#include<math.h>
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#include<stdlib.h>
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#include<gsl/gsl_complex.h>
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#include<gsl/gsl_complex_math.h>
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#include<gsl/gsl_sf_legendre.h>
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#include<gsl/gsl_matrix.h>
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#include<gsl/gsl_vector.h>
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#include<gsl/gsl_linalg.h>
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#include "general.h"
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#include "sh.h"
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#include "shcomplex.h"
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ts_spharm *complex_sph_init(ts_vertex_list *vlist, ts_uint l){
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ts_uint j,i;
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ts_spharm *sph=(ts_spharm *)malloc(sizeof(ts_spharm));
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sph->N=0;
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/* lets initialize Ylm for each vertex. */
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sph->Ylmi=(ts_double ***)calloc(l,sizeof(ts_double **));
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for(i=0;i<l;i++){
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sph->Ylmi[i]=(ts_double **)calloc(2*i+1,sizeof(ts_double *));
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for(j=0;j<(2*i+1);j++){
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sph->Ylmi[i][j]=(ts_double *)calloc(vlist->n,sizeof(ts_double));
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}
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}
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/* lets initialize ulm */
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sph->ulm=(ts_double **)calloc(l,sizeof(ts_double *));
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sph->ulmComplex=(gsl_complex **)calloc(l,sizeof(gsl_complex *));
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for(j=0;j<l;j++){
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sph->ulm[j]=(ts_double *)calloc(2*j+1,sizeof(ts_double));
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sph->ulmComplex[j]=(gsl_complex *)calloc(2*j+1,sizeof(gsl_complex));
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}
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/* lets initialize sum of Ulm2 */
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sph->sumUlm2=(ts_double **)calloc(l,sizeof(ts_double *));
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for(j=0;j<l;j++){
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sph->sumUlm2[j]=(ts_double *)calloc(2*j+1,sizeof(ts_double));
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}
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/* lets initialize co */
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//NOTE: C is has zero based indexing. Code is imported from fortran and to comply with original indexes we actually generate one index more. Also second dimension is 2*j+2 instead of 2*j+2. elements starting with 0 are useles and should be ignored!
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sph->co=(ts_double **)calloc(l+1,sizeof(ts_double *));
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for(j=0;j<=l;j++){
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sph->co[j]=(ts_double *)calloc(2*j+2,sizeof(ts_double));
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}
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sph->l=l;
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/* Calculate coefficients that will remain constant during all the simulation */
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precomputeShCoeff(sph);
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return sph;
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}
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ts_bool complex_sph_free(ts_spharm *sph){
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int i,j;
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if(sph==NULL) return TS_FAIL;
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for(i=0;i<sph->l;i++){
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if(sph->ulm[i]!=NULL) free(sph->ulm[i]);
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if(sph->ulmComplex[i]!=NULL) free(sph->ulmComplex[i]);
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if(sph->sumUlm2[i]!=NULL) free(sph->sumUlm2[i]);
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if(sph->co[i]!=NULL) free(sph->co[i]);
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}
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if(sph->co[sph->l]!=NULL) free(sph->co[sph->l]);
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if(sph->co != NULL) free(sph->co);
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if(sph->ulm !=NULL) free(sph->ulm);
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if(sph->ulmComplex !=NULL) free(sph->ulmComplex);
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if(sph->Ylmi!=NULL) {
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for(i=0;i<sph->l;i++){
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if(sph->Ylmi[i]!=NULL){
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for(j=0;j<i*2+1;j++){
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if(sph->Ylmi[i][j]!=NULL) free (sph->Ylmi[i][j]);
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}
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free(sph->Ylmi[i]);
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}
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}
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free(sph->Ylmi);
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}
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free(sph);
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return TS_SUCCESS;
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}
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ts_bool calculateUlmComplex(ts_vesicle *vesicle){
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ts_int i,j,k,m,l;
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ts_vertex *cvtx;
