trisurf-ng.git - Gitblit

Added spherical harmonics as-is into rbc

Samo Penic

2014-04-09 dc77e8ef10378188ee0a9657cedd1b7991a0a29f

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88f451	1	#include<math.h>
SP	2	#include<stdlib.h>
	3	#include "general.h"
	4	#include "sh.h"
	5
074a17	6
SP	7
	8	ts_spharm sph_init(ts_vertex_list vlist, ts_uint l){
eb8605	9	ts_uint j,i;
074a17	10	ts_spharm sph=(ts_spharm )malloc(sizeof(ts_spharm));
SP	11
262607	12	sph->N=0;
eb8605	13	/* lets initialize Ylm for each vertex. */
SP	14	sph->Ylmi=(ts_double *)calloc(l,sizeof(ts_double ));
5bb11d	15	for(i=0;i<l;i++){
SP	16	sph->Ylmi[i]=(ts_double *)calloc(2i+1,sizeof(ts_double *));
	17	for(j=0;j<(2*i+1);j++){
eb8605	18	sph->Ylmi[i][j]=(ts_double *)calloc(vlist->n,sizeof(ts_double));
074a17	19	}
SP	20	}
	21
	22	/* lets initialize ulm */
	23	sph->ulm=(ts_double *)calloc(l,sizeof(ts_double ));
	24	for(j=0;j<l;j++){
	25	sph->ulm[j]=(ts_double )calloc(2j+1,sizeof(ts_double));
	26	}
	27
262607	28	/* lets initialize sum of Ulm2 */
SP	29	sph->sumUlm2=(ts_double *)calloc(l,sizeof(ts_double ));
	30	for(j=0;j<l;j++){
	31	sph->sumUlm2[j]=(ts_double )calloc(2j+1,sizeof(ts_double));
	32	}
074a17	33
SP	34	/* lets initialize co */
79fc9c	35	//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 2j+2 instead of 2j+2. elements starting with 0 are useles and should be ignored!
SP	36	sph->co=(ts_double *)calloc(l+1,sizeof(ts_double ));
	37	for(j=0;j<=l;j++){
	38	sph->co[j]=(ts_double )calloc(2j+2,sizeof(ts_double));
074a17	39	}
SP	40
5bb11d	41	sph->l=l;
SP	42
	43	/* Calculate coefficients that will remain constant during all the simulation */
	44	precomputeShCoeff(sph);
	45
074a17	46	return sph;
SP	47	}
	48
	49
eb8605	50	ts_bool sph_free(ts_spharm *sph){
SP	51	int i,j;
074a17	52	for(i=0;i<sph->l;i++){
SP	53	if(sph->ulm[i]!=NULL) free(sph->ulm[i]);
262607	54	if(sph->sumUlm2[i]!=NULL) free(sph->sumUlm2[i]);
074a17	55	if(sph->co[i]!=NULL) free(sph->co[i]);
SP	56	}
79fc9c	57	if(sph->co[sph->l]!=NULL) free(sph->co[sph->l]);
074a17	58	if(sph->co != NULL) free(sph->co);
SP	59	if(sph->ulm !=NULL) free(sph->ulm);
	60
eb8605	61	if(sph->Ylmi!=NULL) {
074a17	62	for(i=0;i<sph->l;i++){
eb8605	63	if(sph->Ylmi[i]!=NULL){
5bb11d	64	for(j=0;j<i*2+1;j++){
eb8605	65	if(sph->Ylmi[i][j]!=NULL) free (sph->Ylmi[i][j]);
SP	66	}
	67	free(sph->Ylmi[i]);
	68	}
074a17	69	}
eb8605	70	free(sph->Ylmi);
074a17	71	}
