From 7711c905ae16a03606fa77b97ad0b3323c89f59d Mon Sep 17 00:00:00 2001 From: Qiming Sun Date: Wed, 23 Sep 2020 11:12:33 -0700 Subject: [PATCH] Version 4.0.0 Add polynomial fitting scheme for erfc integral rys roots Bug fixes of erfc integral rys roots --- CMakeLists.txt | 21 +- ChangeLog | 6 + README | 5 +- include/cint.h.in | 5 +- src/cint_const.h | 3 +- src/erfc_roots.c | 48 + src/erfc_roots_xw.dat | 356750 +++++++++++++++++++++++++++++++++ src/fmt.c | 1 - src/g2e.c | 10 +- src/g2e_coulerf.c | 7 +- src/polyfits.c | 284 + src/rys_roots.c | 311 +- src/rys_roots.h | 2 +- testsuite/erfc_tabulate.py | 88 + testsuite/rys_tabulate.py | 20 +- testsuite/test_cint.py | 312 +- testsuite/test_rys_roots.py | 193 + 17 files changed, 357816 insertions(+), 250 deletions(-) create mode 100644 src/erfc_roots.c create mode 100644 src/erfc_roots_xw.dat create mode 100644 src/polyfits.c create mode 100644 testsuite/erfc_tabulate.py create mode 100644 testsuite/test_rys_roots.py diff --git a/CMakeLists.txt b/CMakeLists.txt index 32928cc8..5a4813e4 100644 --- a/CMakeLists.txt +++ b/CMakeLists.txt @@ -1,8 +1,8 @@ cmake_minimum_required (VERSION 2.6) project (cint C) -set(cint_VERSION_MAJOR "3") -set(cint_VERSION_MINOR "1") -set(cint_VERSION_PATCH "1") +set(cint_VERSION_MAJOR "4") +set(cint_VERSION_MINOR "0") +set(cint_VERSION_PATCH "0") set(cint_VERSION_TWEAK "0") set(cint_VERSION "${cint_VERSION_MAJOR}.${cint_VERSION_MINOR}.${cint_VERSION_PATCH}") set(cint_SOVERSION "${cint_VERSION_MAJOR}") @@ -71,6 +71,7 @@ if(WITH_RANGE_COULOMB) # defined in config.h # add_definitions(-DWITH_RANGE_COULOMB) message("Enabled WITH_RANGE_COULOMB") + set(cintSrc ${cintSrc} src/erfc_roots.c src/polyfits.c) endif(WITH_RANGE_COULOMB) if(WITH_COULOMB_ERF) @@ -99,11 +100,16 @@ else() message("P orbitals convention (px, py, pz)") endif(PYPZPX) -if(DEFINED MIN_EXPCUTOFF) +if(MIN_EXPCUTOFF) message("Minimal cutoff in exponent for integral screening ${MIN_EXPCUTOFF}") add_definitions(-DMIN_EXPCUTOFF=${MIN_EXPCUTOFF}) endif() +if(KEEP_GOING) + message("Whether to trigger hard exit for numerical issues in Rys quadrature") + add_definitions(-DKEEP_GOING) +endif() + option(WITH_FORTRAN "Fortran interface" on) if(WITH_FORTRAN) add_definitions(-DWITH_FORTRAN) @@ -143,12 +149,15 @@ if(QUADMATH_FOUND) endif() target_link_libraries(cint "-lm") -install(TARGETS cint DESTINATION "${CMAKE_INSTALL_PREFIX}/${CMAKE_INSTALL_LIBDIR}" COMPONENT "lib") + set(CintHeaders ${PROJECT_SOURCE_DIR}/include/cint_funcs.h ${PROJECT_BINARY_DIR}/include/cint.h) + +install(TARGETS cint DESTINATION "${CMAKE_INSTALL_PREFIX}/${CMAKE_INSTALL_LIBDIR}" COMPONENT "lib") install(FILES ${CintHeaders} DESTINATION ${CMAKE_INSTALL_PREFIX}/${CMAKE_INSTALL_INCLUDEDIR} COMPONENT "dev") + if(ENABLE_EXAMPLE) enable_language(Fortran) find_package(OpenMP) @@ -202,7 +211,7 @@ set("CPACK_DEBIAN_DEV_PACKAGE_NAME" "${CPACK_DEBIAN_LIB_PACKAGE_NAME}-dev") set(CPACK_DEBIAN_LIB_PACKAGE_DEPENDS "libopenblas0-pthread") set(CPACK_DEBIAN_DEV_PACKAGE_DEPENDS "${CPACK_DEBIAN_LIB_PACKAGE_NAME},libopenblas-pthread-dev") if(HAVE_QUADMATH) - set(CPACK_DEBIAN_LIB_PACKAGE_DEPENDS "${CPACK_DEBIAN_LIB_PACKAGE_DEPENDS},libquadmath0") + set(CPACK_DEBIAN_LIB_PACKAGE_DEPENDS "${CPACK_DEBIAN_LIB_PACKAGE_DEPENDS},libquadmath0") endif() set(CPACK_COMPONENTS_GROUPING "IGNORE") diff --git a/ChangeLog b/ChangeLog index 39a3af94..9f9850aa 100644 --- a/ChangeLog +++ b/ChangeLog @@ -1,3 +1,9 @@ +Version 4.0.0 (2020-09-23): + * API Change. PTR_LIGHT_SPEED is replaced with PTR_EXPCUTOFF. + Integral screening parameter can be passed through env[PTR_EXPCUTOFF] + * Add short-range integrals for range-separation + * Handle linear dependency in Rys polynomial + * Avoid calling exit function (issue #41) Version 3.1.1 (2020-08-25): * Fix bug in (py, pz, px) order Version 3.1.0 (2020-08-25): diff --git a/README b/README index caffb0ff..53b86829 100644 --- a/README +++ b/README @@ -1,8 +1,8 @@ libcint ======= -version 3.1.1 -2020-08-25 +version 4.0.0 +2020-09-23 What is libcint @@ -28,6 +28,7 @@ Features - Gaunt interaction - Breit interaction - 2-center, 3-center and 4-center integrals + - Long-range part and short-range part of range-separated Coulomb * Common lisp script to generate C code for new integrals. * Thread safe. * Uniform API for all kind of integrals. diff --git a/include/cint.h.in b/include/cint.h.in index e27ad500..c8364d9b 100644 --- a/include/cint.h.in +++ b/include/cint.h.in @@ -14,11 +14,14 @@ #define FINT int #endif +// This field is not required. Leave here as a placehold for backward compatibility #define PTR_EXPCUTOFF 0 #define PTR_COMMON_ORIG 1 #define PTR_RINV_ORIG 4 #define PTR_RINV_ZETA 7 -// omega parameter in range-separated coulomb operator erf(omega*r12)/r12 +// omega parameter in range-separated coulomb operator +// LR interaction: erf(omega*r12)/r12 if omega > 0 +// SR interaction: erfc(omega*r12)/r12 if omega < 0 #define PTR_RANGE_OMEGA 8 // Yukawa potential and slater-type geminal e^{-zeta r} #define PTR_F12_ZETA 9 diff --git a/src/cint_const.h b/src/cint_const.h index 7119c484..27478a84 100644 --- a/src/cint_const.h +++ b/src/cint_const.h @@ -5,8 +5,6 @@ */ // global parameters in env - -// Overall cutoff for integral prescreening, value needs to be ~ln(threshold) #define PTR_EXPCUTOFF 0 // R_C of (r-R_C) in dipole, GIAO operators #define PTR_COMMON_ORIG 1 @@ -22,6 +20,7 @@ #define PTR_F12_ZETA 9 // Gaussian type geminal e^{-zeta r^2} #define PTR_GTG_ZETA 10 +// Overall cutoff for integral prescreening, value needs to be ~ln(threshold) #define PTR_ENV_START 20 // slots of atm diff --git a/src/erfc_roots.c b/src/erfc_roots.c new file mode 100644 index 00000000..559c2f34 --- /dev/null +++ b/src/erfc_roots.c @@ -0,0 +1,48 @@ +// This function is implemented based on libslater library +// https://github.com/nubakery/libslater + +#include +#include +#include +#include "rys_roots.h" +#include "erfc_roots_xw.dat" + +void _CINT_clenshaw_d1(double *rr, const double *x, double u, FINT nroot); +void _CINT_clenshaw_dc(double *rr, const double *x, double u, FINT nroot); +void _CINT_matmul_14_14(double *imc, double *im, FINT nroot); + +void CINTerfc_rys_polyfits(FINT nroots, double x, double lower, double* u, double* w) +{ + const double* dx = DATA_X + (nroots-1)*nroots/2 * 1960; + const double* dw = DATA_W + (nroots-1)*nroots/2 * 1960; + double ll, t, tt; + FINT k, it; + FINT offset; + double im [14*nroots]; + double imc[14*nroots]; + + t = x; + if (t > 19682.99) t = 19682.99; + if (t > 1.0) { + tt = log(t) * 0.9102392266268373 + 1.0; // log(3)+1 + } else { + tt = sqrt(t); + } + + it = (FINT)tt; + tt = tt - it; + tt = 2.0 * tt - 1.0; + ll = 2.0 * lower - 1.0; + + offset = nroots * 196 * it; + _CINT_clenshaw_dc(im, dx+offset, ll, nroots); + _CINT_matmul_14_14(imc, im, nroots); + _CINT_clenshaw_d1(u, imc, tt, nroots); + _CINT_clenshaw_dc(im, dw+offset, ll, nroots); + _CINT_matmul_14_14(imc, im, nroots); + _CINT_clenshaw_d1(w, imc, tt, nroots); + + for (k = 0; k < nroots; k++) { + u[k] = u[k] / (1 - u[k]); + } +} diff --git a/src/erfc_roots_xw.dat b/src/erfc_roots_xw.dat new file mode 100644 index 00000000..4bea8a4b --- /dev/null +++ b/src/erfc_roots_xw.dat @@ -0,0 +1,356750 @@ +static const double DATA_X[] = { +/* root=1 */ + 1.16670164987695979e+00, + 1.17048381705232529e+00, + 1.17768088315981578e+00, + 1.18757623432476511e+00, + 1.19916038323313723e+00, + 1.21124904839807557e+00, + 1.22266250118688014e+00, + 1.23242877423602470e+00, + 1.23994943502983812e+00, + 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2.59548966994613062e-21, + 2.74487501518455307e-21, + 2.86610690138157352e-21, + 2.95107099333205252e-21, + 