 Mon Sep 17 00:00:00 2001 From: Daniel Kotik Date: Wed, 1 Apr 2020 21:57:07 +0200 Subject: [PATCH 088/145] Make k member variable private --- Laguerre_Gauss_3d/optbeam.pxd | 2 +- Laguerre_Gauss_3d/optbeam.py | 20 ++++++++++---------- 2 files changed, 11 insertions(+), 11 deletions(-) diff --git a/Laguerre_Gauss_3d/optbeam.pxd b/Laguerre_Gauss_3d/optbeam.pxd index 5395494..ae8e3e4 100644 --- a/Laguerre_Gauss_3d/optbeam.pxd +++ b/Laguerre_Gauss_3d/optbeam.pxd @@ -46,7 +46,7 @@ cdef (double complex, double, double) _complex_dblquad(Beam3d func, cdef class Beam3d: cdef: readonly dict params - double x, k + double x, _k public bool called cdef double complex _integrand(self, double x, double y) nogil diff --git a/Laguerre_Gauss_3d/optbeam.py b/Laguerre_Gauss_3d/optbeam.py index 94bc399..b85c694 100644 --- a/Laguerre_Gauss_3d/optbeam.py +++ b/Laguerre_Gauss_3d/optbeam.py @@ -90,7 +90,7 @@ class Beam3d: def __init__(self, x, params, called=False): """...""" self.x = x # TODO: rename x to x_shift - self.k = params['k'] + self._k = params['k'] self.params = params self.called = called @@ -121,7 +121,7 @@ def profile(self, r): print(type(e).__name__ + ":", e) sys.exit() - return self.k**2 * result + return self._k**2 * result def spectrum(self, sin_theta, theta, phi): """Spectrum amplitude function, f.""" @@ -132,7 +132,7 @@ def _phase(self, sin_theta, cos_theta, phi, x, y, z): sin_phi = _sin(phi) cos_phi = _cos(phi) - return self.k*(sin_theta*(y*sin_phi - z*cos_phi) + cos_theta*x) + return self._k*(sin_theta*(y*sin_phi - z*cos_phi) + cos_theta*x) def _integrand(self, theta, phi): """Integrand function.""" @@ -160,7 +160,7 @@ def profile(self, r): (result, real_tol, imag_tol) = _complex_dblquad(self if cython.compiled else self._integrand, - -self.k, self.k, -self.k, self.k) + -self._k, self._k, -self._k, self._k) except Exception as e: print(type(e).__name__ + ":", e) sys.exit() @@ -173,7 +173,7 @@ def spectrum(self, k_y, k_z): def _phase(self, k_y, k_z, x, y, z): """Phase function.""" - return x*_csqrt(self.k**2 - k_y**2 - k_z**2).real + y*k_y + z*k_z + return x*_csqrt(self._k**2 - k_y**2 - k_z**2).real + y*k_y + z*k_z def _integrand(self, k_y, k_z): """Integrand function.""" @@ -201,7 +201,7 @@ def __init__(self, x, params, called=False): def profile(self, r): """...""" if self.x == 0 and self._m == 0: - return _exp(-((r.y**2 + r.z**2) / self._W_y**2)) * 2*math.pi*self.k + return _exp(-((r.y**2 + r.z**2) / self._W_y**2)) * 2*math.pi*self._k else: return super().profile(r) @@ -211,7 +211,7 @@ def spectrum(self, k_y, k_z): return self._f_Gauss_cartesian(k_y, k_z, self._W_y) else: return self._f_Laguerre_Gauss_cartesian(k_y, k_z, - self._W_y, self.k, self._m) + self._W_y, self._k, self._m) def _phi(self, k_y, k_z): """Azimuthal angle. @@ -261,17 +261,17 @@ def __init__(self, x, params, called=False): def profile(self, r): """...""" if self.x == 0 and self._m == 0: - return _exp(-((r.y**2 + r.z**2) / self._W_y**2)) * 2*math.pi*self.k + return _exp(-((r.y**2 + r.z**2) / self._W_y**2)) * 2*math.pi*self._k else: return super().profile(r) def spectrum(self, sin_theta, theta, phi): """Spectrum amplitude function, f.""" if self._m == 0: - return self._f_Gauss_spherical(sin_theta, self._W_y, self.k) + return self._f_Gauss_spherical(sin_theta, self._W_y, self._k) else: return self._f_Laguerre_Gauss_spherical(sin_theta, theta, phi, - self._W_y, self.k, self._m) + self._W_y, self._k, self._m) def _f_Gauss_spherical(self, sin_theta, W_y, k): """2d-Gaussian spectrum amplitude. From a353a66dac83d4dee5f81189a695c4f7dd526efa Mon Sep 17 00:00:00 2001 From: Daniel Kotik Date: Thu, 2 Apr 2020 18:35:25 +0200 Subject: [PATCH 089/145] Make params attribute values read-only: MappingProxyType is a read-only view of the dict type. --- Laguerre_Gauss_3d/optbeam.pxd | 2 +- Laguerre_Gauss_3d/optbeam.py | 3 ++- 2 files changed, 3 insertions(+), 2 deletions(-) diff --git a/Laguerre_Gauss_3d/optbeam.pxd b/Laguerre_Gauss_3d/optbeam.pxd index ae8e3e4..455e928 100644 --- a/Laguerre_Gauss_3d/optbeam.pxd +++ b/Laguerre_Gauss_3d/optbeam.pxd @@ -45,7 +45,7 @@ cdef (double complex, double, double) _complex_dblquad(Beam3d func, # ----------------------------------------------------------------------------- cdef class Beam3d: cdef: - readonly dict params + dict __dict__ double x, _k public bool called diff --git a/Laguerre_Gauss_3d/optbeam.py b/Laguerre_Gauss_3d/optbeam.py index b85c694..db95d4a 100644 --- a/Laguerre_Gauss_3d/optbeam.py +++ b/Laguerre_Gauss_3d/optbeam.py @@ -12,6 +12,7 @@ import sys from scipy.integrate import dblquad +from types import MappingProxyType if not cython.compiled: @@ -91,7 +92,7 @@ def __init__(self, x, params, called=False): """...""" self.x = x # TODO: rename x to x_shift self._k = params['k'] - self.params = params + self.params = MappingProxyType(params) # read-only view of a dict self.called = called def _integrand(self, x, y): From 404fde0ea08d2cc7383862b72168d3171e643a08 Mon Sep 17 00:00:00 2001 From: Daniel Kotik Date: Thu, 2 Apr 2020 18:49:29 +0200 Subject: [PATCH 090/145] Make params a read-only property --- Laguerre_Gauss_3d/optbeam.py | 10 +++++++++- 1 file changed, 9 insertions(+), 1 deletion(-) diff --git a/Laguerre_Gauss_3d/optbeam.py b/Laguerre_Gauss_3d/optbeam.py index db95d4a..f49f80f 100644 --- a/Laguerre_Gauss_3d/optbeam.py +++ b/Laguerre_Gauss_3d/optbeam.py @@ -92,9 +92,17 @@ def __init__(self, x, params, called=False): """...""" self.x = x # TODO: rename x to x_shift self._k = params['k'] - self.params = MappingProxyType(params) # read-only view of a dict + self._params = MappingProxyType(params) # read-only view of a dict self.called = called + @property + def params(self): + """Beam specific parameters. + + This is a read-only property. + """ + return self._params + def _integrand(self, x, y): """Integrand function over two coordinates x and y.""" raise NotImplementedError From af1250711f1157fc2ec842f4db83684eb1766c19 Mon Sep 17 00:00:00 2001 From: Daniel Kotik Date: Thu, 2 Apr 2020 18:58:27 +0200 Subject: [PATCH 091/145] Improve readability of math expression --- Laguerre_Gauss_3d/optbeam.py | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/Laguerre_Gauss_3d/optbeam.py b/Laguerre_Gauss_3d/optbeam.py index f49f80f..2406df7 100644 --- a/Laguerre_Gauss_3d/optbeam.py +++ b/Laguerre_Gauss_3d/optbeam.py @@ -210,7 +210,7 @@ def __init__(self, x, params, called=False): def profile(self, r): """...""" if self.x == 0 and self._m == 0: - return _exp(-((r.y**2 + r.z**2) / self._W_y**2)) * 2*math.pi*self._k + return 2*math.pi*self._k * _exp(-((r.y**2 + r.z**2) / self._W_y**2)) else: return super().profile(r) @@ -270,7 +270,7 @@ def __init__(self, x, params, called=False): def profile(self, r): """...""" if self.x == 0 and self._m == 0: - return _exp(-((r.y**2 + r.z**2) / self._W_y**2)) * 2*math.pi*self._k + return 2*math.pi*self._k * _exp(-((r.y**2 + r.z**2) / self._W_y**2)) else: return super().profile(r) From 3519b36b9de9d43aef87c3caafe78cd3b8bb95ca Mon Sep 17 00:00:00 2001 From: Daniel Kotik Date: Thu, 2 Apr 2020 23:29:18 +0200 Subject: [PATCH 092/145] Minor alignment adjustment --- Laguerre_Gauss_3d/optbeam.pxd | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/Laguerre_Gauss_3d/optbeam.pxd b/Laguerre_Gauss_3d/optbeam.pxd index 455e928..1c21248 100644 --- a/Laguerre_Gauss_3d/optbeam.pxd +++ b/Laguerre_Gauss_3d/optbeam.pxd @@ -56,7 +56,7 @@ cdef class Beam3dSpherical(Beam3d): double _ry, _rz cdef double _phase(self, double sin_theta, double cos_theta, double phi, - double x, double y, double z) nogil + double x, double y, double z) nogil cdef double complex spectrum(self, double sin_theta, double theta, double phi) nogil cdef double complex _integrand(self, double theta, double phi) nogil From 54c47231fc1ef9dbbcf6aff9c0283d0218850346 Mon Sep 17 00:00:00 2001 From: Daniel Kotik Date: Thu, 2 Apr 2020 23:37:40 +0200 Subject: [PATCH 093/145] Move brewster and critical functions to optbeam library --- Laguerre_Gauss_3d/LaguerreGauss3d.py | 19 ++----------------- Laguerre_Gauss_3d/optbeam.py | 11 +++++++++++ 2 files changed, 13 insertions(+), 17 deletions(-) diff --git a/Laguerre_Gauss_3d/LaguerreGauss3d.py b/Laguerre_Gauss_3d/LaguerreGauss3d.py index a6a8b02..daa420b 100644 --- a/Laguerre_Gauss_3d/LaguerreGauss3d.py +++ b/Laguerre_Gauss_3d/LaguerreGauss3d.py @@ -49,32 +49,17 @@ """ import argparse -import cmath import math import meep as mp import sys from datetime import datetime - -from optbeam import PsiSpherical -from optbeam2 import PsiCartesian -# TODO: change in future versions to LaguerreGauss3d, Airy3d etc. +from optbeam import LaguerreGauss3d, critical, brewster print("Meep version:", mp.__version__) -def Critical(n1, n2): - """Calculate critical angle in degrees.""" - assert n1 > n2, "\nWarning: Critical angle is not defined, since n1 <= n2!" - return math.degrees(math.asin(n2/n1)) - - -def Brewster(n1, n2): - """Calculate Brewster angle in degrees.""" - return math.degrees(math.atan(n2/n1)) - - def main(args): print("\nstart time:", datetime.now()) @@ -97,7 +82,7 @@ def main(args): # angle of incidence chi_deg = args.chi_deg #chi_deg = 1.0*Critical(n1, n2) - #chi_deg = 0.95*Brewster(n1, n2) + #chi_deg = 0.95*brewster(n1, n2) test_output = args.test_output diff --git a/Laguerre_Gauss_3d/optbeam.py b/Laguerre_Gauss_3d/optbeam.py index 2406df7..ecc02d0 100644 --- a/Laguerre_Gauss_3d/optbeam.py +++ b/Laguerre_Gauss_3d/optbeam.py @@ -85,6 +85,17 @@ def _complex_dblquad(func, a, b, gfun, hfun): return real + 1j*imag, real_tol, imag_tol +def critical(n1, n2): + """Calculate critical angle in degrees.""" + assert n1 > n2, "\nWarning: Critical angle is not defined, since n1 <= n2!" + return math.degrees(math.asin(n2/n1)) + + +def brewster(n1, n2): + """Calculate Brewster angle in degrees.""" + return math.degrees(math.atan(n2/n1)) + + class Beam3d: """Abstract base class.""" From 3a5ca1cb942fd0900415c0426314c390e29892e7 Mon Sep 17 00:00:00 2001 From: Daniel Kotik Date: Thu, 2 Apr 2020 23:57:10 +0200 Subject: [PATCH 094/145] Remove obsolete test outputs etc. --- Laguerre_Gauss_3d/LaguerreGauss3d.py | 100 ++------------------------- 1 file changed, 7 insertions(+), 93 deletions(-) diff --git a/Laguerre_Gauss_3d/LaguerreGauss3d.py b/Laguerre_Gauss_3d/LaguerreGauss3d.py index daa420b..16e4daa 100644 --- a/Laguerre_Gauss_3d/LaguerreGauss3d.py +++ b/Laguerre_Gauss_3d/LaguerreGauss3d.py @@ -51,11 +51,9 @@ import argparse import math import meep as mp -import sys +import optbeam as op from datetime import datetime -from optbeam import LaguerreGauss3d, critical, brewster - print("Meep version:", mp.__version__) @@ -81,10 +79,8 @@ def main(args): # angle of incidence chi_deg = args.chi_deg - #chi_deg = 1.0*Critical(n1, n2) - #chi_deg = 0.95*brewster(n1, n2) - - test_output = args.test_output + #chi_deg = 1.0*op.critical(n1, n2) + #chi_deg = 0.95*op.brewster(n1, n2) # -------------------------------------------------------------------------- # specific Meep parameters (may need to be adjusted) @@ -156,75 +152,6 @@ def Delta_x(alpha): # set Courant factor (mandatory if either n1 or n2 is smaller than 1) Courant = (n1 if n1 < n2 else n2) / 3 - # -------------------------------------------------------------------------- - # 2d-beam profile distribution (field amplitude) at the waist of the beam - # -------------------------------------------------------------------------- - def Gauss(r, params): - """Gauss profile.""" - W_y = params['W_y'] - - return math.exp(-((r.y**2 + r.z**2) / W_y**2)) - - # -------------------------------------------------------------------------- - # some test outputs - # -------------------------------------------------------------------------- - if test_output: - print("Gauss 2d beam profile:", Gauss(mp.Vector3(0, 0.5, 0.2), params)) - print() - - # -------------------------------------------------------------------------- - # spectrum amplitude distribution(s) - # -------------------------------------------------------------------------- - - # cartesian coordinates (not recommmended) ------------------------- - - - # spherical coordinates -------------------------------------------- - - - # -------------------------------------------------------------------------- - # some test outputs - # -------------------------------------------------------------------------- - if test_output: - k_y, k_z = 1.0, 5.2 - theta_ = theta(k_y, k_z, k1) - phi_ = phi(k_y, k_z) - - print("Gauss spectrum (cartesian):", - f_Gauss_cartesian(k_y, k_z, params)) - print("Gauss spectrum (spherical):", - f_Gauss_spherical(math.sin(theta_), theta_, phi_, params)) - print() - print("L-G spectrum (cartesian):", - f_Laguerre_Gauss_cartesian(k_y, k_z, params)) - print("L-G spectrum (spherical):", - f_Laguerre_Gauss_spherical(math.sin(theta_), theta_, phi_, params)) - print() - - # -------------------------------------------------------------------------- - # plane wave decomposition - # (purpose: calculate field amplitude at light source position if not - # coinciding with beam waist) - # -------------------------------------------------------------------------- - - - # -------------------------------------------------------------------------- - # some test outputs (uncomment if needed) - # -------------------------------------------------------------------------- - if test_output: - k_y, k_z = 1.0, 5.2 - x, y, z = -2.15, 0.3, 0.5 - r = mp.Vector3(0, y, z) - - print("phi:", phi(k_y, k_z)) - print() - print("psi (cartesian):", - psi_cartesian(r, f_Laguerre_Gauss_cartesian, x, params)) - print("psi (spherical):", - psi_spherical(r, lambda st, t, p: f_Laguerre_Gauss_spherical(st, t, p, W_y=w_0, m=m_charge, k=k1), x, k1)) - print("psi (origin, simple):", Gauss(r)) - sys.exit() - # -------------------------------------------------------------------------- # display values of physical variables # -------------------------------------------------------------------------- @@ -278,10 +205,8 @@ def Gauss(r, params): sources = [] - # define beam profile function - psi_spherical = PsiSpherical(x=shift, params=params) - # TODO: change to psi_LaguerreGauss = LaguerreGauss3d.psi(...) in future versions - # f_Laguerre_Gauss = LaguerreGauss3d.f_spectrum(...) + # specify optical beam + LGbeam = op.LaguerreGauss3d(x=shift, params=params) if e_z != 0: source_Ez = mp.Source(src=mp.ContinuousSource(frequency=freq, width=0.5), @@ -289,10 +214,7 @@ def Gauss(r, params): amplitude=e_z, size=mp.Vector3(0, 3, 3), center=mp.Vector3(source_shift, 0, 0), - #amp_func=lambda r: Gauss(r, params) - #amp_func=lambda r: psi_cartesian(r, shift, params) - #amp_func=lambda r: psi_spherical(r)#, shift, params) - amp_func=psi_spherical + amp_func=LGbeam.profile ) sources.append(source_Ez) @@ -302,10 +224,7 @@ def Gauss(r, params): amplitude=e_y, size=mp.Vector3(0, 3, 3), center=mp.Vector3(source_shift, 0, 0), - #amp_func=lambda r: Gauss(r, params) - #amp_func=lambda r: psi_cartesian(r, shift, params) - #amp_func=lambda r: psi_spherical(r)#, shift, params) - amp_func=psi_spherical + amp_func=LGbeam.profile ) sources.append(source_Ey) @@ -423,10 +342,5 @@ def output_efield_imag_squared(sim): default=45, help='incidence angle in degrees (default: %(default)s)') - parser.add_argument('-test_output', - action='store_true', - default=False, - help='switch to enable test print statements') - args = parser.parse_args() main(args) From 51f985dbf06e93a82e212f06cc03713ea4c040c2 Mon Sep 17 00:00:00 2001 From: Daniel Kotik Date: Tue, 7 Apr 2020 18:50:20 +0200 Subject: [PATCH 095/145] Update .gitignore with Cython related stuff --- .gitignore | 8 ++++++++ 1 file changed, 8 insertions(+) diff --git a/.gitignore b/.gitignore index d151ebf..581a345 100644 --- a/.gitignore +++ b/.gitignore @@ -18,9 +18,17 @@ __pycache__/ *.py[cod] *$py.class +### Cython ### # C extensions *.so +# profiling annotions +*.html + +# Cython generated C source code +*.c + + # Distribution / packaging .Python build/ From ba01ed1c7fa8c4d7f98f52f84396a801069deca4 Mon Sep 17 00:00:00 2001 From: Daniel Kotik Date: Fri, 3 Apr 2020 23:58:52 +0200 Subject: [PATCH 096/145] Add empty files optbeam.p* --- Gauss_2d/optbeam.pxd | 9 +++++++++ Gauss_2d/optbeam.py | 9 +++++++++ 2 files changed, 18 insertions(+) create mode 100644 Gauss_2d/optbeam.pxd create mode 100644 Gauss_2d/optbeam.py diff --git a/Gauss_2d/optbeam.pxd b/Gauss_2d/optbeam.pxd new file mode 100644 index 0000000..e2f11e0 --- /dev/null +++ b/Gauss_2d/optbeam.pxd @@ -0,0 +1,9 @@ +# -*- coding: utf-8 -*- +""" +file: optbeam.pxd +brief: ... +author: Daniel Kotik +version: 1.5-beta +release date: xx.xx.2020 +creation date: 03.04.2020 +""" diff --git a/Gauss_2d/optbeam.py b/Gauss_2d/optbeam.py new file mode 100644 index 0000000..0b68630 --- /dev/null +++ b/Gauss_2d/optbeam.py @@ -0,0 +1,9 @@ +# -*- coding: utf-8 -*- +""" +file: optbeam.py +brief: ... +author: Daniel Kotik +version: 1.5-beta +release date: xx.xx.2020 +creation date: 03.04.2020 +""" From c454d9f559e63c899b29ff38434dad2cc806e869 Mon Sep 17 00:00:00 2001 From: Daniel Kotik Date: Sat, 4 Apr 2020 12:32:33 +0200 Subject: [PATCH 097/145] Add content to optbeam.py: MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit This serves as starting point for speed optimisation with Cython. Current execution times: %timeit psi(r) 2.84 ms ± 17 µs per loop (mean ± std. dev. of 7 runs, 100 loops each) --- Gauss_2d/optbeam.py | 81 +++++++++++++++++++++++++++++++++++++++++++++ 1 file changed, 81 insertions(+) diff --git a/Gauss_2d/optbeam.py b/Gauss_2d/optbeam.py index 0b68630..a25a09e 100644 --- a/Gauss_2d/optbeam.py +++ b/Gauss_2d/optbeam.py @@ -7,3 +7,84 @@ release date: xx.xx.2020 creation date: 03.04.2020 """ +import cmath +import math +import sys + +from scipy.integrate import quad + + +def complex_quad(func, a, b, **kwargs): + """Integrate real and imaginary part of the given function.""" + def real_func(x): + return func(x).real + + def imag_func(x): + return func(x).imag + + real, real_tol = quad(real_func, a, b, **kwargs) + imag, imag_tol = quad(imag_func, a, b, **kwargs) + + return real + 1j*imag, real_tol, imag_tol + + +def f_Gauss(k_y, params): + """Gaussian spectrum amplitude.""" + W_y = params['W_y'] + + return math.exp(-(k_y*W_y/2)**2) + + +def psi(r, x, params): + """Field amplitude function.""" + k1 = params["k"] + + try: + getattr(psi, "called") + except AttributeError: + psi.called = True + print("Calculating inital field configuration. " + "This will take some time...") + + def phase(k_y, x, y): + """Phase function.""" + return x*math.sqrt(k1**2 - k_y**2) + k_y*y + + try: + (result, + real_tol, + imag_tol) = complex_quad(lambda k_y: + f_Gauss(k_y, params) + * cmath.exp(1j*phase(k_y, x, r.y)), + -k1, k1) + except Exception as e: + print(type(e).