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ts_coord coord;
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/* set all values to zero */
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for(i=0;i<vesicle->sphHarmonics->l;i++){
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for(j=0;j<2*i+1;j++) GSL_SET_COMPLEX(&(vesicle->sphHarmonics->ulmComplex[i][j]),0.0,0.0);
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}
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for(k=0;k<vesicle->vlist->n; k++){
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cvtx=vesicle->vlist->vtx[k];
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cart2sph(&coord,cvtx->x,cvtx->y,cvtx->z);
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for(i=0;i<vesicle->sphHarmonics->l;i++){
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for(j=0;j<2*i+1;j++){
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m=j-i;
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l=i;
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if(m>=0){
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// fprintf(stderr, "Racunam za l=%d, m=%d\n", l,m);
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vesicle->sphHarmonics->ulmComplex[i][j]=gsl_complex_add(vesicle->sphHarmonics->ulmComplex[i][j], gsl_complex_conjugate(gsl_complex_mul_real(gsl_complex_polar(1.0,(ts_double)m*coord.e2),cvtx->solAngle*cvtx->relR*gsl_sf_legendre_sphPlm(l,m,cos(coord.e3)))) );
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} else {
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// fprintf(stderr, "Racunam za l=%d, abs(m=%d)\n", l,m);
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vesicle->sphHarmonics->ulmComplex[i][j]=gsl_complex_add(vesicle->sphHarmonics->ulmComplex[i][j], gsl_complex_conjugate(gsl_complex_mul_real(gsl_complex_polar(1.0,(ts_double)m*coord.e2),cvtx->solAngle*cvtx->relR*pow(-1,m)*gsl_sf_legendre_sphPlm(l,-m,cos(coord.e3)))) );
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}
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}
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}
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}
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return TS_SUCCESS;
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}
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ts_bool storeUlmComplex2(ts_vesicle *vesicle){
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ts_spharm *sph=vesicle->sphHarmonics;
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ts_int i,j;
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for(i=0;i<sph->l;i++){
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for(j=0;j<2*i+1;j++){
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sph->sumUlm2[i][j]+=gsl_complex_abs2(sph->ulmComplex[i][j]);
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}
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}
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sph->N++;
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return TS_SUCCESS;
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}
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ts_double calculateKc(ts_vesicle *vesicle, ts_int lmin, ts_int lmax){
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ts_int min=lmin;
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ts_int max=lmax; //vesicle->sphHarmonics->l-3;
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ts_long i,j;
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ts_double retval, bval;
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gsl_matrix *A=gsl_matrix_alloc(max-min,2);
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gsl_vector *tau=gsl_vector_alloc(2);
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gsl_vector *b=gsl_vector_alloc(max-min);
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gsl_vector *x=gsl_vector_alloc(2);
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gsl_vector *res=gsl_vector_alloc(max-min);
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//solving (A^T*A)*x=A^T*b
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//fill the data for matrix A and vector b
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for(i=min;i<max;i++){
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gsl_matrix_set(A, i-min,0,(ts_double)((i-1)*(i+2)));
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gsl_matrix_set(A, i-min,1,(ts_double)((i-1)*(i+2)*(i+1)*i));
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// fprintf(stderr,"%e %e\n", gsl_matrix_get(A,i-min,0), gsl_matrix_get(A,i-min,1));
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bval=0.0;
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//average for m from 0..l (only positive m's)
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for(j=0;j<=i;j++){
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bval+=vesicle->sphHarmonics->sumUlm2[i][(j+i)];
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}
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bval=bval/(ts_double)vesicle->sphHarmonics->N/(ts_double)(i+1);
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gsl_vector_set(b,i-min,1.0/bval);
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// fprintf(stderr,"%e\n", 1.0/gsl_vector_get(b,i-min));
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}
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// fprintf(stderr,"b[2]=%e\n",gsl_vector_get(b,1));
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gsl_linalg_QR_decomp(A,tau);
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gsl_linalg_QR_lssolve(A,tau,b,x,res);
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// fprintf(stderr,"kc=%e\n",gsl_vector_get(x,1));
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retval=gsl_vector_get(x,1);
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gsl_matrix_free(A);
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gsl_vector_free(tau);
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gsl_vector_free(b);
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gsl_vector_free(x);
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gsl_vector_free(res);
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return retval;
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}
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