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gradientCalculationV2.py

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+# -*- coding: utf-8 -*-
+"""
+Created on Mon Nov  4 17:02:30 2019
+
+@author: to_reilly
+"""
+
+import numpy as np
+import matplotlib.pyplot as plt
+from scipy import special
+from scipy import spatial
+
+def calcP(mm, aa, bb, kk):
+    mu0 = 4 * np.pi * 10**(-7)
+    dBesselk_m = special.kvp(mm, abs(kk)*aa,1)
+    dBesseli_m = special.ivp(mm, abs(kk)*bb,1)
+    return aa * mu0 * kk * dBesseli_m * dBesselk_m
+
+def calcQ(mm, aa, bb, kk):
+    mu0 = 4 * np.pi * 10**(-7)
+    dBesselk_m = special.kvp(mm,abs(kk)*aa,1)
+    Besseli_m = special.iv(mm, abs(kk) * bb)
+    return mm * aa * mu0 / bb * abs(kk) / kk * Besseli_m * dBesselk_m
+
+def calculateContour(streamF, numWires, phi, z):
+
+    phi2D, z2D= np.meshgrid(phi,z)
+    levels = np.linspace(np.min(streamF), np.max(streamF), numWires*2 + 4)
+    levels = levels[1:-1]
+
+    # Wire should be laid along contours between the isolines, calculate midpoint between isolines
+    midPointLevels = [(levels[i]+levels[i+1])/2 for i in range(np.size(levels)-1)]
+    midPointLevels = np.array(midPointLevels)[np.abs(midPointLevels) >= 1e-6] #remove zeros, account for floating point error
+
+    plt.ioff()
+    plt.figure()
+    contWires = plt.contour(phi2D,z2D,streamF,levels = midPointLevels)
+
+    return contWires
+
+def halbachXgradient(linearLength = 140, coilRad = 135, coilLength = 350,numWires = 10, numHighOrders = 10, \
+                     linearityTerm = 16, apoTerm = .05, resolution = 1e-3):
+
+    gradStrength    = 1e-3
+    a               = coilRad*1e-3     #gradRad
+    b               = 0.001*a
+    d               = linearLength*1e-3     #Linear region 
+    nShape          = linearityTerm
+    res             = resolution
+    Zmax            = coilLength*1e-3
+    N               = numHighOrders
+    h               = apoTerm
+
+    Nsamp           = np.int(2*Zmax/res)
+    z               = np.linspace(-Zmax,Zmax,Nsamp)
+    phi             = np.linspace(-1.5*np.pi,0.5*np.pi,Nsamp)
+
+
+    kfov            = 1/res
+    k               = np.linspace(0.00001,kfov,Nsamp).conj().T
+
+    gradShape       = np.divide(z,1+(z/d)**nShape)
+    gradShape_k     = np.fft.fft(gradShape.conj().T);
+
+    t_k = np.exp(-2*(h*k)**2)       #apodisation term
+
+    n_0    = 2*np.pi*gradShape_k*gradStrength/(calcQ(1,a,b,k)+calcP(1,a,b,k))
+    streamF = 0
+
+    for n in range(N+1):
+        sign = (-1)**(n+1)
+        scale  = 1
+        for m in range(n+1):
+            scale *= np.divide((calcP(2*m-1,a,b,k)-calcQ(2*m-1,a,b,k)),(calcP(2*m+1,a,b,k)+calcQ(2*m+1,a,b,k)))
+        B_apo   = sign*np.fft.ifft(np.divide(np.multiply(n_0,t_k*scale),k)) 
+        streamF += np.outer(B_apo,np.cos((2*n+1)*phi))
+    streamF = np.real(streamF)
+
+
+    return calculateContour(streamF, numWires, phi, z)
+
+def halbachYgradient(linearLength = 140, coilRad = 135, coilLength = 350, numWires = 10, numHighOrders = 10, \
+                     linearityTerm = 16, apoTerm = .05, resolution = 1e-3):
+
+    gradStrength    = 1e-3
+    a               = coilRad*1e-3     #gradRad
+    b               = 0.001*a
+    d               = linearLength*1e-3     #Linear region 
+    Zmax            = 2*coilLength*1e-3
+    N               = numHighOrders
+    h               = apoTerm
+
+    Nsamp           = np.int(2*Zmax/resolution)
+    z               = np.linspace(-Zmax,Zmax,Nsamp)
+    phi             = np.linspace(-1*np.pi,1*np.pi,Nsamp)
+
+    k               = np.linspace(0.00001,1/resolution,Nsamp).conj().T
+
+    gradShape       = 1/(1+(z/d)**linearityTerm) - 1/(1+((z+3.5*d)/(0.5*d))**linearityTerm)-1/(1+((z-3.5*d)/(0.5*d))**linearityTerm)
+
+    gradShape_k     = np.fft.fft(gradShape.conj().T);
+
+    t_k             = np.exp(-2*(h*k)**2)       #apodisation term
+
+    n_0             = b*2*np.pi*gradShape_k*gradStrength/(calcQ(2,a,b,k)+calcP(2,a,b,k))
