Plane wave decomposition now works for the transversal part (not yet longitudinal)

Former-commit-id: 83dadf35d24a66c7576395f6f156f5e7586551cd

qpms/test_planewave_decomposition.c

@@ -22,30 +22,64 @@ char *normstr(qpms_normalisation_t norm) {
 	}
 }
 int test_planewave_decomposition(cart3_t k, ccart3_t E, qpms_l_t lMax, qpms_normalisation_t norm, int npoints, cart3_t *points);
+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);
 
 int main() {
 	gsl_rng *rng =  gsl_rng_alloc(gsl_rng_ranlxs0);
 	gsl_rng_set(rng, 666);
 
-	qpms_l_t lMax = 20;
+	qpms_l_t lMax = 50;
 	int npoints = 10;
 	double sigma = 1.3;
 	cart3_t points[npoints];
+	double relerrs[npoints];
 	memset(points, 0, npoints * sizeof(cart3_t));
-	points[0].x = points[1].y = points[2].z = 1.;
+	points[1].x = points[2].y = points[3].z = 1.;
-	for (unsigned i = 3; i < npoints; ++i) {
+	double relerrthreshold = 1e-11;
+	for (unsigned i = 4; i < npoints; ++i) {
 		cart3_t *w = points+i;
 		w->x = gsl_ran_gaussian(rng, sigma);
 		w->y = gsl_ran_gaussian(rng, sigma);
 		w->z = gsl_ran_gaussian(rng, sigma);
 	}
 	
+	double ksigma = 15;
+
+	for(int i = 1; i < 2; ++i) {
+		cart3_t k = {0, 0, 2};
+		ccart3_t E = {0., 1.1+I, 0.};
+		if(i){
+			k.x = gsl_ran_gaussian(rng, ksigma);
+			k.y = gsl_ran_gaussian(rng, ksigma);
+			k.z = gsl_ran_gaussian(rng, ksigma);
+			E.x = gsl_ran_gaussian(rng, ksigma);
+			E.x += I* gsl_ran_gaussian(rng, ksigma);	
+			E.y = gsl_ran_gaussian(rng, ksigma);
+			E.y += I* gsl_ran_gaussian(rng, ksigma);
+			E.z = gsl_ran_gaussian(rng, ksigma);
+			E.z += I* gsl_ran_gaussian(rng, ksigma);
+		}
+#if 0
+		printf("Test wave k = %gx̂ + %gŷ + %gẑ", k.x, k.y, k.z);
+		printf(", E_0 = (%g+%gj)x̂ + (%g+%gj)ŷ + (%g+%gj)ẑ\n",
+			creal(E.x),cimag(E.x),
+			creal(E.y),cimag(E.y),
+			creal(E.z),cimag(E.z));
+		printf("%d points, sigma = %g, rel. err. threshold = %g\n", npoints, sigma, relerrthreshold);
+		for(int i = 1; i <= 3; ++i){
+			int res = test_planewave_decomposition_silent(k, E, lMax, i, npoints, points, relerrthreshold, relerrs);
+			printf("\n%s %d/%d %s %s\n", res ? "!!" : "OK", npoints-res, npoints, normstr(i), "");
+			for(int p = 0; p < npoints; ++p) printf("%.3g ", relerrs[p]);
+			res = test_planewave_decomposition_silent(k, E, lMax, i |QPMS_NORMALISATION_T_CSBIT, npoints, points, relerrthreshold, relerrs);
+			printf("\n%s %d/%d %s %s\n", res ? "!!" : "OK", npoints-res, npoints, normstr(i), "with C.-S. phase");
+			for(int p = 0; p < npoints; ++p) printf("%.3g ", relerrs[p]);
+		}
+#endif 
+		for(int i = 1; i <= 3; ++i){
+			test_planewave_decomposition(k, E, lMax, i, npoints, points);
+			test_planewave_decomposition(k, E, lMax, i | QPMS_NORMALISATION_T_CSBIT, npoints, points);
+		}
 