2.99469686223991272e-21, + -1.14048086697688211e-21, + -1.16331049277731536e-21, + -1.20861612916886205e-21, + -1.27559138255006627e-21, + -1.36279313777717327e-21, + -1.46789583750954986e-21, + -1.58740910359856222e-21, + -1.71639636273469003e-21, + -1.84830225194556651e-21, + -1.97513514344435326e-21, + -2.08827220858048923e-21, + -2.17979395215062908e-21, + -2.24371726091771277e-21, + -2.27645160467805074e-21, + 7.68383130267689900e-22, + 7.83764260119368003e-22, + 8.14288254617485956e-22, + 8.59411722932823197e-22, + 9.18161997536755780e-22, + 9.88970753636645990e-22, + 1.06948125388942752e-21, + 1.15635339806556671e-21, + 1.24514133117214764e-21, + 1.33041977535039533e-21, + 1.40635161152399427e-21, + 1.46762691261048568e-21, + 1.51031280242956044e-21, + 1.53212665427934710e-21, + -3.86622558936174643e-22, + -3.94361782229791297e-22, + -4.09720335563755895e-22, + -4.32424774884436816e-22, + -4.61985567690492928e-22, + -4.97613117199264650e-22, + -5.38119991905021589e-22, + -5.81821153683477823e-22, + -6.26470466521820161e-22, + -6.69325311151097851e-22, + -7.07440037060194824e-22, + -7.38150915973898823e-22, + -7.59509729111242130e-22, + -7.70410560492341852e-22, +}; diff --git a/src/fmt.c b/src/fmt.c index 17f100a9..05c82adb 100644 --- a/src/fmt.c +++ b/src/fmt.c @@ -290,7 +290,6 @@ void fmt_erfc_like(double *f, double t, double lower, FINT m) } else { turnover_point = 4; } - turnover_point = m + 1.5; if (t < turnover_point) { double b = m + 0.5; diff --git a/src/g2e.c b/src/g2e.c index fca87054..faec2e02 100644 --- a/src/g2e.c +++ b/src/g2e.c @@ -1731,11 +1731,11 @@ int CINTg0_2e(double *g, const double fac, const CINTEnvVars *envs) #ifdef WITH_RANGE_COULOMB const double omega = envs->env[PTR_RANGE_OMEGA]; double theta = 0; - if (omega > 0) { // long-range part of range-separated Coulomb - theta = omega * omega / (omega * omega + a0); - a0 *= theta; - } else if (omega < 0) { // short-range part of range-separated Coulomb + if (omega != 0) { theta = omega * omega / (omega * omega + a0); + if (omega > 0) { // long-range part of range-separated Coulomb + a0 *= theta; + } } #endif @@ -1744,7 +1744,7 @@ int CINTg0_2e(double *g, const double fac, const CINTEnvVars *envs) + rijrkl[2] * rijrkl[2]); #ifdef WITH_RANGE_COULOMB - if (omega < 0) { + if (omega < 0) { // short-range part of range-separated Coulomb // very small erfc() leads to ~0 weights if (theta * x > envs->expcutoff) { return 0; diff --git a/src/g2e_coulerf.c b/src/g2e_coulerf.c index 21bb6ae5..7ca282fd 100644 --- a/src/g2e_coulerf.c +++ b/src/g2e_coulerf.c @@ -13,7 +13,7 @@ #include "rys_roots.h" #include "g2e.h" -void CINTg0_2e_coulerf(double *g, double fac, CINTEnvVars *envs); +int CINTg0_2e_coulerf(double *g, double fac, CINTEnvVars *envs); void CINTinit_int2e_coulerf_EnvVars(CINTEnvVars *envs, FINT *ng, FINT *shls, FINT *atm, FINT natm, FINT *bas, FINT nbas, double *env) @@ -25,7 +25,7 @@ void CINTinit_int2e_coulerf_EnvVars(CINTEnvVars *envs, FINT *ng, FINT *shls, /* * g[i,k,l,j] = < ik | lj > = ( i j | k l ) */ -void CINTg0_2e_coulerf(double *g, double fac, CINTEnvVars *envs) +int CINTg0_2e_coulerf(double *g, double fac, CINTEnvVars *envs) { double aij = envs->aij; double akl = envs->akl; @@ -57,7 +57,7 @@ void CINTg0_2e_coulerf(double *g, double fac, CINTEnvVars *envs) g[0] = 1; g[1] = 1; g[2] *= fac1; - return; + return 1; } FINT irys; @@ -102,4 +102,5 @@ void CINTg0_2e_coulerf(double *g, double fac, CINTEnvVars *envs) } (*envs->f_g0_2d4d)(g, &bc, envs); + return 1; } diff --git a/src/polyfits.c b/src/polyfits.c new file mode 100644 index 00000000..05ee40b8 --- /dev/null +++ b/src/polyfits.c @@ -0,0 +1,284 @@ +#include +#include +#include +#include "rys_roots.h" + +/* +from mpmath import * +mp.dps = 25 +for i in range(14): + for j in range(14): + print(' %.19e' % cos(pi*j*(2*i+1)/28)[-26:]) +*/ +static const double COS_14_14[] = { + 1. , + 9.9371220989324260398e-01, + 9.7492791218182361934e-01, + 9.4388333030836757409e-01, + 9.0096886790241914600e-01, + 8.4672419922828412453e-01, + 7.8183148246802980363e-01, + 7.0710678118654757274e-01, + 6.2348980185873348336e-01, + 5.3203207651533657163e-01, + 4.3388373911755812040e-01, + 3.3027906195516709698e-01, + 2.2252093395631439288e-01, + 1.1196447610330785560e-01, + 1. , + 9.4388333030836757409e-01, + 7.8183148246802980363e-01, + 5.3203207651533657163e-01, + 2.2252093395631439288e-01, +-1.1196447610330785560e-01, +-4.3388373911755812040e-01, +-7.0710678118654757274e-01, +-9.0096886790241914600e-01, +-9.9371220989324260398e-01, +-9.7492791218182361934e-01, +-8.4672419922828412453e-01, +-6.2348980185873348336e-01, +-3.3027906195516709698e-01, + 1. , + 8.4672419922828412453e-01, + 4.3388373911755812040e-01, +-1.1196447610330785560e-01, +-6.2348980185873348336e-01, +-9.4388333030836757409e-01, +-9.7492791218182361934e-01, +-7.0710678118654757274e-01, +-2.2252093395631439288e-01, + 3.3027906195516709698e-01, + 7.8183148246802980363e-01, + 9.9371220989324260398e-01, + 9.0096886790241914600e-01, + 5.3203207651533657163e-01, + 1. , + 7.0710678118654757274e-01, + 0. , +-7.0710678118654757274e-01, +-1. , +-7.0710678118654757274e-01, + 0. , + 7.0710678118654757274e-01, + 1. , + 7.0710678118654757274e-01, + 0. , +-7.0710678118654757274e-01, +-1. , +-7.0710678118654757274e-01, + 1. , + 5.3203207651533657163e-01, +-4.3388373911755812040e-01, +-9.9371220989324260398e-01, +-6.2348980185873348336e-01, + 3.3027906195516709698e-01, + 9.7492791218182361934e-01, + 7.0710678118654757274e-01, +-2.2252093395631439288e-01, +-9.4388333030836757409e-01, +-7.8183148246802980363e-01, + 1.1196447610330785560e-01, + 9.0096886790241914600e-01, + 8.4672419922828412453e-01, + 1. , + 3.3027906195516709698e-01, +-7.8183148246802980363e-01, +-8.4672419922828412453e-01, + 2.2252093395631439288e-01, + 9.9371220989324260398e-01, + 4.3388373911755812040e-01, +-7.0710678118654757274e-01, +-9.0096886790241914600e-01, + 1.1196447610330785560e-01, + 9.7492791218182361934e-01, + 5.3203207651533657163e-01, +-6.2348980185873348336e-01, +-9.4388333030836757409e-01, + 1. , + 1.1196447610330785560e-01, +-9.7492791218182361934e-01, +-3.3027906195516709698e-01, + 9.0096886790241914600e-01, + 5.3203207651533657163e-01, +-7.8183148246802980363e-01, +-7.0710678118654757274e-01, + 6.2348980185873348336e-01, + 8.4672419922828412453e-01, +-4.3388373911755812040e-01, +-9.4388333030836757409e-01, + 2.2252093395631439288e-01, + 9.9371220989324260398e-01, + 1. , +-1.1196447610330785560e-01, +-9.7492791218182361934e-01, + 3.3027906195516709698e-01, + 9.0096886790241914600e-01, +-5.3203207651533657163e-01, +-7.8183148246802980363e-01, + 7.0710678118654757274e-01, + 6.2348980185873348336e-01, +-8.4672419922828412453e-01, +-4.3388373911755812040e-01, + 9.4388333030836757409e-01, + 2.2252093395631439288e-01, +-9.9371220989324260398e-01, + 1. , +-3.3027906195516709698e-01, +-7.8183148246802980363e-01, + 8.4672419922828412453e-01, + 2.2252093395631439288e-01, +-9.9371220989324260398e-01, + 4.3388373911755812040e-01, + 7.0710678118654757274e-01, +-9.0096886790241914600e-01, +-1.1196447610330785560e-01, + 9.7492791218182361934e-01, +-5.3203207651533657163e-01, +-6.2348980185873348336e-01, + 9.4388333030836757409e-01, + 1. , +-5.3203207651533657163e-01, +-4.3388373911755812040e-01, + 9.9371220989324260398e-01, +-6.2348980185873348336e-01, +-3.3027906195516709698e-01, + 9.7492791218182361934e-01, +-7.0710678118654757274e-01, +-2.2252093395631439288e-01, + 9.4388333030836757409e-01, +-7.8183148246802980363e-01, +-1.1196447610330785560e-01, + 9.0096886790241914600e-01, +-8.4672419922828412453e-01, + 1. , +-7.0710678118654757274e-01, + 0. , + 