From 6c274defd904dedd6cb89c002f5eeced6c079d47 Mon Sep 17 00:00:00 2001
From: Samo Penic <samo.penic@gmail.com>
Date: Tue, 11 Dec 2018 11:42:22 +0000
Subject: [PATCH] Added stretching variables
---
src/sh.c | 352 +++++++++++++++++++++++++++++++++++++++++++++++++++++++++-
1 files changed, 345 insertions(+), 7 deletions(-)
diff --git a/src/sh.c b/src/sh.c
index b494b25..3f64939 100644
--- a/src/sh.c
+++ b/src/sh.c
@@ -1,10 +1,84 @@
+/* vim: set ts=4 sts=4 sw=4 noet : */
#include<math.h>
#include<stdlib.h>
#include "general.h"
#include "sh.h"
+#include "io.h"
+#include <string.h>
+
+
+ts_spharm *sph_init(ts_vertex_list *vlist, ts_uint l){
+ ts_uint j,i;
+ ts_spharm *sph=(ts_spharm *)malloc(sizeof(ts_spharm));
+
+ sph->N=0;
+ /* lets initialize Ylm for each vertex. */
+ sph->Ylmi=(ts_double ***)calloc(l,sizeof(ts_double **));
+ for(i=0;i<l;i++){
+ sph->Ylmi[i]=(ts_double **)calloc(2*i+1,sizeof(ts_double *));
+ for(j=0;j<(2*i+1);j++){
+ sph->Ylmi[i][j]=(ts_double *)calloc(vlist->n,sizeof(ts_double));
+ }
+ }
+
+ /* lets initialize ulm */
+ sph->ulm=(ts_double **)calloc(l,sizeof(ts_double *));
+ for(j=0;j<l;j++){
+ sph->ulm[j]=(ts_double *)calloc(2*j+1,sizeof(ts_double));
+ }
+
+ /* lets initialize sum of Ulm2 */
+ sph->sumUlm2=(ts_double **)calloc(l,sizeof(ts_double *));
+ for(j=0;j<l;j++){
+ sph->sumUlm2[j]=(ts_double *)calloc(2*j+1,sizeof(ts_double));
+ }
+
+ /* lets initialize co */
+//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!
+ sph->co=(ts_double **)calloc(l+1,sizeof(ts_double *));
+ for(j=0;j<=l;j++){
+ sph->co[j]=(ts_double *)calloc(2*j+2,sizeof(ts_double));
+ }
+
+ sph->l=l;
+
+ /* Calculate coefficients that will remain constant during all the simulation */
+ precomputeShCoeff(sph);
+
+ return sph;
+}
+
+
+ts_bool sph_free(ts_spharm *sph){
+ int i,j;
+ if(sph==NULL) return TS_FAIL;
+ for(i=0;i<sph->l;i++){
+ if(sph->ulm[i]!=NULL) free(sph->ulm[i]);
+ if(sph->sumUlm2[i]!=NULL) free(sph->sumUlm2[i]);
+ if(sph->co[i]!=NULL) free(sph->co[i]);
+ }
+ if(sph->co[sph->l]!=NULL) free(sph->co[sph->l]);
+ if(sph->co != NULL) free(sph->co);
+ if(sph->ulm !=NULL) free(sph->ulm);
+
+ if(sph->Ylmi!=NULL) {
+ for(i=0;i<sph->l;i++){
+ if(sph->Ylmi[i]!=NULL){
+ for(j=0;j<i*2+1;j++){
+ if(sph->Ylmi[i][j]!=NULL) free (sph->Ylmi[i][j]);
+ }
+ free(sph->Ylmi[i]);
+ }
+ }
+ free(sph->Ylmi);
+ }
+
+ free(sph);
+ return TS_SUCCESS;
+}
/* Gives you legendre polynomials. Taken from NR, p. 254 */
-ts_double plgndr(ts_int l, ts_int m, ts_float x){
+ts_double plgndr(ts_int l, ts_int m, ts_double x){
ts_double fact, pll, pmm, pmmp1, somx2;
ts_int i,ll;
@@ -55,7 +129,39 @@
}
-/*Computes Y(l,m,theta,fi) (Miha's definition that is different from common definition for factor srqt(1/(2*pi)) */
+/** @brief: Precomputes coefficients that are required for spherical harmonics computations.