-	cart3_t k = {0, 0, 1};
-	ccart3_t E = {0., 1., 0.};
-	for(int i = 1; i <= 3; ++i){
-		test_planewave_decomposition(k, E, lMax, i, npoints, points);
-		test_planewave_decomposition(k, E, lMax, i | QPMS_NORMALISATION_T_CSBIT, npoints, points);
 	}
 	gsl_rng_free(rng);
 }
@@ -84,9 +118,9 @@ int test_planewave_decomposition(cart3_t k, ccart3_t E, qpms_l_t lMax, qpms_norm
 		sph_t w_sph = cart2sph(w);
 		printf("Point %d: x = %f, y = %f, z = %f,\n", i, w.x, w.y, w.z);
 		printf("        |r| = %f, θ = %f, φ = %f:\n", w_sph.r, w_sph.theta, w_sph.phi);
-		double ph_2pi = cart3_dot(k,w);
+		double phase = cart3_dot(k,w);
-		printf("  k.r = %f\n", ph_2pi);
+		printf("  k.r = %f\n", phase);
-		double phfac = cexp(2 * M_PI * ph_2pi * I);
+		complex double phfac = cexp(phase * I);
 		ccart3_t Ew = ccart3_scale(phfac, E);
 		printf("  pw  E(r) = (%f+%fj)x̂ + (%f+%fj)ŷ + (%f+%fj)ẑ", 
 			creal(Ew.x),cimag(Ew.x),
@@ -97,6 +131,7 @@ int test_planewave_decomposition(cart3_t k, ccart3_t E, qpms_l_t lMax, qpms_norm
 			creal(Ew_s.rc), cimag(Ew_s.rc), 
 			creal(Ew_s.thetac), cimag(Ew_s.thetac),
 			creal(Ew_s.phic), cimag(Ew_s.phic));
+		w_sph.r *= k_sph.r; /// NEVER FORGET THIS!!!
 		csphvec_t Ew_s_recomp = qpms_eval_vswf(w_sph,
 			lc, mc, ec, lMax, QPMS_BESSEL_REGULAR, norm);
 		ccart3_t Ew_recomp = csphvec2ccart(Ew_s_recomp, w_sph);
@@ -108,13 +143,50 @@ int test_planewave_decomposition(cart3_t k, ccart3_t E, qpms_l_t lMax, qpms_norm
 			creal(Ew_s_recomp.rc), cimag(Ew_s_recomp.rc), 
 			creal(Ew_s_recomp.thetac), cimag(Ew_s_recomp.thetac),
 			creal(Ew_s_recomp.phic), cimag(Ew_s_recomp.phic));
-		printf(" rel. err. magnitude: %e @ r̂, %e @ θ̂, %e @ φ̂\n",
+		double relerrfac = 2/(cabs(Ew_s_recomp.rc) + cabs(Ew_s.rc)
-			2. * cabs(Ew_s_recomp.rc - Ew_s.rc)
+				+cabs(Ew_s_recomp.thetac) + cabs(Ew_s.thetac)
-				/(cabs(Ew_s_recomp.rc) + cabs(Ew_s.rc)),
+				+cabs(Ew_s_recomp.phic) + cabs(Ew_s.phic));
-			2. * cabs(Ew_s_recomp.thetac - Ew_s.thetac)
+		printf(" rel. err. magnitude: %g @ r̂, %g @ θ̂, %g @ φ̂\n",
-				/(cabs(Ew_s_recomp.thetac) + cabs(Ew_s.thetac)),
+			cabs(Ew_s_recomp.rc - Ew_s.rc) * relerrfac,
-			2. * cabs(Ew_s_recomp.phic - Ew_s.phic)
+			cabs(Ew_s_recomp.thetac - Ew_s.thetac) * relerrfac,
-				/(cabs(Ew_s_recomp.phic) + cabs(Ew_s.phic)));
+			cabs(Ew_s_recomp.phic - Ew_s.phic) * relerrfac
+		      );
 	}
 	return 0;
 }
+
+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) {
+	qpms_y_t nelem = qpms_lMax2nelem(lMax);
+	int failcount = 0;
+	complex double lc[nelem], mc[nelem], ec[nelem];
+	if (QPMS_SUCCESS != 
+		qpms_planewave2vswf_fill_cart(k, E, lc, mc, ec, lMax, norm)) {
+		printf("Error\n");
+		return -1;
+	}
+	sph_t k_sph = cart2sph(k);
+	csphvec_t E_s = ccart2csphvec(E, k_sph);
+	for (int i = 0; i < npoints; i++) {
+		cart3_t w = points[i];
+		sph_t w_sph = cart2sph(w);
+		w_sph.r *= k_sph.r;
+		double phase = cart3_dot(k,w);
+		complex double phfac = cexp(phase * I);
+		ccart3_t Ew = ccart3_scale(phfac, E);
+		csphvec_t Ew_s = ccart2csphvec(Ew, w_sph);
+		csphvec_t Ew_s_recomp = qpms_eval_vswf(w_sph,
+			lc, mc, ec, lMax, QPMS_BESSEL_REGULAR, norm);
+		ccart3_t Ew_recomp = csphvec2ccart(Ew_s_recomp, w_sph);
+		double relerrfac = 2/(cabs(Ew_s_recomp.rc) + cabs(Ew_s.rc)
+				+cabs(Ew_s_recomp.thetac) + cabs(Ew_s.thetac)
+				+cabs(Ew_s_recomp.phic) + cabs(Ew_s.phic));
+			
+		double relerr = (cabs(Ew_s_recomp.rc - Ew_s.rc) 
+			+	cabs(Ew_s_recomp.thetac - Ew_s.thetac)
+			+ 	cabs(Ew_s_recomp.phic - Ew_s.phic)
+			) * relerrfac;
+		if(relerrs) relerrs[i] = relerr;
+		if(relerr > relerrthreshold) ++failcount;
+	}
+	return failcount;
+}

