Computing translation coefficients with precalculated multipliers now

working


Former-commit-id: 7a7b8fd403f1624661a198119080937193f4a8c7

qpms/test_translations2.c

@@ -0,0 +1,54 @@
+#include "translations.h"
+#include <stdio.h>
+//#include <math.h>
+#include <complex.h>
+
+typedef struct {
+	int m, n, mu, nu;
+	sph_t kdlj;
+	qpms_bessel_t J;
+	complex double result_A, result_B;
+} testcase_single_trans_t;
+
+testcase_single_trans_t testcases_Taylor[] = {
+#include "testcases_taylor"
+};
+
+int lMax=10;
+
+int main() {
+	qpms_trans_calculator *c = qpms_trans_calculator_init(lMax, QPMS_NORMALIZATION_TAYLOR);
+
+	for(testcase_single_trans_t *tc = testcases_Taylor; tc->J != QPMS_BESSEL_UNDEF; tc++) {
+		if (!tc->n || !tc->nu || tc->n > lMax || tc->nu > lMax ) continue;
+
+		printf("m=%d, n=%d, mu=%d, nu=%d,\n", tc->m,tc->n,tc->mu,tc->nu);
+		complex double A = qpms_trans_single_A_Taylor(tc->m, tc->n, tc->mu, tc->nu, tc->kdlj, true, tc->J);
+		complex double B = qpms_trans_single_B_Taylor(tc->m, tc->n, tc->mu, tc->nu, tc->kdlj, true, tc->J);
+		complex double A2 = qpms_trans_calculator_get_A(c, tc->m, tc->n, tc->mu, tc->nu, tc->kdlj, true, tc->J);
+		complex double B2 = qpms_trans_calculator_get_B(c, tc->m, tc->n, tc->mu, tc->nu, tc->kdlj, true, tc->J);
+		printf("A  = %.16f+%.16fj, relerr=%.16f, J=%d\n",
+				creal(A), cimag(A),  (0 == cabs(tc->result_A - A)) ? 0 :
+				cabs(tc->result_A - A)/((cabs(A) < cabs(tc->result_A)) ? cabs(A) : cabs(tc->result_A)),
+				tc->J);
+		printf("A' = %.16f+%.16fj, relerr=%.16f, relerr2=%.3e\n",
+				creal(A2), cimag(A2),  (0 == cabs(tc->result_A - A2)) ? 0 :
+				cabs(tc->result_A - A2)/((cabs(A2) < cabs(tc->result_A)) ? cabs(A2) : cabs(tc->result_A)),
+				(0 == cabs(A - A2)) ? 0 :
+				cabs(A - A2)/((cabs(A2) < cabs(A)) ? cabs(A2) : cabs(A))
+		      );
+		printf("B  = %.16f+%.16fj, relerr=%.16f, J=%d\n",
+				creal(B), cimag(B),  (0 == cabs(tc->result_B - B)) ? 0 :
+				cabs(tc->result_B - B)/((cabs(B) < cabs(tc->result_B)) ? cabs(B) : cabs(tc->result_B)),
+				tc->J);
+		printf("B' = %.16f+%.16fj, relerr=%.16f, relerr2=%.3e\n",
+				creal(B2), cimag(B2),  (0 == cabs(tc->result_B - B2)) ? 0 :
+				cabs(tc->result_B - B2)/((cabs(B2) < cabs(tc->result_B)) ? cabs(B2) : cabs(tc->result_B)),
+				(0 == cabs(B - B2)) ? 0 :
+				cabs(B - B2)/((cabs(B2) < cabs(B)) ? cabs(B2) : cabs(B))
+		      );
+	}
+	qpms_trans_calculator_free(c);
+}
+
+

qpms/translations.c

@@ -84,7 +84,8 @@ complex double qpms_trans_single_A_Taylor(int m, int n, int mu, int nu, sph_t kd
     for(int q = 0; q <= qmax; ++q) {
 	    int p = n+nu-2*q;
 	    int Pp_order = mu-m;
-	    if(p < abs(Pp_order)) continue; // FIXME raději nastav lépe meze
+	    //if(p < abs(Pp_order)) continue; // FIXME raději nastav lépe meze
+	    assert(p >= abs(Pp_order));
 	    double a1q_n = a1q[q] / a1q0;
 	    double Pp = leg[gsl_sf_legendre_array_index(p, abs(Pp_order))];
 	    if (Pp_order < 0) Pp *= min1pow(mu-m) * exp(lgamma(1+p+Pp_order)-lgamma(1+p-Pp_order));
@@ -105,7 +106,7 @@ complex double qpms_trans_single_A_Taylor(int m, int n, int mu, int nu, sph_t kd
 }
 
 complex double qpms_trans_single_B_Taylor(int m, int n, int mu, int nu, sph_t kdlj,
-		bool r_ge_d, qpms_bessel_t J) { // TODO make J enum
+		bool r_ge_d, qpms_bessel_t J) { 
     if(r_ge_d) J = QPMS_BESSEL_REGULAR;
     double costheta = cos(kdlj.theta);
     