7.0710678118654757274e-01, +-1. , + 7.0710678118654757274e-01, + 0. , +-7.0710678118654757274e-01, + 1. , +-7.0710678118654757274e-01, + 0. , + 7.0710678118654757274e-01, +-1. , + 7.0710678118654757274e-01, + 1. , +-8.4672419922828412453e-01, + 4.3388373911755812040e-01, + 1.1196447610330785560e-01, +-6.2348980185873348336e-01, + 9.4388333030836757409e-01, +-9.7492791218182361934e-01, + 7.0710678118654757274e-01, +-2.2252093395631439288e-01, +-3.3027906195516709698e-01, + 7.8183148246802980363e-01, +-9.9371220989324260398e-01, + 9.0096886790241914600e-01, +-5.3203207651533657163e-01, + 1. , +-9.4388333030836757409e-01, + 7.8183148246802980363e-01, +-5.3203207651533657163e-01, + 2.2252093395631439288e-01, + 1.1196447610330785560e-01, +-4.3388373911755812040e-01, + 7.0710678118654757274e-01, +-9.0096886790241914600e-01, + 9.9371220989324260398e-01, +-9.7492791218182361934e-01, + 8.4672419922828412453e-01, +-6.2348980185873348336e-01, + 3.3027906195516709698e-01, + 1. , +-9.9371220989324260398e-01, + 9.7492791218182361934e-01, +-9.4388333030836757409e-01, + 9.0096886790241914600e-01, +-8.4672419922828412453e-01, + 7.8183148246802980363e-01, +-7.0710678118654757274e-01, + 6.2348980185873348336e-01, +-5.3203207651533657163e-01, + 4.3388373911755812040e-01, +-3.3027906195516709698e-01, + 2.2252093395631439288e-01, +-1.1196447610330785560e-01, +}; + +void _CINT_clenshaw_dc(double *rr, const double *x, double u, FINT nroot) +{ + double d[14]; + double g[14]; + double u2 = u * 2.; + FINT i, j, k; + + for (i = 0; i < nroot; ++i) { + for (j = 0; j < 14; j++) { + d[j] = 0; + g[j] = x[13*14+j]; + } + for (k = 11; k >= 1; k-=2) { + for (j = 0; j < 14; j++) { + d[j] = u2 * g[j] - d[j] + x[(k+1)*14+j ]; + } + for (j = 0; j < 14; j++){ + g[j] = u2 * d[j] - g[j] + x[k*14+j]; + } + } + for (j = 0; j < 14; j++) { + rr[j+14*i] = u * g[j] - d[j] + x[j] * 0.5; + } + x += 196; + } +} + +void _CINT_clenshaw_d1(double *rr, const double *x, double u, FINT nroot) +{ + FINT i; + double d0, d1, g0, g1; + double u2 = u * 2.; + + for (i = 0; i < nroot; i++) { + d0 = 0; + g0 = x[13+14*i]; + d0 = u2 * g0 - d0 + x[12+14*i]; + g0 = u2 * d0 - g0 + x[11+14*i]; + d0 = u2 * g0 - d0 + x[10+14*i]; + g0 = u2 * d0 - g0 + x[9 +14*i]; + d0 = u2 * g0 - d0 + x[8 +14*i]; + g0 = u2 * d0 - g0 + x[7 +14*i]; + d0 = u2 * g0 - d0 + x[6 +14*i]; + g0 = u2 * d0 - g0 + x[5 +14*i]; + d0 = u2 * g0 - d0 + x[4 +14*i]; + g0 = u2 * d0 - g0 + x[3 +14*i]; + d0 = u2 * g0 - d0 + x[2 +14*i]; + g0 = u2 * d0 - g0 + x[1 +14*i]; + rr[i] = u * g0 - d0 + x[14*i] * 0.5; + } +} + +void _CINT_matmul_14_14(double *imc, double *im, FINT nroot) +{ + double o7 = 0.14285714285714285714; + double s; + double d0[14]; + FINT i, j, k; + for (i = 0; i < nroot; i++) { + for (j = 0; j < 14; j++) { + d0[j] = 0; + } + for (j = 0; j < 14; j++) { + s = im[j+14*i]; + for (k = 0; k < 14; ++k) { + d0[k] += s * COS_14_14[j*14+k]; + } + } + for (j = 0; j < 14; j++) { + imc[j+14*i] = o7 * d0[j]; + } + } +} diff --git a/src/rys_roots.c b/src/rys_roots.c index ed1be160..90cd01c1 100644 --- a/src/rys_roots.c +++ b/src/rys_roots.c @@ -32,62 +32,130 @@ static void rys_root2(double x, double *roots, double *weights); static void rys_root3(double x, double *roots, double *weights); static void rys_root4(double x, double *roots, double *weights); static void rys_root5(double x, double *roots, double *weights); -static void R_droot(FINT nroots, double x, double *roots, double *weights); -static void erfc_rys_roots(FINT nroots, double x, double lower, double *roots, double *weights); +static int R_droot(FINT nroots, double x, double *roots, double *weights); #ifdef HAVE_QUADMATH_H -static void R_qroot(FINT nroots, double x, double *roots, double *weights); +static int R_qroot(FINT nroots, double x, double *roots, double *weights); #else -static void R_lroot(FINT nroots, double x, double *roots, double *weights); +static int R_lroot(FINT nroots, double x, double *roots, double *weights); +#endif +#ifdef WITH_RANGE_COULOMB +static int erfc_rys_roots(FINT nroots, double x, double lower, double *roots, double *weights); #endif // FIXME: R_dsmit causes big errors for nroots > 13 void CINTrys_roots(FINT nroots, double x, double *u, double *w) { + FINT error; switch (nroots) { - case 1: - rys_root1(x, u, w); - break; - case 2: - rys_root2(x, u, w); - break; - case 3: - rys_root3(x, u, w); - break; - case 4: - rys_root4(x, u, w); - break; - case 5: - rys_root5(x, u, w); - break; - case 6: case 7: case 8: case 9: - R_droot(nroots, x, u, w); - break; + case 1: + rys_root1(x, u, w); + break; + case 2: + rys_root2(x, u, w); + break; + case 3: + rys_root3(x, u, w); + break; + case 4: + rys_root4(x, u, w); + break; + case 5: + rys_root5(x, u, w); + break; #ifdef HAVE_QUADMATH_H - default: + case 6: case 7: case 8: case 9: + error = R_droot(nroots, x, u, w); + if (error == 1) { R_qroot(nroots, x, u, w); -#else - case 10: case 11: case 12: case 13: - R_lroot(nroots, x, u, w); - break; - default: - fprintf(stderr, "libcint needs quadmath library to support nroots=%d\n", nroots); + } + break; + default: + error = R_qroot(nroots, x, u, w); + if (error == 1) { #ifndef KEEP_GOING exit(1); #else + fprintf(stderr, "libcint R_lroot fails. nroots=%d\n", nroots); +#endif + } +#else // QUADMATH + case 6: case 7: case 8: case 9: + error = R_droot(nroots, x, u, w); + if (error == 1) { R_lroot(nroots, x, u, w); + } + break; + case 10: case 11: case 12: case 13: + R_lroot(nroots, x, u, w); + break; + default: + fprintf(stderr, "libcint needs quadmath library to support nroots=%d\n", nroots); +#ifndef KEEP_GOING + exit(1); +#else + error = R_lroot(nroots, x, u, w); + if (error == 1) { + fprintf(stderr, "libcint R_lroot fails. nroots=%d\n", nroots); + } #endif #endif } } +#ifdef WITH_RANGE_COULOMB /* * lower is the lower bound of the erfc integral */ +static void erfc_rys_aug_polyfits(FINT nroots, double x, double lower, + double *u, double *w, FINT turnover_point) +{ + int error; + if (lower < turnover_point) { + error = erfc_rys_roots(nroots, x, lower, u, w); + } + if (error == 1 || lower >= turnover_point) { + // call polyfits for erfc roots and weights. It has + // on average errors ~1e-7 + CINTerfc_rys_polyfits(nroots, x, lower, u, w); + } + +} void CINTerfc_rys_roots(FINT nroots, double x, double lower, double *u, double *w) { - erfc_rys_roots(nroots, x, lower, u, w); + FINT error; + switch (nroots) { + case 1: case 2: case 3: case 4: + error = erfc_rys_roots(nroots, x, lower, u, w); + if (error == 1) { + CINTerfc_rys_polyfits(nroots, x, lower, u, w); + } + break; + case 5: + erfc_rys_aug_polyfits(nroots, x, lower, u, w, 0.8); + break; + case 6: + erfc_rys_aug_polyfits(nroots, x, lower, u, w, 0.6); + break; + case 7: + erfc_rys_aug_polyfits(nroots, x, lower, u, w, 0.4); + break; + case 8: + erfc_rys_aug_polyfits(nroots, x, lower, u, w, 0.3); + break; + case 9: case 10: case 11: case 12: case 13: + CINTerfc_rys_polyfits(nroots, x, lower, u, w); + break; + default: + fprintf(stderr, "libcint erfc_rys_roots does not support nroots=%d\n", nroots); +#ifndef KEEP_GOING + exit(1); +#else + erfc_rys_roots(nroots, x, lower, u, w); +#endif + } } +#endif static void rys_root1(double X, double *roots, double *weights) { @@ -1457,6 +1525,7 @@ static int R_dnode(double *a, double *rt, FINT order) { const double accrt = 1e-15; double x0, x1, xi, x1init, p0, p1, pi, p1init; + double roots[order]; FINT i, m, n; x1init = 0; @@ -1487,10 +1556,10 @@ static int R_dnode(double *a, double *rt, FINT order) } // interpolate/extrapolate between [x0,x1] if (p1 == 0) { - rt[m] = x1; + roots[m] = x1; continue; } else if (p0 == 0) { - rt[m] = x0; + roots[m] = x0; continue; } else { xi = x0 + (x0 - x1) / (p1 - p0) * p0; @@ -1500,7 +1569,7 @@ static int R_dnode(double *a, double *rt, FINT order) n++; if (n > 200) { fprintf(stderr, "libcint::rys_roots NO CONV. IN R_dnode\n"); - return 2; + return 1; } POLYNOMIAL_VALUE1(pi, a, order, xi); if (pi == 0) { @@ -1527,11 +1596,21 @@ static int R_dnode(double *a, double *rt, FINT order) xi = x0 + (x0 - x1) / (p1 - p0) * p0; } - rt[m] = xi; + roots[m] = xi; + } + for (m = 0; m < order; ++m) { + rt[m] = roots[m]; } return 0; } +#define SET_ZERO(a, n, start) \ + for (k = start; k < n; ++k) { \ + for (i = 0; i < n; ++i) { \ + a[i + k * MXROOTS1] = 0; \ + } \ + } \ + static int R_dsmit(double *cs, double *fmt_ints, FINT n) { int i, j, k; @@ -1539,7 +1618,15 @@ static int R_dsmit(double *cs, double *fmt_ints, FINT n) double v[MXROOTS1]; fac = -fmt_ints[1] / fmt_ints[0]; - tmp = 1 / sqrt(fmt_ints[2] + fac * fmt_ints[1]); + tmp = fmt_ints[2] + fac * fmt_ints[1]; + if (tmp <= 0) { +#ifndef KEEP_GOING + fprintf(stderr, "libcint::rys_roots negative value in sqrt for roots %d (j=1)\n", n-1); +#endif + SET_ZERO(cs, n, 1); + return 1; + } + tmp = 1 / sqrt(tmp); cs[0+0*MXROOTS1] = 1 / sqrt(fmt_ints[0]); cs[0+1*MXROOTS1] = fac * tmp; cs[1+1*MXROOTS1] = tmp; @@ -1562,15 +1649,11 @@ static int R_dsmit(double *cs, double *fmt_ints, FINT n) if (fac <= 0) { #ifndef KEEP_GOING - fprintf(stderr, "libcint::rys_roots negative value in sqrt for roots %d\n", n); + fprintf(stderr, "libcint::rys_roots negative value in sqrt for roots %d (j=%d)\n", n-1, j); #endif // set rest coefficients to 0 - for (k = j; k < n; ++k) { - for (i = 0; i < n; ++i) { - cs[i + k * MXROOTS1] = 0; - } - } - return 4; + SET_ZERO(cs, n, j); + return j; } fac = 1 / sqrt(fac); cs[j + j * MXROOTS1] = fac; @@ -1585,8 +1668,8 @@ static int R_dsmit(double *cs, double *fmt_ints, FINT n) * Using RDK algorithm (based on Schmidt orthogonalization to search rys roots * and weights */ -static void _rdk_rys_roots(FINT nroots, double *fmt_ints, - double *roots, double *weights) +static int _rdk_rys_roots(FINT nroots, double *fmt_ints, + double *roots, double *weights) { FINT i, k, j, m, order; FINT nroots1 = nroots + 1; @@ -1601,12 +1684,12 @@ static void _rdk_rys_roots(FINT nroots, double *fmt_ints, roots[k] = 0; weights[k] = 0; } - return; + return 0; } if (nroots == 1) { roots[k] = fmt_ints[1] / (fmt_ints[0] - fmt_ints[1]); weights[k] = fmt_ints[0]; - return; + return 0; } FINT error = R_dsmit(cs, fmt_ints, nroots1); @@ -1614,6 +1697,10 @@ static void _rdk_rys_roots(FINT nroots, double *fmt_ints, if (error) { exit(error); } +#else + if (error == 1) { + return 1; + } #endif dum = sqrt(cs[2*MXROOTS1+1] * cs[2*MXROOTS1+1] - 4 * cs[2*MXROOTS1+0] * cs[2*MXROOTS1+2]); @@ -1627,9 +1714,11 @@ static void _rdk_rys_roots(FINT nroots, double *fmt_ints, order = k + 1; a = cs + (k + 1) * MXROOTS1; error = R_dnode(a, rt, order); -#ifndef KEEP_GOING if (error) { +#ifndef KEEP_GOING exit(error); +#else + return error; } #endif } @@ -1657,23 +1746,26 @@ static void _rdk_rys_roots(FINT nroots, double *fmt_ints, roots[k] = root / (1 - root); weights[k] = 1 / dum; } + return 0; } -static void R_droot(FINT nroots, double x, - double roots[], double weights[]) +static int R_droot(FINT nroots, double x, + double roots[], double weights[]) { double fmt_ints[nroots*2+1]; gamma_inc_like(fmt_ints, x, nroots*2); - _rdk_rys_roots(nroots, fmt_ints, roots, weights); + return _rdk_rys_roots(nroots, fmt_ints, roots, weights); } -static void erfc_rys_roots(FINT nroots, double x, double lower, +#ifdef WITH_RANGE_COULOMB +static int erfc_rys_roots(FINT nroots, double x, double lower, double *roots, double *weights) { double fmt_ints[nroots*2+1]; fmt_erfc_like(fmt_ints, x, lower, nroots*2); - _rdk_rys_roots(nroots, fmt_ints, roots, weights); + return _rdk_rys_roots(nroots, fmt_ints, roots, weights); } +#endif #ifndef HAVE_QUADMATH_H @@ -1715,6 +1807,7 @@ static void R_lnode(long double *a, long double *rt, FINT order) const long double accrt = 1e-15; #endif long double x0, x1, xi, x1init, p0, p1, pi, p1init; + long double roots[order]; FINT i, m, n; x1init = 0; @@ -1742,11 +1835,11 @@ static void R_lnode(long double *a, long double *rt, FINT order) p0 = p1init; } // interpolate/extrapolate between [x0,x1] - if (p0 == 0) { - rt[m] = x0; + if (p1 == 0) { + roots[m] = x1; continue; - } else if (p1 == 0) { - rt[m] = x1; + } else if (p0 == 0) { + roots[m] = x0; continue; } else { xi = x0 + (x0 - x1) / (p1 - p0) * p0; @@ -1756,7 +1849,7 @@ static void R_lnode(long double *a, long double *rt, FINT order) n++; if (n > 200) { fprintf(stderr, "libcint::rys_roots NO CONV. IN R_lnode\n"); - return 2; + return 1; } POLYNOMIAL_VALUE1(pi, a, order, xi); if (pi == 0) { @@ -1783,18 +1876,30 @@ static void R_lnode(long double *a, long double *rt, FINT order) xi = x0 + (x0 - x1) / (p1 - p0) * p0; } - rt[m] = xi; + roots[m] = xi; + } + for (m = 0; m < order; ++m) { + rt[m] = roots[m]; } + return 0; } -static void R_lsmit(long double *cs, long double *fmt_ints, FINT n) +static FINT R_lsmit(long double *cs, long double *fmt_ints, FINT n) { FINT i, j, k; long double fac, dot, tmp; long double v[MXROOTS1]; fac = -fmt_ints[1] / fmt_ints[0]; - tmp = 1 / SQRTL(fmt_ints[2] + fac * fmt_ints[1]); + tmp = fmt_ints[2] + fac * fmt_ints[1]; + if (tmp <= 0) { +#ifndef KEEP_GOING + fprintf(stderr, "libcint::rys_roots negative value in sqrt for roots %d (j=1)\n", n-1); +#endif + SET_ZERO(cs, n, 1); + return 1; + } + tmp = 1 / SQRTL(tmp); cs[0+0*MXROOTS1] = 1 / SQRTL(fmt_ints[0]); cs[0+1*MXROOTS1] = fac * tmp; cs[1+1*MXROOTS1] = tmp; @@ -1817,15 +1922,11 @@ static void R_lsmit(long double *cs, long double *fmt_ints, FINT n) if (fac <= 0) { #ifndef KEEP_GOING - fprintf(stderr, "libcint::rys_roots negative value in sqrt for roots %d\n", n); + fprintf(stderr, "libcint::rys_roots negative value in sqrt for roots %d (j=%d)\n", n-1, j); #endif // set rest coefficients to 0 - for (k = j; k < n; ++k) { - for (i = 0; i < n; ++i) { - cs[i + k * MXROOTS1] = 0; - } - } - return 4; + SET_ZERO(cs, n, j); + return j; } fac = 1 / SQRTL(fac); cs[j + j * MXROOTS1] = fac; @@ -1833,10 +1934,11 @@ static void R_lsmit(long double *cs, long double *fmt_ints, FINT n) cs[k + j * MXROOTS1] = fac * v[k]; } } + return 0; } -static void R_lroot(FINT nroots, double x, - double roots[], double weights[]) +static int R_lroot(FINT nroots, double x, + double roots[], double weights[]) { FINT i, k, j, m, order; FINT nroots1 = nroots + 1; @@ -1852,7 +1954,7 @@ static void R_lroot(FINT nroots, double x, roots[k] = 0; weights[k] = 0; } - return; + return 0; } FINT error = R_lsmit(cs, fmt_ints, nroots1); @@ -1860,6 +1962,10 @@ static void R_lroot(FINT nroots, double x, if (error) { exit(error); } +#else + if (error == 1) { + return 1; + } #endif if (nroots == 1) { @@ -1877,11 +1983,13 @@ static void R_lroot(FINT nroots, double x, order = k + 1; a = cs + (k + 1) * MXROOTS1; error = R_lnode(a, rt, order); -#ifndef KEEP_GOING if (error) { +#ifndef KEEP_GOING exit(error); - } +#else + return error; #endif + } } for (k = 0; k < nroots; ++k) { @@ -1903,6 +2011,7 @@ static void R_lroot(FINT nroots, double x, roots[k] = root / (1 - root); weights[k] = 1 / dum; } + return 0; } #else // defined HAVE_QUADMATH_H @@ -1910,6 +2019,7 @@ static int R_qnode(__float128 *a, __float128 *rt, FINT order) { const __float128 accrt = 1e-20q; __float128 x0, x1, xi, x1init, p0, p1, pi, p1init; + __float128 roots[order]; FINT i, m, n; x1init = 0; @@ -1919,6 +2029,9 @@ static int R_qnode(__float128 *a, __float128 *rt, FINT order) p0 = p1init; x1init = rt[m]; POLYNOMIAL_VALUE1(p1init, a, order, x1init); + + // When all