__name__ + ":", e) + sys.exit() + + return result + + +def main(): + class Vector3: + """Simple 3d vector class.""" + + def __init__(self, x, y, z): + self.x = x + self.y = y + self.z = z + + x, y, z = -2.15, 0.3, 0.5 + + r = Vector3(0, y, z) + # alternative: + # import meep; r = meep.Vector3(0, y, z) + + k1 = 116.11326447667875 + w_0 = 0.1061032953945969 + params = dict(W_y=w_0, k=k1) + + return (lambda r: psi(r, x, params), r) + + +if __name__ == '__main__': + main() From 6725a7162dade7fb4e79a8f649dd98f4cbb0cdbe Mon Sep 17 00:00:00 2001 From: Daniel Kotik Date: Sat, 4 Apr 2020 18:38:24 +0200 Subject: [PATCH 098/145] Rewrite psi as profile method of class Beam2d --- Gauss_2d/optbeam.py | 79 +++++++++++++++++++++++++++------------------ 1 file changed, 47 insertions(+), 32 deletions(-) diff --git a/Gauss_2d/optbeam.py b/Gauss_2d/optbeam.py index a25a09e..0a249fc 100644 --- a/Gauss_2d/optbeam.py +++ b/Gauss_2d/optbeam.py @@ -28,40 +28,53 @@ def imag_func(x): return real + 1j*imag, real_tol, imag_tol -def f_Gauss(k_y, params): - """Gaussian spectrum amplitude.""" - W_y = params['W_y'] - - return math.exp(-(k_y*W_y/2)**2) - - -def psi(r, x, params): - """Field amplitude function.""" - k1 = params["k"] - - try: - getattr(psi, "called") - except AttributeError: - psi.called = True - print("Calculating inital field configuration. " - "This will take some time...") - - def phase(k_y, x, y): +class Beam2d: + """...""" + + def __init__(self, x, params, called=False): + """...""" + self.x = x + self._k = params['k'] + self._params = params + self.called = called + + self._W_y = params['W_y'] + + def profile(self, r): + """Field amplitude function.""" + self._ry = r.y + self._rz = r.z + + if not self.called: + print("Calculating inital field configuration. " + "This will take some time...") + self.called = True + + try: + (result, + real_tol, + imag_tol) = complex_quad(self._integrand, -self._k, self._k) + except Exception as e: + print(type(e).__name__ + ":", e) + sys.exit() + + return result + + def spectrum(self, k_y): + """Spectrum amplitude function, f.""" + return self._f_Gauss(k_y, self._W_y) + + def _phase(self, k_y, x, y): """Phase function.""" - return x*math.sqrt(k1**2 - k_y**2) + k_y*y + return x*math.sqrt(self._k**2 - k_y**2) + k_y*y - try: - (result, - real_tol, - imag_tol) = complex_quad(lambda k_y: - f_Gauss(k_y, params) - * cmath.exp(1j*phase(k_y, x, r.y)), - -k1, k1) - except Exception as e: - print(type(e).__name__ + ":", e) - sys.exit() + def _integrand(self, k_y): + """Integrand function.""" + return self.spectrum(k_y) * cmath.exp(1j*self._phase(k_y, self.x, self._ry)) - return result + def _f_Gauss(self, k_y, W_y): + """Gaussian spectrum amplitude.""" + return math.exp(-(k_y*W_y/2)**2) def main(): @@ -83,7 +96,9 @@ def __init__(self, x, y, z): w_0 = 0.1061032953945969 params = dict(W_y=w_0, k=k1) - return (lambda r: psi(r, x, params), r) + beam = Beam2d(x=x, params=params) + + return (beam, r) if __name__ == '__main__': From 6b232b744b7dddbb9c402ef6c400a49d7cec0a5e Mon Sep 17 00:00:00 2001 From: Daniel Kotik Date: Sat, 4 Apr 2020 23:55:07 +0200 Subject: [PATCH 099/145] Add superclass Beam2dCartesian --- Gauss_2d/optbeam.py | 40 +++++++++++++++++++++++++++++++++++----- 1 file changed, 35 insertions(+), 5 deletions(-) diff --git a/Gauss_2d/optbeam.py b/Gauss_2d/optbeam.py index 0a249fc..f6b2183 100644 --- a/Gauss_2d/optbeam.py +++ b/Gauss_2d/optbeam.py @@ -12,6 +12,7 @@ import sys from scipy.integrate import quad +from types import MappingProxyType def complex_quad(func, a, b, **kwargs): @@ -28,17 +29,23 @@ def imag_func(x): return real + 1j*imag, real_tol, imag_tol -class Beam2d: +class Beam2dCartesian: """...""" def __init__(self, x, params, called=False): """...""" self.x = x self._k = params['k'] - self._params = params + self._params = MappingProxyType(params) # read-only view of a dict self.called = called - self._W_y = params['W_y'] + @property + def params(self): + """Beam specific parameters. + + This is a read-only property. + """ + return self._params def profile(self, r): """Field amplitude function.""" @@ -62,7 +69,7 @@ def profile(self, r): def spectrum(self, k_y): """Spectrum amplitude function, f.""" - return self._f_Gauss(k_y, self._W_y) + raise NotImplementedError def _phase(self, k_y, x, y): """Phase function.""" @@ -72,6 +79,29 @@ def _integrand(self, k_y): """Integrand function.""" return self.spectrum(k_y) * cmath.exp(1j*self._phase(k_y, self.x, self._ry)) + +# ----------------------------------------------------------------------------- +# specific beam implementations based on Beam2dCartesian base class +# ----------------------------------------------------------------------------- +class Gauss2d(Beam2dCartesian): + """2d Gauss beam.""" + + def __init__(self, x, params, called=False): + """...""" + self._W_y = params['W_y'] + super().__init__(x, params, called) + + def profile(self, r): + """...""" + if self.x == 0: + return NotImplemented + else: + return super().profile(r) + + def spectrum(self, k_y): + """Spectrum amplitude function, f.""" + return self._f_Gauss(k_y, self._W_y) + def _f_Gauss(self, k_y, W_y): """Gaussian spectrum amplitude.""" return math.exp(-(k_y*W_y/2)**2) @@ -96,7 +126,7 @@ def __init__(self, x, y, z): w_0 = 0.1061032953945969 params = dict(W_y=w_0, k=k1) - beam = Beam2d(x=x, params=params) + beam = Gauss2d(x=x, params=params) return (beam, r) From 2cf84222e4900344ff917fad7dfa3f31916ab1d6 Mon Sep 17 00:00:00 2001 From: Daniel Kotik Date: Sun, 5 Apr 2020 12:07:32 +0200 Subject: [PATCH 100/145] Preliminary work for Cython takeover --- Gauss_2d/optbeam.pxd | 10 ++++++++++ Gauss_2d/optbeam.py | 37 ++++++++++++++++++++++++++----------- 2 files changed, 36 insertions(+), 11 deletions(-) diff --git a/Gauss_2d/optbeam.pxd b/Gauss_2d/optbeam.pxd index e2f11e0..76386bb 100644 --- a/Gauss_2d/optbeam.pxd +++ b/Gauss_2d/optbeam.pxd @@ -7,3 +7,13 @@ version: 1.5-beta release date: xx.xx.2020 creation date: 03.04.2020 """ +cimport cython +from cpython.pycapsule cimport PyCapsule_New +from cpython cimport bool + +cdef extern from "math.h": + cpdef double _exp "exp" (double x) nogil + cpdef double _sqrt "sqrt" (double x) nogil + +cdef extern from "complex.h": + cpdef double complex _cexp "cexp" (double complex z) nogil diff --git a/Gauss_2d/optbeam.py b/Gauss_2d/optbeam.py index f6b2183..303ec65 100644 --- a/Gauss_2d/optbeam.py +++ b/Gauss_2d/optbeam.py @@ -7,6 +7,7 @@ release date: xx.xx.2020 creation date: 03.04.2020 """ +import cython import cmath import math import sys @@ -15,16 +16,30 @@ from types import MappingProxyType -def complex_quad(func, a, b, **kwargs): - """Integrate real and imaginary part of the given function.""" - def real_func(x): - return func(x).real +if not cython.compiled: + from math import (exp as _exp, + sqrt as _sqrt) + from cmath import exp as _cexp + print("\nPlease consider compiling `%s.py` via Cython: " + "`$ cythonize -3 -i %s.py`\n" % (__name__, __name__)) +else: + from scipy import LowLevelCallable + + +def _real_1d_func(x, func): + """Return real part of a 1d function.""" + return func(x).real - def imag_func(x): - return func(x).imag - real, real_tol = quad(real_func, a, b, **kwargs) - imag, imag_tol = quad(imag_func, a, b, **kwargs) +def _imag_1d_func(x, func): + """Return imag part of a 1d function.""" + return func(x).imag + + +def complex_quad(func, a, b, **kwargs): + """Integrate real and imaginary part of the given function.""" + real, real_tol = quad(_real_1d_func, a, b, (func,)) + imag, imag_tol = quad(_imag_1d_func, a, b, (func,)) return real + 1j*imag, real_tol, imag_tol @@ -73,11 +88,11 @@ def spectrum(self, k_y): def _phase(self, k_y, x, y): """Phase function.""" - return x*math.sqrt(self._k**2 - k_y**2) + k_y*y + return x*_sqrt(self._k**2 - k_y**2) + k_y*y def _integrand(self, k_y): """Integrand function.""" - return self.spectrum(k_y) * cmath.exp(1j*self._phase(k_y, self.x, self._ry)) + return self.spectrum(k_y) * _cexp(1j*self._phase(k_y, self.x, self._ry)) # ----------------------------------------------------------------------------- @@ -104,7 +119,7 @@ def spectrum(self, k_y): def _f_Gauss(self, k_y, W_y): """Gaussian spectrum amplitude.""" - return math.exp(-(k_y*W_y/2)**2) + return _exp(-(k_y*W_y/2)**2) def main(): From 16361ce5dc6ade8e4d8e650c359360284c6fcc7c Mon Sep 17 00:00:00 2001 From: Daniel Kotik Date: Wed, 8 Apr 2020 14:37:18 +0200 Subject: [PATCH 101/145] Declare functions and classes cdef --- Gauss_2d/optbeam.pxd | 32 ++++++++++++++++++++++++++++++++ Gauss_2d/optbeam.py | 2 +- 2 files changed, 33 insertions(+), 1 deletion(-) diff --git a/Gauss_2d/optbeam.pxd b/Gauss_2d/optbeam.pxd index 76386bb..bdd8f16 100644 --- a/Gauss_2d/optbeam.pxd +++ b/Gauss_2d/optbeam.pxd @@ -11,9 +11,41 @@ cimport cython from cpython.pycapsule cimport PyCapsule_New from cpython cimport bool +# ----------------------------------------------------------------------------- +# declare C functions as "cpdef" to export them to the module +# ----------------------------------------------------------------------------- cdef extern from "math.h": cpdef double _exp "exp" (double x) nogil cpdef double _sqrt "sqrt" (double x) nogil cdef extern from "complex.h": cpdef double complex _cexp "cexp" (double complex z) nogil + +# ----------------------------------------------------------------------------- +# function declarations +# ----------------------------------------------------------------------------- +@cython.locals(real=cython.double, imag=cython.double, real_tol=cython.double, + imag_tol=cython.double) +cdef (double complex, double, double) complex_quad(func, double a, double b) + +# ----------------------------------------------------------------------------- +# class declarations +# ----------------------------------------------------------------------------- +cdef class Beam2dCartesian: + cdef: + dict __dict__ + double x, _k + public bool called + + double _ry, _rz + + cdef double spectrum(self, double k_y) nogil + cdef double _phase(self, double k_y, double x, double y) nogil + cpdef double complex _integrand(self, double k_y) + +cdef class Gauss2d(Beam2dCartesian): + cdef: + double _W_y + + cdef double _f_Gauss(self, double k_y, double W_y) nogil + cdef double spectrum(self, double k_y) nogil diff --git a/Gauss_2d/optbeam.py b/Gauss_2d/optbeam.py index 303ec65..91c1653 100644 --- a/Gauss_2d/optbeam.py +++ b/Gauss_2d/optbeam.py @@ -36,7 +36,7 @@ def _imag_1d_func(x, func): return func(x).imag -def complex_quad(func, a, b, **kwargs): +def complex_quad(func, a, b): """Integrate real and imaginary part of the given function.""" real, real_tol = quad(_real_1d_func, a, b, (func,)) imag, imag_tol = quad(_imag_1d_func, a, b, (func,)) From b16a63fe820876e88959c6eaa75cc8f063882da0 Mon Sep 17 00:00:00 2001 From: Daniel Kotik Date: Wed, 8 Apr 2020 14:50:09 +0200 Subject: [PATCH 102/145] Add C functions for obtaining real/imag part of func --- Gauss_2d/optbeam.pxd | 3 +++ Gauss_2d/optbeam.py | 20 ++++++++++++++++++++ 2 files changed, 23 insertions(+) diff --git a/Gauss_2d/optbeam.pxd b/Gauss_2d/optbeam.pxd index bdd8f16..5f08e5f 100644 --- a/Gauss_2d/optbeam.pxd +++ b/Gauss_2d/optbeam.pxd @@ -24,6 +24,9 @@ cdef extern from "complex.h": # ----------------------------------------------------------------------------- # function declarations # ----------------------------------------------------------------------------- +cdef double _imag_1d_func_c(int n, double *arr, void *func_ptr) +cdef double _real_1d_func_c(int n, double *arr, void *func_ptr) + @cython.locals(real=cython.double, imag=cython.double, real_tol=cython.double, imag_tol=cython.double) cdef (double complex, double, double) complex_quad(func, double a, double b) diff --git a/Gauss_2d/optbeam.py b/Gauss_2d/optbeam.py index 91c1653..c85ffdb 100644 --- a/Gauss_2d/optbeam.py +++ b/Gauss_2d/optbeam.py @@ -36,6 +36,26 @@ def _imag_1d_func(x, func): return func(x).imag +def _imag_1d_func_c(n, arr, func_ptr): + """Return imag part of a 1d function. + + Cython implementation. + """ + # pure python formulation of: + # return (func_ptr)(arr[0], arr[1]).imag + return cython.cast(Beam2dCartesian, func_ptr)._integrand(arr[0]).imag + + +def _real_1d_func_c(n, arr, func_ptr): + """Return real part of a 1d function. + + Cython implementation. + """ + # pure python formulation of: + # return (func_ptr)(arr[0], arr[1]).real + return cython.cast(Beam2dCartesian, func_ptr)._integrand(arr[0]).real + + def complex_quad(func, a, b): """Integrate real and imaginary part of the given function.""" real, real_tol = quad(_real_1d_func, a, b, (func,)) From 9040e22f22fc3ebb16bdfb68aa0d1a979b735f7a Mon Sep 17 00:00:00 2001 From: Daniel Kotik Date: Wed, 8 Apr 2020 18:49:47 +0200 Subject: [PATCH 103/145] Allow access to LowLevelCallable integrand --- Gauss_2d/optbeam.pxd | 4 ++-- Gauss_2d/optbeam.py | 26 ++++++++++++++++++++++---- 2 files changed, 24 insertions(+), 6 deletions(-) diff --git a/Gauss_2d/optbeam.pxd b/Gauss_2d/optbeam.pxd index 5f08e5f..87e39b4 100644 --- a/Gauss_2d/optbeam.pxd +++ b/Gauss_2d/optbeam.pxd @@ -29,7 +29,7 @@ cdef double _real_1d_func_c(int n, double *arr, void *func_ptr) @cython.locals(real=cython.double, imag=cython.double, real_tol=cython.double, imag_tol=cython.double) -cdef (double complex, double, double) complex_quad(func, double a, double b) +cdef (double complex, double, double) _complex_quad(func, double a, double b) # ----------------------------------------------------------------------------- # class declarations @@ -44,7 +44,7 @@ cdef class Beam2dCartesian: cdef double spectrum(self, double k_y) nogil cdef double _phase(self, double k_y, double x, double y) nogil - cpdef double complex _integrand(self, double k_y) + cdef double complex _integrand(self, double k_y) nogil cdef class Gauss2d(Beam2dCartesian): cdef: diff --git a/Gauss_2d/optbeam.py b/Gauss_2d/optbeam.py index c85ffdb..d217851 100644 --- a/Gauss_2d/optbeam.py +++ b/Gauss_2d/optbeam.py @@ -56,10 +56,27 @@ def _real_1d_func_c(n, arr, func_ptr): return cython.cast(Beam2dCartesian, func_ptr)._integrand(arr[0]).real -def complex_quad(func, a, b): +def _complex_quad(func, a, b): """Integrate real and imaginary part of the given function.""" - real, real_tol = quad(_real_1d_func, a, b, (func,)) - imag, imag_tol = quad(_imag_1d_func, a, b, (func,)) + if cython.compiled: + # pure python formulation of: cdef void *f_ptr = func + f_ptr = cython.declare(cython.p_void, cython.cast(cython.p_void, func)) + + func_capsule = PyCapsule_New(f_ptr, cython.NULL, cython.NULL) + + current_module = sys.modules[__name__] + + ll_real_1d_func_c = LowLevelCallable.from_cython(current_module, + '_real_1d_func_c', + func_capsule) + ll_imag_1d_func_c = LowLevelCallable.from_cython(current_module, + '_imag_1d_func_c', + func_capsule) + real, real_tol = quad(ll_real_1d_func_c, a, b) + imag, imag_tol = quad(ll_imag_1d_func_c, a, b) + else: + real, real_tol = quad(_real_1d_func, a, b, (func,)) + imag, imag_tol = quad(_imag_1d_func, a, b, (func,)) return real + 1j*imag, real_tol, imag_tol @@ -95,7 +112,8 @@ def profile(self, r): try: (result, real_tol, - imag_tol) = complex_quad(self._integrand, -self._k, self._k) + imag_tol) = _complex_quad(self if cython.compiled else self._integrand, + -self._k, self._k) except Exception as e: print(type(e).