+    streamF = 0
+
+    for n in range(N+1):
+        amp = (-1)**(n+1)
+        scale = 1
+        for m in range(1,n+1):
+            scale *= np.divide((calcP(2*m,a,b,k)-calcQ(2*m,a,b,k)),(calcP(2*m+2,a,b,k)+calcQ(2*m+2,a,b,k)))
+        B_apo   = np.fft.ifft((2/np.pi)*amp*(np.divide(1,k))*n_0*scale*t_k)
+        streamF +=  np.outer(B_apo,np.sin((2*n+2)*phi))
+
+    #remove sidelobes       
+    d_samp=d/resolution
+    streamF = streamF[int(Nsamp/2-1.5*d_samp):int(Nsamp/2+1.5*d_samp)]
+    z = z[int(Nsamp/2-1.5*d_samp):int(Nsamp/2+1.5*d_samp)]
+    phi2D, z2D= np.meshgrid(phi,z)
+
+    return calculateContour(streamF, numWires, phi, z)
+
+def halbachZgradient(linearLength = 140, coilRad = 135, coilLength = 350, numWires = 10, numHighOrders = 10, \
+                     linearityTerm = 16, apoTerm = .05, resolution = 1e-3):
+
+    gradStrength    = 1e-3
+    a               = coilRad*1e-3     #gradRad
+    b               = 0.001*a
+    d               = linearLength*1e-3     #Linear region 
+    Zmax            = 2*coilLength*1e-3
+    N               = numHighOrders
+    h               = apoTerm
+
+    Nsamp           = np.int(2*Zmax/resolution)
+    z               = np.linspace(-Zmax,Zmax,Nsamp)
+    phi             = np.linspace(-0.75*np.pi,1.25*np.pi,Nsamp)
+
+    k               = np.linspace(0.00001,1/resolution,Nsamp).conj().T
+
+    gradShape       = 1/(1+(z/d)**linearityTerm) - 1/(1+((z+3.5*d)/(0.5*d))**linearityTerm)-1/(1+((z-3.5*d)/(0.5*d))**linearityTerm)
+    gradShape_k     = np.fft.fft(gradShape.conj().T);
+
+    t_k             = np.exp(-2*(h*k)**2)       #apodisation term
+
+    n_0             = b*2*np.pi*gradShape_k*gradStrength/(calcQ(2,a,b,k)+calcP(2,a,b,k))
+    streamF         = 0
+
+    for n in range(N+1):
+        amp = (-1)**(n+1)
+        scale = 1
+        for m in range(1,n+1):
+            scale *= np.divide((calcP(2*m,a,b,k)-calcQ(2*m,a,b,k)),(calcP(2*m+2,a,b,k)+calcQ(2*m+2,a,b,k)))
+        B_apo   = np.fft.ifft((2/np.pi)*amp*(np.divide(1,k))*n_0*scale*t_k)
+        streamF +=  np.outer(B_apo,np.cos((2*n+2)*phi))
+
+    #remove sideloabs    
+    d_samp=d/resolution
+    streamF = streamF[int(Nsamp/2-1.5*d_samp):int(Nsamp/2+1.5*d_samp)]
+    z = z[int(Nsamp/2-1.5*d_samp):int(Nsamp/2+1.5*d_samp)]
+    phi2D, z2D= np.meshgrid(phi,z)
+
+    return calculateContour(streamF, numWires, phi, z)
+
+def calculateBfield(contours, DSV, resolution, coilRad, direction):
+    import numexpr as ne
+
+    radius = np.float32(DSV/2)
+
+    phi = np.linspace(0, 2*np.pi, 2*np.pi*radius/resolution, dtype = np.float32)
+    theta = np.linspace(0, np.pi, np.pi*radius/resolution, dtype = np.float32)
+    phiGrid, thetaGrid = np.meshgrid(phi,theta)
+    xSphere = radius*np.multiply(np.sin(thetaGrid), np.cos(phiGrid))
+    ySphere = radius*np.multiply(np.sin(thetaGrid), np.sin(phiGrid))
+    zSphere = radius*np.cos(thetaGrid)
+
+    points = np.stack((np.ravel(xSphere),np.ravel(ySphere),np.ravel(zSphere)),axis=1)
+
+    wireLevels = contours.allsegs
+    gradCurrent = np.float32(contours.levels[1] - contours.levels[0])
+
+    bField = np.zeros(np.shape(points)[0], dtype = np.float32)
+
+    import time
+    startTime = time.time()
+    wireCounter = 1
+    for wireLevel in wireLevels:
+        for wire in wireLevel:
+            print("Simulating wire %.0f of %0.f"%(wireCounter, np.size(wireLevels)))
+            wire = np.array(wire, dtype = np.float32)
+            wirePath3D =  np.stack((np.cos(wire[:,0])*np.float32(coilRad),np.sin(wire[:,0])*np.float32(coilRad),wire[:,1]),axis=1)
+            idS = 1e-7*gradCurrent*(wirePath3D[1:,:] - wirePath3D[:-1,:])
+            r = points[:,np.newaxis] - wirePath3D[:-1,:]
+            r3 = ne.evaluate("sum(r**2, axis = 2)")[:,:,np.newaxis]
+            rNorm = ne.evaluate("r/r3**1.5")
+            bField += np.matmul(rNorm[:,:,2], idS[:,1]) - np.matmul(rNorm[:,:,1],idS[:,2])
+            wireCounter += 1
+    print("Execution time: %.2f seconds"%(time.time()-startTime))