@@ -186,7 +187,8 @@ static inline size_t qpms_mn2y(int m, int n) {
 }
 
 static inline int qpms_y2n(size_t y) {
-	return (sqrt(5+y)-2)/2; // the cast will truncate the fractional part, which is what we want
+	//return (sqrt(5+y)-2)/2; // the cast will truncate the fractional part, which is what we want
+	return sqrt(y+1);
 }
 
 static inline int qpms_yn2m(size_t y, int n) {
@@ -207,8 +209,148 @@ static inline size_t qpms_trans_calculator_index_yyu(const qpms_trans_calculator
 	return c->nelem * y + yu;
 }
 
+
 #define SQ(x) ((x)*(x))
 
+//#if 0
+static void qpms_trans_calculator_multipliers_A_Taylor(
+		complex double *dest, int m, int n, int mu, int nu, int qmax) {
+	assert(qmax == gaunt_q_max(-m,n,mu,nu));
+	double a1q[qmax+1];
+	int err;
+	gaunt_xu(-m,n,mu,nu,qmax,a1q,&err);
+	if (err) abort();
+	double a1q0 = a1q[0];
+
+	double exponent=(lgamma(2*n+1)-lgamma(n+2)+lgamma(2*nu+3)-lgamma(nu+2)
+                +lgamma(n+nu+m-mu+1)-lgamma(n-m+1)-lgamma(nu+mu+1)
+                +lgamma(n+nu+1) - lgamma(2*(n+nu)+1)) - 0.5*( // ex-prenormratio
+                lgamma(n+m+1)-lgamma(n-m+1)+lgamma(nu-mu+1)-lgamma(nu+mu+1));
+	double presum = exp(exponent);
+	presum *=  min1pow(m+n) * sqrt((2.*n+1)/(2.*nu+1)) / (4*n);
+
+	for(int q = 0; q <= qmax; q++) {
+		int p = n+nu-2*q;
+		int Pp_order = mu - m;
+		assert(p >= abs(Pp_order));
+		double a1q_n = a1q[q] / a1q0;
+		// Assuming non_normalized legendre polynomials!
+		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;
+		// FIXME I might not need complex here
+	}
+}
+//#endif
+#if 0
+static void qpms_trans_calculator_multipliers_A_Taylor(
+		complex double *dest, int m, int n, int mu, int nu, int qmax) {
+	assert(qmax == gaunt_q_max(-m,n,mu,nu));
+	double a1q[qmax+1];
+	int err;
+	gaunt_xu(-m,n,mu,nu,qmax,a1q,&err);
+	if (err) abort();
+	double a1q0 = a1q[0];
+	for(int q = 0; q <= qmax; ++q) {
+		int p = n+nu-2*q;
+		int Pp_order = mu-m;
+		//if(p < abs(Pp_order)) continue; // FIXME raději nastav lépe meze
+		assert(p >= abs(Pp_order));
+		double a1q_n = a1q[q] / a1q0;
+		//double Pp = leg[gsl_sf_legendre_array_index(p, abs(Pp_order))];
+		//complex double zp = bes[p];
+		 dest[q] = (n*(n+1) + nu*(nu+1) - p*(p+1)) * min1pow(q) * a1q_n /* * zp * Pp*/;
+		if (Pp_order < 0) dest[q] *= min1pow(mu-m) * exp(lgamma(1+p+Pp_order)-lgamma(1+p-Pp_order));
+		//sum += summandq;
+	}
+
+	double exponent=(lgamma(2*n+1)-lgamma(n+2)+lgamma(2*nu+3)-lgamma(nu+2)
+			+lgamma(n+nu+m-mu+1)-lgamma(n-m+1)-lgamma(nu+mu+1)
+			+lgamma(n+nu+1) - lgamma(2*(n+nu)+1));
+	complex double presum = exp(exponent);
+	presum *=/* cexp(I*(mu-m)*kdlj.phi) * */  min1pow(m) * ipow(nu+n) / (4*n);
+
+	complex double prenormratio = ipow(nu-n) *  sqrt(((2.*nu+1)/(2.*n+1))* exp(
+				lgamma(n+m+1)-lgamma(n-m+1)+lgamma(nu-mu+1)-lgamma(nu+mu+1)));
+	//return (presum / prenormratio) * sum;
+	for(int q=0;q<=qmax;++q) dest[q] *= presum / prenormratio;
+}
+#endif	
+
+
+
+static void qpms_trans_calculator_multipliers_B_Taylor(
+		complex double *dest, int m, int n, int mu, int nu, int Qmax) {
+	assert(Qmax == gaunt_q_max(-m,n+1,mu,nu));
+	int q2max = gaunt_q_max(-m-1,n+1,mu+1,nu);
+	assert(Qmax == q2max);
+	// FIXME remove the q2max variable altogether, as it is probably equal