__name__ + ":", e) sys.exit() From c861365bc7d84ac8b445927474d41b0a45a2f7db Mon Sep 17 00:00:00 2001 From: Daniel Kotik Date: Thu, 9 Apr 2020 15:11:39 +0200 Subject: [PATCH 104/145] Add profile function for special case x=0 --- Gauss_2d/optbeam.py | 5 +++-- 1 file changed, 3 insertions(+), 2 deletions(-) diff --git a/Gauss_2d/optbeam.py b/Gauss_2d/optbeam.py index d217851..8f66512 100644 --- a/Gauss_2d/optbeam.py +++ b/Gauss_2d/optbeam.py @@ -113,7 +113,7 @@ def profile(self, r): (result, real_tol, imag_tol) = _complex_quad(self if cython.compiled else self._integrand, - -self._k, self._k) + -self._k, self._k) except Exception as e: print(type(e).__name__ + ":", e) sys.exit() @@ -142,12 +142,13 @@ class Gauss2d(Beam2dCartesian): def __init__(self, x, params, called=False): """...""" self._W_y = params['W_y'] + self._norm = 2 * math.sqrt(math.pi) / self._W_y super().__init__(x, params, called) def profile(self, r): """...""" if self.x == 0: - return NotImplemented + return self._norm * math.exp(-(r.y / self._W_y)**2) else: return super().profile(r) From 2b5a6c729e6815ff554f5c6045b8a7e18a195151 Mon Sep 17 00:00:00 2001 From: Daniel Kotik Date: Thu, 9 Apr 2020 15:58:54 +0200 Subject: [PATCH 105/145] Optimize calculation at x=0 for speed --- Gauss_2d/optbeam.pxd | 1 + Gauss_2d/optbeam.py | 4 ++-- 2 files changed, 3 insertions(+), 2 deletions(-) diff --git a/Gauss_2d/optbeam.pxd b/Gauss_2d/optbeam.pxd index 87e39b4..63ac447 100644 --- a/Gauss_2d/optbeam.pxd +++ b/Gauss_2d/optbeam.pxd @@ -49,6 +49,7 @@ cdef class Beam2dCartesian: cdef class Gauss2d(Beam2dCartesian): cdef: double _W_y + double _norm cdef double _f_Gauss(self, double k_y, double W_y) nogil cdef double spectrum(self, double k_y) nogil diff --git a/Gauss_2d/optbeam.py b/Gauss_2d/optbeam.py index 8f66512..ce37d1c 100644 --- a/Gauss_2d/optbeam.py +++ b/Gauss_2d/optbeam.py @@ -142,13 +142,13 @@ class Gauss2d(Beam2dCartesian): def __init__(self, x, params, called=False): """...""" self._W_y = params['W_y'] - self._norm = 2 * math.sqrt(math.pi) / self._W_y + self._norm = 2 * _sqrt(math.pi) / self._W_y super().__init__(x, params, called) def profile(self, r): """...""" if self.x == 0: - return self._norm * math.exp(-(r.y / self._W_y)**2) + return self._norm * _exp(-(r.y / self._W_y)**2) else: return super().profile(r) From 8ecf9bff8c2edea8e26098a3df7d6ad51075f0f2 Mon Sep 17 00:00:00 2001 From: Daniel Kotik Date: Thu, 9 Apr 2020 16:01:43 +0200 Subject: [PATCH 106/145] Update docstrings --- Gauss_2d/optbeam.py | 8 ++++++-- 1 file changed, 6 insertions(+), 2 deletions(-) diff --git a/Gauss_2d/optbeam.py b/Gauss_2d/optbeam.py index ce37d1c..14ec8f3 100644 --- a/Gauss_2d/optbeam.py +++ b/Gauss_2d/optbeam.py @@ -100,7 +100,11 @@ def params(self): return self._params def profile(self, r): - """Field amplitude function.""" + """Field amplitude function. + + Plane wave decomposition, to calculate field amplitude at light source + position if not coinciding with beam waist. + """ self._ry = r.y self._rz = r.z @@ -121,7 +125,7 @@ def profile(self, r): return result def spectrum(self, k_y): - """Spectrum amplitude function, f.""" + """Spectrum amplitude distribution function, f.""" raise NotImplementedError def _phase(self, k_y, x, y): From 52008777abb3d0ac3520ecda24c4d98cd7f41e03 Mon Sep 17 00:00:00 2001 From: Daniel Kotik Date: Thu, 9 Apr 2020 16:02:17 +0200 Subject: [PATCH 107/145] Remove cmath import --- Gauss_2d/optbeam.py | 1 - 1 file changed, 1 deletion(-) diff --git a/Gauss_2d/optbeam.py b/Gauss_2d/optbeam.py index 14ec8f3..81426a6 100644 --- a/Gauss_2d/optbeam.py +++ b/Gauss_2d/optbeam.py @@ -8,7 +8,6 @@ creation date: 03.04.2020 """ import cython -import cmath import math import sys From 8378dda29b0192e5c01f9e7c4f14d1e07ac81fcc Mon Sep 17 00:00:00 2001 From: Daniel Kotik Date: Sat, 11 Apr 2020 13:19:39 +0200 Subject: [PATCH 108/145] Fix normalization factor for special case x=0, m=0 --- Laguerre_Gauss_3d/optbeam.pxd | 2 ++ Laguerre_Gauss_3d/optbeam.py | 6 ++++-- 2 files changed, 6 insertions(+), 2 deletions(-) diff --git a/Laguerre_Gauss_3d/optbeam.pxd b/Laguerre_Gauss_3d/optbeam.pxd index 1c21248..e739b85 100644 --- a/Laguerre_Gauss_3d/optbeam.pxd +++ b/Laguerre_Gauss_3d/optbeam.pxd @@ -72,6 +72,7 @@ cdef class LaguerreGauss3d(Beam3dSpherical): cdef: int _m double _W_y + double _norm cdef double complex _f_Gauss_spherical(self, double sin_theta, double _W_y, double k) nogil cdef double complex _f_Laguerre_Gauss_spherical(self, double sin_theta, double theta, double phi, @@ -82,6 +83,7 @@ cdef class LaguerreGauss3dCartesian(Beam3dCartesian): cdef: int _m double _W_y + double _norm cdef double _phi(self, double k_y, double k_z) nogil cdef double _theta(self, double k_y, double k_z, double k) nogil diff --git a/Laguerre_Gauss_3d/optbeam.py b/Laguerre_Gauss_3d/optbeam.py index ecc02d0..97b4049 100644 --- a/Laguerre_Gauss_3d/optbeam.py +++ b/Laguerre_Gauss_3d/optbeam.py @@ -217,11 +217,12 @@ def __init__(self, x, params, called=False): super().__init__(x, params, called) self._W_y = params['W_y'] self._m = params['m'] + self._norm = 4 * math.pi / (self._W_y**2) def profile(self, r): """...""" if self.x == 0 and self._m == 0: - return 2*math.pi*self._k * _exp(-((r.y**2 + r.z**2) / self._W_y**2)) + return self._norm * _exp(-((r.y**2 + r.z**2) / self._W_y**2)) else: return super().profile(r) @@ -277,11 +278,12 @@ def __init__(self, x, params, called=False): super().__init__(x, params, called) self._W_y = params['W_y'] self._m = params['m'] + self._norm = 4 * math.pi / (self._W_y**2) def profile(self, r): """...""" if self.x == 0 and self._m == 0: - return 2*math.pi*self._k * _exp(-((r.y**2 + r.z**2) / self._W_y**2)) + return self._norm * _exp(-((r.y**2 + r.z**2) / self._W_y**2)) else: return super().profile(r) From 8eb3ce3d2b5b04c1aa770364a52e2b2725668e3f Mon Sep 17 00:00:00 2001 From: Daniel Kotik Date: Sat, 11 Apr 2020 19:22:21 +0200 Subject: [PATCH 109/145] Finalize import of Gauss beam from optbeam module --- Gauss_2d/Gauss2d.py | 107 +++----------------------------------------- Gauss_2d/optbeam.py | 14 +++++- 2 files changed, 20 insertions(+), 101 deletions(-) diff --git a/Gauss_2d/Gauss2d.py b/Gauss_2d/Gauss2d.py index 5d1a0f7..756050e 100644 --- a/Gauss_2d/Gauss2d.py +++ b/Gauss_2d/Gauss2d.py @@ -38,13 +38,11 @@ """ import argparse -import cmath import math import meep as mp -import sys +import optbeam as op from datetime import datetime -from scipy.integrate import quad print("Meep version:", mp.__version__) @@ -61,31 +59,6 @@ def interfaceType(string): return value -def complex_quad(func, a, b, **kwargs): - """Integrate real and imaginary part of the given function.""" - def real_func(x): - return func(x).real - - def imag_func(x): - return func(x).imag - - real, real_tol = quad(real_func, a, b, **kwargs) - imag, imag_tol = quad(imag_func, a, b, **kwargs) - - return real + 1j*imag, real_tol, imag_tol - - -def Critical(n1, n2): - """Calculate critical angle in degrees.""" - assert n1 > n2, "\nWarning: Critical angle is not defined, since n1 <= n2!" - return math.degrees(math.asin(n2/n1)) - - -def Brewster(n1, n2): - """Calculate Brewster angle in degrees.""" - return math.degrees(math.atan(n2/n1)) - - def main(args): print("\nstart time:", datetime.now()) @@ -106,8 +79,8 @@ def main(args): # angle of incidence chi_deg = args.chi_deg - #chi_deg = 1.0*Critical(n1, n2) - #chi_deg = 0.95*Brewster(n1, n2) + #chi_deg = 1.0*op.critical(n1, n2) + #chi_deg = 0.95*op.brewster(n1, n2) test_output = args.test_output @@ -198,69 +171,6 @@ def Delta_x(alpha): # set Courant factor (mandatory if either n1 or n2 is smaller than 1) Courant = (n1 if n1 < n2 else n2) / 2 - # -------------------------------------------------------------------------- - # beam profile distribution (field amplitude) at the waist of the beam - # -------------------------------------------------------------------------- - def Gauss(r, params): - """Gauss profile.""" - W_y = params['W_y'] - - return math.exp(-(r.y / W_y)**2) - - # -------------------------------------------------------------------------- - # spectrum amplitude distribution - # -------------------------------------------------------------------------- - def f_Gauss(k_y, params): - """Gaussian spectrum amplitude.""" - W_y = params['W_y'] - - return math.exp(-(k_y*W_y/2)**2) - - if test_output: - print("Gauss spectrum:", f_Gauss(0.2, params)) - - # -------------------------------------------------------------------------- - # plane wave decomposition - # (purpose: calculate field amplitude at light source position if not - # coinciding with beam waist) - # -------------------------------------------------------------------------- - def psi(r, x, params): - """Field amplitude function.""" - try: - getattr(psi, "called") - except AttributeError: - psi.called = True - print("Calculating inital field configuration. " - "This will take some time...") - - def phase(k_y, x, y): - """Phase function.""" - return x*math.sqrt(k1**2 - k_y**2) + k_y*y - - try: - (result, - real_tol, - imag_tol) = complex_quad(lambda k_y: - f_Gauss(k_y, params) * - cmath.exp(1j*phase(k_y, x, r.y)), - -k1, k1) - except Exception as e: - print(type(e).__name__ + ":", e) - sys.exit() - - return result - - # -------------------------------------------------------------------------- - # some test outputs (uncomment if needed) - # -------------------------------------------------------------------------- - if test_output: - x, y, z = -2.15, 0.3, 0.5 - r = mp.Vector3(0, y, z) - - print() - print("psi :", psi(r, x, params)) - sys.exit() - # -------------------------------------------------------------------------- # display values of physical variables # -------------------------------------------------------------------------- @@ -286,12 +196,14 @@ def phase(k_y, x, y): eps_averaging = True # default: True filename_prefix = None + # specify optical beam + beam = op.Gauss2d(x=shift, params=params) + sources = [mp.Source(src=mp.ContinuousSource(frequency=freq, width=0.5), component=mp.Ez if s_pol else mp.Ey, size=mp.Vector3(0, 2, 0), center=mp.Vector3(source_shift, 0, 0), - #amp_func=lambda r: Gauss(r, params) - amp_func=lambda r: psi(r, shift, params) + amp_func=beam.profile ) ] @@ -389,10 +301,5 @@ def output_efield2(sim): default=45, help='incidence angle in degrees (default: %(default)s)') - parser.add_argument('-test_output', - action='store_true', - default=False, - help='switch to enable test print statements') - args = parser.parse_args() main(args) diff --git a/Gauss_2d/optbeam.py b/Gauss_2d/optbeam.py index 81426a6..fdb83ba 100644 --- a/Gauss_2d/optbeam.py +++ b/Gauss_2d/optbeam.py @@ -80,6 +80,17 @@ def _complex_quad(func, a, b): return real + 1j*imag, real_tol, imag_tol +def critical(n1, n2): + """Calculate critical angle in degrees.""" + assert n1 > n2, "\nWarning: Critical angle is not defined, since n1 <= n2!" + return math.degrees(math.asin(n2/n1)) + + +def brewster(n1, n2): + """Calculate Brewster angle in degrees.""" + return math.degrees(math.atan(n2/n1)) + + class Beam2dCartesian: """...""" @@ -101,7 +112,7 @@ def params(self): def profile(self, r): """Field amplitude function. - Plane wave decomposition, to calculate field amplitude at light source + Plane wave decomposition: calculate field amplitude at light source position if not coinciding with beam waist. """ self._ry = r.y @@ -150,6 +161,7 @@ def __init__(self, x, params, called=False): def profile(self, r): """...""" + # beam profile distribution (field amplitude) at the waist of the beam if self.x == 0: return self._norm * _exp(-(r.y / self._W_y)**2) else: From 0741e4ba62a2de4ceed008cd3bae038f6a18a2fc Mon Sep 17 00:00:00 2001 From: Daniel Kotik Date: Sat, 11 Apr 2020 19:26:55 +0200 Subject: [PATCH 110/145] Improve test of correct interface argument --- Gauss_2d/Gauss2d.py | 11 ++++------- 1 file changed, 4 insertions(+), 7 deletions(-) diff --git a/Gauss_2d/Gauss2d.py b/Gauss_2d/Gauss2d.py index 756050e..0df7d89 100644 --- a/Gauss_2d/Gauss2d.py +++ b/Gauss_2d/Gauss2d.py @@ -47,16 +47,13 @@ print("Meep version:", mp.__version__) -def interfaceType(string): +def interfaceType(string_val): """Provide interface argument type.""" - value = string - if (value != "planar" and - value != "concave" and - value != "convex"): + if string_val not in ["planar", "concave", "convex"]: raise argparse.ArgumentTypeError('Value has to be either concave, ' 'convex or planar (but %s is provided)' - % value) - return value + % string_val) + return string_val def main(args): From bad0665debc10fb5449664b221675a1f784be47d Mon Sep 17 00:00:00 2001 From: Daniel Kotik Date: Sun, 12 Apr 2020 11:29:09 +0200 Subject: [PATCH 111/145] Add optbeam.p* files --- Airy_2d/optbeam.pxd | 55 ++++++++++++ Airy_2d/optbeam.py | 210 ++++++++++++++++++++++++++++++++++++++++++++ 2 files changed, 265 insertions(+) create mode 100644 Airy_2d/optbeam.pxd create mode 100644 Airy_2d/optbeam.py diff --git a/Airy_2d/optbeam.pxd b/Airy_2d/optbeam.pxd new file mode 100644 index 0000000..63ac447 --- /dev/null +++ b/Airy_2d/optbeam.pxd @@ -0,0 +1,55 @@ +# -*- coding: utf-8 -*- +""" +file: optbeam.pxd +brief: ... +author: Daniel Kotik +version: 1.5-beta +release date: xx.xx.2020 +creation date: 03.04.2020 +""" +cimport cython +from cpython.pycapsule cimport PyCapsule_New +from cpython cimport bool + +# ----------------------------------------------------------------------------- +# declare C functions as "cpdef" to export them to the module +# ----------------------------------------------------------------------------- +cdef extern from "math.h": + cpdef double _exp "exp" (double x) nogil + cpdef double _sqrt "sqrt" (double x) nogil + +cdef extern from "complex.h": + cpdef double complex _cexp "cexp" (double complex z) nogil + +# ----------------------------------------------------------------------------- +# function declarations +# ----------------------------------------------------------------------------- +cdef double _imag_1d_func_c(int n, double *arr, void *func_ptr) +cdef double _real_1d_func_c(int n, double *arr, void *func_ptr) + +@cython.locals(real=cython.double, imag=cython.double, real_tol=cython.double, + imag_tol=cython.double) +cdef (double complex, double, double) _complex_quad(func, double a, double b) + +# ----------------------------------------------------------------------------- +# class declarations +# ----------------------------------------------------------------------------- +cdef class Beam2dCartesian: + cdef: + dict __dict__ + double x, _k + public bool called + + double _ry, _rz + + cdef double spectrum(self, double k_y) nogil + cdef double _phase(self, double k_y, double x, double y) nogil + cdef double complex _integrand(self, double k_y) nogil + +cdef class Gauss2d(Beam2dCartesian): + cdef: + double _W_y + double _norm + + cdef double _f_Gauss(self, double k_y, double W_y) nogil + cdef double spectrum(self, double k_y) nogil diff --git a/Airy_2d/optbeam.py b/Airy_2d/optbeam.py new file mode 100644 index 0000000..b506efc --- /dev/null +++ b/Airy_2d/optbeam.py @@ -0,0 +1,210 @@ +# -*- coding: utf-8 -*- +""" +file: optbeam.py +brief: ... +author: Daniel Kotik +version: 1.5-beta +release date: xx.xx.2020 +creation date: 12.04.2020 +""" +import cython +import math +import sys + +from scipy.integrate import quad +from types import MappingProxyType + + +if not cython.compiled: + from math import (exp as _exp, + sqrt as _sqrt) + from cmath import exp as _cexp + print("\nPlease consider compiling `%s.py` via Cython: " + "`$ cythonize -3 -i %s.py`\n" % (__name__, __name__)) +else: + from scipy import LowLevelCallable + + +def _real_1d_func(x, func): + """Return real part of a 1d function.""" + return func(x).real + + +def _imag_1d_func(x, func): + """Return imag part of a 1d function.""" + return func(x).imag + + +def _imag_1d_func_c(n, arr, func_ptr): + """Return imag part of a 1d function. + + Cython implementation. + """ + # pure python formulation of: + # return (func_ptr)(arr[0], arr[1]).imag + return cython.cast(Beam2dCartesian, func_ptr)._integrand(arr[0]).imag + + +def _real_1d_func_c(n, arr, func_ptr): + """Return real part of a 1d function. + + Cython implementation. + """ + # pure python formulation of: + # return (func_ptr)(arr[0], arr[1]).real + return cython.cast(Beam2dCartesian, func_ptr)._integrand(arr[0]).real + + +def _complex_quad(func, a, b): + """Integrate real and imaginary part of the given function.""" + if cython.compiled: + # pure python formulation of: cdef void *f_ptr = func + f_ptr = cython.declare(cython.p_void, cython.cast(cython.p_void, func)) + + func_capsule = PyCapsule_New(f_ptr, cython.NULL, cython.NULL) + + current_module = sys.modules[__name__] + + ll_real_1d_func_c = LowLevelCallable.from_cython(current_module, + '_real_1d_func_c', + func_capsule) + ll_imag_1d_func_c = LowLevelCallable.from_cython(current_module, + '_imag_1d_func_c', + func_capsule) + real, real_tol = quad(ll_real_1d_func_c, a, b) + imag, imag_tol = quad(ll_imag_1d_func_c, a, b) + else: + real, real_tol = quad(_real_1d_func, a, b, (func,)) + imag, imag_tol = quad(_imag_1d_func, a, b, (func,)) + + return real + 1j*imag, real_tol, imag_tol + + +def critical(n1, n2): + """Calculate critical angle in degrees.""" + assert n1 > n2, "\nWarning: Critical angle is not defined, since n1 <= n2!" + return math.degrees(math.asin(n2/n1)) + + +def brewster(n1, n2): + """Calculate Brewster angle in degrees.""" + return math.degrees(math.atan(n2/n1)) + + +class Beam2dCartesian: + """...""" + + def __init__(self, x, params, called=False): + """...""" + self.x = x + self._k = params['k'] + self._params = MappingProxyType(params) # read-only view of a dict + self.called = called + + @property + def params(self): + """Beam specific parameters. + + This is a read-only property. + """ + return self._params + + def profile(self, r): + """Field amplitude function. + + Plane wave decomposition: calculate field amplitude at light source + position if not coinciding with beam waist. + """ + self._ry = r.y + self._rz = r.z + + if not self.called: + print("Calculating inital field configuration. " + "This will take some time...") + self.called = True + + try: + (result, + real_tol, + imag_tol) = _complex_quad(self if cython.compiled else self._integrand, + -self._k, self._k) + except Exception as e: + print(type(e).