Found a working set of parameters for the VSWF translation.
Former-commit-id: 3b36597e152bd89e6251e34d549fe1db3ecfd955
This commit is contained in:
Marek Nečada
parent
430e5b2a6b
commit
f943cc0cdb
26
BUGS.rst
26
BUGS.rst
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@ -8,6 +8,32 @@ B(1,0,n,n)/B(1,0,n,-n) == -(2n)! at (x,y,z) = (x,0,0)
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(expected plus or minus 1).
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A-coefficients seem to behave correctly.
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Translation coefficients inconsistent
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-------------------------------------
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The translation coefficients currently do not work correctly except for certain
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combinations of additional i-factors (defined by the [AB][NMF][123] macros
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in translations.c) and only for certain normalisations.
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QPMS_NORMALISATION_KRISTENSSON_CS does not work at all
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QPMS_NORMALISATION_NONE_CS does not work at all
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QPMS_NORMALISATION_TAYLOR_CS works for the following macros defined:
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AN1 AM0 BN1 BM0 BF0
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AN1 AM0 BN3 BM2 BF2
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AN3 AM2 BN1 BM0 BF0
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AN3 AM2 BN3 BM2 BF2
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QPMS_NORMALISATION_TAYLOR works for the following macros defined:
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AN1 AM2 BN1 BM3 BF0
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AN1 AM2 BN3 BM0 BF2
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AN3 AM0 BN1 BM2 BF0
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AN3 AM0 BN3 BM0 BF2
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The default behaviour is now that the QPMS_NORMALISATION_TAYLOR_CS works.
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Longitudinal waves
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------------------
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Plane wave decompositions gives wrong value on the longitudinal part.
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The implementation of the L coefficients OR the longitudinal waves
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is thus probably wrong.
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Scattering result asymmetry
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---------------------------
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The lattice scattering code (such as finitesqlatzsym-scattery.py) produces
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@ -1,3 +1,4 @@
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// c99 -o test_planewave_decomposition -ggdb -I .. test_planewave_decomposition.c ../vswf.c -lgsl -lm -lblas ../legendre.c ../bessel.c
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#include <gsl/gsl_rng.h>
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#include <gsl/gsl_math.h>
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#include <gsl/gsl_randist.h>
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@ -1,3 +1,4 @@
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//c99 -o test_vswf_translations -ggdb -I .. test_vswf_translations.c ../translations.c ../gaunt.c -lgsl -lm -lblas ../vecprint.c ../vswf.c ../legendre.c
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#include "translations.h"
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#include "vswf.h"
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#include <stdio.h>
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@ -1,3 +1,5 @@
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// c99 -o ../../tests/raytests/n_nu0 -ggdb -I .. vswf_translation_test_rays.c ../translations.c ../vswf.c ../gaunt.c ../legendre.c -lgsl -lm -lblas
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#include "translations.h"
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#include "vswf.h"
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#include <stdio.h>
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@ -58,7 +60,7 @@ int main(int argc, char **argv) {
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qpms_y_t y1 = qpms_mn2y(m1, l1);
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//qpms_l_t viewlMax = 2;
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int npoints = 10;
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int npoints = 3;
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double sigma = 4.;
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//double shiftsigma = 0.01;
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@ -66,9 +68,9 @@ int main(int argc, char **argv) {
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// o2minuso1.x = gsl_ran_gaussian(rng, shiftsigma);
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// o2minuso1.y = gsl_ran_gaussian(rng, shiftsigma);
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// o2minuso1.z = gsl_ran_gaussian(rng, shiftsigma);
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o2minuso1_max.x = 6;
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o2minuso1_max.y = 0;
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o2minuso1_max.z = 0;
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o2minuso1_max.x = 1;
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o2minuso1_max.y = 2;
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o2minuso1_max.z = 5;
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int nraysteps = 512;
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cart3_t o2mo1_step = cart3_scale(1./nraysteps, o2minuso1_max);
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@ -235,189 +237,3 @@ int main(int argc, char **argv) {
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return 0;