qpms/vecprint.c

@@ -0,0 +1,33 @@
+#include <assert.h>
+#include "vectors.h"
+#include "complex.h"
+#include <stdio.h>
+
+void print_csphvec(csphvec_t v)
+{
+	printf("(%f+%fj)r̂ + (%f+%fj)θ̂ + (%f+%fj)φ̂",
+			creal(v.rc), cimag(v.rc),
+			creal(v.thetac), cimag(v.thetac),
+			creal(v.phic), cimag(v.phic)
+	      );
+}
+
+
+void print_cart3(cart3_t v)
+{
+	printf("%fx̂ + %fŷ + %fẑ", v.x, v.y, v.z);
+}
+
+void print_ccart3(ccart3_t v)
+{
+	printf("(%f+%fj)x̂ + (%f+%fj)ŷ + (%f+%fj)ẑ",
+			creal(v.x), cimag(v.x),
+			creal(v.y), cimag(v.y),
+			creal(v.z), cimag(v.z)
+	      );
+}
+
+void print_sph(sph_t r)
+{
+	printf("(r=%g, θ=%g, φ=%g)", r.r, r.theta, r.phi);
+}

qpms/vectors.h

@@ -107,4 +107,9 @@ static inline csphvec_t ccart2csphvec(const ccart3_t cartvec, const sph_t at) {
 	return res;
 }
 
+void print_csphvec(csphvec_t);
+void print_ccart3(ccart3_t);
+void print_cart3(cart3_t);
+void print_sph(sph_t);
+
 #endif //VECTORS_H

qpms/vswf.c

@@ -374,8 +374,8 @@ qpms_errno_t qpms_vecspharm_dual_fill(csphvec_t *const a1target, csphvec_t *cons
 				p3->phic = 0;
 				++p3;
 			}
+			++pleg; ++ppi; ++ptau;
 		}
-		++pleg; ++ppi; ++ptau;
 	}
 	qpms_pitau_free(pt);
 	return QPMS_SUCCESS;