eb8605	72
074a17	73	free(sph);
SP	74	return TS_SUCCESS;
	75	}
	76
88f451	77	/* Gives you legendre polynomials. Taken from NR, p. 254 */
3b3902	78	ts_double plgndr(ts_int l, ts_int m, ts_double x){
88f451	79	ts_double fact, pll, pmm, pmmp1, somx2;
SP	80	ts_int i,ll;
	81
	82	#ifdef TS_DOUBLE_DOUBLE
	83	if(m<0 \|\| m>l \|\| fabs(x)>1.0)
	84	fatal("Bad arguments in routine plgndr",1);
	85	#endif
	86	#ifdef TS_DOUBLE_FLOAT
	87	if(m<0 \|\| m>l \|\| fabsf(x)>1.0)
	88	fatal("Bad arguments in routine plgndr",1);
	89	#endif
	90	#ifdef TS_DOUBLE_LONGDOUBLE
	91	if(m<0 \|\| m>l \|\| fabsl(x)>1.0)
	92	fatal("Bad arguments in routine plgndr",1);
	93	#endif
	94	pmm=1.0;
	95	if (m>0) {
	96	#ifdef TS_DOUBLE_DOUBLE
	97	somx2=sqrt((1.0-x)*(1.0+x));
	98	#endif
	99	#ifdef TS_DOUBLE_FLOAT
	100	somx2=sqrtf((1.0-x)*(1.0+x));
	101	#endif
	102	#ifdef TS_DOUBLE_LONGDOUBLE
	103	somx2=sqrtl((1.0-x)*(1.0+x));
	104	#endif
	105	fact=1.0;
	106	for (i=1; i<=m;i++){
	107	pmm = -factsomx2;
	108	fact +=2.0;
	109	}
	110	}
	111
	112	if (l == m) return pmm;
	113	else {
	114	pmmp1=x(2m+1)*pmm;
	115	if(l==(m+1)) return(pmmp1);
	116	else {
	117	pll=0; /* so it can not be uninitialized */
	118	for(ll=m+2;ll<=l;ll++){
	119	pll=(x(2ll-1)pmmp1-(ll+m-1)pmm)/(ll-m);
	120	pmm=pmmp1;
	121	pmmp1=pll;
	122	}
	123	return(pll);
	124	}
	125	}
	126	}
	127
	128
9bf6ee	129	/** @brief: Precomputes coefficients that are required for spherical harmonics computations.
523bf1	130
9bf6ee	131	*/
523bf1	132	ts_bool precomputeShCoeff(ts_spharm *sph){
074a17	133	ts_int i,j,al,am;
SP	134	ts_double **co=sph->co;
79fc9c	135	for(i=1;i<=sph->l;i++){
SP	136	al=i;
074a17	137	sph->co[i][i+1]=sqrt((2.0*al+1.0)/2.0/M_PI);
79fc9c	138	for(j=1;j<=i-1;j++){
SP	139	am=j;
008026	140	sph->co[i][i+1+j]=co[i][i+j]*sqrt(1.0/(al-am+1.0)/(al+am));
074a17	141	sph->co[i][i+1-j]=co[i][i+1+j];
523bf1	142	}
79fc9c	143	co[i][2i+1]=co[i][2i]sqrt(1.0/(2.0al));
SP	144	co[i][1]=co[i][2*i+1];
074a17	145	co[i][i+1]=sqrt((2.0*al+1.0)/4.0/M_PI);
523bf1	146	}
SP	147	return TS_SUCCESS;
	148
	149	}
	150
	151
c9d07c	152	/** @brief: Computes Y(l,m,theta,fi)
SP	153	*
	154	* Function calculates Y^l_m for vertex with given (\theta, \fi) coordinates in
	155	* spherical coordinate system.
	156	* @param l is an ts_int argument.
	157	* @param m is an ts_int argument.
	158	* @param theta is ts_double argument.
	159	* @param fi is a ts_double argument.