__name__ + ":", e) + sys.exit() + + return result + + def spectrum(self, k_y): + """Spectrum amplitude distribution function, f.""" + raise NotImplementedError + + def _phase(self, k_y, x, y): + """Phase function.""" + return x*_sqrt(self._k**2 - k_y**2) + k_y*y + + def _integrand(self, k_y): + """Integrand function.""" + return self.spectrum(k_y) * _cexp(1j*self._phase(k_y, self.x, self._ry)) + + +# ----------------------------------------------------------------------------- +# specific beam implementations based on Beam2dCartesian base class +# ----------------------------------------------------------------------------- +class IncAiry2d(Beam2dCartesian): + """2d incomplete Airy beam.""" + + pass + + +class Gauss2d(Beam2dCartesian): + """2d Gauss beam.""" + + def __init__(self, x, params, called=False): + """...""" + self._W_y = params['W_y'] + self._norm = 2 * _sqrt(math.pi) / self._W_y + super().__init__(x, params, called) + + def profile(self, r): + """...""" + # beam profile distribution (field amplitude) at the waist of the beam + if self.x == 0: + return self._norm * _exp(-(r.y / self._W_y)**2) + else: + return super().profile(r) + + def spectrum(self, k_y): + """Spectrum amplitude function, f.""" + return self._f_Gauss(k_y, self._W_y) + + def _f_Gauss(self, k_y, W_y): + """Gaussian spectrum amplitude.""" + return _exp(-(k_y*W_y/2)**2) + + +def main(): + class Vector3: + """Simple 3d vector class.""" + + def __init__(self, x, y, z): + self.x = x + self.y = y + self.z = z + + x, y, z = -2.15, 0.3, 0.5 + + r = Vector3(0, y, z) + # alternative: + # import meep; r = meep.Vector3(0, y, z) + + k1 = 116.11326447667875 + w_0 = 0.1061032953945969 + params = dict(W_y=w_0, k=k1) + + beam = Gauss2d(x=x, params=params) + + return (beam, r) + + +if __name__ == '__main__': + main() From f93c6c40cc8b92c6199359ab53f6dce58d285c05 Mon Sep 17 00:00:00 2001 From: Daniel Kotik Date: Sun, 12 Apr 2020 21:50:36 +0200 Subject: [PATCH 112/145] Update class IncAiry2d --- Airy_2d/optbeam.py | 41 ++++++++++++++++++++++++----------------- 1 file changed, 24 insertions(+), 17 deletions(-) diff --git a/Airy_2d/optbeam.py b/Airy_2d/optbeam.py index b506efc..66f1286 100644 --- a/Airy_2d/optbeam.py +++ b/Airy_2d/optbeam.py @@ -153,33 +153,38 @@ def _integrand(self, k_y): class IncAiry2d(Beam2dCartesian): """2d incomplete Airy beam.""" - pass - - -class Gauss2d(Beam2dCartesian): - """2d Gauss beam.""" - def __init__(self, x, params, called=False): """...""" self._W_y = params['W_y'] - self._norm = 2 * _sqrt(math.pi) / self._W_y + self._M = params['M'] + self._W = params['W'] + #self._norm = 2 * _sqrt(math.pi) / self._W_y super().__init__(x, params, called) def profile(self, r): """...""" # beam profile distribution (field amplitude) at the waist of the beam if self.x == 0: - return self._norm * _exp(-(r.y / self._W_y)**2) + # replace integrand function + return super().profile(r) + #return self._norm * _exp(-(r.y / self._W_y)**2) else: return super().profile(r) def spectrum(self, k_y): - """Spectrum amplitude function, f.""" - return self._f_Gauss(k_y, self._W_y) + """...""" + return self._f_Airy(k_y, self._W_y, self._M, self._W) + + def _f_Airy(self, k_y, W_y, M, W): + """Airy spectrum amplitude.""" + return W_y * _cexp(1.0j*(-1/3)*(k_y*W_y)**3) \ + * self._heaviside(W_y * k_y - (M - W)) \ + * self._heaviside((M + W) - W_y * k_y) + + def _heaviside(x): + """Theta (Heaviside step) function.""" + return 0 if x < 0 else 1 - def _f_Gauss(self, k_y, W_y): - """Gaussian spectrum amplitude.""" - return _exp(-(k_y*W_y/2)**2) def main(): @@ -197,11 +202,13 @@ def __init__(self, x, y, z): # alternative: # import meep; r = meep.Vector3(0, y, z) - k1 = 116.11326447667875 - w_0 = 0.1061032953945969 - params = dict(W_y=w_0, k=k1) + k1 = 75.39822368615503 + w_0 = 0.09284038347027228 + M = 0 + W = 4 + params = dict(W_y=w_0, k=k1, M=M, W=W) - beam = Gauss2d(x=x, params=params) + beam = IncAiry2d(x=x, params=params) return (beam, r) From cefddcae08569ea399e18f2ce82f9193442b2754 Mon Sep 17 00:00:00 2001 From: Daniel Kotik Date: Mon, 13 Apr 2020 15:30:52 +0200 Subject: [PATCH 113/145] Fix class IncAiry2d --- Airy_2d/optbeam.pxd | 13 ++++++++----- Airy_2d/optbeam.py | 2 +- 2 files changed, 9 insertions(+), 6 deletions(-) diff --git a/Airy_2d/optbeam.pxd b/Airy_2d/optbeam.pxd index 63ac447..df3affd 100644 --- a/Airy_2d/optbeam.pxd +++ b/Airy_2d/optbeam.pxd @@ -42,14 +42,17 @@ cdef class Beam2dCartesian: double _ry, _rz - cdef double spectrum(self, double k_y) nogil + cdef double complex spectrum(self, double k_y) nogil cdef double _phase(self, double k_y, double x, double y) nogil cdef double complex _integrand(self, double k_y) nogil -cdef class Gauss2d(Beam2dCartesian): +cdef class IncAiry2d(Beam2dCartesian): cdef: double _W_y - double _norm + double _M + double _W + #double _norm - cdef double _f_Gauss(self, double k_y, double W_y) nogil - cdef double spectrum(self, double k_y) nogil + cdef double _heaviside(self, double x) nogil + cdef double complex _f_Airy(self, double k_y, double W_y, double M, double W) nogil + cdef double complex spectrum(self, double k_y) nogil diff --git a/Airy_2d/optbeam.py b/Airy_2d/optbeam.py index 66f1286..5cb54af 100644 --- a/Airy_2d/optbeam.py +++ b/Airy_2d/optbeam.py @@ -181,7 +181,7 @@ def _f_Airy(self, k_y, W_y, M, W): * self._heaviside(W_y * k_y - (M - W)) \ * self._heaviside((M + W) - W_y * k_y) - def _heaviside(x): + def _heaviside(self, x): """Theta (Heaviside step) function.""" return 0 if x < 0 else 1 From 31067e4524015fd092ec46ea36c235b8e6c496f6 Mon Sep 17 00:00:00 2001 From: Daniel Kotik Date: Tue, 14 Apr 2020 12:03:15 +0200 Subject: [PATCH 114/145] Add profile distribution at x=0 --- Airy_2d/optbeam.pxd | 2 -- Airy_2d/optbeam.py | 13 ++++++++----- 2 files changed, 8 insertions(+), 7 deletions(-) diff --git a/Airy_2d/optbeam.pxd b/Airy_2d/optbeam.pxd index df3affd..cd8bf0c 100644 --- a/Airy_2d/optbeam.pxd +++ b/Airy_2d/optbeam.pxd @@ -39,7 +39,6 @@ cdef class Beam2dCartesian: dict __dict__ double x, _k public bool called - double _ry, _rz cdef double complex spectrum(self, double k_y) nogil @@ -51,7 +50,6 @@ cdef class IncAiry2d(Beam2dCartesian): double _W_y double _M double _W - #double _norm cdef double _heaviside(self, double x) nogil cdef double complex _f_Airy(self, double k_y, double W_y, double M, double W) nogil diff --git a/Airy_2d/optbeam.py b/Airy_2d/optbeam.py index 5cb54af..13fc3df 100644 --- a/Airy_2d/optbeam.py +++ b/Airy_2d/optbeam.py @@ -158,16 +158,19 @@ def __init__(self, x, params, called=False): self._W_y = params['W_y'] self._M = params['M'] self._W = params['W'] - #self._norm = 2 * _sqrt(math.pi) / self._W_y super().__init__(x, params, called) def profile(self, r): """...""" - # beam profile distribution (field amplitude) at the waist of the beam if self.x == 0: - # replace integrand function - return super().profile(r) - #return self._norm * _exp(-(r.y / self._W_y)**2) + self._ry = r.y + # beam profile distribution (field amplitude) at the waist of the beam + (result, + real_tol, + imag_tol) = _complex_quad(lambda xi: + _cexp(1.0j*(-(xi**3)/3 + (xi * self._ry/self._W_y))), + self._M-self._W, self._M+self._W) + return result else: return super().profile(r) From 0b07fbd5a4ead8bcb4aaaba2bb2467a82c7205cd Mon Sep 17 00:00:00 2001 From: Daniel Kotik Date: Tue, 14 Apr 2020 13:27:42 +0200 Subject: [PATCH 115/145] Replace integrand function for special case x=0: Additionally, for x=0 the integration boundaries need to be adjusted. This must be realized in the profile function. --- Airy_2d/optbeam.pxd | 2 ++ Airy_2d/optbeam.py | 31 ++++++++++++++++++++----------- 2 files changed, 22 insertions(+), 11 deletions(-) diff --git a/Airy_2d/optbeam.pxd b/Airy_2d/optbeam.pxd index cd8bf0c..3821539 100644 --- a/Airy_2d/optbeam.pxd +++ b/Airy_2d/optbeam.pxd @@ -40,6 +40,7 @@ cdef class Beam2dCartesian: double x, _k public bool called double _ry, _rz + double _a, _b cdef double complex spectrum(self, double k_y) nogil cdef double _phase(self, double k_y, double x, double y) nogil @@ -50,6 +51,7 @@ cdef class IncAiry2d(Beam2dCartesian): double _W_y double _M double _W + double xi cdef double _heaviside(self, double x) nogil cdef double complex _f_Airy(self, double k_y, double W_y, double M, double W) nogil diff --git a/Airy_2d/optbeam.py b/Airy_2d/optbeam.py index 13fc3df..86ab38c 100644 --- a/Airy_2d/optbeam.py +++ b/Airy_2d/optbeam.py @@ -101,6 +101,10 @@ def __init__(self, x, params, called=False): self._params = MappingProxyType(params) # read-only view of a dict self.called = called + # integration boundaries + self._a = -self._k + self._b = self._k + @property def params(self): """Beam specific parameters. @@ -127,7 +131,7 @@ def profile(self, r): (result, real_tol, imag_tol) = _complex_quad(self if cython.compiled else self._integrand, - -self._k, self._k) + self._a, self._b) except Exception as e: print(type(e).__name__ + ":", e) sys.exit() @@ -163,16 +167,11 @@ def __init__(self, x, params, called=False): def profile(self, r): """...""" if self.x == 0: - self._ry = r.y - # beam profile distribution (field amplitude) at the waist of the beam - (result, - real_tol, - imag_tol) = _complex_quad(lambda xi: - _cexp(1.0j*(-(xi**3)/3 + (xi * self._ry/self._W_y))), - self._M-self._W, self._M+self._W) - return result - else: - return super().profile(r) + # adjust integration boundaries + self._a = self._M-self._W + self._b = self._M+self._W + + return super().profile(r) def spectrum(self, k_y): """...""" @@ -188,6 +187,16 @@ def _heaviside(self, x): """Theta (Heaviside step) function.""" return 0 if x < 0 else 1 + def _integrand(self, k_y): + """...""" + if self.x == 0: + xi = k_y + return _cexp(1.0j*(-(xi**3)/3 + (xi * self._ry/self._W_y))) + else: + # FIXME: return super()._integrand(k_y) results in: + # RuntimeError: super(): __class__ cell not found + return self.spectrum(k_y) * _cexp(1j*self._phase(k_y, self.x, self._ry)) + def main(): From 1f240c7c0d5037223186c7bf80d03af523c51def Mon Sep 17 00:00:00 2001 From: Daniel Kotik Date: Tue, 14 Apr 2020 15:45:21 +0200 Subject: [PATCH 116/145] Add comment regarding content of previous commit --- Airy_2d/optbeam.py | 8 +++++--- 1 file changed, 5 insertions(+), 3 deletions(-) diff --git a/Airy_2d/optbeam.py b/Airy_2d/optbeam.py index 86ab38c..ba5951e 100644 --- a/Airy_2d/optbeam.py +++ b/Airy_2d/optbeam.py @@ -193,8 +193,10 @@ def _integrand(self, k_y): xi = k_y return _cexp(1.0j*(-(xi**3)/3 + (xi * self._ry/self._W_y))) else: - # FIXME: return super()._integrand(k_y) results in: - # RuntimeError: super(): __class__ cell not found + # next line needs _integrand declared cpdef without nogil attribute, + # and will execute slower than repeating the super class integration + # routine function here + #return super(IncAiry2d, self)._integrand(k_y) return self.spectrum(k_y) * _cexp(1j*self._phase(k_y, self.x, self._ry)) @@ -220,7 +222,7 @@ def __init__(self, x, y, z): W = 4 params = dict(W_y=w_0, k=k1, M=M, W=W) - beam = IncAiry2d(x=x, params=params) + beam = IncAiry2d(x=0, params=params) return (beam, r) From c022f8abc9572ba37cd87dd96afbd4cfe268fa99 Mon Sep 17 00:00:00 2001 From: Daniel Kotik Date: Tue, 14 Apr 2020 15:50:45 +0200 Subject: [PATCH 117/145] Remove unused import --- Airy_2d/optbeam.py | 3 +-- 1 file changed, 1 insertion(+), 2 deletions(-) diff --git a/Airy_2d/optbeam.py b/Airy_2d/optbeam.py index ba5951e..a2d2853 100644 --- a/Airy_2d/optbeam.py +++ b/Airy_2d/optbeam.py @@ -16,8 +16,7 @@ if not cython.compiled: - from math import (exp as _exp, - sqrt as _sqrt) + from math import sqrt as _sqrt from cmath import exp as _cexp print("\nPlease consider compiling `%s.py` via Cython: " "`$ cythonize -3 -i %s.py`\n" % (__name__, __name__)) From 1eefc275634b83cb46b3dc3444c73e191105b737 Mon Sep 17 00:00:00 2001 From: Daniel Kotik Date: Tue, 14 Apr 2020 16:41:47 +0200 Subject: [PATCH 118/145] Clean up Airy2d.py --- Airy_2d/Airy2d.py | 140 +++------------------------------------------- 1 file changed, 8 insertions(+), 132 deletions(-) diff --git a/Airy_2d/Airy2d.py b/Airy_2d/Airy2d.py index da232eb..a5985a9 100644 --- a/Airy_2d/Airy2d.py +++ b/Airy_2d/Airy2d.py @@ -41,44 +41,16 @@ """ import argparse -import cmath import math import meep as mp -import sys +import optbeam as op from datetime import datetime -from scipy.integrate import quad print("Meep version:", mp.__version__) -def complex_quad(func, a, b, **kwargs): - """Integrate real and imaginary part of the given function.""" - def real_func(x): - return func(x).real - - def imag_func(x): - return func(x).imag - - real, real_tol = quad(real_func, a, b, **kwargs) - imag, imag_tol = quad(imag_func, a, b, **kwargs) - - return real + 1j*imag, real_tol, imag_tol - - -def Critical(n1, n2): - """Calculate critical angle in degrees.""" - assert n1 > n2, "\nWarning: Critical angle is not defined, since n1 <= n2!" - return math.degrees(math.asin(n2/n1)) - - -def Brewster(n1, n2): - """Calculate Brewster angle in degrees.""" - return math.degrees(math.atan(n2/n1)) - - def main(args): - """Main function.""" print("\nstart time:", datetime.now()) # -------------------------------------------------------------------------- @@ -100,10 +72,8 @@ def main(args): # angle of incidence chi_deg = args.chi_deg - #chi_deg = 1.0*Critical(n1, n2) - #chi_deg = 0.95*Brewster(n1, n2) - - test_output = args.test_output + #chi_deg = 1.0*op.critical(n1, n2) + #chi_deg = 0.95*op.brewster(n1, n2) # -------------------------------------------------------------------------- # specific Meep parameters (may need to be adjusted) @@ -171,95 +141,6 @@ def Delta_x(alpha): # set Courant factor (mandatory if either n1 or n2 is smaller than 1) Courant = (n1 if n1 < n2 else n2) / 2 - # -------------------------------------------------------------------------- - # beam profile distribution (field amplitude) at the waist of the beam - # -------------------------------------------------------------------------- - def Gauss(r, params): - """Gauss profile.""" - W_y = params['W_y'] - - return math.exp(-(r.y / W_y)**2) - - def Ai_inc(r, params): - """Incomplete Airy function.""" - W_y, M, W = params['W_y'], params['M'], params['W'] - - (result, - real_tol, - imag_tol) = complex_quad(lambda xi: - cmath.exp(1.0j*(-(xi**3)/3 + (xi * r.y/W_y))), - M-W, M+W) - return result - - if test_output: - print("w_0:", params['W_y']) - print("Airy function 1:", Ai_inc(mp.Vector3(1, -0.3, 1), params)) - - # -------------------------------------------------------------------------- - # spectrum amplitude distribution - # -------------------------------------------------------------------------- - def Heaviside(x): - """Theta (Heaviside step) function.""" - return 0 if x < 0 else 1 - - def f_Gauss(k_y, params): - """Gaussian spectrum amplitude.""" - W_y = params['W_y'] - - return math.exp(-(k_y*W_y/2)**2) - - def f_Airy(k_y, params): - """Airy spectrum amplitude.""" - W_y, M, W = params['W_y'], params['M'], params['W'] - - return W_y*cmath.exp(1.0j*(-1/3)*(k_y*W_y)**3) \ - * Heaviside(W_y*k_y - (M-W)) * Heaviside((M+W) - (W_y*k_y)) - - if test_output: - print("Airy spectrum:", f_Airy(0.2, params)) - - # -------------------------------------------------------------------------- - # plane wave decomposition - # (purpose: calculate field amplitude at light source position if not - # coinciding with beam waist) - # -------------------------------------------------------------------------- - def psi(r, f, x, params): - """Field amplitude function.""" - try: - getattr(psi, "called") - except AttributeError: - psi.called = True - print("Calculating inital field configuration. " - "This will take some time...") - - def phase(k_y, x, y): - """Phase function.""" - return x*math.sqrt(k1**2 - k_y**2) + k_y*y - - try: - (result, - real_tol, - imag_tol) = complex_quad(lambda k_y: - f(k_y, params) * - cmath.exp(1j*phase(k_y, x, r.y)), - -k1, k1, limit=100) - except Exception as e: - print(type(e).