+
+*/
+ts_bool precomputeShCoeff(ts_spharm *sph){
+ ts_int i,j,al,am;
+ ts_double **co=sph->co;
+ for(i=1;i<=sph->l;i++){
+ al=i;
+ sph->co[i][i+1]=sqrt((2.0*al+1.0)/2.0/M_PI);
+ for(j=1;j<=i-1;j++){
+ am=j;
+ sph->co[i][i+1+j]=co[i][i+j]*sqrt(1.0/(al-am+1.0)/(al+am));
+ sph->co[i][i+1-j]=co[i][i+1+j];
+ }
+ co[i][2*i+1]=co[i][2*i]*sqrt(1.0/(2.0*al));
+ co[i][1]=co[i][2*i+1];
+ co[i][i+1]=sqrt((2.0*al+1.0)/4.0/M_PI);
+ }
+ return TS_SUCCESS;
+
+}
+
+
+/** @brief: Computes Y(l,m,theta,fi)
+ *
+ * Function calculates Y^l_m for vertex with given (\theta, \fi) coordinates in
+ * spherical coordinate system.
+ * @param l is an ts_int argument.
+ * @param m is an ts_int argument.
+ * @param theta is ts_double argument.
+ * @param fi is a ts_double argument.
+ *
+ * (Miha's definition that is different from common definition for factor srqt(1/(2*pi)) */
ts_double shY(ts_int l,ts_int m,ts_double theta,ts_double fi){
ts_double fac1, fac2, K;
int i;
@@ -64,11 +170,11 @@
fatal("Error using shY function!",1);
fac1=1.0;
- for(i=1; i<=l-m;i++){
+ for(i=1; i<=l-abs(m);i++){
fac1 *= i;
}
fac2=1.0;
- for(i=1; i<=l+m;i++){
+ for(i=1; i<=l+abs(m);i++){
fac2 *= i;
}
@@ -81,10 +187,242 @@
else {
//K=pow(-1.0,abs(m))*sqrt(1.0/(2.0*M_PI))*cos(m*fi);
if(abs(m)%2==0)
- K=sqrt(1.0/(M_PI))*sin(m*fi);
+ K=sqrt(1.0/(M_PI))*cos(m*fi);
else
- K=-sqrt(1.0/(M_PI))*sin(m*fi);
+ K=-sqrt(1.0/(M_PI))*cos(m*fi);
}
- return K*sqrt((2.0*l+1.0)/2.0*fac1/fac2)*plgndr(l,abs(m),cos(theta));
+ return K*sqrt((2.0*l+1.0)/2.0*(ts_double)(fac1/fac2))*plgndr(l,abs(m),cos(theta));
+}
+
+
+/* Function transforms coordinates from cartesian to spherical coordinates
+ * (r,phi, theta). */
+ts_bool *cart2sph(ts_coord *coord, ts_double x, ts_double y, ts_double z){
+ coord->coord_type=TS_COORD_SPHERICAL;
+#ifdef TS_DOUBLE_DOUBLE
+ coord->e1=sqrt(x*x+y*y+z*z);
+ if(z==0) coord->e3=M_PI/2.0;
+ else coord->e3=atan2(sqrt(x*x+y*y),z);
+ coord->e2=atan2(y,x);
+#endif
+#ifdef TS_DOUBLE_FLOAT
+ coord->e1=sqrtf(x*x+y*y+z*z);
+ if(z==0) coord->e3=M_PI/2.0;
+ else coord->e3=atanf(sqrtf(x*x+y*y)/z);
+ coord->e2=atan2f(y,x);
+#endif
+#ifdef TS_DOUBLE_LONGDOUBLE
+ coord->e1=sqrtl(x*x+y*y+z*z);
+ if(z==0) coord->e3=M_PI/2.0;
+ else coord->e3=atanl(sqrtl(x*x+y*y)/z);
+ coord->e2=atan2l(y,x);
+#endif
+
+ return TS_SUCCESS;
+}
+
+
+ts_bool sph2cart(ts_coord *coord){
+ coord->coord_type=TS_COORD_CARTESIAN;
+ ts_double x,y,z;
+
+ x=coord->e1*cos(coord->e2)*sin(coord->e3);
+ y=coord->e1*sin(coord->e2)*sin(coord->e3);
+ z=coord->e1*cos(coord->e3);
+
+ coord->e1=x;
+ coord->e2=y;
+ coord->e3=z;
+
+ return TS_SUCCESS;
+}
+
+