	160	*
	161	* (Miha's definition that is different from common definition for factor srqt(1/(2pi)) /
88f451	162	ts_double shY(ts_int l,ts_int m,ts_double theta,ts_double fi){
SP	163	ts_double fac1, fac2, K;
	164	int i;
	165
	166	if(l<0 \|\| m>l \|\| m<-l)
	167	fatal("Error using shY function!",1);
	168
	169	fac1=1.0;
af3bad	170	for(i=1; i<=l-abs(m);i++){
88f451	171	fac1 *= i;
SP	172	}
	173	fac2=1.0;
af3bad	174	for(i=1; i<=l+abs(m);i++){
88f451	175	fac2 *= i;
SP	176	}
	177
	178	if(m==0){
	179	K=sqrt(1.0/(2.0*M_PI));
	180	}
	181	else if (m>0) {
	182	K=sqrt(1.0/(M_PI))cos(mfi);
	183	}
	184	else {
	185	//K=pow(-1.0,abs(m))sqrt(1.0/(2.0M_PI))cos(mfi);
	186	if(abs(m)%2==0)
af3bad	187	K=sqrt(1.0/(M_PI))cos(mfi);
88f451	188	else
af3bad	189	K=-sqrt(1.0/(M_PI))cos(mfi);
88f451	190	}
SP	191
	192	return Ksqrt((2.0l+1.0)/2.0fac1/fac2)plgndr(l,abs(m),cos(theta));
	193	}
523bf1	194
SP	195
	196	/* Function transforms coordinates from cartesian to spherical coordinates
	197	* (r,phi, theta). */
	198	ts_bool cart2sph(ts_coord coord, ts_double x, ts_double y, ts_double z){
	199	coord->coord_type=TS_COORD_SPHERICAL;
	200	#ifdef TS_DOUBLE_DOUBLE
	201	coord->e1=sqrt(xx+yy+z*z);
	202	if(z==0) coord->e3=M_PI/2.0;
	203	else coord->e3=atan(sqrt(xx+yy)/z);
	204	coord->e2=atan2(y,x);
	205	#endif
	206	#ifdef TS_DOUBLE_FLOAT
	207	coord->e1=sqrtf(xx+yy+z*z);
	208	if(z==0) coord->e3=M_PI/2.0;
	209	else coord->e3=atanf(sqrtf(xx+yy)/z);
	210	coord->e2=atan2f(y,x);
	211	#endif
	212	#ifdef TS_DOUBLE_LONGDOUBLE
	213	coord->e1=sqrtl(xx+yy+z*z);
	214	if(z==0) coord->e3=M_PI/2.0;
	215	else coord->e3=atanl(sqrtl(xx+yy)/z);
	216	coord->e2=atan2l(y,x);
	217	#endif
	218
	219	return TS_SUCCESS;
	220	}
	221
	222	/* Function returns radius of the sphere with the same volume as vesicle (r0) */
	223	ts_double getR0(ts_vesicle *vesicle){
	224	ts_double r0;
	225	#ifdef TS_DOUBLE_DOUBLE
	226	r0=pow(vesicle->volume*3.0/4.0/M_PI,1.0/3.0);
	227	#endif
	228	#ifdef TS_DOUBLE_FLOAT
	229	r0=powf(vesicle->volume*3.0/4.0/M_PI,1.0/3.0);
	230	#endif
	231	#ifdef TS_DOUBLE_LONGDOUBLE
	232	r0=powl(vesicle->volume*3.0/4.0/M_PI,1.0/3.0);
	233	#endif
	234	return r0;
	235	}
	236
	237
	238	ts_bool preparationSh(ts_vesicle *vesicle, ts_double r0){
	239	//TODO: before calling or during the call calculate area of each triangle! Can
	240	//be also done after vertexmove and bondflip //
919555	241	//DONE: in energy calculation! //
523bf1	242	ts_uint i,j;
SP	243	ts_vertex **vtx=vesicle->vlist->vtx;
	244	ts_vertex *cvtx;
	245	ts_triangle *ctri;
	246	ts_double centroid[3];
	247	ts_double r;