__name__ + ":", e) - sys.exit() - - return result - - # -------------------------------------------------------------------------- - # some test outputs (uncomment if needed) - # -------------------------------------------------------------------------- - if test_output: - x, y, z = -2.15, 0.3, 0.5 - r = mp.Vector3(0, y, z) - - print() - print("psi :", psi(r, f_Airy, x, params)) - sys.exit() - # -------------------------------------------------------------------------- # display values of physical variables # -------------------------------------------------------------------------- @@ -282,15 +163,15 @@ def phase(k_y, x, y): eps_averaging = True # default: True filename_prefix = None + # specify optical beam + beam = op.IncAiry2d(x=shift, params=params) + sources = [mp.Source(src=mp.ContinuousSource(frequency=freq, width=0.5), component=mp.Ez if s_pol else mp.Ey, size=mp.Vector3(0, 9, 0), center=mp.Vector3(source_shift, 0, 0), - #amp_func=lambda r: Gauss(r, params) - #amp_func=lambda r: Ai_inc(r, params) - #amp_func=lambda r: psi(r, f_Gauss, shift, params) - amp_func=lambda r: psi(r, f_Airy, shift, params) - ) + amp_func=beam.profile + ) ] sim = mp.Simulation(cell_size=cell, @@ -385,10 +266,5 @@ def output_efield2(sim): default=45, help='incidence angle in degrees (default: %(default)s)') - parser.add_argument('-test_output', - action='store_true', - default=False, - help='switch to enable test print statements') - args = parser.parse_args() main(args) From d526842e42fb102e678a45ca3e11b219e3529131 Mon Sep 17 00:00:00 2001 From: Daniel Kotik Date: Thu, 16 Apr 2020 17:07:15 +0200 Subject: [PATCH 119/145] Add kwargs parameter to _complex_quad --- Airy_2d/optbeam.pxd | 2 +- Airy_2d/optbeam.py | 14 +++++++------- Gauss_2d/optbeam.pxd | 2 +- Gauss_2d/optbeam.py | 10 +++++----- Laguerre_Gauss_3d/optbeam.pxd | 3 ++- Laguerre_Gauss_3d/optbeam.py | 10 +++++----- 6 files changed, 21 insertions(+), 20 deletions(-) diff --git a/Airy_2d/optbeam.pxd b/Airy_2d/optbeam.pxd index 3821539..95570f9 100644 --- a/Airy_2d/optbeam.pxd +++ b/Airy_2d/optbeam.pxd @@ -29,7 +29,7 @@ cdef double _real_1d_func_c(int n, double *arr, void *func_ptr) @cython.locals(real=cython.double, imag=cython.double, real_tol=cython.double, imag_tol=cython.double) -cdef (double complex, double, double) _complex_quad(func, double a, double b) +cdef (double complex, double, double) _complex_quad(func, double a, double b, dict kwargs=*) # ----------------------------------------------------------------------------- # class declarations diff --git a/Airy_2d/optbeam.py b/Airy_2d/optbeam.py index a2d2853..55fed01 100644 --- a/Airy_2d/optbeam.py +++ b/Airy_2d/optbeam.py @@ -54,7 +54,7 @@ def _real_1d_func_c(n, arr, func_ptr): return cython.cast(Beam2dCartesian, func_ptr)._integrand(arr[0]).real -def _complex_quad(func, a, b): +def _complex_quad(func, a, b, kwargs={}): """Integrate real and imaginary part of the given function.""" if cython.compiled: # pure python formulation of: cdef void *f_ptr = func @@ -70,11 +70,11 @@ def _complex_quad(func, a, b): ll_imag_1d_func_c = LowLevelCallable.from_cython(current_module, '_imag_1d_func_c', func_capsule) - real, real_tol = quad(ll_real_1d_func_c, a, b) - imag, imag_tol = quad(ll_imag_1d_func_c, a, b) + real, real_tol = quad(ll_real_1d_func_c, a, b, **kwargs) + imag, imag_tol = quad(ll_imag_1d_func_c, a, b, **kwargs) else: - real, real_tol = quad(_real_1d_func, a, b, (func,)) - imag, imag_tol = quad(_imag_1d_func, a, b, (func,)) + real, real_tol = quad(_real_1d_func, a, b, (func,), **kwargs) + imag, imag_tol = quad(_imag_1d_func, a, b, (func,), **kwargs) return real + 1j*imag, real_tol, imag_tol @@ -130,7 +130,7 @@ def profile(self, r): (result, real_tol, imag_tol) = _complex_quad(self if cython.compiled else self._integrand, - self._a, self._b) + self._a, self._b, dict(limit=100)) except Exception as e: print(type(e).__name__ + ":", e) sys.exit() @@ -221,7 +221,7 @@ def __init__(self, x, y, z): W = 4 params = dict(W_y=w_0, k=k1, M=M, W=W) - beam = IncAiry2d(x=0, params=params) + beam = IncAiry2d(x=x, params=params) return (beam, r) diff --git a/Gauss_2d/optbeam.pxd b/Gauss_2d/optbeam.pxd index 63ac447..0a0bcef 100644 --- a/Gauss_2d/optbeam.pxd +++ b/Gauss_2d/optbeam.pxd @@ -29,7 +29,7 @@ cdef double _real_1d_func_c(int n, double *arr, void *func_ptr) @cython.locals(real=cython.double, imag=cython.double, real_tol=cython.double, imag_tol=cython.double) -cdef (double complex, double, double) _complex_quad(func, double a, double b) +cdef (double complex, double, double) _complex_quad(func, double a, double b, dict kwargs=*) # ----------------------------------------------------------------------------- # class declarations diff --git a/Gauss_2d/optbeam.py b/Gauss_2d/optbeam.py index fdb83ba..c3a0baa 100644 --- a/Gauss_2d/optbeam.py +++ b/Gauss_2d/optbeam.py @@ -55,7 +55,7 @@ def _real_1d_func_c(n, arr, func_ptr): return cython.cast(Beam2dCartesian, func_ptr)._integrand(arr[0]).real -def _complex_quad(func, a, b): +def _complex_quad(func, a, b, kwargs={}): """Integrate real and imaginary part of the given function.""" if cython.compiled: # pure python formulation of: cdef void *f_ptr = func @@ -71,11 +71,11 @@ def _complex_quad(func, a, b): ll_imag_1d_func_c = LowLevelCallable.from_cython(current_module, '_imag_1d_func_c', func_capsule) - real, real_tol = quad(ll_real_1d_func_c, a, b) - imag, imag_tol = quad(ll_imag_1d_func_c, a, b) + real, real_tol = quad(ll_real_1d_func_c, a, b, **kwargs) + imag, imag_tol = quad(ll_imag_1d_func_c, a, b, **kwargs) else: - real, real_tol = quad(_real_1d_func, a, b, (func,)) - imag, imag_tol = quad(_imag_1d_func, a, b, (func,)) + real, real_tol = quad(_real_1d_func, a, b, (func,), **kwargs) + imag, imag_tol = quad(_imag_1d_func, a, b, (func,), **kwargs) return real + 1j*imag, real_tol, imag_tol diff --git a/Laguerre_Gauss_3d/optbeam.pxd b/Laguerre_Gauss_3d/optbeam.pxd index e739b85..2d3aa1c 100644 --- a/Laguerre_Gauss_3d/optbeam.pxd +++ b/Laguerre_Gauss_3d/optbeam.pxd @@ -38,7 +38,8 @@ cdef double _real_2d_func_c(int n, double *arr, void *func_ptr) imag_tol=cython.double) cdef (double complex, double, double) _complex_dblquad(Beam3d func, double a, double b, - double gfun, double hfun) + double gfun, double hfun, + dict kwargs=*) # ----------------------------------------------------------------------------- # class declarations diff --git a/Laguerre_Gauss_3d/optbeam.py b/Laguerre_Gauss_3d/optbeam.py index 97b4049..9756e7c 100644 --- a/Laguerre_Gauss_3d/optbeam.py +++ b/Laguerre_Gauss_3d/optbeam.py @@ -60,7 +60,7 @@ def _real_2d_func_c(n, arr, func_ptr): return cython.cast(Beam3d, func_ptr)._integrand(arr[0], arr[1]).real -def _complex_dblquad(func, a, b, gfun, hfun): +def _complex_dblquad(func, a, b, gfun, hfun, kwargs={}): """Integrate real and imaginary part of the given function.""" if cython.compiled: # pure python formulation of: cdef void *f_ptr = func @@ -76,11 +76,11 @@ def _complex_dblquad(func, a, b, gfun, hfun): ll_imag_2d_func_c = LowLevelCallable.from_cython(current_module, '_imag_2d_func_c', func_capsule) - real, real_tol = dblquad(ll_real_2d_func_c, a, b, gfun, hfun) - imag, imag_tol = dblquad(ll_imag_2d_func_c, a, b, gfun, hfun) + real, real_tol = dblquad(ll_real_2d_func_c, a, b, gfun, hfun, **kwargs) + imag, imag_tol = dblquad(ll_imag_2d_func_c, a, b, gfun, hfun, **kwargs) else: - real, real_tol = dblquad(_real_2d_func, a, b, gfun, hfun, (func,)) - imag, imag_tol = dblquad(_imag_2d_func, a, b, gfun, hfun, (func,)) + real, real_tol = dblquad(_real_2d_func, a, b, gfun, hfun, (func,), **kwargs) + imag, imag_tol = dblquad(_imag_2d_func, a, b, gfun, hfun, (func,), **kwargs) return real + 1j*imag, real_tol, imag_tol From b05bada1c420675840a43314f860d357a05a5320 Mon Sep 17 00:00:00 2001 From: Daniel Kotik Date: Thu, 16 Apr 2020 17:10:26 +0200 Subject: [PATCH 120/145] Remove obsolete test_output variable --- Gauss_2d/Gauss2d.py | 2 -- 1 file changed, 2 deletions(-) diff --git a/Gauss_2d/Gauss2d.py b/Gauss_2d/Gauss2d.py index 0df7d89..3ce82bb 100644 --- a/Gauss_2d/Gauss2d.py +++ b/Gauss_2d/Gauss2d.py @@ -79,8 +79,6 @@ def main(args): #chi_deg = 1.0*op.critical(n1, n2) #chi_deg = 0.95*op.brewster(n1, n2) - test_output = args.test_output - # -------------------------------------------------------------------------- # specific Meep parameters (may need to be adjusted) # -------------------------------------------------------------------------- From f58c97ccaafaf1982cfd135a5c66686395f8f597 Mon Sep 17 00:00:00 2001 From: Daniel Kotik Date: Mon, 2 Aug 2021 21:27:10 +0200 Subject: [PATCH 121/145] Fix comment --- Airy_2d/optbeam.py | 5 ++--- Gauss_2d/optbeam.py | 4 ++-- 2 files changed, 4 insertions(+), 5 deletions(-) diff --git a/Airy_2d/optbeam.py b/Airy_2d/optbeam.py index 55fed01..72aeca0 100644 --- a/Airy_2d/optbeam.py +++ b/Airy_2d/optbeam.py @@ -40,7 +40,7 @@ def _imag_1d_func_c(n, arr, func_ptr): Cython implementation. """ # pure python formulation of: - # return (func_ptr)(arr[0], arr[1]).imag + # return (func_ptr)(arr[0]).imag return cython.cast(Beam2dCartesian, func_ptr)._integrand(arr[0]).imag @@ -50,7 +50,7 @@ def _real_1d_func_c(n, arr, func_ptr): Cython implementation. """ # pure python formulation of: - # return (func_ptr)(arr[0], arr[1]).real + # return (func_ptr)(arr[0]).real return cython.cast(Beam2dCartesian, func_ptr)._integrand(arr[0]).real @@ -199,7 +199,6 @@ def _integrand(self, k_y): return self.spectrum(k_y) * _cexp(1j*self._phase(k_y, self.x, self._ry)) - def main(): class Vector3: """Simple 3d vector class.""" diff --git a/Gauss_2d/optbeam.py b/Gauss_2d/optbeam.py index c3a0baa..2bcf4f2 100644 --- a/Gauss_2d/optbeam.py +++ b/Gauss_2d/optbeam.py @@ -41,7 +41,7 @@ def _imag_1d_func_c(n, arr, func_ptr): Cython implementation. """ # pure python formulation of: - # return (func_ptr)(arr[0], arr[1]).imag + # return (func_ptr)(arr[0]).imag return cython.cast(Beam2dCartesian, func_ptr)._integrand(arr[0]).imag @@ -51,7 +51,7 @@ def _real_1d_func_c(n, arr, func_ptr): Cython implementation. """ # pure python formulation of: - # return (func_ptr)(arr[0], arr[1]).real + # return (func_ptr)(arr[0]).real return cython.cast(Beam2dCartesian, func_ptr)._integrand(arr[0]).real From a162bf7a8a9ccb60b7142c8cfd8916213057f2a9 Mon Sep 17 00:00:00 2001 From: Daniel Kotik Date: Wed, 4 Aug 2021 15:55:15 +0200 Subject: [PATCH 122/145] Establish package structure --- optbeam/2d/__init__.py | 0 optbeam/3d/__init__.py | 0 optbeam/__init__.py | 0 3 files changed, 0 insertions(+), 0 deletions(-) create mode 100644 optbeam/2d/__init__.py create mode 100644 optbeam/3d/__init__.py create mode 100644 optbeam/__init__.py diff --git a/optbeam/2d/__init__.py b/optbeam/2d/__init__.py new file mode 100644 index 0000000..e69de29 diff --git a/optbeam/3d/__init__.py b/optbeam/3d/__init__.py new file mode 100644 index 0000000..e69de29 diff --git a/optbeam/__init__.py b/optbeam/__init__.py new file mode 100644 index 0000000..e69de29 From 5b763335fe28e177ccedc7701e6d45151eaa41de Mon Sep 17 00:00:00 2001 From: Daniel Kotik Date: Wed, 4 Aug 2021 16:38:52 +0200 Subject: [PATCH 123/145] Move `critical` and `brewster` functions top level --- optbeam/__init__.py | 12 ++++++++++++ 1 file changed, 12 insertions(+) diff --git a/optbeam/__init__.py b/optbeam/__init__.py index e69de29..7dbee0b 100644 --- a/optbeam/__init__.py +++ b/optbeam/__init__.py @@ -0,0 +1,12 @@ +import math + + +def critical(n1, n2): + """Calculate critical angle in degrees.""" + assert n1 > n2, "\nWarning: Critical angle is not defined, since n1 <= n2!" + return math.degrees(math.asin(n2/n1)) + + +def brewster(n1, n2): + """Calculate Brewster angle in degrees.""" + return math.degrees(math.atan(n2/n1)) From 3fbd04d03a4dd07d1f0edc7e125b2804dc6d5fe0 Mon Sep 17 00:00:00 2001 From: Daniel Kotik Date: Wed, 4 Aug 2021 16:41:08 +0200 Subject: [PATCH 124/145] Add helper modules containing private functions used internally --- optbeam/2d/_helpers.py | 0 optbeam/3d/_helpers.py | 0 2 files changed, 0 insertions(+), 0 deletions(-) create mode 100644 optbeam/2d/_helpers.py create mode 100644 optbeam/3d/_helpers.py diff --git a/optbeam/2d/_helpers.py b/optbeam/2d/_helpers.py new file mode 100644 index 0000000..e69de29 diff --git a/optbeam/3d/_helpers.py b/optbeam/3d/_helpers.py new file mode 100644 index 0000000..e69de29 From 8d3998092ac6b2ea8baf31b5a0a6643d5019cbca Mon Sep 17 00:00:00 2001 From: Daniel Kotik Date: Wed, 4 Aug 2021 16:46:43 +0200 Subject: [PATCH 125/145] Add `beams.py` holding beam class definitions --- optbeam/2d/beams.py | 0 optbeam/3d/beams.py | 0 2 files changed, 0 insertions(+), 0 deletions(-) create mode 100644 optbeam/2d/beams.py create mode 100644 optbeam/3d/beams.py diff --git a/optbeam/2d/beams.py b/optbeam/2d/beams.py new file mode 100644 index 0000000..e69de29 diff --git a/optbeam/3d/beams.py b/optbeam/3d/beams.py new file mode 100644 index 0000000..e69de29 From 6db65d076a3ef978ca722d0ccb1f6999788338f5 Mon Sep 17 00:00:00 2001 From: Daniel Kotik Date: Fri, 6 Aug 2021 13:26:40 +0200 Subject: [PATCH 126/145] Add helper functions to `_helpers:py` --- optbeam/2d/_helpers.py | 53 ++++++++++++++++++++++++++++++++++++++++ optbeam/3d/_helpers.py | 55 ++++++++++++++++++++++++++++++++++++++++++ 2 files changed, 108 insertions(+) diff --git a/optbeam/2d/_helpers.py b/optbeam/2d/_helpers.py index e69de29..990ba50 100644 --- a/optbeam/2d/_helpers.py +++ b/optbeam/2d/_helpers.py @@ -0,0 +1,53 @@ +def _real_1d_func(x, func): + """Return real part of a 1d function.""" + return func(x).real + + +def _imag_1d_func(x, func): + """Return imag part of a 1d function.""" + return func(x).imag + + +def _imag_1d_func_c(n, arr, func_ptr): + """Return imag part of a 1d function. + + Cython implementation. + """ + # pure python formulation of: + # return (func_ptr)(arr[0]).imag + return cython.cast(Beam2dCartesian, func_ptr)._integrand(arr[0]).imag + + +def _real_1d_func_c(n, arr, func_ptr): + """Return real part of a 1d function. + + Cython implementation. + """ + # pure python formulation of: + # return (func_ptr)(arr[0]).real + return cython.cast(Beam2dCartesian, func_ptr)._integrand(arr[0]).real + + +def _complex_quad(func, a, b, kwargs={}): + """Integrate real and imaginary part of the given function.""" + if cython.compiled: + # pure python formulation of: cdef void *f_ptr = func + f_ptr = cython.declare(cython.p_void, cython.cast(cython.p_void, func)) + + func_capsule = PyCapsule_New(f_ptr, cython.NULL, cython.NULL) + + current_module = sys.modules[__name__] + + ll_real_1d_func_c = LowLevelCallable.from_cython(current_module, + '_real_1d_func_c', + func_capsule) + ll_imag_1d_func_c = LowLevelCallable.from_cython(current_module, + '_imag_1d_func_c', + func_capsule) + real, real_tol = quad(ll_real_1d_func_c, a, b, **kwargs) + imag, imag_tol = quad(ll_imag_1d_func_c, a, b, **kwargs) + else: + real, real_tol = quad(_real_1d_func, a, b, (func,), **kwargs) + imag, imag_tol = quad(_imag_1d_func, a, b, (func,), **kwargs) + + return real + 1j*imag, real_tol, imag_tol diff --git a/optbeam/3d/_helpers.py b/optbeam/3d/_helpers.py index e69de29..c00e00a 100644 --- a/optbeam/3d/_helpers.py +++ b/optbeam/3d/_helpers.py @@ -0,0 +1,55 @@ +def _real_2d_func(x, y, func): + """Return real part of a 2d function.""" + return func(x, y).real + + +def _imag_2d_func(x, y, func): + """Return imag part of a 2d function.""" + return func(x, y).imag + + +def _imag_2d_func_c(n, arr, func_ptr): + """Return imag part of a 2d function. + + Cython implementation. + """ + # pure python formulation of: + # return (func_ptr)(arr[0], arr[1]).imag + return cython.cast(Beam3d, func_ptr)._integrand(arr[0], arr[1]).imag + + +def _real_2d_func_c(n, arr, func_ptr): + """Return real part of a 2d function. + + Cython implementation. + """ + # pure python formulation of: + # return (func_ptr)(arr[0], arr[1]).real + return cython.cast(Beam3d, func_ptr)._integrand(arr[0], arr[1]).real + + +def _complex_dblquad(func, a, b, gfun, hfun, kwargs={}): + """Integrate real and imaginary part of the given function.""" + if cython.compiled: + # pure python formulation of: cdef void *f_ptr = func + f_ptr = cython.declare(cython.p_void, cython.cast(cython.p_void, func)) + + func_capsule = PyCapsule_New(f_ptr, cython.NULL, cython.NULL) + + current_module = sys.modules[__name__] + + ll_real_2d_func_c = LowLevelCallable.from_cython(current_module, + '_real_2d_func_c', + func_capsule) + ll_imag_2d_func_c = LowLevelCallable.from_cython(current_module, + '_imag_2d_func_c', + func_capsule) + real, real_tol = dblquad(ll_real_2d_func_c, a, b, gfun, hfun, **kwargs) + imag, imag_tol = dblquad(ll_imag_2d_func_c, a, b, gfun, hfun, **kwargs) + else: + real, real_tol = dblquad( + _real_2d_func, a, b, gfun, hfun, (func,), **kwargs) + imag, imag_tol = dblquad( + _imag_2d_func, a, b, gfun, hfun, (func,), **kwargs) + + return real + 1j*imag, real_tol, imag_tol From 8900d69d3625f2f7d520e05014e9a12b2514f2fa Mon Sep 17 00:00:00 2001 From: Daniel Kotik Date: Fri, 6 Aug 2021 13:34:08 +0200 Subject: [PATCH 127/145] Add beam classes to `beams.py` --- optbeam/2d/beams.py | 132 +++++++++++++++++++++++++++ optbeam/3d/beams.py | 215 ++++++++++++++++++++++++++++++++++++++++++++ 2 files changed, 347 insertions(+) diff --git a/optbeam/2d/beams.py b/optbeam/2d/beams.py index e69de29..d861b57 100644 --- a/optbeam/2d/beams.py +++ b/optbeam/2d/beams.py @@ -0,0 +1,132 @@ +from ._helpers import _complex_quad + + +class Beam2dCartesian: + """...""" + + def __init__(self, x, params, called=False): + """...""" + self.x = x + self._k = params['k'] + self._params = MappingProxyType(params) # read-only view of a dict + self.called = called + + @property + def params(self): + """Beam specific parameters. + + This is a read-only property. + """ + return self._params + + def profile(self, r): + """Field amplitude function. + + Plane wave decomposition: calculate field amplitude at light source + position if not coinciding with beam waist. + """ + self._ry = r.y + self._rz = r.z + + if not self.called: + print("Calculating inital field configuration. " + "This will take some time...") + self.called = True + + try: + (result, + real_tol, + imag_tol) = _complex_quad(self if cython.compiled else self._integrand, + -self._k, self._k) + except Exception as e: + print(type(e).