+	// to Qmax
+	double a2q[q2max+1], a3q[Qmax+1], a2q0, a3q0;
+	int err;
+	if (mu == nu) {
+	for (int q = 0; q <= q2max; ++q)
+                a2q[q] = 0;
+          	a2q0 = 1;
+    	}
+    	else {
+            	gaunt_xu(-m-1,n+1,mu+1,nu,q2max,a2q,&err); if (err) abort();
+            	a2q0 = a2q[0];
+    	}
+    	gaunt_xu(-m,n+1,mu,nu,Qmax,a3q,&err); if (err) abort();
+    	a3q0 = a3q[0];
+
+	double exponent=(lgamma(2*n+3)-lgamma(n+2)+lgamma(2*nu+3)-lgamma(nu+2)
+			+lgamma(n+nu+m-mu+2)-lgamma(n-m+1)-lgamma(nu+mu+1)
+			+lgamma(n+nu+2) - lgamma(2*(n+nu)+3)) - 0.5 * (
+				lgamma(n+m+1)-lgamma(n-m+1)+lgamma(nu-mu+1)
+				-lgamma(nu+mu+1));
+	complex double presum = exp(exponent);
+	presum *= I * (min1pow(m+n) *sqrt((2.*n+1)/(2.*nu+1)) / (
+			(4*n)*(n+1)*(n+m+1)));
+
+	for (int q = 0; q <= Qmax; ++q) {
+		int p = n+nu-2*q;
+		double a2q_n = a2q[q]/a2q0;
+		double a3q_n = a3q[q]/a3q0;
+		int Pp_order_ = mu-m;
+		//if(p+1 < abs(Pp_order_)) continue; // FIXME raději nastav lépe meze
+		assert(p+1 >= abs(Pp_order_));
+		double Ppfac = (Pp_order_ >= 0) ? 1 :		
+			
+			min1pow(mu-m) * exp(lgamma(1+1+p+Pp_order_)-lgamma(1+1+p-Pp_order_));
+		double summandq = ((2*(n+1)*(nu-mu)*a2q_n
+					-(-nu*(nu+1) - n*(n+3) - 2*mu*(n+1)+p*(p+3))* a3q_n)
+				*min1pow(q));
+		dest[q] = Ppfac * summandq * presum;
+	}
+}
+
+int qpms_trans_calculator_multipliers_A(qpms_normalization_t norm, complex double *dest, int m, int n, int mu, int nu, int qmax) {
+	switch (norm) {
+		case QPMS_NORMALIZATION_TAYLOR:
+			qpms_trans_calculator_multipliers_A_Taylor(dest,m,n,mu,nu,qmax);
+			return 0;
+			break;
+		default:
+			abort();
+	}
+	assert(0);
+}
+
+int qpms_trans_calculator_multipliers_B(qpms_normalization_t norm, complex double *dest, int m, int n, int mu, int nu, int qmax) {
+	switch (norm) {
+		case QPMS_NORMALIZATION_TAYLOR:
+			qpms_trans_calculator_multipliers_B_Taylor(dest,m,n,mu,nu,qmax);
+			return 0;
+			break;
+		default:
+			abort();
+	}
+	assert(0);
+}
+
 qpms_trans_calculator
 *qpms_trans_calculator_init (int lMax, qpms_normalization_t normalization) {
 	qpms_trans_calculator *c = malloc(sizeof(qpms_trans_calculator));
@@ -224,14 +366,24 @@ qpms_trans_calculator
 			int m,n, mu, nu;
 			qpms_y2mn_p(y,&m,&n);
 			qpms_y2mn_p(yu,&mu,&nu);
-			qmaxsum += (qmaxes[qpms_trans_calculator_index_yyu(c,y,yu)] = gaunt_q_max(-m,n,mu,nu));
+			qmaxsum += 1 + (
+				qmaxes[qpms_trans_calculator_index_yyu(c,y,yu)] 
+				= gaunt_q_max(-m,n,mu,nu));
 		}
 	c->A_multipliers[0] = malloc(qmaxsum * sizeof(complex double));
-	for(size_t i = 0; i < SQ(c->nelem); ++i)
+	// calculate multiplier beginnings
-		c->A_multipliers[i+1] = c->A_multipliers[i] + qmaxes[i];
+	for(size_t i = 0; i < SQ(c->nelem); ++i) 
-	// TODO here comes the filling of A_multipliers
+		c->A_multipliers[i+1] = c->A_multipliers[i] + qmaxes[i] + 1;
-	
+	// calculate the multipliers
-
+	for(size_t y = 0; y < c->nelem; ++y)
+		for(size_t yu = 0; yu < c->nelem; ++yu) {
+			size_t i = y * c->nelem + yu;
+			int m, n, mu, nu;
+			qpms_y2mn_p(y, &m, &n);
+			qpms_y2mn_p(yu, &mu, &nu);
+			qpms_trans_calculator_multipliers_A(normalization,
+				c->A_multipliers[i], m, n, mu, nu, qmaxes[i]);
+		}
 