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}
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#if 0
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int test_sphwave_translation(const qpms_trans_calculator *c, qpms_bessel_t wavetype,
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cart3_t sc, int npoints, cart3_t *points) {
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puts("==============================================================");
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printf("Test translation o2-o1 = %fx̂ + %fŷ + %fẑ", sc.x, sc.y, sc.z);
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sph_t ss = cart2sph(sc);
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printf(" = %fr̂ @ o1, θ = %f, φ = %f\n", ss.r, ss.theta, ss.phi);
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printf("lMax = %d, norm: %s, csphase = %d\n",
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(int)c->lMax, normstr(c->normalisation), qpms_normalisation_t_csphase(c->normalisation));
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printf("wave type J = %d\n", wavetype);
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qpms_l_t lMax = c->lMax;
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qpms_y_t nelem = c->nelem;
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csphvec_t N1[nelem], /* N2[nelem], */ M1[nelem] /*, M2[nelem]*/;
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for (int i = 0; i < npoints; i++) {
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printf("-------- Point %d --------\n", i);
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cart3_t w1c = points[i];
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// cart3_t w2c = cart3_add(w1c, cart3_scale(-1, sc));
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cart3_t w2c = cart3_add(w1c, sc);
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sph_t w1s = cart2sph(w1c);
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sph_t w2s = cart2sph(w2c);
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printf(" = %fx̂ + %fŷ + %fẑ @o1\n", w1c.x, w1c.y, w1c.z);
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printf(" = %fx̂ + %fŷ + %fẑ @o2\n", w2c.x, w2c.y, w2c.z);
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printf(" = %fr̂ @ o1, θ = %f, φ = %f\n", w1s.r, w1s.theta, w1s.phi);
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printf(" = %fr̂ @ o2, θ = %f, φ = %f\n", w2s.r, w2s.theta, w2s.phi);
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printf("Outside the sphere centered in o1 intersecting o2: %s; by %f\n", (w1s.r > ss.r) ? "true" : "false",
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w1s.r - ss.r);
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if(QPMS_SUCCESS != qpms_vswf_fill(NULL, M1, N1, lMax, w1s, wavetype, c->normalisation))
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abort(); // original wave set
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for(qpms_y_t y1 = 0; y1 < nelem; ++y1) { //index of the wave originating in o1 that will be reconstructed in o2
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qpms_m_t m1;
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qpms_l_t l1;
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qpms_y2mn_p(y1, &m1, &l1);
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printf("*** wave l = %d, m = %d ***\n", l1, m1);
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complex double A[nelem], B[nelem];
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for(qpms_y_t y2 = 0; y2 < nelem; ++y2){
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qpms_m_t m2; qpms_l_t l2;
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qpms_y2mn_p(y2, &m2, &l2);
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if(qpms_trans_calculator_get_AB_p(c, A+y2, B+y2, m2, l2, m1, l1, ss, (w1s.r > ss.r), wavetype))
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abort();
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}
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printf("M = ");
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print_csphvec(M1[y1]);
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printf(" @ o1\n = ");
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ccart3_t M1c = csphvec2ccart(M1[y1], w1s);
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print_ccart3(M1c);
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printf("\n = ");
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csphvec_t M1s2 = ccart2csphvec(M1c, w2s);
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print_csphvec(M1s2);
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printf(" @ o2\n");
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csphvec_t M2s2 = qpms_eval_vswf(w2s, NULL, A, B, lMax, wavetype, c->normalisation);
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printf("Mr= ");
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print_csphvec(M2s2);
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printf(" @ o2\n");
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printf("N = ");
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print_csphvec(N1[y1]);
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printf(" @ o1\n = ");
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ccart3_t N1c = csphvec2ccart(N1[y1], w1s);
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print_ccart3(N1c);
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printf("\n = ");
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csphvec_t N1s2 = ccart2csphvec(N1c, w2s);
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print_csphvec(N1s2);
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printf(" @o2\nNr= ");
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csphvec_t N2s2 = qpms_eval_vswf(w2s, NULL, B, A, lMax, wavetype, c->normalisation);
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print_csphvec(N2s2);
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printf(" @o2\n");
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}
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}
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return 0; // FIXME something more meaningful here...