coefficients a are 0, short-circuit the rest code to + // ensure the roots from the lower order polynomials are preserved if (p1init == 0) { continue; } @@ -1937,11 +2050,11 @@ static int R_qnode(__float128 *a, __float128 *rt, FINT order) p0 = p1init; } // interpolate/extrapolate between [x0,x1] - if (p0 == 0) { - rt[m] = x0; + if (p1 == 0) { + roots[m] = x1; continue; - } else if (p1 == 0) { - rt[m] = x1; + } else if (p0 == 0) { + roots[m] = x0; continue; } else { xi = x0 + (x0 - x1) / (p1 - p0) * p0; @@ -1951,7 +2064,7 @@ static int R_qnode(__float128 *a, __float128 *rt, FINT order) n++; if (n > 600) { fprintf(stderr, "libcint::rys_roots NO CONV. IN R_qnode\n"); - return 2; + return 1; } POLYNOMIAL_VALUE1(pi, a, order, xi); if (pi == 0) { @@ -1978,8 +2091,12 @@ static int R_qnode(__float128 *a, __float128 *rt, FINT order) xi = x0 + (x0 - x1) / (p1 - p0) * p0; } - rt[m] = xi; + roots[m] = xi; + } + for (m = 0; m < order; ++m) { + rt[m] = roots[m]; } + return 0; } static int R_qsmit(__float128 *cs, __float128 *fmt_ints, FINT n) @@ -1989,12 +2106,20 @@ static int R_qsmit(__float128 *cs, __float128 *fmt_ints, FINT n) __float128 v[MXROOTS1]; fac = -fmt_ints[1] / fmt_ints[0]; - tmp = 1 / sqrtq(fmt_ints[2] + fac * fmt_ints[1]); + tmp = fmt_ints[2] + fac * fmt_ints[1]; + if (tmp <= 0) { +#ifndef KEEP_GOING + fprintf(stderr, "libcint::rys_roots negative value in sqrt for roots %d (j=1)\n", n-1); +#endif + SET_ZERO(cs, n, 1); + return 1; + } + tmp = 1 / sqrtq(tmp); cs[0+0*MXROOTS1] = 1 / sqrtq(fmt_ints[0]); cs[0+1*MXROOTS1] = fac * tmp; cs[1+1*MXROOTS1] = tmp; - for (i = 2; i < n; ++i) { + for (j = 2; j < n; ++j) { for (k = 0; k < j; ++k) { v[k] = 0; } @@ -2012,15 +2137,11 @@ static int R_qsmit(__float128 *cs, __float128 *fmt_ints, FINT n) if (fac <= 0) { #ifndef KEEP_GOING - fprintf(stderr, "libcint::rys_roots negative value in sqrt\n"); + fprintf(stderr, "libcint::rys_roots negative value in sqrt for roots %d (j=%d)\n", n-1, j); #endif // set rest coefficients to 0 - for (k = j; k < n; ++k) { - for (i = 0; i < n; ++i) { - cs[i + k * MXROOTS1] = 0; - } - } - return 4; + SET_ZERO(cs, n, j); + return j; } fac = 1.q / sqrtq(fac); cs[j + j * MXROOTS1] = fac; @@ -2030,8 +2151,7 @@ static int R_qsmit(__float128 *cs, __float128 *fmt_ints, FINT n) } } -static void R_qroot(FINT nroots, double x, - double roots[], double weights[]) +static int R_qroot(FINT nroots, double x, double *roots, double *weights) { FINT i, k, j, m, order; FINT nroots1 = nroots + 1; @@ -2047,7 +2167,7 @@ static void R_qroot(FINT nroots, double x, roots[k] = 0; weights[k] = 0; } - return; + return 0; } FINT error = R_qsmit(cs, fmt_ints, nroots1); @@ -2055,6 +2175,10 @@ static void R_qroot(FINT nroots, double x, if (error) { exit(error); } +#else + if (error == 1) { + return 1; + } #endif if (nroots == 1) { @@ -2072,11 +2196,13 @@ static void R_qroot(FINT nroots, double x, order = k + 1; a = cs + (k + 1) * MXROOTS1; error = R_qnode(a, rt, order); -#ifndef KEEP_GOING if (error) { +#ifndef KEEP_GOING exit(error); - } +#else + return error; #endif + } } for (k = 0; k < nroots; ++k) { @@ -2098,6 +2224,7 @@ static void R_qroot(FINT nroots, double x, roots[k] = root / (1 - root); weights[k] = 1 / dum; } + return 0; } #endif diff --git a/src/rys_roots.h b/src/rys_roots.h index bb866989..0fe4fe5a 100644 --- a/src/rys_roots.h +++ b/src/rys_roots.h @@ -2,5 +2,5 @@ void CINTrys_roots(FINT nroots, double x, double *u, double *w); void CINTstg_roots(FINT nroots, double ta, double ua, double* rr, double* ww); -void CINTerfc_roots(FINT nroots, double x, double lower, double *u, double *w); void CINTerfc_rys_roots(FINT nroots, double x, double lower, double *u, double *w); +void CINTerfc_rys_polyfits(FINT nroots, double x, double lower, double *u, double *w); diff --git a/testsuite/erfc_tabulate.py b/testsuite/erfc_tabulate.py new file mode 100644 index 00000000..c83fa436 --- /dev/null +++ b/testsuite/erfc_tabulate.py @@ -0,0 +1,88 @@ +import os +import mpmath +import numpy as np +mpmath.mp.dps = 60 + +#https://www.ams.org/journals/mcom/1981-36-153/S0025-5718-1981-0595058-X/home.html +table_ref = np.array([ +mpmath.mpf('0.1177578934567401754080e+01'), +mpmath.mpf('-0.4590054580646477331e-02'), +mpmath.mpf('-0.84249133366517915584e-01'), +mpmath.mpf('0.59209939998191890498e-01'), +mpmath.mpf('-0.26658668435305752277e-01'), +mpmath.mpf('0.9074997670705265094e-02'), +mpmath.mpf('-0.2413163540417608191e-02'), +mpmath.mpf('0.490775836525808632e-03'), +mpmath.mpf('-0.69169733025012064e-04'), +mpmath.mpf('0.4139027986073010e-05'), +mpmath.mpf('0.774038306619849e-06'), +mpmath.mpf('-0.218864010492344e-06'), +mpmath.mpf('0.10764999465671e-07'), +mpmath.mpf('0.4521959811218e-08'), +mpmath.mpf('-0.775440020883e-09'), +mpmath.mpf('-0.63180883409e-10'), +mpmath.mpf('0.28687950109e-10'), +mpmath.mpf('0.194558685e-12'), +mpmath.mpf('-0.965469675e-12'), +mpmath.mpf('0.32525481e-13'), +mpmath.mpf('0.33473119e-13'), +mpmath.mpf('-0.1864563e-14'), +mpmath.mpf('-0.1250795e-14'), +mpmath.mpf('0.74182e-16'), +mpmath.mpf('0.50631e-16'), +mpmath.mpf('-0.2237e-17'), +mpmath.mpf('-0.2187e-17'), +mpmath.mpf('0.27e-19'), +mpmath.mpf('0.97e-19'), +mpmath.mpf('0.3e-20'), +mpmath.mpf('-0.4e-20'), +]) + +def chebyshev_roots(n): + return [mpmath.cos(mpmath.pi * (k + .5) / n) for k in range(n)] + +def clenshaw_points(n): + out = [] + for j in range(n): + c = [mpmath.cos(mpmath.pi * j * (k + 0.5) / n) for k in range(n)] + out.append(c) + return out + +ngrids = 31 +chebrt = np.array(chebyshev_roots(ngrids)) +cs = np.array(clenshaw_points(ngrids)) + +def tabulate_erfc(): + k = mpmath.mpf('3.75') + values = [] + for t in chebrt: + x = k*(t+1)/(1-t) + values.append((1+2*x)*mpmath.exp(x*x)*mpmath.erfc(x)) + values = np.array(values) + fac = mpmath.mpf(2) / ngrids + tab = values.dot(cs.T) * fac + tab[0] /= 2 + return tab + +def clenshaw_d1(tab, t): + d0 = 0 + d1 = tab[ngrids-1] + for k in reversed(range(1, ngrids-1)): + d1, d0 = t * 2 * d1 - d0 + tab[k], d1 + return t * d1 - d0 + tab[0] + +def erfc(x, tab=None): + if tab is None: + tab = tabulate_erfc().astype(float) + k = 3.75 + t = (x-k)/ (x+k) + v = clenshaw_d1(tab, t) + return v / (1 + 2*x) / np.exp(x * x) + +if __name__ == '__main__': + table = tabulate_erfc().astype(float) + for c in np.arange(-20, 8): + x = mpmath.mpf('1.5')**c + ref = mpmath.erfc(x) + v = erfc(float(x), table) + print('erfc',1.5**c, 'erfc(x)', v, 'error', float(v / ref - 1)) diff --git a/testsuite/rys_tabulate.py b/testsuite/rys_tabulate.py index d1643e3b..e3b18d25 100644 --- a/testsuite/rys_tabulate.py +++ b/testsuite/rys_tabulate.py @@ -57,7 +57,7 @@ def tabulate_erfc(nroots, tbase): Tp = (Tmin + Tmax) / 2 tabulate_points = get_tabulate_points(tbase, Tp) - boundary_points = [r/2 + 0.5 for r in chebrt] + boundary_points = [(r/2 + 0.5)**2 for r in chebrt] fac = mpmath.mpf(2) / ngrids @@ -82,8 +82,8 @@ def clenshaw_d1(x, u, nroots): for i in range(nroots): xi = x[i] d0 = 0 - d1 = xi[13] - for k in reversed(range(1, 13)): + d1 = xi[ngrids-1] + for k in reversed(range(1, ngrids-1)): d1, d0 = u2 * d1 - d0 + xi[k], d1 rr.append(u * d1 - d0 + xi[0] * 0.5) return rr @@ -100,13 +100,15 @@ def polyfit_erf(nroots, x): tt = mpmath.sqrt(t) it = int(tt) - tt = tt - it + if isinstance(x, float): + tt = float(tt) - it + else: + tt = tt - it tt = 2.0 * tt - 1.0 tab_rs, tab_ws = tabulate_erf(nroots, it) - - rr = clenshaw_d1(tab_rs, tt, nroots) - ww = clenshaw_d1(tab_ws, tt, nroots) + rr = clenshaw_d1(tab_rs.astype(float), tt, nroots) + ww = clenshaw_d1(tab_ws.astype(float), tt, nroots) rr = [r/(1-r) for r in rr] return rr, ww @@ -131,12 +133,12 @@ def polyfit_erfc(nroots, x, low): u = low * 