 	qmaxsum = 0;
 	for(size_t y=0; y < c->nelem; y++)
@@ -239,16 +391,122 @@ qpms_trans_calculator
 			int m, n, mu, nu;
 			qpms_y2mn_p(y,&m,&n);
 			qpms_y2mn_p(yu,&mu,&nu);
-			qmaxsum += (qmaxes[qpms_trans_calculator_index_yyu(c,y,yu)] = gaunt_q_max(-m,n+1,mu,nu));
+			qmaxsum += 1 + (
+				qmaxes[qpms_trans_calculator_index_yyu(c,y,yu)] 
+				= gaunt_q_max(-m,n+1,mu,nu));
 		}
 	c->B_multipliers[0] = malloc(qmaxsum * sizeof(complex double));
-	for(size_t i = 0; i < SQ(c->nelem); ++i)
+	// calculate multiplier beginnings
-		c->B_multipliers[i+1] = c->B_multipliers[i] + qmaxes[i];
+	for(size_t i = 0; i < SQ(c->nelem); ++i) 
-
+		c->B_multipliers[i+1] = c->B_multipliers[i] + qmaxes[i] + 1;
-	// TODO here comes the filling of B_multipliers
+	// calculate the multipliers
+	for(size_t y = 0; y < c->nelem; ++y)
+		for(size_t yu = 0; yu < c->nelem; ++yu) {
+			size_t i = y * c->nelem + yu;
+			int m, n, mu, nu;
+			qpms_y2mn_p(y, &m, &n);
+			qpms_y2mn_p(yu, &mu, &nu);
+			qpms_trans_calculator_multipliers_B(normalization,
+				c->B_multipliers[i], m, n, mu, nu, qmaxes[i]);
+		}
 
 	free(qmaxes);
 	return c;
 }
 
+complex double qpms_trans_calculator_get_A_buf(const qpms_trans_calculator *c,
+		int m, int n, int mu, int nu, sph_t kdlj,
+		bool r_ge_d, qpms_bessel_t J,
+		complex double *bessel_buf, double *legendre_buf) {
+	if (r_ge_d) J = QPMS_BESSEL_REGULAR;
+	switch(c->normalization) {
+		case QPMS_NORMALIZATION_TAYLOR:
+			{
+				double costheta = cos(kdlj.theta);
+				if (gsl_sf_legendre_array_e(GSL_SF_LEGENDRE_NONE,n+nu,costheta,-1,legendre_buf)) abort();
+				if (qpms_sph_bessel_array(J, n+nu, kdlj.r, bessel_buf)) abort();
+				size_t i = qpms_trans_calculator_index_mnmunu(c, m, n, mu, nu);
+				size_t qmax = c->A_multipliers[i+1] - c->A_multipliers[i] - 1;
+				assert(qmax == gaunt_q_max(-m,n,mu,nu));
+				complex double sum = 0;
+				for(size_t q = 0; q <= qmax; ++q) {
+					int p = n+nu-2*q;
+					double Pp = legendre_buf[gsl_sf_legendre_array_index(p, abs(mu-m))];
+					complex double zp = bessel_buf[p];
+					complex double multiplier = c->A_multipliers[i][q];
+					sum += Pp * zp *  multiplier;
+				}
+				complex double eimf =  cexp(I*(mu-m)*kdlj.phi);
+				return sum * eimf;
+			}
+			break;
+		default:
+			abort();
+	}
+	assert(0);
+}
 