__name__ + ":", e) + sys.exit() + + return result + + def spectrum(self, k_y): + """Spectrum amplitude distribution function, f.""" + raise NotImplementedError + + def _phase(self, k_y, x, y): + """Phase function.""" + return x*_sqrt(self._k**2 - k_y**2) + k_y*y + + def _integrand(self, k_y): + """Integrand function.""" + return self.spectrum(k_y) * _cexp(1j*self._phase(k_y, self.x, self._ry)) + + +# ----------------------------------------------------------------------------- +# specific beam implementations based on Beam2dCartesian base class +# ----------------------------------------------------------------------------- +class Gauss2d(Beam2dCartesian): + """2d Gauss beam.""" + + def __init__(self, x, params, called=False): + """...""" + self._W_y = params['W_y'] + self._norm = 2 * _sqrt(math.pi) / self._W_y + super().__init__(x, params, called) + + def profile(self, r): + """...""" + # beam profile distribution (field amplitude) at the waist of the beam + if self.x == 0: + return self._norm * _exp(-(r.y / self._W_y)**2) + else: + return super().profile(r) + + def spectrum(self, k_y): + """Spectrum amplitude function, f.""" + return self._f_Gauss(k_y, self._W_y) + + def _f_Gauss(self, k_y, W_y): + """Gaussian spectrum amplitude.""" + return _exp(-(k_y*W_y/2)**2) + + +class IncAiry2d(Beam2dCartesian): + """2d incomplete Airy beam.""" + + def __init__(self, x, params, called=False): + """...""" + self._W_y = params['W_y'] + self._M = params['M'] + self._W = params['W'] + super().__init__(x, params, called) + + def profile(self, r): + """...""" + if self.x == 0: + # adjust integration boundaries + self._a = self._M-self._W + self._b = self._M+self._W + + return super().profile(r) + + def spectrum(self, k_y): + """...""" + return self._f_Airy(k_y, self._W_y, self._M, self._W) + + def _f_Airy(self, k_y, W_y, M, W): + """Airy spectrum amplitude.""" + return W_y * _cexp(1.0j*(-1/3)*(k_y*W_y)**3) \ + * self._heaviside(W_y * k_y - (M - W)) \ + * self._heaviside((M + W) - W_y * k_y) + + def _heaviside(self, x): + """Theta (Heaviside step) function.""" + return 0 if x < 0 else 1 + + def _integrand(self, k_y): + """...""" + if self.x == 0: + xi = k_y + return _cexp(1.0j*(-(xi**3)/3 + (xi * self._ry/self._W_y))) + else: + # next line needs _integrand declared cpdef without nogil attribute, + # and will execute slower than repeating the super class integration + # routine function here + #return super(IncAiry2d, self)._integrand(k_y) + return self.spectrum(k_y) * _cexp(1j*self._phase(k_y, self.x, self._ry)) diff --git a/optbeam/3d/beams.py b/optbeam/3d/beams.py index e69de29..438b5c6 100644 --- a/optbeam/3d/beams.py +++ b/optbeam/3d/beams.py @@ -0,0 +1,215 @@ +from ._helpers import _complex_dblquad + +class Beam3d: + """Abstract base class.""" + + def __init__(self, x, params, called=False): + """...""" + self.x = x # TODO: rename x to x_shift + self._k = params['k'] + self._params = MappingProxyType(params) # read-only view of a dict + self.called = called + + @property + def params(self): + """Beam specific parameters. + + This is a read-only property. + """ + return self._params + + def _integrand(self, x, y): + """Integrand function over two coordinates x and y.""" + raise NotImplementedError + + +class Beam3dSpherical(Beam3d): + """Reference implementaion of a 3d beam in spherical coordinates.""" + + def profile(self, r): + """Beam profile function, psi.""" + self._ry = r.y + self._rz = r.z + + if not self.called: + print("Calculating inital field configuration. " + "This will take some time...") + self.called = True + + try: + (result, + real_tol, + imag_tol) = _complex_dblquad(self if cython.compiled else self._integrand, + 0, 2*math.pi, 0, math.pi/2) + except Exception as e: + print(type(e).__name__ + ":", e) + sys.exit() + + return self._k**2 * result + + def spectrum(self, sin_theta, theta, phi): + """Spectrum amplitude function, f.""" + raise NotImplementedError + + def _phase(self, sin_theta, cos_theta, phi, x, y, z): + """Phase function.""" + sin_phi = _sin(phi) + cos_phi = _cos(phi) + + return self._k*(sin_theta*(y*sin_phi - z*cos_phi) + cos_theta*x) + + def _integrand(self, theta, phi): + """Integrand function.""" + sin_theta = _sin(theta) + cos_theta = _cos(theta) + + return sin_theta * cos_theta * self.spectrum(sin_theta, theta, phi) * \ + _cexp(1j*self._phase(sin_theta, cos_theta, phi, self.x, self._ry, self._rz)) + + +class Beam3dCartesian(Beam3d): + """Reference implementaion of a 3d beam in Cartesian coordinates.""" + + def profile(self, r): + """Beam profile function, psi.""" + self._ry = r.y + self._rz = r.z + + if not self.called: + print("Calculating inital field configuration. " + "This will take some time...") + self.called = True + + try: + (result, + real_tol, + imag_tol) = _complex_dblquad(self if cython.compiled else self._integrand, + -self._k, self._k, -self._k, self._k) + except Exception as e: + print(type(e).__name__ + ":", e) + sys.exit() + + return result + + def spectrum(self, k_y, k_z): + """Spectrum amplitude function, f.""" + raise NotImplementedError + + def _phase(self, k_y, k_z, x, y, z): + """Phase function.""" + return x*_csqrt(self._k**2 - k_y**2 - k_z**2).real + y*k_y + z*k_z + + def _integrand(self, k_y, k_z): + """Integrand function.""" + return self.spectrum(k_y, k_z) * \ + _cexp(1j*self._phase(k_y, k_z, self.x, self._ry, self._rz)) + + +# ----------------------------------------------------------------------------- +# specific beam implementations based on Beam3dSpherical or Beam3dCartesian +# base classes depending on the choice of a suitable coordinate system +# ----------------------------------------------------------------------------- +class LaguerreGauss3dCartesian(Beam3dCartesian): + """Cartesian implementaion of a 3d Laguerre-Gauss beam. + + This class serves only as an example for a will be removed in future + versions. + """ + + def __init__(self, x, params, called=False): + """Laguerre-Gauss beam specifc parameters.""" + super().__init__(x, params, called) + self._W_y = params['W_y'] + self._m = params['m'] + self._norm = 4 * math.pi / (self._W_y**2) + + def profile(self, r): + """...""" + if self.x == 0 and self._m == 0: + return self._norm * _exp(-((r.y**2 + r.z**2) / self._W_y**2)) + else: + return super().profile(r) + + def spectrum(self, k_y, k_z): + """Spectrum amplitude function, f.""" + if self._m == 0: + return self._f_Gauss_cartesian(k_y, k_z, self._W_y) + else: + return self._f_Laguerre_Gauss_cartesian(k_y, k_z, + self._W_y, self._k, self._m) + + def _phi(self, k_y, k_z): + """Azimuthal angle. + + Part of coordinate transformation from k-space to (theta, phi)-space. + """ + return _atan2(k_y, -k_z) + + def _theta(self, k_y, k_z, k): + """Polar angle. + + Part of coordinate transformation from k-space to (theta, phi)-space. + """ + return _acos(_csqrt(k**2 - k_y**2 - k_z**2).real / k) + + def _f_Gauss_cartesian(self, k_y, k_z, W_y): + """2d-Gaussian spectrum amplitude. + + Impementation for Cartesian coordinates. + """ + return _exp(-W_y**2 * (k_y**2 + k_z**2)/4) + + def _f_Laguerre_Gauss_cartesian(self, k_y, k_z, W_y, k, m): + """Laguerre-Gaussian spectrum amplitude. + + Impementation for Cartesian coordinates. + """ + return self._f_Gauss_cartesian(k_y, k_z, W_y) * \ + _cexp(1j*m*self._phi(k_y, k_z)) * self._theta(k_y, k_z, k)**_abs(m) + + +class LaguerreGauss3d(Beam3dSpherical): + """3d Laguerre-Gauss beam. + + Usage: + LGbeam = LaguerreGauss3d(x=x, params=params) + LGbeam.profile(r) + LGbeam.spectrum(sin_theta, theta, phi) + """ + + def __init__(self, x, params, called=False): + """Laguerre-Gauss beam specifc parameters.""" + super().__init__(x, params, called) + self._W_y = params['W_y'] + self._m = params['m'] + self._norm = 4 * math.pi / (self._W_y**2) + + def profile(self, r): + """...""" + if self.x == 0 and self._m == 0: + return self._norm * _exp(-((r.y**2 + r.z**2) / self._W_y**2)) + else: + return super().profile(r) + + def spectrum(self, sin_theta, theta, phi): + """Spectrum amplitude function, f.""" + if self._m == 0: + return self._f_Gauss_spherical(sin_theta, self._W_y, self._k) + else: + return self._f_Laguerre_Gauss_spherical(sin_theta, theta, phi, + self._W_y, self._k, self._m) + + def _f_Gauss_spherical(self, sin_theta, W_y, k): + """2d-Gaussian spectrum amplitude. + + Implementation for spherical coordinates. + """ + return _exp(-(k*W_y*sin_theta/2)**2) + + def _f_Laguerre_Gauss_spherical(self, sin_theta, theta, phi, W_y, k, m): + """Laguerre-Gaussian spectrum amplitude. + + Implementation for spherical coordinates. + """ + return self._f_Gauss_spherical(sin_theta, W_y, k) * theta**_abs(m) * \ + _cexp(1j*m*phi) From 6ff057e1e910b9475593b178193cce493d6ff45f Mon Sep 17 00:00:00 2001 From: Daniel Kotik Date: Wed, 11 Aug 2021 14:48:25 +0200 Subject: [PATCH 128/145] Fix imports for 2d subpackage --- optbeam/2d/_helpers.py | 12 ++++++++++++ optbeam/2d/beams.py | 14 ++++++++++++++ 2 files changed, 26 insertions(+) diff --git a/optbeam/2d/_helpers.py b/optbeam/2d/_helpers.py index 990ba50..64ae007 100644 --- a/optbeam/2d/_helpers.py +++ b/optbeam/2d/_helpers.py @@ -1,3 +1,15 @@ + +import cython +import sys + +if cython.compiled: + from scipy import LowLevelCallable + +from scipy.integrate import quad + +from .beams import Beam2dCartesian + + def _real_1d_func(x, func): """Return real part of a 1d function.""" return func(x).real diff --git a/optbeam/2d/beams.py b/optbeam/2d/beams.py index d861b57..039b3bb 100644 --- a/optbeam/2d/beams.py +++ b/optbeam/2d/beams.py @@ -1,3 +1,17 @@ + +import cython +import math +import sys + +if not cython.compiled: + from math import (exp as _exp, + sqrt as _sqrt) + from cmath import exp as _cexp + print("\nPlease consider compiling `%s.py` via Cython: " + "`$ cythonize -3 -i %s.py`\n" % (__name__, __name__)) + +from types import MappingProxyType + from ._helpers import _complex_quad From 345699bb87116ae99846cd05f5c805d93da14a1b Mon Sep 17 00:00:00 2001 From: Daniel Kotik Date: Wed, 11 Aug 2021 15:10:00 +0200 Subject: [PATCH 129/145] Fix imports for 3d subpackage --- optbeam/3d/_helpers.py | 12 ++++++++++++ optbeam/3d/beams.py | 25 ++++++++++++++++++++++++- 2 files changed, 36 insertions(+), 1 deletion(-) diff --git a/optbeam/3d/_helpers.py b/optbeam/3d/_helpers.py index c00e00a..99a30d2 100644 --- a/optbeam/3d/_helpers.py +++ b/optbeam/3d/_helpers.py @@ -1,3 +1,15 @@ + +import cython +import sys + +if cython.compiled: + from scipy import LowLevelCallable + +from scipy.integrate import dblquad + +from .beams import Beam3d + + def _real_2d_func(x, y, func): """Return real part of a 2d function.""" return func(x, y).real diff --git a/optbeam/3d/beams.py b/optbeam/3d/beams.py index 438b5c6..d9f70a9 100644 --- a/optbeam/3d/beams.py +++ b/optbeam/3d/beams.py @@ -1,5 +1,25 @@ + +import cython +import math +import sys + +if not cython.compiled: + from math import (sin as _sin, + cos as _cos, + exp as _exp, + acos as _acos, + atan2 as _atan2) + from cmath import (exp as _cexp, + sqrt as _csqrt) + from builtins import abs as _abs + print("\nPlease consider compiling `%s.py` via Cython: " + "`$ cythonize -3 -i %s.py`\n" % (__name__, __name__)) + +from types import MappingProxyType + from ._helpers import _complex_dblquad + class Beam3d: """Abstract base class.""" @@ -64,7 +84,8 @@ def _integrand(self, theta, phi): cos_theta = _cos(theta) return sin_theta * cos_theta * self.spectrum(sin_theta, theta, phi) * \ - _cexp(1j*self._phase(sin_theta, cos_theta, phi, self.x, self._ry, self._rz)) + _cexp(1j*self._phase(sin_theta, cos_theta, + phi, self.x, self._ry, self._rz)) class Beam3dCartesian(Beam3d): @@ -213,3 +234,5 @@ def _f_Laguerre_Gauss_spherical(self, sin_theta, theta, phi, W_y, k, m): """ return self._f_Gauss_spherical(sin_theta, W_y, k) * theta**_abs(m) * \ _cexp(1j*m*phi) + return self._f_Gauss_spherical(sin_theta, W_y, k) * theta**_abs(m) * \ + _cexp(1j*m*phi) From 1c9d70c571ed4e34b86bb72711eefadb5920ce46 Mon Sep 17 00:00:00 2001 From: Daniel Kotik Date: Thu, 12 Aug 2021 10:30:03 +0200 Subject: [PATCH 130/145] Rename subpackage names to be valid identifiers: Identifiers must start with a letter or an underscore (can't start with a numeral). --- optbeam/{2d => _2d}/__init__.py | 0 optbeam/{2d => _2d}/_helpers.py | 0 optbeam/{2d => _2d}/beams.py | 0 optbeam/{3d => _3d}/__init__.py | 0 optbeam/{3d => _3d}/_helpers.py | 0 optbeam/{3d => _3d}/beams.py | 0 6 files changed, 0 insertions(+), 0 deletions(-) rename optbeam/{2d => _2d}/__init__.py (100%) rename optbeam/{2d => _2d}/_helpers.py (100%) rename optbeam/{2d => _2d}/beams.py (100%) rename optbeam/{3d => _3d}/__init__.py (100%) rename optbeam/{3d => _3d}/_helpers.py (100%) rename optbeam/{3d => _3d}/beams.py (100%) diff --git a/optbeam/2d/__init__.py b/optbeam/_2d/__init__.py similarity index 100% rename from optbeam/2d/__init__.py rename to optbeam/_2d/__init__.py diff --git a/optbeam/2d/_helpers.py b/optbeam/_2d/_helpers.py similarity index 100% rename from optbeam/2d/_helpers.py rename to optbeam/_2d/_helpers.py diff --git a/optbeam/2d/beams.py b/optbeam/_2d/beams.py similarity index 100% rename from optbeam/2d/beams.py rename to optbeam/_2d/beams.py diff --git a/optbeam/3d/__init__.py b/optbeam/_3d/__init__.py similarity index 100% rename from optbeam/3d/__init__.py rename to optbeam/_3d/__init__.py diff --git a/optbeam/3d/_helpers.py b/optbeam/_3d/_helpers.py similarity index 100% rename from optbeam/3d/_helpers.py rename to optbeam/_3d/_helpers.py diff --git a/optbeam/3d/beams.py b/optbeam/_3d/beams.py similarity index 100% rename from optbeam/3d/beams.py rename to optbeam/_3d/beams.py From 8d2dfc333d1907c57477512b968fbb5f8680f0bf Mon Sep 17 00:00:00 2001 From: Daniel Kotik Date: Thu, 12 Aug 2021 10:39:41 +0200 Subject: [PATCH 131/145] Import only necessary functions and classes: Avoid namespace cluttering by importing with prefixed underscore. --- optbeam/__init__.py | 12 +++++++++--- 1 file changed, 9 insertions(+), 3 deletions(-) diff --git a/optbeam/__init__.py b/optbeam/__init__.py index 7dbee0b..cafd6ff 100644 --- a/optbeam/__init__.py +++ b/optbeam/__init__.py @@ -1,12 +1,18 @@ -import math + +from math import (degrees as _degrees, + asin as _asin, + atan as _atan) + +from ._2d.beams import Gauss2d, IncAiry2d +from ._3d.beams import LaguerreGauss3d def critical(n1, n2): """Calculate critical angle in degrees.""" assert n1 > n2, "\nWarning: Critical angle is not defined, since n1 <= n2!" - return math.degrees(math.asin(n2/n1)) + return _degrees(_asin(n2/n1)) def brewster(n1, n2): """Calculate Brewster angle in degrees.""" - return math.degrees(math.atan(n2/n1)) + return _degrees(_atan(n2/n1)) From ba1d89a93142eed7b7de39ffcf3a1c1f79598bd9 Mon Sep 17 00:00:00 2001 From: Daniel Kotik Date: Thu, 12 Aug 2021 11:00:30 +0200 Subject: [PATCH 132/145] Avoid circular import of `Beam3d` class --- optbeam/_3d/_helpers.py | 26 ++++++++++++++++++++++++-- optbeam/_3d/beams.py | 27 +-------------------------- 2 files changed, 25 insertions(+), 28 deletions(-) diff --git a/optbeam/_3d/_helpers.py b/optbeam/_3d/_helpers.py index 99a30d2..f919353 100644 --- a/optbeam/_3d/_helpers.py +++ b/optbeam/_3d/_helpers.py @@ -6,8 +6,7 @@ from scipy import LowLevelCallable from scipy.integrate import dblquad - -from .beams import Beam3d +from types import MappingProxyType def _real_2d_func(x, y, func): @@ -65,3 +64,26 @@ def _complex_dblquad(func, a, b, gfun, hfun, kwargs={}): _imag_2d_func, a, b, gfun, hfun, (func,), **kwargs) return real + 1j*imag, real_tol, imag_tol + + +class Beam3d: + """Abstract base class.""" + + def __init__(self, x, params, called=False): + """...""" + self.x = x # TODO: rename x to x_shift + self._k = params['k'] + self._params = MappingProxyType(params) # read-only view of a dict + self.called = called + + @property + def params(self): + """Beam specific parameters. + + This is a read-only property. + """ + return self._params + + def _integrand(self, x, y): + """Integrand function over two coordinates x and y.""" + raise NotImplementedError diff --git a/optbeam/_3d/beams.py b/optbeam/_3d/beams.py index d9f70a9..9a9e57e 100644 --- a/optbeam/_3d/beams.py +++ b/optbeam/_3d/beams.py @@ -15,32 +15,7 @@ print("\nPlease consider compiling `%s.py` via Cython: " "`$ cythonize -3 -i %s.py`\n" % (__name__, __name__)) -from types import MappingProxyType - -from ._helpers import _complex_dblquad - - -class Beam3d: - """Abstract base class.""" - - def __init__(self, x, params, called=False): - """...""" - self.x = x # TODO: rename x to x_shift - self._k = params['k'] - self._params = MappingProxyType(params) # read-only view of a dict - self.called = called - - @property - def params(self): - """Beam specific parameters. - - This is a read-only property. - """ - return self._params - - def _integrand(self, x, y): - """Integrand function over two coordinates x and y.""" - raise NotImplementedError +from ._helpers import _complex_dblquad, Beam3d class Beam3dSpherical(Beam3d): From 96e8ae0b5169c552b4d3cca90d8774cd35c8cec1 Mon Sep 17 00:00:00 2001 From: Daniel Kotik Date: Thu, 12 Aug 2021 11:23:28 +0200 Subject: [PATCH 133/145] Introduce abstract base class `Beam2d`: This is to align with the 3d case where there is already an ABC. --- optbeam/_2d/_helpers.py | 6 +++--- optbeam/_2d/beams.py | 12 ++++++++++-- 2 files changed, 13 insertions(+), 5 deletions(-) diff --git a/optbeam/_2d/_helpers.py b/optbeam/_2d/_helpers.py index 64ae007..8e358d5 100644 --- a/optbeam/_2d/_helpers.py +++ b/optbeam/_2d/_helpers.py @@ -7,7 +7,7 @@ from scipy.integrate import quad -from .beams import Beam2dCartesian +from .beams import Beam2d def _real_1d_func(x, func): @@ -27,7 +27,7 @@ def _imag_1d_func_c(n, arr, func_ptr): """ # pure python formulation of: # return (func_ptr)(arr[0]).imag - return cython.cast(Beam2dCartesian, func_ptr)._integrand(arr[0]).imag + return cython.cast(Beam2d, func_ptr)._integrand(arr[0]).imag def _real_1d_func_c(n, arr, func_ptr): @@ -37,7 +37,7 @@ def _real_1d_func_c(n, arr, func_ptr): """ # pure python formulation of: # return (func_ptr)(arr[0]).real - return cython.cast(Beam2dCartesian, func_ptr)._integrand(arr[0]).real + return cython.cast(Beam2d, func_ptr)._integrand(arr[0]).real def _complex_quad(func, a, b, kwargs={}): diff --git a/optbeam/_2d/beams.py b/optbeam/_2d/beams.py index 039b3bb..1c9ceec 100644 --- a/optbeam/_2d/beams.py +++ b/optbeam/_2d/beams.py @@ -15,8 +15,8 @@ from ._helpers import _complex_quad -class Beam2dCartesian: - """...""" +class Beam2d: + """Abstract base class.""" def __init__(self, x, params, called=False): """...""" @@ -33,6 +33,14 @@ def params(self): """ return self._params + def _integrand(self, x): + """Integrand function over one coordinate x.""" + raise NotImplementedError + + +class Beam2dCartesian(Beam2d): + """...""" + def profile(self, r): """Field amplitude function. From a3cd99e242e3d87825a47e00ba40acfa385d37e8 Mon Sep 17 00:00:00 2001 From: Daniel Kotik Date: Thu, 12 Aug 2021 11:35:04 +0200 Subject: [PATCH 134/145] Avoid circular import of `Beam2d` class --- optbeam/_2d/_helpers.py | 26 ++++++++++++++++++++++++-- optbeam/_2d/beams.py | 27 +-------------------------- 2 files changed, 25 insertions(+), 28 deletions(-) diff --git a/optbeam/_2d/_helpers.py b/optbeam/_2d/_helpers.py index 8e358d5..0e2c46c 100644 --- a/optbeam/_2d/_helpers.py +++ b/optbeam/_2d/_helpers.py @@ -6,8 +6,7 @@ from scipy import LowLevelCallable from scipy.integrate import quad - -from .beams import Beam2d +from types import MappingProxyType def _real_1d_func(x, func): @@ -63,3 +62,26 @@ def _complex_quad(func, a, b, kwargs={}): imag, imag_tol = quad(_imag_1d_func, a, b, (func,), **kwargs) return real + 1j*imag, real_tol, imag_tol + + +class Beam2d: + """Abstract base class.""" + + def __init__(self, x, params, called=False): + """...""" + self.x = x + self._k = params['k'] + self._params = MappingProxyType(params) # read-only view of a dict + self.called = called + + @property + def params(self): + """Beam specific parameters. + + This is a read-only property. + """ + return self._params + + def _integrand(self, x): + """Integrand function over one coordinate x.""" + raise NotImplementedError diff --git a/optbeam/_2d/beams.py b/optbeam/_2d/beams.py index 1c9ceec..a48f31e 100644 --- a/optbeam/_2d/beams.py +++ b/optbeam/_2d/beams.py @@ -10,32 +10,7 @@ print("\nPlease consider compiling `%s.py` via Cython: " "`$ cythonize -3 -i %s.py`\n" % (__name__, __name__)) -from types import MappingProxyType - -from ._helpers import _complex_quad - - -class Beam2d: - """Abstract base class.""" - - def __init__(self, x, params, called=False): - """...""" - self.x = x - self._k = params['k'] - self._params = MappingProxyType(params) # read-only view of a dict - self.called = called - - @property - def params(self): - """Beam specific parameters. - - This is a read-only property. - """ - return self._params - - def _integrand(self, x): - """Integrand function over one coordinate x.""" - raise NotImplementedError +from ._helpers import _complex_quad, Beam2d class Beam2dCartesian(Beam2d): From 670053b80be56844b3ed41e240a9f2ac8494965d Mon Sep 17 00:00:00 2001 From: Daniel Kotik Date: Thu, 12 Aug 2021 21:32:39 +0200 Subject: [PATCH 135/145] Remove `optbeam.py` files from script folders --- Airy_2d/optbeam.py | 229 ----------------------- Gauss_2d/optbeam.py | 204 --------------------- Laguerre_Gauss_3d/optbeam.py | 342 ----------------------------------- 3 files changed, 775 deletions(-) delete mode 100644 Airy_2d/optbeam.py delete mode 100644 Gauss_2d/optbeam.py delete mode 100644 Laguerre_Gauss_3d/optbeam.py diff --git a/Airy_2d/optbeam.py b/Airy_2d/optbeam.py deleted file mode 100644 index 72aeca0..0000000 --- a/Airy_2d/optbeam.py +++ /dev/null @@ -1,229 +0,0 @@ -# -*- coding: utf-8 -*- -""" -file: optbeam.py -brief: ... -author: Daniel Kotik -version: 1.5-beta -release date: xx.xx.2020 -creation date: 12.04.2020 -""" -import cython -import math -import sys - -from scipy.integrate import quad -from types import MappingProxyType - - -if not cython.compiled: - from math import sqrt as _sqrt - from cmath import exp as _cexp - print("\nPlease consider compiling `%s.py` via Cython: " - "`$ cythonize -3 -i %s.py`\n" % (__name__, __name__)) -else: - from scipy import LowLevelCallable - - -def _real_1d_func(x, func): - """Return real part of a 1d function.""" - return func(x).real - - -def _imag_1d_func(x, func): - """Return imag part of a 1d function.""" - return func(x).imag - - -def _imag_1d_func_c(n, arr, func_ptr): - """Return imag part of a 1d function. - - Cython implementation. - """ - # pure python formulation of: - # return (func_ptr)(arr[0]).imag - return cython.cast(Beam2dCartesian, func_ptr)._integrand(arr[0]).imag - - -def _real_1d_func_c(n, arr, func_ptr): - """Return real part of a 1d function. - - Cython implementation. - """ - # pure python formulation of: - # return (func_ptr)(arr[0]).real - return cython.cast(Beam2dCartesian, func_ptr)._integrand(arr[0]).real - - -def _complex_quad(func, a, b, kwargs={}): - """Integrate real and imaginary part of the given function.""" - if cython.compiled: - # pure python formulation of: cdef void *f_ptr = func - f_ptr = cython.declare(cython.p_void, cython.cast(cython.p_void, func)) - - func_capsule = PyCapsule_New(f_ptr, cython.NULL, cython.NULL) - - current_module = sys.modules[__name__] - - ll_real_1d_func_c = LowLevelCallable.from_cython(current_module, - '_real_1d_func_c', - func_capsule) - ll_imag_1d_func_c = LowLevelCallable.from_cython(current_module, - '_imag_1d_func_c', - func_capsule) - real, real_tol = quad(ll_real_1d_func_c, a, b, **kwargs) - imag, imag_tol = quad(ll_imag_1d_func_c, a, b, **kwargs) - else: - real, real_tol = quad(_real_1d_func, a, b, (func,), **kwargs) - imag, imag_tol = quad(_imag_1d_func, a, b, (func,), **kwargs) - - return real + 1j*imag, real_tol, imag_tol - - -def critical(n1, n2): - """Calculate critical angle in degrees.""" - assert n1 > n2, "\nWarning: Critical angle is not defined, since n1 <= n2!" - return math.degrees(math.asin(n2/n1)) - - -def brewster(n1, n2): - """Calculate Brewster angle in degrees.""" - return math.degrees(math.atan(n2/n1)) - - -class Beam2dCartesian: - """...""" - - def __init__(self, x, params, called=False): - """...""" - self.x = x - self._k = params['k'] - self._params = MappingProxyType(params) # read-only view of a dict - self.called = called - - # integration boundaries - self._a = -self._k - self._b = self._k - - @property - def params(self): - """Beam specific parameters. - - This is a read-only property. - """ - return self._params - - def profile(self, r): - """Field amplitude function. - - Plane wave decomposition: calculate field amplitude at light source - position if not coinciding with beam waist. - """ - self._ry = r.y - self._rz = r.z - - if not self.called: - print("Calculating inital field configuration. " - "This will take some time...") - self.called = True - - try: - (result, - real_tol, - imag_tol) = _complex_quad(self if cython.compiled else self._integrand, - self._a, self._b, dict(limit=100)) - except Exception as e: - print(type(e).__name__ + ":", e) - sys.exit() - - return result - - def spectrum(self, k_y): - """Spectrum amplitude distribution function, f.""" - raise NotImplementedError - - def _phase(self, k_y, x, y): - """Phase function.""" - return x*_sqrt(self._k**2 - k_y**2) + k_y*y - - def _integrand(self, k_y): - """Integrand function.""" - return self.spectrum(k_y) * _cexp(1j*self._phase(k_y, self.x, self._ry)) - - -# ----------------------------------------------------------------------------- -# specific beam implementations based on Beam2dCartesian base class -# ----------------------------------------------------------------------------- -class IncAiry2d(Beam2dCartesian): - """2d incomplete Airy beam.""" - - def __init__(self, x, params, called=False): - """...""" - self._W_y = params['W_y'] - self._M = params['M'] - self._W = params['W'] - super().__init__(x, params, called) - - def profile(self, r): - """...""" - if self.x == 0: - # adjust integration boundaries - self._a = self._M-self._W - self._b = self._M+self._W - - return super().profile(r) - - def spectrum(self, k_y): - """...""" - return self._f_Airy(k_y, self._W_y, self._M, self._W) - - def _f_Airy(self, k_y, W_y, M, W): - """Airy spectrum amplitude.""" - return W_y * _cexp(1.0j*(-1/3)*(k_y*W_y)**3) \ - * self._heaviside(W_y * k_y - (M - W)) \ - * self._heaviside((M + W) - W_y * k_y) - - def _heaviside(self, x): - """Theta (Heaviside step) function.""" - return 0 if x < 0 else 1 - - def _integrand(self, k_y): - """...""" - if self.x == 0: - xi = k_y - return _cexp(1.0j*(-(xi**3)/3 + (xi * self._ry/self._W_y))) - else: - # next line needs _integrand declared cpdef without nogil attribute, - # and will execute slower than repeating the super class integration - # routine function here - #return super(IncAiry2d, self)._integrand(k_y) - return self.spectrum(k_y) * _cexp(1j*self._phase(k_y, self.x, self._ry)) - - -def main(): - class Vector3: - """Simple 3d vector class.""" - - def __init__(self, x, y, z): - self.x = x - self.y = y - self.z = z - - x, y, z = -2.15, 0.3, 0.5 - - r = Vector3(0, y, z) - # alternative: - # import meep; r = meep.Vector3(0, y, z) - - k1 = 75.39822368615503 - w_0 = 0.09284038347027228 - M = 0 - W = 4 - params = dict(W_y=w_0, k=k1, M=M, W=W) - - beam = IncAiry2d(x=x, params=params) - - return (beam, r) - - -if __name__ == '__main__': - main() diff --git a/Gauss_2d/optbeam.py b/Gauss_2d/optbeam.py deleted file mode 100644 index 2bcf4f2..0000000 --- a/Gauss_2d/optbeam.py +++ /dev/null @@ -1,204 +0,0 @@ -# -*- coding: utf-8 -*- -""" -file: optbeam.py -brief: ... -author: Daniel Kotik -version: 1.5-beta -release date: xx.xx.2020 -creation date: 03.04.2020 -""" -import cython -import math -import sys - -from scipy.integrate import quad -from types import MappingProxyType - - -if not cython.compiled: - from math import (exp as _exp, - sqrt as _sqrt) - from cmath import exp as _cexp - print("\nPlease consider compiling `%s.py` via Cython: " - "`$ cythonize -3 -i %s.py`\n" % (__name__, __name__)) -else: - from scipy import LowLevelCallable - - -def _real_1d_func(x, func): - """Return real part of a 1d function.""" - return func(x).real - - -def _imag_1d_func(x, func): - """Return imag part of a 1d function.""" - return func(x).imag - - -def _imag_1d_func_c(n, arr, func_ptr): - """Return imag part of a 1d function. - - Cython implementation. - """ - # pure python formulation of: - # return (func_ptr)(arr[0]).imag - return cython.cast(Beam2dCartesian, func_ptr)._integrand(arr[0]).imag - - -def _real_1d_func_c(n, arr, func_ptr): - """Return real part of a 1d function. - - Cython implementation. - """ - # pure python formulation of: - # return (func_ptr)(arr[0]).real - return cython.cast(Beam2dCartesian, func_ptr)._integrand(arr[0]).real - - -def _complex_quad(func, a, b, kwargs={}): - """Integrate real and imaginary part of the given function.""" - if cython.compiled: - # pure python formulation of: cdef void *f_ptr = func - f_ptr = cython.declare(cython.p_void, cython.cast(cython.p_void, func)) - - func_capsule = PyCapsule_New(f_ptr, cython.NULL, cython.NULL) - - current_module = sys.modules[__name__] - - ll_real_1d_func_c = LowLevelCallable.from_cython(current_module, - '_real_1d_func_c', - func_capsule) - ll_imag_1d_func_c = LowLevelCallable.from_cython(current_module, - '_imag_1d_func_c', - func_capsule) - real, real_tol = quad(ll_real_1d_func_c, a, b, **kwargs) - imag, imag_tol = quad(ll_imag_1d_func_c, a, b, **kwargs) - else: - real, real_tol = quad(_real_1d_func, a, b, (func,), **kwargs) - imag, imag_tol = quad(_imag_1d_func, a, b, (func,), **kwargs) - - return real + 1j*imag, real_tol, imag_tol - - -def critical(n1, n2): - """Calculate critical angle in degrees.""" - assert n1 > n2, "\nWarning: Critical angle is not defined, since n1 <= n2!" - return math.degrees(math.asin(n2/n1)) - - -def brewster(n1, n2): - """Calculate Brewster angle in degrees.""" - return math.degrees(math.atan(n2/n1)) - - -class Beam2dCartesian: - """...""" - - def __init__(self, x, params, called=False): - """...""" - self.x = x - self._k = params['k'] - self._params = MappingProxyType(params) # read-only view of a dict - self.called = called - - @property - def params(self): - """Beam specific parameters. - - This is a read-only property. - """ - return self._params - - def profile(self, r): - """Field amplitude function. - - Plane wave decomposition: calculate field amplitude at light source - position if not coinciding with beam waist. - """ - self._ry = r.y - self._rz = r.z - - if not self.called: - print("Calculating inital field configuration. " - "This will take some time...") - self.called = True - - try: - (result, - real_tol, - imag_tol) = _complex_quad(self if cython.compiled else self._integrand, - -self._k, self._k) - except Exception as e: - print(type(e).__name__ + ":", e) - sys.exit() - - return result - - def spectrum(self, k_y): - """Spectrum amplitude distribution function, f.""" - raise NotImplementedError - - def _phase(self, k_y, x, y): - """Phase function.""" - return x*_sqrt(self._k**2 - k_y**2) + k_y*y - - def _integrand(self, k_y): - """Integrand function.""" - return self.spectrum(k_y) * _cexp(1j*self._phase(k_y, self.x, self._ry)) - - -# ----------------------------------------------------------------------------- -# specific beam implementations based on Beam2dCartesian base class -# ----------------------------------------------------------------------------- -class Gauss2d(Beam2dCartesian): - """2d Gauss beam.""" - - def __init__(self, x, params, called=False): - """...""" - self._W_y = params['W_y'] - self._norm = 2 * _sqrt(math.pi) / self._W_y - super().