2 - 1 # map [0, 1] to [-1, 1] tab_rs, tab_ws = tabulate_erfc(nroots, it) - im = clenshaw_d1(tab_rs, u, nroots) + im = clenshaw_d1(tab_rs.astype(float), u, nroots) imc = intermediate(im) rr = clenshaw_d1(imc, tt, nroots) rr = [r/(1-r) for r in rr] - im = clenshaw_d1(tab_ws, u, nroots) + im = clenshaw_d1(tab_ws.astype(float), u, nroots) imc = intermediate(im) ww = clenshaw_d1(imc, tt, nroots) return rr, ww diff --git a/testsuite/test_cint.py b/testsuite/test_cint.py index db796797..be78cba6 100644 --- a/testsuite/test_cint.py +++ b/testsuite/test_cint.py @@ -17,11 +17,12 @@ _cint = numpy.ctypeslib.load_library('libcint', '.') -PTR_LIGHT_SPEED = 0 PTR_COMMON_ORIG = 1 PTR_SHIELDING_ORIG = 4 PTR_RINV_ORIG = 4 PTR_RINV_ZETA = 7 +PTR_RANGE_OMEGA = 8 +PTR_EXPCUTOFF = 11 PTR_ENV_START = 20 CHARGE_OF = 0 @@ -157,7 +158,7 @@ def test_int1e_sph(name, vref, dim, place): di = (bas[i,ANG_OF] * 2 + 1) * bas[i,NCTR_OF] dj = (bas[j,ANG_OF] * 2 + 1) * bas[j,NCTR_OF] shls = (ctypes.c_int * 2)(i, j) - intor(op, shls, c_atm, natm, c_bas, nbas, c_env); + intor(op, shls, c_atm, natm, c_bas, nbas, c_env) v1 += abs(numpy.array(op[:di*dj*dim])).sum() cnt += di*dj*dim if close(v1, vref, cnt, place): @@ -179,7 +180,7 @@ def test_int1e_spinor(name, vref, dim, place): di = _cint.CINTlen_spinor(i, c_bas, nbas) * bas[i,NCTR_OF] dj = _cint.CINTlen_spinor(j, c_bas, nbas) * bas[j,NCTR_OF] shls = (ctypes.c_int * 2)(i, j) - intor(op, shls, c_atm, natm, c_bas, nbas, c_env); + intor(op, shls, c_atm, natm, c_bas, nbas, c_env) v1 += abs(cdouble_to_cmplx(op[:di*dj*dim*2])).sum() cnt += di*dj*dim*2 if close(v1, vref, cnt, place): @@ -216,9 +217,9 @@ def test_comp1e_spinor(name1, name_ref, shift, dim, place): di = _cint.CINTlen_spinor(i, c_bas, nbas) * bas[i,NCTR_OF] dj = _cint.CINTlen_spinor(j, c_bas, nbas) * bas[j,NCTR_OF] shls = (ctypes.c_int * 2)(i+shift[0], j+shift[1]) - intor(op, shls, c_atm, natm, c_bas, nbas, c_env); + intor(op, shls, c_atm, natm, c_bas, nbas, c_env) shls_ref = (ctypes.c_int * 2)(i, j) - intor_ref(op_ref, shls_ref, c_atm, natm, c_bas, nbas, c_env); + intor_ref(op_ref, shls_ref, c_atm, natm, c_bas, nbas, c_env) dd = abs(pfac * cdouble_to_cmplx(op[:di*dj*dim*2]).reshape(di,dj,dim) - cdouble_to_cmplx(op_ref[:di*dj*dim*2]).reshape(di,dj,dim)) if numpy.round(dd, place).sum(): @@ -245,7 +246,7 @@ def test_int2e_sph(name, vref, dim, place): dk = (bas[k,ANG_OF] * 2 + 1) * bas[k,NCTR_OF] dl = (bas[l,ANG_OF] * 2 + 1) * bas[l,NCTR_OF] shls = (ctypes.c_int * 4)(i, j, k, l) - intor(op, shls, c_atm, natm, c_bas, nbas, c_env, opt); + intor(op, shls, c_atm, natm, c_bas, nbas, c_env, opt) v1 += abs(numpy.array(op[:di*dj*dk*dl*dim])).sum() cnt += di*dj*dk*dl*dim if close(v1, vref, cnt, place): @@ -253,6 +254,56 @@ def test_int2e_sph(name, vref, dim, place): else: print("* FAIL: ", name, ". err:", '%.16g' % abs(v1-vref), "/", vref) +def test_erf(name, omega, place): + intor = getattr(_cint, name) + intor.restype = ctypes.c_void_p + env_lr = env.copy() + env_lr[PTR_RANGE_OMEGA] = omega + env_sr = env.copy() + env_sr[PTR_RANGE_OMEGA] = -omega + c_env_lr = env_lr.ctypes.data_as(ctypes.c_void_p) + c_env_sr = env_sr.ctypes.data_as(ctypes.c_void_p) + + op_lr = numpy.empty(10000) + op_sr = numpy.empty(10000) + op = numpy.empty(10000) + v1 = 0 + cnt = 0 + shls = (ctypes.c_int * 4)(3,3,3,3) + intor(op.ctypes.data_as(ctypes.c_void_p), shls, c_atm, natm, c_bas, nbas, c_env, opt) + intor(op_lr.ctypes.data_as(ctypes.c_void_p), shls, c_atm, natm, c_bas, nbas, c_env_lr, opt) + intor(op_sr.ctypes.data_as(ctypes.c_void_p), shls, c_atm, natm, c_bas, nbas, c_env_sr, opt) + print(numpy.sort(op[:9**4]-op_lr[:9**4]-op_sr[:9**4])) + print((op[:9**4]-op_lr[:9**4]-op_sr[:9**4]).argsort()) + print(op[3126], op_lr[3126], op_sr[3126]) + print(op[0], op_lr[0], op_sr[0]) + exit() + for l in range(nbas.value): + for k in range(l+1): + for j in range(l+1): + for i in range(j+1): + di = (bas[i,ANG_OF] * 2 + 1) * bas[i,NCTR_OF] + dj = (bas[j,ANG_OF] * 2 + 1) * bas[j,NCTR_OF] + dk = (bas[k,ANG_OF] * 2 + 1) * bas[k,NCTR_OF] + dl = (bas[l,ANG_OF] * 2 + 1) * bas[l,NCTR_OF] + shls = (ctypes.c_int * 4)(i, j, k, l) + intor(op.ctypes.data_as(ctypes.c_void_p), shls, c_atm, natm, c_bas, nbas, c_env, opt) + intor(op_lr.ctypes.data_as(ctypes.c_void_p), shls, c_atm, natm, c_bas, nbas, c_env_lr, opt) + intor(op_sr.ctypes.data_as(ctypes.c_void_p), shls, c_atm, natm, c_bas, nbas, c_env_sr, opt) + cnt = di * dj * dk * dl + dd = abs(op_lr[:cnt] + op_sr[:cnt] - op[:cnt]) + print(dd.max()) + #with numpy.errstate(invalid='ignore'): + # dd[dd > 1e-7] / op[:cnt][dd > 1e-7] + #if numpy.round(dd.max(), place) > 0: + # maxi = dd.argmax() + # print("* FAIL: erf+erfc", name, "omega=", omega, + # " shell:", i, j, k, l, + # "erf:", op_lr[maxi], "erfc:", op_sr[maxi], + # "regular:", op[maxi], "err:", dd[maxi]) + # return + print("pass: erf+erfc", name, "omega=", omega) + def test_int2e_spinor(name, vref, dim, place): intor = getattr(_cint, name) intor.restype = ctypes.c_void_p @@ -268,7 +319,7 @@ def test_int2e_spinor(name, vref, dim, place): dk = _cint.CINTlen_spinor(k, c_bas, nbas) * bas[k,NCTR_OF] dl = _cint.CINTlen_spinor(l, c_bas, nbas) * bas[l,NCTR_OF] shls = (ctypes.c_int * 4)(i, j, k, l) - intor(op, shls, c_atm, natm, c_bas, nbas, c_env, opt); + intor(op, shls, c_atm, natm, c_bas, nbas, c_env, opt) v1 += abs(cdouble_to_cmplx(op[:di*dj*dk*dl*dim*2])).sum() cnt += di*dj*dk*dl*dim*2 if close(v1, vref, cnt, place): @@ -323,124 +374,129 @@ def test_comp2e_spinor(name1, name_ref, shift, dim, place): def close(v1, vref, count, place): return round(abs(v1-vref), place) == 0 - for f in (('cint1e_ovlp_sph' , 320.9470780962389, 1, 11), - ('cint1e_nuc_sph' , 3664.898206036863, 1, 10), - ('cint1e_kin_sph' , 887.2525599069498, 1, 11), - ('cint1e_ia01p_sph' , 210.475021425001 , 3, 12), - ('cint1e_cg_irxp_sph', 3464.41761486531, 3, 10), - ('cint1e_giao_irjxp_sph', 2529.89787038728, 3, 10), - ('cint1e_igkin_sph' , 107.6417224161130, 3, 11), - ('cint1e_igovlp_sph', 37.94968860771099, 3, 12), - ('cint1e_ignuc_sph' , 478.5594827282386, 3, 11), - ('cint1e_ipovlp_sph', 429.5284222008585, 3, 11), - ('cint1e_ipkin_sph' , 1307.395170673386, 3, 10), - ('cint1e_ipnuc_sph' , 8358.422626593954, 3, 10), - ('cint1e_iprinv_sph', 385.1108471512923, 3, 11), - ('cint1e_prinvxp_sph',210.475021425001, 3, 11), - ('cint1e_z_sph' , 651.8811101988866, 1, 11), - ('cint1e_zz_sph' , 1881.075059037941, 1, 10), - ('cint1e_r_sph' , 1803.13043674652 , 3, 10), - ('cint1e_rr_sph' , 13379.47937680471, 9, 9), - ('cint1e_r2_sph' , 5237.899221349136, 1, 10), - ): - test_int1e_sph(*f) - - for f in (('cint1e_ovlp' , 284.4528456839759, 1, 11), - ('cint1e_nuc' , 3025.766689838620, 1, 10), - ('cint1e_gnuc' , 296.6160944673867, 3, 11), - ('cint1e_srsr' , 1430.424389624617, 1, 10), - ('cint1e_sr' , 240.4064385362524, 1, 11), - ('cint1e_srsp' , 1022.805155947573, 1, 10), - ('cint1e_spsp' , 1554.251610462129, 1, 10), - ('cint1e_sp' , 265.2448605537422, 1, 11), - ('cint1e_spspsp' , 1551.856568558924, 1, 10), - ('cint1e_spnuc' , 3905.024862120781, 1, 10), - ('cint1e_spnucsp' , 20689.33926165072, 1, 9 ), - ('cint1e_srnucsr' , 13408.06084488522, 1, 9 ), - ('cint1e_cg_sa10sa01', 319.6545034966355, 9, 11), - ('cint1e_cg_sa10sp' , 1705.563585675829, 3, 10), - ('cint1e_cg_sa10nucsp',16506.04502697362, 3, 9 ), - ('cint1e_giao_sa10sa01' , 358.7833729392868, 9, 11), - ('cint1e_giao_sa10sp' , 1070.550400465705, 3, 10), - ('cint1e_giao_sa10nucsp', 12819.05472701636, 3, 9 ), - ('cint1e_govlp' , 23.2674074483772, 3, 12), - ('cint1e_sa01sp' , 218.244203172625, 3, 11), - ('cint1e_spgsp' , 96.9346217249868, 3, 12), - ('cint1e_spgnucsp' , 1659.37670007911, 3, 