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}
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#endif
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#if 0
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int test_planewave_decomposition(cart3_t k, ccart3_t E, qpms_l_t lMax, qpms_normalisation_t norm, int npoints, cart3_t *points){
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qpms_y_t nelem = qpms_lMax2nelem(lMax);
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complex double lc[nelem], mc[nelem], ec[nelem];
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if (QPMS_SUCCESS !=
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qpms_planewave2vswf_fill_cart(k, E, lc, mc, ec, lMax, norm)) {
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printf("Error\n");
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return -1;
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}
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printf("==============================================================\n");
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printf("Test wave k = %fx̂ + %fŷ + %fẑ", k.x, k.y, k.z);
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sph_t k_sph = cart2sph(k);
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printf(" = %fr̂ @ θ = %f, φ = %f\n", k_sph.r, k_sph.theta, k_sph.phi);
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printf(" E_0 = (%f+%fj)x̂ + (%f+%fj)ŷ + (%f+%fj)ẑ",
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creal(E.x),cimag(E.x),
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creal(E.y),cimag(E.y),
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creal(E.z),cimag(E.z));
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csphvec_t E_s = ccart2csphvec(E, k_sph);
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printf(" = (%f+%fj)r̂ + (%f+%fj)θ̂ + (%f+%fj)φ̂ @ k\n",
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creal(E_s.rc), cimag(E_s.rc), creal(E_s.thetac), cimag(E_s.thetac),
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creal(E_s.phic), cimag(E_s.phic));
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printf(" lMax = %d, norm: %s, csphase = %d\n",
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(int)lMax, normstr(norm), qpms_normalisation_t_csphase(norm));
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printf("a_L: ");
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for(qpms_y_t y = 0; y < nelem; ++y) printf("%g+%gj ", creal(lc[y]), cimag(lc[y]));
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printf("\na_M: ");
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for(qpms_y_t y = 0; y < nelem; ++y) printf("%g+%gj ", creal(mc[y]), cimag(mc[y]));
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printf("\na_N: ");
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for(qpms_y_t y = 0; y < nelem; ++y) printf("%g+%gj ", creal(ec[y]), cimag(ec[y]));
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printf("\n");
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for (int i = 0; i < npoints; i++) {
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cart3_t w = points[i];
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sph_t w_sph = cart2sph(w);
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printf("Point %d: x = %f, y = %f, z = %f,\n", i, w.x, w.y, w.z);
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printf(" |r| = %f, θ = %f, φ = %f:\n", w_sph.r, w_sph.theta, w_sph.phi);
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double phase = cart3_dot(k,w);
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printf(" k.r = %f\n", phase);
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complex double phfac = cexp(phase * I);
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ccart3_t Ew = ccart3_scale(phfac, E);
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printf(" pw E(r) = (%f+%fj)x̂ + (%f+%fj)ŷ + (%f+%fj)ẑ",
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creal(Ew.x),cimag(Ew.x),
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creal(Ew.y),cimag(Ew.y),
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creal(Ew.z),cimag(Ew.z));
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csphvec_t Ew_s = ccart2csphvec(Ew, w_sph);
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printf(" = (%f+%fj)r̂ + (%f+%fj)θ̂ + (%f+%fj)φ̂ @ r\n",
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creal(Ew_s.rc), cimag(Ew_s.rc),
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creal(Ew_s.thetac), cimag(Ew_s.thetac),
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creal(Ew_s.phic), cimag(Ew_s.phic));
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w_sph.r *= k_sph.r; /// NEVER FORGET THIS!!!
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csphvec_t Ew_s_recomp = qpms_eval_vswf(w_sph,
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lc, mc, ec, lMax, QPMS_BESSEL_REGULAR, norm);
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ccart3_t Ew_recomp = csphvec2ccart(Ew_s_recomp, w_sph);
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printf(" rec E(r) = (%f+%fj)x̂ + (%f+%fj)ŷ + (%f+%fj)ẑ",
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creal(Ew_recomp.x),cimag(Ew_recomp.x),
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creal(Ew_recomp.y),cimag(Ew_recomp.y),
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creal(Ew_recomp.z),cimag(Ew_recomp.z));
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printf(" = (%f+%fj)r̂ + (%f+%fj)θ̂ + (%f+%fj)φ̂ @ r\n",
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creal(Ew_s_recomp.rc), cimag(Ew_s_recomp.rc),
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creal(Ew_s_recomp.thetac), cimag(Ew_s_recomp.thetac),
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creal(Ew_s_recomp.phic), cimag(Ew_s_recomp.phic));
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double relerrfac = 2/(cabs(Ew_s_recomp.rc) + cabs(Ew_s.rc)
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+cabs(Ew_s_recomp.thetac) + cabs(Ew_s.thetac)
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+cabs(Ew_s_recomp.phic) + cabs(Ew_s.phic));
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printf(" rel. err. magnitude: %g @ r̂, %g @ θ̂, %g @ φ̂\n",
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cabs(Ew_s_recomp.rc - Ew_s.rc) * relerrfac,
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cabs(Ew_s_recomp.thetac - Ew_s.thetac) * relerrfac,
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cabs(Ew_s_recomp.phic - Ew_s.phic) * relerrfac
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);
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}
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return 0;
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}
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int test_planewave_decomposition_silent(cart3_t k, ccart3_t E, qpms_l_t lMax, qpms_normalisation_t norm, int npoints, cart3_t *points, double relerrthreshold, double *relerrs) {