+complex double qpms_trans_calculator_get_B_buf(const qpms_trans_calculator *c,
+		int m, int n, int mu, int nu, sph_t kdlj,
+		bool r_ge_d, qpms_bessel_t J,
+		complex double *bessel_buf, double *legendre_buf) {
+	if (r_ge_d) J = QPMS_BESSEL_REGULAR;
+	switch(c->normalization) {
+		case QPMS_NORMALIZATION_TAYLOR:
+			{
+				double costheta = cos(kdlj.theta);
+				if (gsl_sf_legendre_array_e(GSL_SF_LEGENDRE_NONE,n+nu+1,
+																costheta,-1,legendre_buf)) abort();
+				if (qpms_sph_bessel_array(J, n+nu+2, kdlj.r, bessel_buf)) abort();
+				size_t i = qpms_trans_calculator_index_mnmunu(c, m, n, mu, nu);
+				size_t qmax = c->B_multipliers[i+1] - c->B_multipliers[i] - 1;
+				assert(qmax == gaunt_q_max(-m,n+1,mu,nu));
+				complex double sum = 0;
+				for(int q = 0; q <= qmax; ++q) {
+					int p = n+nu-2*q;
+					double Pp_ = legendre_buf[gsl_sf_legendre_array_index(p+1, abs(mu-m))];
+					complex double eimf = cexp(I * kdlj.phi);
+					complex double zp_ = bessel_buf[p+1];
+					complex double multiplier = c->B_multipliers[i][q];
+					sum += Pp_ * zp_ * multiplier;
+				}
+				complex double eimf =  cexp(I*(mu-m)*kdlj.phi);
+				return sum * eimf;
+			}
+			break;
+		default:
+			abort();
+	}
+	assert(0);
+}
+
+complex double qpms_trans_calculator_get_A(const qpms_trans_calculator *c,
+                int m, int n, int mu, int nu, sph_t kdlj,
+                bool r_ge_d, qpms_bessel_t J) {
+	double leg[gsl_sf_legendre_array_n(n+nu)];
+	complex double bes[n+nu+1];
+	return qpms_trans_calculator_get_A_buf(c,m,n,mu,nu,kdlj,r_ge_d,J,
+			bes,leg);
+}
+
+complex double qpms_trans_calculator_get_B(const qpms_trans_calculator *c,
+                int m, int n, int mu, int nu, sph_t kdlj,
+                bool r_ge_d, qpms_bessel_t J) {
+	double leg[gsl_sf_legendre_array_n(n+nu+1)];
+	complex double bes[n+nu+2];
+	return qpms_trans_calculator_get_B_buf(c,m,n,mu,nu,kdlj,r_ge_d,J,
+			bes,leg);
+}
+
+#if 0
+int qpms_trans_calculator_get_AB_p(const qpms_trans_calculator *c,
+                complex double *Adest, complex double *Bdest,
+                int m, int n, int mu, int nu, sph_t kdlj,
+                bool r_ge_d, qpms_bessel_t J) {
+	double leg[gsl_sf_legendre_array_n(n+nu+1)];
+	complex double bes[n+nu+2];
+	return qpms_trans_calculator_get_AB_buf(c,Adest,Bdest,
+			m,n,mu,nu,kdlj,r_ge_d,J,
+			bes,leg);
+}
+#endif

qpms/translations.h

@@ -46,4 +46,18 @@ typedef struct qpms_trans_calculator {
 qpms_trans_calculator *qpms_trans_calculator_init(int lMax, qpms_normalization_t nt);
 void qpms_trans_calculator_free(qpms_trans_calculator *);
 
+complex double qpms_trans_calculator_get_A(const qpms_trans_calculator *c,
+		int m, int n, int mu, int nu, sph_t kdlj,
+		bool r_ge_d, qpms_bessel_t J);
+complex double qpms_trans_calculator_get_B(const qpms_trans_calculator *c,
+		int m, int n, int mu, int nu, sph_t kdlj,
+		bool r_ge_d, qpms_bessel_t J);
+#if 0
+int qpms_trans_calculator_get_AB_p(const qpms_trans_calculator *c,
+		complex double *Adest, complex double *Bdest,
+		int m, int n, int mu, int nu, sph_t kdlj,
+		bool r_ge_d, qpms_bessel_t J);
+#endif
+
+
 #endif // QPMS_TRANSLATIONS_H