+/* Function returns radius of the sphere with the same volume as vesicle (r0) */
+ts_double getR0(ts_vesicle *vesicle){
+ ts_double r0;
+ #ifdef TS_DOUBLE_DOUBLE
+ r0=pow(vesicle->volume*3.0/4.0/M_PI,1.0/3.0);
+#endif
+#ifdef TS_DOUBLE_FLOAT
+ r0=powf(vesicle->volume*3.0/4.0/M_PI,1.0/3.0);
+#endif
+#ifdef TS_DOUBLE_LONGDOUBLE
+ r0=powl(vesicle->volume*3.0/4.0/M_PI,1.0/3.0);
+#endif
+ return r0;
+}
+
+
+ts_bool preparationSh(ts_vesicle *vesicle, ts_double r0){
+//TODO: before calling or during the call calculate area of each triangle! Can
+//be also done after vertexmove and bondflip //
+//DONE: in energy calculation! //
+ ts_uint i,j;
+ ts_vertex **vtx=vesicle->vlist->vtx;
+ ts_vertex *cvtx;
+ ts_triangle *ctri;
+ ts_double centroid[3];
+ ts_double r;
+ for (i=0; i<vesicle->vlist->n; i++){
+ cvtx=vtx[i];
+ //cvtx->projArea=4.0*M_PI/1447.0*(cvtx->x*cvtx->x+cvtx->y*cvtx->y+cvtx->z*cvtx->z)/r0/r0;
+ cvtx->projArea=0.0;
+
+ /* go over all triangles that have a common vertex i */
+ for(j=0; j<cvtx->tristar_no; j++){
+ ctri=cvtx->tristar[j];
+ centroid[0]=(ctri->vertex[0]->x + ctri->vertex[1]->x + ctri->vertex[2]->x)/3.0;
+ centroid[1]=(ctri->vertex[0]->y + ctri->vertex[1]->y + ctri->vertex[2]->y)/3.0;
+ centroid[2]=(ctri->vertex[0]->z + ctri->vertex[1]->z + ctri->vertex[2]->z)/3.0;
+ /* calculating projArea+= area(triangle)*cos(theta) */
+#ifdef TS_DOUBLE_DOUBLE
+ 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]);
+#endif
+#ifdef TS_DOUBLE_FLOAT
+ 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]);
+#endif
+#ifdef TS_DOUBLE_LONGDOUBLE
+ 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]);
+#endif
+ }
+
+ cvtx->projArea=cvtx->projArea/3.0;
+ //we dont store spherical coordinates of vertex, so we have to calculate
+ //r(i) at this point.
+#ifdef TS_DOUBLE_DOUBLE
+ r=sqrt(cvtx->x*cvtx->x+cvtx->y*cvtx->y+cvtx->z*cvtx->z);
+#endif
+#ifdef TS_DOUBLE_FLOAT
+ r=sqrtf(cvtx->x*cvtx->x+cvtx->y*cvtx->y+cvtx->z*cvtx->z);
+#endif
+#ifdef TS_DOUBLE_LONGDOUBLE
+ r=sqrtl(cvtx->x*cvtx->x+cvtx->y*cvtx->y+cvtx->z*cvtx->z);
+#endif
+ cvtx->relR=(r-r0)/r0;
+ cvtx->solAngle=cvtx->projArea/r/r;
+ }
+ return TS_SUCCESS;
+}
+
+
+
+ts_bool calculateYlmi(ts_vesicle *vesicle){
+ ts_int i,j,k;
+ ts_spharm *sph=vesicle->sphHarmonics;
+ ts_coord *coord=(ts_coord *)malloc(sizeof(ts_coord));
+ ts_double fi, theta;
+ ts_int m;
+ ts_vertex *cvtx;
+ for(k=0;k<vesicle->vlist->n;k++){
+ cvtx=vesicle->vlist->vtx[k];
+ sph->Ylmi[0][0][k]=sqrt(1.0/4.0/M_PI);
+ cart2sph(coord,cvtx->x, cvtx->y, cvtx->z);
+ fi=coord->e2;
+ theta=coord->e3;
+ for(i=1; i<sph->l; i++){
+ for(j=0;j<i;j++){
+ m=j+1;
+//Nastudiraj!!!!!