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qpms_y_t nelem = qpms_lMax2nelem(lMax);
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int failcount = 0;
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complex double lc[nelem], mc[nelem], ec[nelem];
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if (QPMS_SUCCESS !=
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qpms_planewave2vswf_fill_cart(k, E, lc, mc, ec, lMax, norm)) {
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printf("Error\n");
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return -1;
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}
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sph_t k_sph = cart2sph(k);
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csphvec_t E_s = ccart2csphvec(E, k_sph);
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for (int i = 0; i < npoints; i++) {
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cart3_t w = points[i];
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sph_t w_sph = cart2sph(w);
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w_sph.r *= k_sph.r;
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double phase = cart3_dot(k,w);
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complex double phfac = cexp(phase * I);
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ccart3_t Ew = ccart3_scale(phfac, E);
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csphvec_t Ew_s = ccart2csphvec(Ew, w_sph);
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csphvec_t Ew_s_recomp = qpms_eval_vswf(w_sph,
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lc, mc, ec, lMax, QPMS_BESSEL_REGULAR, norm);
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ccart3_t Ew_recomp = csphvec2ccart(Ew_s_recomp, w_sph);
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double relerrfac = 2/(cabs(Ew_s_recomp.rc) + cabs(Ew_s.rc)
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+cabs(Ew_s_recomp.thetac) + cabs(Ew_s.thetac)
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+cabs(Ew_s_recomp.phic) + cabs(Ew_s.phic));
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double relerr = (cabs(Ew_s_recomp.rc - Ew_s.rc)
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+ cabs(Ew_s_recomp.thetac - Ew_s.thetac)
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+ cabs(Ew_s_recomp.phic - Ew_s.phic)
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) * relerrfac;
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if(relerrs) relerrs[i] = relerr;
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if(relerr > relerrthreshold) ++failcount;
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}
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return failcount;
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}
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#endif
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@ -0,0 +1,43 @@
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for an in 0 1 2 3 ; do
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for am in 0 2 ; do
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for bn in 0 1 2 3 ; do
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for bm in 0 2 ; do
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for bf in 0 1 2 3 ; do
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c99 -o ../../tests/raytests/z/AN${an}M${am}BN${bn}M${bm}F${bf} -DAN${an} -DAM${am} -DBN${bn} -DBM${bm} -DBF${bf} -ggdb -O2 -I .. vswf_translation_test_rays.c ../translations.c ../vswf.c ../gaunt.c ../legendre.c -lgsl -lm -lblas
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done
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done
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done
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done
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done
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export NORM="129"
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for an in 0 1 2 3 ; do
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for am in 0 2 ; do
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for bn in 0 1 2 3 ; do
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for bm in 0 2 ; do
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for bf in 0 1 2 3 ; do
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./AN${an}M${am}BN${bn}M${bm}F${bf} an${an}m${am}bn${bn}m${bm}f${bf}_${NORM} 1 0 ${NORM}
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sed -e 's/\./,/g' an${an}m${am}bn${bn}m${bm}f${bf}_${NORM}.0 > an${an}m${am}bn${bn}m${bm}f${bf}_${NORM}.0.tsv
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sed -e 's/\./,/g' an${an}m${am}bn${bn}m${bm}f${bf}_${NORM}.1 > an${an}m${am}bn${bn}m${bm}f${bf}_${NORM}.1.tsv
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sed -e 's/\./,/g' an${an}m${am}bn${bn}m${bm}f${bf}_${NORM}.2 > an${an}m${am}bn${bn}m${bm}f${bf}_${NORM}.2.tsv
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# for i in an${an}m${am}bn${bn}m${bm}_130.? ; do
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# sed -e 's/\./,/g' $i >${i}.tsv
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# done
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done
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done
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done
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done
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done
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export NORM="129"
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export smer="125"
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export an=1 am=0 bn=1 bm=0 bf=0
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c99 -o ../../tests/raytests/$smer/AN${an}M${am}BN${bn}M${bm}F${bf} -DAN${an} -DAM${am} -DBN${bn} -DBM${bm} -DBF${bf} -ggdb -I .. vswf_translation_test_rays.c ../translations.c ../vswf.c ../gaunt.c ../legendre.c -lgsl -lm -lblas
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cd ../../tests/raytests/$smer
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./AN${an}M${am}BN${bn}M${bm}F${bf} an${an}m${am}bn${bn}m${bm}f${bf}_${NORM} 1 0 ${NORM}
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sed -e 's/\./,/g' an${an}m${am}bn${bn}m${bm}f${bf}_${NORM}.0 > an${an}m${am}bn${bn}m${bm}f${bf}_${NORM}.0.tsv
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sed -e 's/\./,/g' an${an}m${am}bn${bn}m${bm}f${bf}_${NORM}.1 > an${an}m${am}bn${bn}m${bm}f${bf}_${NORM}.1.tsv
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sed -e 's/\./,/g' an${an}m${am}bn${bn}m${bm}f${bf}_${NORM}.2 > an${an}m${am}bn${bn}m${bm}f${bf}_${NORM}.2.tsv
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cd -
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@ -11,6 +11,35 @@
|
|||
#include <stdlib.h> //abort()
|
||||
#include <gsl/gsl_sf_coupling.h>
|
||||
|
||||
|
||||
/*
|
||||
* Define macros with additional factors that "should not be there" according
|
||||
* to the "original" formulae but are needed to work with my vswfs.