10), - ('cint1e_spgsa01' , 37.8884662927634, 9, 12), - ('cint1e_ipovlp' , 153.860148521121, 3, 12), - ('cint1e_ipkin' , 497.249399637873, 3, 11), - ('cint1e_ipnuc' , 4506.61348255897, 3, 10), - ('cint1e_iprinv' , 240.036283917245, 3, 11), - ('cint1e_ipspnucsp', 35059.4071347107, 3, 9), - ('cint1e_ipsprinvsp',1166.20850563398, 3, 10), - ): - test_int1e_spinor(*f) - - for f in (# rys_roots for i,j,k,l=3,3,3,3 has round-off error ~ 1e-5 - ('cint2e_sph' , 56243.88328768107 , 1, 8 ), - ('cint2e_ip1_sph', 115489.8643866550 , 3, 8 ), - ): - test_int2e_sph(*f) - if "--quick" not in sys.argv: - # Four tests marked with "# *" may fail in quadmath mode - for f in (('cint2e_ip1_sph', 115489.8643866550 , 3, 8 ), - ('cint2e_p1vxp1_sph', 89014.88169743448, 3, 9), - ): - test_int2e_sph(*f) - for f in (('cint2e' , 37737.11365710611, 1, 8), - ('cint2e_spsp1' , 221528.4764668166, 1, 8), - ('cint2e_spsp1spsp2' , 1391716.876869147, 1, 7), # * - ('cint2e_srsr1' , 178572.7398308939, 1, 8), - ('cint2e_srsr1srsr2' , 860883.6288270953, 1, 8), # * - ('cint2e_cg_sa10sp1' , 241519.2143647713, 3, 8), - ('cint2e_cg_sa10sp1spsp2' , 1419443.469767018, 3, 7), # * - ('cint2e_giao_sa10sp1' , 153861.920807804 , 3, 8), - ('cint2e_giao_sa10sp1spsp2', 918284.9464686266, 3, 8), # * - ('cint2e_g1' , 3755.251591892025, 3, 10), - ('cint2e_spgsp1' , 16626.99103794526, 3, 9 ), - ('cint2e_g1spsp2' , 22186.56654833549, 3, 9 ), - ('cint2e_spgsp1spsp2' , 107110.2340526177, 3, 8 ), - ('cint2e_ip1' , 34912.85433806438, 3, 9 ), - ('cint2e_ipspsp1' , 221092.5556043494, 3, 8 ), - ('cint2e_ip1spsp2' , 212447.1029358293, 3, 8 ), - ('cint2e_ipspsp1spsp2', 1443972.936563201, 3, 7 ), - ): - test_int2e_spinor(*f) - - test_comp2e_spinor('cint2e_spsp1', 'cint2e', (4,4,0,0), 1, 11) - test_comp2e_spinor('cint2e_spsp1spsp2', 'cint2e', (4,4,4,4), 1, 11) - test_comp2e_spinor('cint2e_spsp1spsp2', 'cint2e_spsp1', (0,0,4,4), 1, 11) - test_comp2e_spinor('cint2e_spgsp1', 'cint2e_g1', (4,4,0,0), 3, 11) - test_comp2e_spinor('cint2e_g1spsp2', 'cint2e_g1', (0,0,4,4), 3, 11) - test_comp2e_spinor('cint2e_spgsp1spsp2', 'cint2e_g1', (4,4,4,4), 3, 11) - test_comp2e_spinor('cint2e_ipspsp1', 'cint2e_ip1', (4,4,0,0), 3, 11) - test_comp2e_spinor('cint2e_ip1spsp2', 'cint2e_ip1', (0,0,4,4), 3, 11) - test_comp2e_spinor('cint2e_ipspsp1spsp2', 'cint2e_ip1', (4,4,4,4), 3, 11) - - fz = getattr(_cint, 'cint1e_z_sph') - fzz = getattr(_cint, 'cint1e_zz_sph') - fr = getattr(_cint, 'cint1e_r_sph') - fr2 = getattr(_cint, 'cint1e_r2_sph') - frr = getattr(_cint, 'cint1e_rr_sph') - v1 = 0 - for j in range(nbas.value*2): - for i in range(j+1): - di = (bas[i,ANG_OF] * 2 + 1) * bas[i,NCTR_OF] - dj = (bas[j,ANG_OF] * 2 + 1) * bas[j,NCTR_OF] - opz = numpy.empty((di,dj) , order='F') - opzz = numpy.empty((di,dj) , order='F') - opr = numpy.empty((di,dj,3), order='F') - opr2 = numpy.empty((di,dj) , order='F') - oprr = numpy.empty((di,dj,9), order='F') - shls = (ctypes.c_int * 2)(i, j) - fz ( opz.ctypes.data_as(ctypes.c_void_p), shls, c_atm, natm, c_bas, nbas, c_env) - fzz(opzz.ctypes.data_as(ctypes.c_void_p), shls, c_atm, natm, c_bas, nbas, c_env) - fr ( opr.ctypes.data_as(ctypes.c_void_p), shls, c_atm, natm, c_bas, nbas, c_env) - fr2(opr2.ctypes.data_as(ctypes.c_void_p), shls, c_atm, natm, c_bas, nbas, c_env) - frr(oprr.ctypes.data_as(ctypes.c_void_p), shls, c_atm, natm, c_bas, nbas, c_env) - v1 = abs(opz-opr[:,:,2]).sum() - v1 += abs(opzz-oprr[:,:,8]).sum() - v1 += abs(opr2-oprr[:,:,0]-oprr[:,:,4]-oprr[:,:,8]).sum() - if round(v1/(di*dj), 13): - print("* FAIL: ", i, j, v1) +# for f in (('cint1e_ovlp_sph' , 320.9470780962389, 1, 11), +# ('cint1e_nuc_sph' , 3664.898206036863, 1, 10), +# ('cint1e_kin_sph' , 887.2525599069498, 1, 11), +# ('cint1e_ia01p_sph' , 210.475021425001 , 3, 12), +# ('cint1e_cg_irxp_sph', 3464.41761486531, 3, 10), +# ('cint1e_giao_irjxp_sph', 2529.89787038728, 3, 10), +# ('cint1e_igkin_sph' , 107.6417224161130, 3, 11), +# ('cint1e_igovlp_sph', 37.94968860771099, 3, 12), +# ('cint1e_ignuc_sph' , 478.5594827282386, 3, 11), +# ('cint1e_ipovlp_sph', 429.5284222008585, 3, 11), +# ('cint1e_ipkin_sph' , 1307.395170673386, 3, 10), +# ('cint1e_ipnuc_sph' , 8358.422626593954, 3, 10), +# ('cint1e_iprinv_sph', 385.1108471512923, 3, 11), +# ('cint1e_prinvxp_sph',210.475021425001, 3, 11), +# ('cint1e_z_sph' , 651.8811101988866, 1, 11), +# ('cint1e_zz_sph' , 1881.075059037941, 1, 10), +# ('cint1e_r_sph' , 1803.13043674652 , 3, 10), +# ('cint1e_rr_sph' , 13379.47937680471, 9, 9), +# ('cint1e_r2_sph' , 5237.899221349136, 1, 10), +# ): +# test_int1e_sph(*f) +# +# for f in (('cint1e_ovlp' , 284.4528456839759, 1, 11), +# ('cint1e_nuc' , 3025.766689838620, 1, 10), +# ('cint1e_gnuc' , 296.6160944673867, 3, 11), +# ('cint1e_srsr' , 1430.424389624617, 1, 10), +# ('cint1e_sr' , 240.4064385362524, 1, 11), +# ('cint1e_srsp' , 1022.805155947573, 1, 10), +# ('cint1e_spsp' , 1554.251610462129, 1, 10), +# ('cint1e_sp' , 265.2448605537422, 1, 11), +# ('cint1e_spspsp' , 1551.856568558924, 1, 10), +# ('cint1e_spnuc' , 3905.024862120781, 1, 10), +# ('cint1e_spnucsp' , 20689.33926165072, 1, 9 ), +# ('cint1e_srnucsr' , 13408.06084488522, 1, 9 ), +# ('cint1e_cg_sa10sa01', 319.6545034966355, 9, 11), +# ('cint1e_cg_sa10sp' , 1705.563585675829, 3, 10), +# ('cint1e_cg_sa10nucsp',16506.04502697362, 3, 9 ), +# ('cint1e_giao_sa10sa01' , 358.7833729392868, 9, 11), +# ('cint1e_giao_sa10sp' , 1070.550400465705, 3, 10), +# ('cint1e_giao_sa10nucsp', 12819.05472701636, 3, 9 ), +# ('cint1e_govlp' , 23.2674074483772, 3, 12), +# ('cint1e_sa01sp' , 218.244203172625, 3, 11), +# ('cint1e_spgsp' , 96.9346217249868, 3, 12), +# ('cint1e_spgnucsp' , 1659.37670007911, 3, 10), +# ('cint1e_spgsa01' , 37.8884662927634, 9, 12), +# ('cint1e_ipovlp' , 153.860148521121, 3, 12), +# ('cint1e_ipkin' , 497.249399637873, 3, 11), +# ('cint1e_ipnuc' , 4506.61348255897, 3, 10), +# ('cint1e_iprinv' , 240.036283917245, 3, 11), +# ('cint1e_ipspnucsp', 35059.4071347107, 3, 9), +# ('cint1e_ipsprinvsp',1166.20850563398, 3, 10), +# ): +# test_int1e_spinor(*f) +# +# for f in (# rys_roots for i,j,k,l=3,3,3,3 has round-off error ~ 1e-5 +# ('cint2e_sph' , 56243.88328768107 , 1, 8 ), +# ('cint2e_ip1_sph', 115489.8643866550 , 3, 8 ), +# ): +# test_int2e_sph(*f) + +# test_erf('cint2e_sph', 0.2, 9) +# test_erf('cint2e_sph', 0.5, 9) + test_erf('cint2e_sph', 0.8, 9) + +# if "--quick" not in sys.argv: +# # Four tests marked with "# *" may fail in quadmath mode +# for f in (('cint2e_ip1_sph', 115489.8643866550 , 3, 8 ), +# ('cint2e_p1vxp1_sph', 89014.88169743448, 3, 9), +# ): +# test_int2e_sph(*f) +# for f in (('cint2e' , 37737.11365710611, 1, 8), +# ('cint2e_spsp1' , 221528.4764668166, 1, 8), +# ('cint2e_spsp1spsp2' , 1391716.876869147, 1, 7), # * +# ('cint2e_srsr1' , 178572.7398308939, 1, 8), +# ('cint2e_srsr1srsr2' , 860883.6288270953, 1, 8), # * +# ('cint2e_cg_sa10sp1' , 241519.2143647713, 3, 8), +# ('cint2e_cg_sa10sp1spsp2' , 1419443.469767018, 3, 7), # * +# ('cint2e_giao_sa10sp1' , 153861.920807804 , 3, 8), +# ('cint2e_giao_sa10sp1spsp2', 918284.9464686266, 3, 8), # * +# ('cint2e_g1' , 3755.251591892025, 3, 10), +# ('cint2e_spgsp1' , 16626.99103794526, 3, 9 ), +# ('cint2e_g1spsp2' , 22186.56654833549, 3, 9 ), +# ('cint2e_spgsp1spsp2' , 107110.2340526177, 3, 8 ), +# ('cint2e_ip1' , 34912.85433806438, 3, 9 ), +# ('cint2e_ipspsp1' , 221092.5556043494, 3, 8 ), +# ('cint2e_ip1spsp2' , 212447.1029358293, 3, 8 ), +# ('cint2e_ipspsp1spsp2', 1443972.936563201, 3, 7 ), +# ): +# test_int2e_spinor(*f) +# +# test_comp2e_spinor('cint2e_spsp1', 'cint2e', (4,4,0,0), 1, 11) +# test_comp2e_spinor('cint2e_spsp1spsp2', 'cint2e', (4,4,4,4), 1, 11) +# test_comp2e_spinor('cint2e_spsp1spsp2', 