+    error = calculateError(points, bField, direction)
+    return [xSphere*1e3, ySphere*1e3, zSphere*1e3], np.reshape(bField, (np.size(theta), np.size(phi))), error
+
+def calculateError(coords, bField, direction):
+    if(direction == 0):
+        coordAxis = coords[:,2]
+    elif(direction == 1):
+        coordAxis = coords[:,1]
+    else:
+        coordAxis = coords[:,0]
+
+    argMin = np.argmin(coordAxis)
+    argMax = np.argmax(coordAxis)
+
+    posRange = np.max(coordAxis) - np.min(coordAxis)
+
+    bRange = bField[argMax] - bField[argMin]
+
+    efficiency = bRange/posRange
+
+    coordAxis[np.abs(coordAxis) < 0.01*posRange] = 'NaN'
+
+    return np.nanmax((bField - efficiency*coordAxis)/(efficiency*coordAxis))
+
+def exportWires(contours, coilRad, direction, conjoined):
+
+    wireNum = 0
+    contourDict = {}
+    wireLevels = contours.allsegs
+
+    if ((direction == 0) and conjoined):        #for the X gradient the center of the smallest contour is needed for joining the wires
+        minLength = np.inf
+        for wireLevel in wireLevels:
+            for wire in wireLevel:
+                if(np.size(wire,0) < minLength):
+                    centerHeight = np.abs(np.mean(wire[:,1])*1e3)
+
+    for wireLevel in wireLevels:
+        for wire in wireLevel:
+            wirePath3D = np.stack((np.cos(wire[:,0])*coilRad,np.sin(wire[:,0])*coilRad,wire[:,1]*1e3),axis=1)
+            if(conjoined):
+                gapSize = 8 #gap in which the sections are joined
+                gapAngle = gapSize/coilRad      
+                centerAngle = np.mean(wire[:,0])
+
+                if(direction == 0):
+                    mask = (np.abs(wire[:,0] - centerAngle) > gapAngle) | (np.abs(wirePath3D[:,2]) < centerHeight)
+                else:
+                    mask = (np.abs(wire[:,0] - centerAngle) > gapAngle) | (wirePath3D[:,2] < 0)
+
+                while mask[0]:
+                    mask = np.roll(mask,1)
+                    wirePath3D = np.roll(wirePath3D, 1, axis = 0)
+
+                contourDict[str(wireNum)] = np.stack((wirePath3D[mask, 0],wirePath3D[mask, 1],wirePath3D[mask, 2]),axis=1)
+            else:
+                contourDict[str(wireNum)] = wirePath3D
+            wireNum += 1
+
+    if(not conjoined):
+        return contourDict
+    else:
+
+        #############################################
+        # Join the wires with a gap in to one array #
+        #############################################
+
+        numCoilSegments = 4             #Number of quadrants
+
+        joinedContour = {}
+        joinedContour[str(0)] = contourDict[str(0)]
+        joinedContour[str(1)] = contourDict[str(1)]
+        joinedContour[str(2)] = contourDict[str(int(2*wireNum/numCoilSegments))]
+        joinedContour[str(3)] = contourDict[str(int(2*wireNum/numCoilSegments)+1)]
+
+        for idx in range(1,int(wireNum/numCoilSegments)):
+            joinedContour[str(0)] = np.append(joinedContour[str(0)], contourDict[str(2*idx)], axis = 0)
+            joinedContour[str(1)] = np.append(joinedContour[str(1)], contourDict[str(2*idx+1)], axis = 0)
+            joinedContour[str(2)] = np.append(joinedContour[str(2)], contourDict[str(int(2*wireNum/numCoilSegments) + idx*2 )], axis = 0)
+            joinedContour[str(3)] = np.append(joinedContour[str(3)], contourDict[str(int(2*wireNum/numCoilSegments) + idx*2 +1)], axis = 0)
+
+
+        ############################################
+        # Check for consecutive identical elements #
+        ############################################
+        tol = 1e-5
+        for key in joinedContour:
+            delta = joinedContour[key][1:,:] - joinedContour[key][:-1,:]
+            delta = np.sum(np.square(delta), axis = 1)
+            zeroElements = delta < tol
+            joinedContour[key] = np.delete(joinedContour[key],np.nonzero(zeroElements), axis = 0)
+
+        return joinedContour
+
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