	248	for (i=0; i<vesicle->vlist->n; i++){
	249	cvtx=vtx[i];
	250	//cvtx->projArea=4.0M_PI/1447.0(cvtx->xcvtx->x+cvtx->ycvtx->y+cvtx->z*cvtx->z)/r0/r0;
	251	cvtx->projArea=0.0;
	252
	253	/* go over all triangles that have a common vertex i */
	254	for(j=0; j<cvtx->tristar_no; j++){
	255	ctri=cvtx->tristar[j];
	256	centroid[0]=(ctri->vertex[0]->x + ctri->vertex[1]->x + ctri->vertex[2]->x)/3.0;
	257	centroid[1]=(ctri->vertex[0]->y + ctri->vertex[1]->y + ctri->vertex[2]->y)/3.0;
	258	centroid[2]=(ctri->vertex[0]->z + ctri->vertex[1]->z + ctri->vertex[2]->z)/3.0;
	259	/* calculating projArea+= area(triangle)cos(theta) /
	260	#ifdef TS_DOUBLE_DOUBLE
	261	cvtx->projArea = cvtx->projArea + ctri->area(-centroid[0]ctri->xnorm - centroid[1]ctri->ynorm - centroid[2]ctri->znorm)/ sqrt(centroid[0]centroid[0]+centroid[1]centroid[1]+centroid[2]*centroid[2]);
	262	#endif
	263	#ifdef TS_DOUBLE_FLOAT
	264	cvtx->projArea = cvtx->projArea + ctri->area(-centroid[0]ctri->xnorm - centroid[1]ctri->ynorm - centroid[2]ctri->znorm)/ sqrtf(centroid[0]centroid[0]+centroid[1]centroid[1]+centroid[2]*centroid[2]);
	265	#endif
	266	#ifdef TS_DOUBLE_LONGDOUBLE
	267	cvtx->projArea = cvtx->projArea + ctri->area(-centroid[0]ctri->xnorm - centroid[1]ctri->ynorm - centroid[2]ctri->znorm)/ sqrtl(centroid[0]centroid[0]+centroid[1]centroid[1]+centroid[2]*centroid[2]);
	268	#endif
	269	}
	270
	271	cvtx->projArea=cvtx->projArea/3.0;
	272	//we dont store spherical coordinates of vertex, so we have to calculate
	273	//r(i) at this point.
	274	#ifdef TS_DOUBLE_DOUBLE
	275	r=sqrt(cvtx->xcvtx->x+cvtx->ycvtx->y+cvtx->z*cvtx->z);
	276	#endif
	277	#ifdef TS_DOUBLE_FLOAT
	278	r=sqrtf(cvtx->xcvtx->x+cvtx->ycvtx->y+cvtx->z*cvtx->z);
	279	#endif
	280	#ifdef TS_DOUBLE_LONGDOUBLE
	281	r=sqrtl(cvtx->xcvtx->x+cvtx->ycvtx->y+cvtx->z*cvtx->z);
	282	#endif
	283	cvtx->relR=(r-r0)/r0;
3b3902	284	cvtx->solAngle=cvtx->projArea/r/r;
523bf1	285	}
SP	286	return TS_SUCCESS;
	287	}
	288
	289
	290
	291	ts_bool calculateYlmi(ts_vesicle *vesicle){
3b3902	292	ts_int i,j,k;
523bf1	293	ts_spharm *sph=vesicle->sphHarmonics;
SP	294	ts_coord coord=(ts_coord )malloc(sizeof(ts_coord));
	295	ts_double fi, theta;
79048f	296	ts_int m;
074a17	297	ts_vertex *cvtx;
523bf1	298	for(k=0;k<vesicle->vlist->n;k++){
074a17	299	cvtx=vesicle->vlist->vtx[k];
eb8605	300	sph->Ylmi[0][0][k]=sqrt(1.0/4.0/M_PI);
074a17	301	cart2sph(coord,cvtx->x, cvtx->y, cvtx->z);
523bf1	302	fi=coord->e2;
SP	303	theta=coord->e3;
79048f	304	for(i=1; i<sph->l; i++){
523bf1	305	for(j=0;j<i;j++){
79048f	306	m=j+1;
3b3902	307	//Nastudiraj!!!!!