__init__(x, params, called) - - def profile(self, r): - """...""" - # beam profile distribution (field amplitude) at the waist of the beam - if self.x == 0: - return self._norm * _exp(-(r.y / self._W_y)**2) - else: - return super().profile(r) - - def spectrum(self, k_y): - """Spectrum amplitude function, f.""" - return self._f_Gauss(k_y, self._W_y) - - def _f_Gauss(self, k_y, W_y): - """Gaussian spectrum amplitude.""" - return _exp(-(k_y*W_y/2)**2) - - -def main(): - class Vector3: - """Simple 3d vector class.""" - - def __init__(self, x, y, z): - self.x = x - self.y = y - self.z = z - - x, y, z = -2.15, 0.3, 0.5 - - r = Vector3(0, y, z) - # alternative: - # import meep; r = meep.Vector3(0, y, z) - - k1 = 116.11326447667875 - w_0 = 0.1061032953945969 - params = dict(W_y=w_0, k=k1) - - beam = Gauss2d(x=x, params=params) - - return (beam, r) - - -if __name__ == '__main__': - main() diff --git a/Laguerre_Gauss_3d/optbeam.py b/Laguerre_Gauss_3d/optbeam.py deleted file mode 100644 index 9756e7c..0000000 --- a/Laguerre_Gauss_3d/optbeam.py +++ /dev/null @@ -1,342 +0,0 @@ -# -*- coding: utf-8 -*- -""" -file: optbeam.py -brief: ... -author: Daniel Kotik -version: 1.5-beta -release date: xx.xx.2020 -creation date: 22.02.2020 -""" -import cython -import math -import sys - -from scipy.integrate import dblquad -from types import MappingProxyType - - -if not cython.compiled: - from math import (sin as _sin, - cos as _cos, - exp as _exp, - acos as _acos, - atan2 as _atan2) - from cmath import (exp as _cexp, - sqrt as _csqrt) - from builtins import abs as _abs - print("\nPlease consider compiling `%s.py` via Cython: " - "`$ cythonize -3 -i %s.py`\n" % (__name__, __name__)) -else: - from scipy import LowLevelCallable - - -def _real_2d_func(x, y, func): - """Return real part of a 2d function.""" - return func(x, y).real - - -def _imag_2d_func(x, y, func): - """Return imag part of a 2d function.""" - return func(x, y).imag - - -def _imag_2d_func_c(n, arr, func_ptr): - """Return imag part of a 2d function. - - Cython implementation. - """ - # pure python formulation of: - # return (func_ptr)(arr[0], arr[1]).imag - return cython.cast(Beam3d, func_ptr)._integrand(arr[0], arr[1]).imag - - -def _real_2d_func_c(n, arr, func_ptr): - """Return real part of a 2d function. - - Cython implementation. - """ - # pure python formulation of: - # return (func_ptr)(arr[0], arr[1]).real - return cython.cast(Beam3d, func_ptr)._integrand(arr[0], arr[1]).real - - -def _complex_dblquad(func, a, b, gfun, hfun, kwargs={}): - """Integrate real and imaginary part of the given function.""" - if cython.compiled: - # pure python formulation of: cdef void *f_ptr = func - f_ptr = cython.declare(cython.p_void, cython.cast(cython.p_void, func)) - - func_capsule = PyCapsule_New(f_ptr, cython.NULL, cython.NULL) - - current_module = sys.modules[__name__] - - ll_real_2d_func_c = LowLevelCallable.from_cython(current_module, - '_real_2d_func_c', - func_capsule) - ll_imag_2d_func_c = LowLevelCallable.from_cython(current_module, - '_imag_2d_func_c', - func_capsule) - real, real_tol = dblquad(ll_real_2d_func_c, a, b, gfun, hfun, **kwargs) - imag, imag_tol = dblquad(ll_imag_2d_func_c, a, b, gfun, hfun, **kwargs) - else: - real, real_tol = dblquad(_real_2d_func, a, b, gfun, hfun, (func,), **kwargs) - imag, imag_tol = dblquad(_imag_2d_func, a, b, gfun, hfun, (func,), **kwargs) - - return real + 1j*imag, real_tol, imag_tol - - -def critical(n1, n2): - """Calculate critical angle in degrees.""" - assert n1 > n2, "\nWarning: Critical angle is not defined, since n1 <= n2!" - return math.degrees(math.asin(n2/n1)) - - -def brewster(n1, n2): - """Calculate Brewster angle in degrees.""" - return math.degrees(math.atan(n2/n1)) - - -class Beam3d: - """Abstract base class.""" - - def __init__(self, x, params, called=False): - """...""" - self.x = x # TODO: rename x to x_shift - self._k = params['k'] - self._params = MappingProxyType(params) # read-only view of a dict - self.called = called - - @property - def params(self): - """Beam specific parameters. - - This is a read-only property. - """ - return self._params - - def _integrand(self, x, y): - """Integrand function over two coordinates x and y.""" - raise NotImplementedError - - -class Beam3dSpherical(Beam3d): - """Reference implementaion of a 3d beam in spherical coordinates.""" - - def profile(self, r): - """Beam profile function, psi.""" - self._ry = r.y - self._rz = r.z - - if not self.called: - print("Calculating inital field configuration. " - "This will take some time...") - self.called = True - - try: - (result, - real_tol, - imag_tol) = _complex_dblquad(self if cython.compiled else self._integrand, - 0, 2*math.pi, 0, math.pi/2) - except Exception as e: - print(type(e).__name__ + ":", e) - sys.exit() - - return self._k**2 * result - - def spectrum(self, sin_theta, theta, phi): - """Spectrum amplitude function, f.""" - raise NotImplementedError - - def _phase(self, sin_theta, cos_theta, phi, x, y, z): - """Phase function.""" - sin_phi = _sin(phi) - cos_phi = _cos(phi) - - return self._k*(sin_theta*(y*sin_phi - z*cos_phi) + cos_theta*x) - - def _integrand(self, theta, phi): - """Integrand function.""" - sin_theta = _sin(theta) - cos_theta = _cos(theta) - - return sin_theta * cos_theta * self.spectrum(sin_theta, theta, phi) * \ - _cexp(1j*self._phase(sin_theta, cos_theta, phi, self.x, self._ry, self._rz)) - - -class Beam3dCartesian(Beam3d): - """Reference implementaion of a 3d beam in Cartesian coordinates.""" - - def profile(self, r): - """Beam profile function, psi.""" - self._ry = r.y - self._rz = r.z - - if not self.called: - print("Calculating inital field configuration. " - "This will take some time...") - self.called = True - - try: - (result, - real_tol, - imag_tol) = _complex_dblquad(self if cython.compiled else self._integrand, - -self._k, self._k, -self._k, self._k) - except Exception as e: - print(type(e).__name__ + ":", e) - sys.exit() - - return result - - def spectrum(self, k_y, k_z): - """Spectrum amplitude function, f.""" - raise NotImplementedError - - def _phase(self, k_y, k_z, x, y, z): - """Phase function.""" - return x*_csqrt(self._k**2 - k_y**2 - k_z**2).real + y*k_y + z*k_z - - def _integrand(self, k_y, k_z): - """Integrand function.""" - return self.spectrum(k_y, k_z) * \ - _cexp(1j*self._phase(k_y, k_z, self.x, self._ry, self._rz)) - - -# ----------------------------------------------------------------------------- -# specific beam implementations based on Beam3dSpherical or Beam3dCartesian -# base classes depending on the choice of a suitable coordinate system -# ----------------------------------------------------------------------------- -class LaguerreGauss3dCartesian(Beam3dCartesian): - """Cartesian implementaion of a 3d Laguerre-Gauss beam. - - This class serves only as an example for a will be removed in future - versions. - """ - - def __init__(self, x, params, called=False): - """Laguerre-Gauss beam specifc parameters.""" - super().__init__(x, params, called) - self._W_y = params['W_y'] - self._m = params['m'] - self._norm = 4 * math.pi / (self._W_y**2) - - def profile(self, r): - """...""" - if self.x == 0 and self._m == 0: - return self._norm * _exp(-((r.y**2 + r.z**2) / self._W_y**2)) - else: - return super().profile(r) - - def spectrum(self, k_y, k_z): - """Spectrum amplitude function, f.""" - if self._m == 0: - return self._f_Gauss_cartesian(k_y, k_z, self._W_y) - else: - return self._f_Laguerre_Gauss_cartesian(k_y, k_z, - self._W_y, self._k, self._m) - - def _phi(self, k_y, k_z): - """Azimuthal angle. - - Part of coordinate transformation from k-space to (theta, phi)-space. - """ - return _atan2(k_y, -k_z) - - def _theta(self, k_y, k_z, k): - """Polar angle. - - Part of coordinate transformation from k-space to (theta, phi)-space. - """ - return _acos(_csqrt(k**2 - k_y**2 - k_z**2).real / k) - - def _f_Gauss_cartesian(self, k_y, k_z, W_y): - """2d-Gaussian spectrum amplitude. - - Impementation for Cartesian coordinates. - """ - return _exp(-W_y**2 * (k_y**2 + k_z**2)/4) - - def _f_Laguerre_Gauss_cartesian(self, k_y, k_z, W_y, k, m): - """Laguerre-Gaussian spectrum amplitude. - - Impementation for Cartesian coordinates. - """ - return self._f_Gauss_cartesian(k_y, k_z, W_y) * \ - _cexp(1j*m*self._phi(k_y, k_z)) * self._theta(k_y, k_z, k)**_abs(m) - - -class LaguerreGauss3d(Beam3dSpherical): - """3d Laguerre-Gauss beam. - - Usage: - LGbeam = LaguerreGauss3d(x=x, params=params) - LGbeam.profile(r) - LGbeam.spectrum(sin_theta, theta, phi) - """ - - def __init__(self, x, params, called=False): - """Laguerre-Gauss beam specifc parameters.""" - super().__init__(x, params, called) - self._W_y = params['W_y'] - self._m = params['m'] - self._norm = 4 * math.pi / (self._W_y**2) - - def profile(self, r): - """...""" - if self.x == 0 and self._m == 0: - return self._norm * _exp(-((r.y**2 + r.z**2) / self._W_y**2)) - else: - return super().profile(r) - - def spectrum(self, sin_theta, theta, phi): - """Spectrum amplitude function, f.""" - if self._m == 0: - return self._f_Gauss_spherical(sin_theta, self._W_y, self._k) - else: - return self._f_Laguerre_Gauss_spherical(sin_theta, theta, phi, - self._W_y, self._k, self._m) - - def _f_Gauss_spherical(self, sin_theta, W_y, k): - """2d-Gaussian spectrum amplitude. - - Implementation for spherical coordinates. - """ - return _exp(-(k*W_y*sin_theta/2)**2) - - def _f_Laguerre_Gauss_spherical(self, sin_theta, theta, phi, W_y, k, m): - """Laguerre-Gaussian spectrum amplitude. - - Implementation for spherical coordinates. - """ - return self._f_Gauss_spherical(sin_theta, W_y, k) * theta**_abs(m) * \ - _cexp(1j*m*phi) - - -def main(): - class Vector3: - """Simple vector class.""" - - def __init__(self, x, y, z): - self.x = x - self.y = y - self.z = z - - x, y, z = -2.15, 0.3, 0.5 - - r = Vector3(0, y, z) - # alternative: - # import meep; r = meep.Vector3(0, y, z) - - k1 = 31.41592653589793 - w_0 = 0.25464790894703254 - m_charge = 2 - - params = dict(W_y=w_0, m=m_charge, k=k1) - - LGbeam = LaguerreGauss3d(x=x, params=params) - LGbeamCartesian = LaguerreGauss3dCartesian(x=x, params=params) - - return (LGbeam, LGbeamCartesian, r) - - -if __name__ == '__main__': - main() From 34a421305dc63daa51e968723ede30388f934a3b Mon Sep 17 00:00:00 2001 From: Daniel Kotik Date: Thu, 12 Aug 2021 21:40:44 +0200 Subject: [PATCH 136/145] Move beam specific folders with scripts into separate `scripts` folder --- .gitignore | 10 +++++----- README.md | 18 +++++++++--------- {Airy_2d => scripts/Airy_2d}/Airy2d.ctl | 0 {Airy_2d => scripts/Airy_2d}/Airy2d.py | 0 .../img/Airy_beam_M_0_W_4_free_space.png | Bin .../img/Airy_beam_M_0_W_4_scattering.png | Bin {Airy_2d => scripts/Airy_2d}/optbeam.pxd | 0 {Gauss_2d => scripts/Gauss_2d}/Gauss2d.ctl | 0 {Gauss_2d => scripts/Gauss_2d}/Gauss2d.py | 0 .../img/concave_cropped_rotated_resized.png | Bin ...cave_intensity_cropped_rotated_resized.png | Bin .../img/convex_cropped_rotated_resized.png | Bin ...nvex_intensity_cropped_rotated_resized.png | Bin .../img/planar_cropped_rotated_resized.png | Bin ...anar_intensity_cropped_rotated_resized.png | Bin {Gauss_2d => scripts/Gauss_2d}/optbeam.pxd | 0 .../Gauss_2d/planar/Gauss2d-e2_s-000003696.h5 | Bin 0 -> 6832256 bytes .../planar/Gauss2d-e2_s-000003696.png | Bin 0 -> 340158 bytes .../Gauss_2d/planar/Gauss2d-eps-000000000.h5 | Bin 0 -> 6832256 bytes .../Gauss_2d/planar/Gauss2d-ez-000003696.h5 | Bin 0 -> 6832256 bytes .../Gauss_2d/planar/Gauss2d-ez-000003696.png | Bin 0 -> 848589 bytes .../Laguerre_Gauss_3d}/LaguerreGauss3d.ctl | 0 .../Laguerre_Gauss_3d}/LaguerreGauss3d.py | 0 .../img/vortex_beam_m_2_3d_full_resized.png | Bin .../img/vortex_beam_m_2_3d_half_resized.png | Bin .../vortex_beam_m_2_longitudinal_resized.png | Bin .../vortex_beam_m_2_transverse_resized.png | Bin .../Laguerre_Gauss_3d}/integration_test.ipynb | 0 .../Laguerre_Gauss_3d}/optbeam.pxd | 0 .../Laguerre_Gauss_3d}/plot_2d_matplotlib.py | 0 .../Laguerre_Gauss_3d}/plot_3d_mayavi.py | 0 31 files changed, 14 insertions(+), 14 deletions(-) rename {Airy_2d => scripts/Airy_2d}/Airy2d.ctl (100%) rename {Airy_2d => scripts/Airy_2d}/Airy2d.py (100%) rename {Airy_2d => scripts/Airy_2d}/img/Airy_beam_M_0_W_4_free_space.png (100%) rename {Airy_2d => scripts/Airy_2d}/img/Airy_beam_M_0_W_4_scattering.png (100%) rename {Airy_2d => scripts/Airy_2d}/optbeam.pxd (100%) rename {Gauss_2d => scripts/Gauss_2d}/Gauss2d.ctl (100%) rename {Gauss_2d => scripts/Gauss_2d}/Gauss2d.py (100%) rename {Gauss_2d => scripts/Gauss_2d}/img/concave_cropped_rotated_resized.png (100%) rename {Gauss_2d => scripts/Gauss_2d}/img/concave_intensity_cropped_rotated_resized.png (100%) rename {Gauss_2d => scripts/Gauss_2d}/img/convex_cropped_rotated_resized.png (100%) rename {Gauss_2d => scripts/Gauss_2d}/img/convex_intensity_cropped_rotated_resized.png (100%) rename {Gauss_2d => scripts/Gauss_2d}/img/planar_cropped_rotated_resized.png (100%) rename {Gauss_2d => scripts/Gauss_2d}/img/planar_intensity_cropped_rotated_resized.png (100%) rename {Gauss_2d => scripts/Gauss_2d}/optbeam.pxd (100%) create mode 100644 scripts/Gauss_2d/planar/Gauss2d-e2_s-000003696.h5 create mode 100644 scripts/Gauss_2d/planar/Gauss2d-e2_s-000003696.png create mode 100644 scripts/Gauss_2d/planar/Gauss2d-eps-000000000.h5 create mode 100644 scripts/Gauss_2d/planar/Gauss2d-ez-000003696.h5 create mode 100644 scripts/Gauss_2d/planar/Gauss2d-ez-000003696.png rename {Laguerre_Gauss_3d => scripts/Laguerre_Gauss_3d}/LaguerreGauss3d.ctl (100%) rename {Laguerre_Gauss_3d => scripts/Laguerre_Gauss_3d}/LaguerreGauss3d.py (100%) rename {Laguerre_Gauss_3d => scripts/Laguerre_Gauss_3d}/img/vortex_beam_m_2_3d_full_resized.png (100%) rename {Laguerre_Gauss_3d => scripts/Laguerre_Gauss_3d}/img/vortex_beam_m_2_3d_half_resized.png (100%) rename {Laguerre_Gauss_3d => scripts/Laguerre_Gauss_3d}/img/vortex_beam_m_2_longitudinal_resized.png (100%) rename {Laguerre_Gauss_3d => scripts/Laguerre_Gauss_3d}/img/vortex_beam_m_2_transverse_resized.png (100%) rename {Laguerre_Gauss_3d => scripts/Laguerre_Gauss_3d}/integration_test.ipynb (100%) rename {Laguerre_Gauss_3d => scripts/Laguerre_Gauss_3d}/optbeam.pxd (100%) rename {Laguerre_Gauss_3d => scripts/Laguerre_Gauss_3d}/plot_2d_matplotlib.py (100%) rename {Laguerre_Gauss_3d => scripts/Laguerre_Gauss_3d}/plot_3d_mayavi.py (100%) diff --git a/.gitignore b/.gitignore index 581a345..08bdb97 100644 --- a/.gitignore +++ b/.gitignore @@ -1,8 +1,8 @@ -Airy_2d/Airy2d-out/* -Laguerre_Gauss_3d/LaguerreGauss3d-out/* -Gauss_2d/planar/* -Gauss_2d/concave/* -Gauss_2d/convex/* +scripts/Airy_2d/Airy2d-out/* +scripts/Laguerre_Gauss_3d/LaguerreGauss3d-out/* +scripts/Gauss_2d/planar/* +scripts/Gauss_2d/concave/* +scripts/Gauss_2d/convex/* ### Jupyter ### .ipynb_checkpoints diff --git a/README.md b/README.md index bce3cf2..10bd736 100644 --- a/README.md +++ b/README.md @@ -1,12 +1,12 @@ -![concave](Gauss_2d/img/concave_intensity_cropped_rotated_resized.png) -![planar](Gauss_2d/img/planar_intensity_cropped_rotated_resized.png) -![convex](Gauss_2d/img/convex_intensity_cropped_rotated_resized.png) -![Airy](Airy_2d/img/Airy_beam_M_0_W_4_scattering.png) - -![snap](Laguerre_Gauss_3d/img/vortex_beam_m_2_longitudinal_resized.png) -![snap](Laguerre_Gauss_3d/img/vortex_beam_m_2_transverse_resized.png) -![snap](Laguerre_Gauss_3d/img/vortex_beam_m_2_3d_half_resized.png) -![Airy](Airy_2d/img/Airy_beam_M_0_W_4_free_space.png) +![concave](scripts/Gauss_2d/img/concave_intensity_cropped_rotated_resized.png) +![planar](scripts/Gauss_2d/img/planar_intensity_cropped_rotated_resized.png) +![convex](scripts/Gauss_2d/img/convex_intensity_cropped_rotated_resized.png) +![Airy](scripts/Airy_2d/img/Airy_beam_M_0_W_4_scattering.png) + +![snap](scripts/Laguerre_Gauss_3d/img/vortex_beam_m_2_longitudinal_resized.png) +![snap](scripts/Laguerre_Gauss_3d/img/vortex_beam_m_2_transverse_resized.png) +![snap](scripts/Laguerre_Gauss_3d/img/vortex_beam_m_2_3d_half_resized.png) +![Airy](scripts/Airy_2d/img/Airy_beam_M_0_W_4_free_space.png) # Optical-beams-MEEP [![DOI](https://zenodo.org/badge/91711821.svg)](https://zenodo.org/badge/latestdoi/91711821) diff --git a/Airy_2d/Airy2d.ctl b/scripts/Airy_2d/Airy2d.ctl similarity index 100% rename from Airy_2d/Airy2d.ctl rename to scripts/Airy_2d/Airy2d.ctl diff --git a/Airy_2d/Airy2d.py b/scripts/Airy_2d/Airy2d.py similarity index 100% rename from Airy_2d/Airy2d.py rename to scripts/Airy_2d/Airy2d.py diff --git a/Airy_2d/img/Airy_beam_M_0_W_4_free_space.png b/scripts/Airy_2d/img/Airy_beam_M_0_W_4_free_space.png similarity index 100% rename from Airy_2d/img/Airy_beam_M_0_W_4_free_space.png rename to scripts/Airy_2d/img/Airy_beam_M_0_W_4_free_space.png diff --git a/Airy_2d/img/Airy_beam_M_0_W_4_scattering.png b/scripts/Airy_2d/img/Airy_beam_M_0_W_4_scattering.png similarity index 100% rename from Airy_2d/img/Airy_beam_M_0_W_4_scattering.png rename to scripts/Airy_2d/img/Airy_beam_M_0_W_4_scattering.png diff --git a/Airy_2d/optbeam.pxd b/scripts/Airy_2d/optbeam.pxd similarity index 100% rename from Airy_2d/optbeam.pxd rename to scripts/Airy_2d/optbeam.pxd diff --git a/Gauss_2d/Gauss2d.ctl b/scripts/Gauss_2d/Gauss2d.ctl similarity index 100% rename from Gauss_2d/Gauss2d.ctl rename to scripts/Gauss_2d/Gauss2d.ctl diff --git a/Gauss_2d/Gauss2d.py b/scripts/Gauss_2d/Gauss2d.py similarity index 100% rename from Gauss_2d/Gauss2d.py rename to scripts/Gauss_2d/Gauss2d.py diff --git a/Gauss_2d/img/concave_cropped_rotated_resized.png 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