'cint2e_spsp1', (0,0,4,4), 1, 11) +# test_comp2e_spinor('cint2e_spgsp1', 'cint2e_g1', (4,4,0,0), 3, 11) +# test_comp2e_spinor('cint2e_g1spsp2', 'cint2e_g1', (0,0,4,4), 3, 11) +# test_comp2e_spinor('cint2e_spgsp1spsp2', 'cint2e_g1', (4,4,4,4), 3, 11) +# test_comp2e_spinor('cint2e_ipspsp1', 'cint2e_ip1', (4,4,0,0), 3, 11) +# test_comp2e_spinor('cint2e_ip1spsp2', 'cint2e_ip1', (0,0,4,4), 3, 11) +# test_comp2e_spinor('cint2e_ipspsp1spsp2', 'cint2e_ip1', (4,4,4,4), 3, 11) +# +# fz = getattr(_cint, 'cint1e_z_sph') +# fzz = getattr(_cint, 'cint1e_zz_sph') +# fr = getattr(_cint, 'cint1e_r_sph') +# fr2 = getattr(_cint, 'cint1e_r2_sph') +# frr = getattr(_cint, 'cint1e_rr_sph') +# v1 = 0 +# for j in range(nbas.value*2): +# for i in range(j+1): +# di = (bas[i,ANG_OF] * 2 + 1) * bas[i,NCTR_OF] +# dj = (bas[j,ANG_OF] * 2 + 1) * bas[j,NCTR_OF] +# opz = numpy.empty((di,dj) , order='F') +# opzz = numpy.empty((di,dj) , order='F') +# opr = numpy.empty((di,dj,3), order='F') +# opr2 = numpy.empty((di,dj) , order='F') +# oprr = numpy.empty((di,dj,9), order='F') +# shls = (ctypes.c_int * 2)(i, j) +# fz ( opz.ctypes.data_as(ctypes.c_void_p), shls, c_atm, natm, c_bas, nbas, c_env) +# fzz(opzz.ctypes.data_as(ctypes.c_void_p), shls, c_atm, natm, c_bas, nbas, c_env) +# fr ( opr.ctypes.data_as(ctypes.c_void_p), shls, c_atm, natm, c_bas, nbas, c_env) +# fr2(opr2.ctypes.data_as(ctypes.c_void_p), shls, c_atm, natm, c_bas, nbas, c_env) +# frr(oprr.ctypes.data_as(ctypes.c_void_p), shls, c_atm, natm, c_bas, nbas, c_env) +# v1 = abs(opz-opr[:,:,2]).sum() +# v1 += abs(opzz-oprr[:,:,8]).sum() +# v1 += abs(opr2-oprr[:,:,0]-oprr[:,:,4]-oprr[:,:,8]).sum() +# if round(v1/(di*dj), 13): +# print("* FAIL: ", i, j, v1) diff --git a/testsuite/test_rys_roots.py b/testsuite/test_rys_roots.py new file mode 100644 index 00000000..9346d902 --- /dev/null +++ b/testsuite/test_rys_roots.py @@ -0,0 +1,193 @@ +import ctypes +import numpy +from rys_roots import * +import rys_tabulate + +def fp(a): + a = numpy.asarray(a) + return a.ravel().dot(numpy.cos(numpy.arange(a.size))) + +def cint_call(fname, nroots, x, low=None): + cint = ctypes.CDLL('../build/libcint.so') + r = numpy.zeros(nroots) + w = numpy.zeros(nroots) + fun = getattr(cint, fname) + if low is None: + fun(ctypes.c_int(nroots), ctypes.c_double(x), + r.ctypes.data_as(ctypes.c_void_p), + w.ctypes.data_as(ctypes.c_void_p)) + else: + fun(ctypes.c_int(nroots), ctypes.c_double(x), ctypes.c_double(low), + r.ctypes.data_as(ctypes.c_void_p), + w.ctypes.data_as(ctypes.c_void_p)) + return r, w + +def check_turnover_point(fun1, fun2): + es = 2**numpy.arange(-2, 5, .5) + turnover_points = [] + for i in range(1, 14): + for x in es: + f1 = fun1(x, i) + f2 = fun2(x, i) + diff = (f1[i] - f2[i])/f1[i] + if diff < 2.2e-16: + turnover_points.append(x) + break + return turnover_points + +def test_turnover_point(): + import functools + import mpmath + mpmath.mp.dps = 15 + print(check_turnover_point(fmt1, fmt2)) + tps = [] + for low in 2**numpy.arange(-4, 5, .5): + tp = check_turnover_point(functools.partial(fmt1_erfc, low=low), + functools.partial(fmt2_erfc, low=low)) + print(low, tp) + tps.append(tp) + print(numpy.array(tps).max(axis=0)) + print(fmt1_erfc(0.9, 2, .6)) + print(fmt1_erfc(1.1, 2, .2)) + print(fmt2_erfc(1.1, 2, .2)) + print(fmt1_erfc(8.1, 2, .2)) + print(fmt2_erfc(8.1, 2, .2)) + print(fmt1(1.1, 2)) + print(fmt2(1.1, 2)) + print(fmt1(8.1, 2)) + print(fmt2(8.1, 2)) + + print(abs(fmt(1, 2) - [0.746824132812427, 0.18947234582049235, 0.10026879814501737]).max()) + print(abs(fmt(7, 2) - [0.3349010581765593, 0.023856369729357483, 0.005046944801608424]).max()) + +def test_rys_roots_mpmath(): + numpy.random.seed(4) + a = numpy.random.rand(4,4) + a = a.T.dot(a) + cs = R_dsmit(a, 4) + print(fp(cs) - -1.1566333099933561) + r, w = rys_roots_weights(6, .4) + print(fp(r) - 2.898038115730877) + print(fp(w) - 0.1193288112731978) + + print(fp(rys_roots_weights(1, .3)) - 0.93475892362307533) + print(fp(rys_roots_weights(2, .8)) - 0.94983728587499205) + print(fp(rys_roots_weights(3, .5)) - -2.7165192846520481) + print(fp(rys_roots_weights(4, .5)) - -11.442155925744938) + + ff = fmt_erfc(.4, 6*2, 0.2) + r, w = rys_roots_weights(6, .4, ff) + print(fp(r) - 3.0557596858378053) + print(fp(w) - 0.00070334763896715) + +def test_rys_roots_weights(): + def check(nroots, x): + r_ref, w_ref = rys_roots_weights(nroots, x) + r, w = cint_call('CINTrys_roots', nroots, x) + return np.array([abs(r-r_ref).max(), abs(w-w_ref).max()]).astype(float) + + failed = False + es = 2**numpy.arange(-3, 7, .25) + for i in range(1, 12): + for x in es: + diffs = check(i, x) + if any(s > 1e-8 for s in diffs): + print(i, x, diffs) + failed |= any(s > 1e-5 for s in diffs) + es = [50, 40, 36, 24, 20, 16, 12, 8, 4, 2, 0.5, 6e-8] + for i in range(1, 5): + for x in es: + diffs = check(i, x) + if any(s > 1e-8 for s in diffs): + print(i, x, diffs) + failed |= any(s > 1e-5 for s in diffs) + if failed: + print('test_rys_roots_weights .. failed') + else: + print('test_rys_roots_weights .. pass') + + +def test_rys_roots_weights_erfc(): + def check(nroots, x, lower): + r_ref, w_ref = rys_roots_weights(nroots, x, lower) + # Needs to remove keyword "static" for erfc_rys_roots + # r, w = cint_call('erfc_rys_roots', nroots, x, lower) + r, w = cint_call('CINTerfc_rys_roots', nroots, x, lower) + return np.array([abs(r-r_ref).max(), abs(w-w_ref).max()]).astype(float) + + es = 2**numpy.arange(-3, 6, .25) + failed = False + for i in range(1, 12): + for x in es: + for low in [.1, .2, .3, .4, .5, .6, .7, .8, .9]: + diffs = check(i, x, low) + if any(s > 1e-7 for s in diffs): + print(i, x, low, diffs) + failed |= any(s > 1e-4 for s in diffs) + if failed: + print('test_rys_roots_weights_erfc .. failed') + else: + print('test_rys_roots_weights_erfc .. pass') + +def test_stg_roots(): + def stg(nroots, t, u): + r = numpy.zeros(nroots) + w = numpy.zeros(nroots) + cint.CINTstg_roots(ctypes.c_int(nroots), + ctypes.c_double(t), ctypes.c_double(u), + r.ctypes.data_as(ctypes.c_void_p), + w.ctypes.data_as(ctypes.c_void_p)) + return r, w + + print(fp(stg(1, 2.2, 1.5)) - 0.653262713484748 ) + print(fp(stg(2, 0.2, 8.5)) - 1.2362174210548105) + print(fp(stg(4, 1.0, 0.5)) - -0.6907781084439245) + + +def test_polyfit(): + def check(nroots, x, low=None): + r0, w0 = rys_roots_weights(nroots, x, low) + if low is None: + r1, w1 = rys_tabulate.polyfit_erf(nroots, x) + else: + r1, w1 = rys_tabulate.polyfit_erfc(nroots, x, low) + return np.array([abs(r0 - r1).max(), abs(w0 - w1).max()]).astype(float) + + es = 2**numpy.arange(-3, 6, .25) + failed = False + for i in range(1, 12): + for low in [None, 0.2, 0.5, 0.8]: + for x in es: + diffs = check(i, x, low) + if any(s > 1e-8 for s in diffs): + print(i, x, low, diffs) + failed |= any(s > 1e-5 for s in diffs) + if failed: + print('test_polyfit .. failed') + else: + print('test_polyfit .. pass') + +def test_rys_roots_vs_polyfit(): + def check(nroots, x, low): + r_ref, w_ref = rys_roots_weights(nroots, x, low) + r0, w0 = cint_call('erfc_rys_roots', nroots, x, low) + r1, w1 = cint_call('CINTerfc_roots', nroots, x, low) + return np.array([abs(r0 - r_ref).max(), + abs(r1 - r_ref).max(), + abs(w0 - w_ref).max(), + abs(w1 - w_ref).max()]).astype(float) + + es = 2**numpy.arange(-6, 6, .5) + for i in range(6, 12): + for low in [0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9]: + for x in es: + diffs = check(i, x, low) + print(i, x, low, diffs, abs(diffs[0])>abs(diffs[1]), abs(diffs[2])>abs(diffs[3])) + + +if __name__ == '__main__': + # test_rys_roots_mpmath() + # test_polyfit() + # test_rys_roots_vs_polyfit() + test_rys_roots_weights() + test_rys_roots_weights_erfc()