79048f	308	sph->Ylmi[i][j][k]=sph->co[i][m]cos((m-i-1)fi)pow(-1,m-i-1)plgndr(i,abs(m-i-1),cos(theta));
3b3902	309	if(i==2 && j==0){
SP	310	/* fprintf(stderr," ** vtx %d **\n", k+1);
	311	fprintf(stderr,"m-i-1 =%d\n",m-i-1);
	312	fprintf(stderr,"fi =%e\n",fi);
	313	fprintf(stderr,"(m-i-1)fi =%e\n",((ts_double)(m-i-1))fi);
	314	fprintf(stderr,"-2fi =%e\n",-2fi);
	315	fprintf(stderr,"m =%d\n",m);
	316
	317	fprintf(stderr," cos(m-i-1)=%e\n",cos((m-i-1)*fi));
	318	fprintf(stderr," cos(-2fi)=%e\n",cos(-2fi));
	319	fprintf(stderr," sph->co[i][m]=%e\n",sph->co[i][m]);
	320	fprintf(stderr," plgndr(i,abs(m-i-1),cos(theta))=%e\n",plgndr(i,abs(m-i-1),cos(theta)));
	321	*/
	322	}
523bf1	323	}
3b3902	324	//Nastudiraj!!!!!
SP	325	j=i;
	326	m=j+1;
	327	sph->Ylmi[i][j][k]=sph->co[i][m]*plgndr(i,0,cos(theta));
	328	for(j=i+1;j<2*i+1;j++){
79048f	329	m=j+1;
3b3902	330	//Nastudiraj!!!!!
79048f	331	sph->Ylmi[i][j][k]=sph->co[i][m]sin((m-i-1)fi)*plgndr(i,m-i-1,cos(theta));
523bf1	332	}
SP	333	}
	334
	335	}
	336	free(coord);
	337	return TS_SUCCESS;
	338	}
	339
	340
	341
	342	ts_bool calculateUlm(ts_vesicle *vesicle){
	343	ts_uint i,j,k;
	344	ts_vertex *cvtx;
	345	for(i=0;i<vesicle->sphHarmonics->l;i++){
8e58b4	346	for(j=0;j<2*i+1;j++) vesicle->sphHarmonics->ulm[i][j]=0.0;
523bf1	347	}
SP	348
	349	//TODO: call calculateYlmi !!!
	350
	351
	352	for(k=0;k<vesicle->vlist->n; k++){
	353	cvtx=vesicle->vlist->vtx[k];
	354	for(i=0;i<vesicle->sphHarmonics->l;i++){
3b3902	355	for(j=0;j<2*i+1;j++){
eb8605	356	vesicle->sphHarmonics->ulm[i][j]+= cvtx->solAnglecvtx->relRvesicle->sphHarmonics->Ylmi[i][j][k];
523bf1	357	}
SP	358
	359	}
	360	}
	361
	362	return TS_SUCCESS;
	363	}
262607	364
SP	365
	366
	367
	368
	369	ts_bool storeUlm2(ts_vesicle *vesicle){
	370
	371	ts_spharm *sph=vesicle->sphHarmonics;
	372	ts_int i,j;
	373	for(i=0;i<sph->l;i++){
	374	for(j=0;j<2*i+1;j++){
8e58b4	375	/* DEBUG fprintf(stderr,"sph->sumUlm2[%d][%d]=%e\n",i,j,sph->ulm[i][j]* sph->ulm[i][j]); */
443ba1	376	sph->sumUlm2[i][j]+=sph->ulm[i][j]* sph->ulm[i][j];
262607	377	}
SP	378	}
	379	sph->N++;
	380	return TS_SUCCESS;
	381	}
dc77e8	382
SP	383
	384	ts_bool saveAvgUlm2(ts_vesicle *vesicle){
	385
	386	FILE *fh;
	387
	388	fh=fopen("sph2out.dat", "w");
	389	if(fh==NULL){
	390	err("Cannot open file %s for writing");
	391	return TS_FAIL;
	392	}
	393
	394	ts_spharm *sph=vesicle->sphHarmonics;
	395	ts_int i,j;
	396	fprintf(fh,"l,\tm,\tulm^2avg\n");
	397	for(i=0;i<sph->l;i++){
	398	for(j=0;j<2*i+1;j++){
	399	fprintf(fh,"%d,\t%d,\t%e\n", i, j-i, sph->sumUlm2[i][j]/(ts_double)sph->N);
	400
	401	}
	402	fprintf(fh,"\n");
	403	}
	404	fclose(fh);
	405	return TS_SUCCESS;
	406	}