+ 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));
+ if(i==2 && j==0){
+ /* fprintf(stderr," **** vtx %d ****\n", k+1);
+ fprintf(stderr,"m-i-1 =%d\n",m-i-1);
+ fprintf(stderr,"fi =%e\n",fi);
+ fprintf(stderr,"(m-i-1)*fi =%e\n",((ts_double)(m-i-1))*fi);
+ fprintf(stderr,"-2*fi =%e\n",-2*fi);
+ fprintf(stderr,"m =%d\n",m);
+
+ fprintf(stderr," cos(m-i-1)=%e\n",cos((m-i-1)*fi));
+ fprintf(stderr," cos(-2*fi)=%e\n",cos(-2*fi));
+ fprintf(stderr," sph->co[i][m]=%e\n",sph->co[i][m]);
+ fprintf(stderr," plgndr(i,abs(m-i-1),cos(theta))=%e\n",plgndr(i,abs(m-i-1),cos(theta)));
+*/
+ }
+ }
+//Nastudiraj!!!!!
+ j=i;
+ m=j+1;
+ sph->Ylmi[i][j][k]=sph->co[i][m]*plgndr(i,0,cos(theta));
+ for(j=i+1;j<2*i+1;j++){
+ m=j+1;
+//Nastudiraj!!!!!
+ sph->Ylmi[i][j][k]=sph->co[i][m]*sin((m-i-1)*fi)*plgndr(i,m-i-1,cos(theta));
+ }
+ }
+
+ }
+ free(coord);
+ return TS_SUCCESS;
+}
+
+
+
+ts_bool calculateUlm(ts_vesicle *vesicle){
+ ts_uint i,j,k;
+ ts_vertex *cvtx;
+ for(i=0;i<vesicle->sphHarmonics->l;i++){
+ for(j=0;j<2*i+1;j++) vesicle->sphHarmonics->ulm[i][j]=0.0;
+ }
+
+//TODO: call calculateYlmi !!!
+
+
+ for(k=0;k<vesicle->vlist->n; k++){
+ cvtx=vesicle->vlist->vtx[k];
+ for(i=0;i<vesicle->sphHarmonics->l;i++){
+ for(j=0;j<2*i+1;j++){
+ vesicle->sphHarmonics->ulm[i][j]+= cvtx->solAngle*cvtx->relR*vesicle->sphHarmonics->Ylmi[i][j][k];
+ }
+
+ }
+ }
+
+ return TS_SUCCESS;
+}
+
+
+
+
+
+ts_bool storeUlm2(ts_vesicle *vesicle){
+
+ts_spharm *sph=vesicle->sphHarmonics;
+ts_int i,j;
+for(i=0;i<sph->l;i++){
+ for(j=0;j<2*i+1;j++){
+ /* DEBUG fprintf(stderr,"sph->sumUlm2[%d][%d]=%e\n",i,j,sph->ulm[i][j]* sph->ulm[i][j]); */
+ sph->sumUlm2[i][j]+=sph->ulm[i][j]* sph->ulm[i][j];
+ }
+}
+ sph->N++;
+return TS_SUCCESS;
+}
+
+
+ts_bool saveAvgUlm2(ts_vesicle *vesicle){
+
+ FILE *fh;
+ char filename[10000];
+ strcpy(filename, command_line_args.path);
+ strcat(filename, "sph2out.dat");
+ fh=fopen(filename, "w");
+ if(fh==NULL){
+ err("Cannot open file %s for writing");
+ return TS_FAIL;
+ }
+
+ ts_spharm *sph=vesicle->sphHarmonics;
+ ts_int i,j;
+ fprintf(fh,"l,\tm,\tulm^2avg\n");
+ for(i=0;i<sph->l;i++){
+ for(j=0;j<2*i+1;j++){
+ fprintf(fh,"%d,\t%d,\t%e\n", i, j-i, sph->sumUlm2[i][j]/(ts_double)sph->N);
+
+ }
+ fprintf(fh,"\n");
+ }
+ fclose(fh);
+ return TS_SUCCESS;
}
--
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