|
||||
* (actually, I don't know whether the error is in using "wrong" implementation
|
||||
* of vswfs, "wrong" implementation of Xu's translation coefficient formulae,
|
||||
* error/inconsintency in Xu's paper or something else)
|
||||
* Anyway, the zeroes give the correct _numerical_ values according to Xu's
|
||||
* paper tables (without Xu's typos, of course), while
|
||||
* the predefined macros give the correct translations of the VSWFs.
|
||||
*/
|
||||
#if !(defined AN0 || defined AN1 || defined AN2 || defined AN3)
|
||||
#pragma message "using AN1 macro as default"
|
||||
#define AN1
|
||||
#endif
|
||||
//#if !(defined AM0 || defined AM2)
|
||||
//#define AM1
|
||||
//#endif
|
||||
#if !(defined BN0 || defined BN1 || defined BN2 || defined BN3)
|
||||
#pragma message "using BN1 macro as default"
|
||||
#define BN1
|
||||
#endif
|
||||
//#if !(defined BM0 || defined BM2)
|
||||
//#define BM1
|
||||
//#endif
|
||||
//#if !(defined BF0 || defined BF1 || defined BF2 || defined BF3)
|
||||
//#define BF1
|
||||
//#endif
|
||||
|
||||
// if defined, the pointer B_multipliers[y] corresponds to the q = 1 element;
|
||||
// otherwise, it corresponds to the q = 0 element, which should be identically zero
|
||||
#ifdef QPMS_PACKED_B_MULTIPLIERS
|
||||
|
|
@ -483,7 +512,18 @@ static void qpms_trans_calculator_multipliers_A_general(
|
|||
double Ppfac = (Pp_order >= 0) ? 1 :
|
||||
min1pow(mu-m) * exp(lgamma(1+p+Pp_order)-lgamma(1+p-Pp_order));
|
||||
double summandfac = (n*(n+1) + nu*(nu+1) - p*(p+1)) * min1pow(q) * a1q_n;
|
||||
dest[q] = presum * summandfac * Ppfac /* * ipow(n-nu) */;
|
||||
dest[q] = presum * summandfac * Ppfac
|
||||
#ifdef AN1
|
||||
* ipow(n-nu)
|
||||
#elif defined AN2
|
||||
* min1pow(-n+nu)
|
||||
#elif defined AN3
|
||||
* ipow (nu - n)
|
||||
#endif
|
||||
#ifdef AM2
|
||||
* min1pow(-m+mu)
|
||||
#endif //NNU
|
||||
;
|
||||
// FIXME I might not need complex here
|
||||
}
|
||||
}
|
||||
|
|
@ -533,7 +573,25 @@ void qpms_trans_calculator_multipliers_B_general(
|
|||
* (isq(n+nu+1)-isq(p+1))
|
||||
);
|
||||
dest[q-BQ_OFFSET] = presum * t * Ppfac_
|
||||
* cruzan_bfactor(-m,n,mu,nu,p) * ipow(p+1) /* * ipow(n-nu) */;
|
||||
* cruzan_bfactor(-m,n,mu,nu,p) * ipow(p+1)
|
||||
#ifdef BN1
|
||||
* ipow(n-nu)
|
||||
#elif defined BN2
|
||||
* min1pow(-n+nu)
|
||||
#elif defined BN3
|
||||
* ipow (nu - n)
|
||||
#endif
|
||||
#ifdef BM2
|
||||
* min1pow(-m+mu)
|
||||
#endif
|
||||
#ifdef BF1
|
||||
* I
|
||||
#elif defined BF2
|
||||
* (-1)
|
||||
#elif defined BF3
|
||||
* (-I)
|
||||
#endif
|
||||
;// NNU
|
||||
}
|
||||
}
|
||||
|
||||
|
|
|
|||
Loading…
Reference in New Issue