From 384af9d04809481663a9fb350212b5e5880955aa Mon Sep 17 00:00:00 2001
From: Samo Penic <samo.penic@gmail.com>
Date: Mon, 06 Jul 2020 12:13:19 +0000
Subject: [PATCH] Eigenvalues calculated wrongly
---
src/energy.c | 286 +++++++++++++++++++++++++++++++++++---------------------
1 files changed, 178 insertions(+), 108 deletions(-)
diff --git a/src/energy.c b/src/energy.c
index 7c29c0b..e67eadc 100644
--- a/src/energy.c
+++ b/src/energy.c
@@ -3,10 +3,12 @@
#include "general.h"
#include "energy.h"
#include "vertex.h"
+#include "bond.h"
#include<math.h>
#include<stdio.h>
-
-
+#include <gsl/gsl_vector_complex.h>
+#include <gsl/gsl_matrix.h>
+#include <gsl/gsl_eigen.h>
/** @brief Wrapper that calculates energy of every vertex in vesicle
*
* Function calculated energy of every vertex in vesicle. It can be used in
@@ -44,9 +46,12 @@
return TS_SUCCESS;
};
-/** @brief Calculation of energy of the vertex
+/** @brief Calculation of the bending energy of the vertex.
*
- * Main function that calculates energy of the vertex \f$i\f$. Nearest neighbors (NN) must be ordered in counterclockwise direction for this function to work.
+ * Main function that calculates energy of the vertex \f$i\f$. Function returns \f$\frac{1}{2}(c_1+c_2-c)^2 s\f$, where \f$(c_1+c_2)/2\f$ is mean curvature,
+ * \f$c/2\f$ is spontaneous curvature and \f$s\f$ is area per vertex \f$i\f$.
+ *
+ * Nearest neighbors (NN) must be ordered in counterclockwise direction for this function to work.
* Firstly NNs that form two neighboring triangles are found (\f$j_m\f$, \f$j_p\f$ and common \f$j\f$). Later, the scalar product of vectors \f$x_1=(\mathbf{i}-\mathbf{j_p})\cdot (\mathbf{i}-\mathbf{j_p})(\mathbf{i}-\mathbf{j_p})\f$, \f$x_2=(\mathbf{j}-\mathbf{j_p})\cdot (\mathbf{j}-\mathbf{j_p})\f$ and \f$x_3=(\mathbf{j}-\mathbf{j_p})\cdot (\mathbf{i}-\mathbf{j_p})\f$ are calculated. From these three vectors the \f$c_{tp}=\frac{1}{\tan(\varphi_p)}\f$ is calculated, where \f$\varphi_p\f$ is the inner angle at vertex \f$j_p\f$. The procedure is repeated for \f$j_m\f$ instead of \f$j_p\f$ resulting in \f$c_{tn}\f$.
*
\begin{tikzpicture}{
@@ -84,109 +89,170 @@
* @returns TS_SUCCESS on successful calculation.
*/
inline ts_bool energy_vertex(ts_vertex *vtx){
- ts_uint jj;
- ts_uint jjp,jjm;
- ts_vertex *j,*jp, *jm;
- ts_triangle *jt;
- ts_double s=0.0,xh=0.0,yh=0.0,zh=0.0,txn=0.0,tyn=0.0,tzn=0.0;
- ts_double x1,x2,x3,ctp,ctm,tot,xlen;
- ts_double h,ht;
- for(jj=1; jj<=vtx->neigh_no;jj++){
- jjp=jj+1;
- if(jjp>vtx->neigh_no) jjp=1;
- jjm=jj-1;
- if(jjm<1) jjm=vtx->neigh_no;
- j=vtx->neigh[jj-1];
- jp=vtx->neigh[jjp-1];
- jm=vtx->neigh[jjm-1];
- jt=vtx->tristar[jj-1];
- x1=vtx_distance_sq(vtx,jp); //shouldn't be zero!
- x2=vtx_distance_sq(j,jp); // shouldn't be zero!
- x3=(j->x-jp->x)*(vtx->x-jp->x)+
- (j->y-jp->y)*(vtx->y-jp->y)+
- (j->z-jp->z)*(vtx->z-jp->z);
-
-#ifdef TS_DOUBLE_DOUBLE
- ctp=x3/sqrt(x1*x2-x3*x3);
-#endif
-#ifdef TS_DOUBLE_FLOAT
- ctp=x3/sqrtf(x1*x2-x3*x3);
-#endif
-#ifdef TS_DOUBLE_LONGDOUBLE
- ctp=x3/sqrtl(x1*x2-x3*x3);
-#endif
- x1=vtx_distance_sq(vtx,jm);
- x2=vtx_distance_sq(j,jm);
- x3=(j->x-jm->x)*(vtx->x-jm->x)+
- (j->y-jm->y)*(vtx->y-jm->y)+
- (j->z-jm->z)*(vtx->z-jm->z);
-#ifdef TS_DOUBLE_DOUBLE
- ctm=x3/sqrt(x1*x2-x3*x3);
-#endif
-#ifdef TS_DOUBLE_FLOAT
- ctm=x3/sqrtf(x1*x2-x3*x3);
-#endif
-#ifdef TS_DOUBLE_LONGDOUBLE
- ctm=x3/sqrtl(x1*x2-x3*x3);
-#endif
- tot=ctp+ctm;
- tot=0.5*tot;
+ ts_uint jj, i, j;
+ ts_double edge_vector_x[7]={0,0,0,0,0,0,0};
+ ts_double edge_vector_y[7]={0,0,0,0,0,0,0};
+ ts_double edge_vector_z[7]={0,0,0,0,0,0,0};
+ ts_double edge_normal_x[7]={0,0,0,0,0,0,0};
+ ts_double edge_normal_y[7]={0,0,0,0,0,0,0};
+ ts_double edge_normal_z[7]={0,0,0,0,0,0,0};
+ ts_double edge_binormal_x[7]={0,0,0,0,0,0,0};
+ ts_double edge_binormal_y[7]={0,0,0,0,0,0,0};
+ ts_double edge_binormal_z[7]={0,0,0,0,0,0,0};
+ ts_double vertex_normal_x=0.0;
+ ts_double vertex_normal_y=0.0;
+ ts_double vertex_normal_z=0.0;
+// ts_triangle *triedge[2]={NULL,NULL};
- xlen=vtx_distance_sq(j,vtx);
-/*
-#ifdef TS_DOUBLE_DOUBLE
- vtx->bond[jj-1]->bond_length=sqrt(xlen);
-#endif
-#ifdef TS_DOUBLE_FLOAT
- vtx->bond[jj-1]->bond_length=sqrtf(xlen);
-#endif
-#ifdef TS_DOUBLE_LONGDOUBLE
- vtx->bond[jj-1]->bond_length=sqrtl(xlen);
-#endif
+ ts_uint nei,neip,neim;
+ ts_vertex *it, *k, *kp,*km;
+ ts_triangle *lm=NULL, *lp=NULL;
+ ts_double sumnorm;
- vtx->bond[jj-1]->bond_length_dual=tot*vtx->bond[jj-1]->bond_length;
-*/
- s+=tot*xlen;
- xh+=tot*(j->x - vtx->x);
- yh+=tot*(j->y - vtx->y);
- zh+=tot*(j->z - vtx->z);
- txn+=jt->xnorm;
- tyn+=jt->ynorm;
- tzn+=jt->znorm;
- }
-
- h=xh*xh+yh*yh+zh*zh;
- ht=txn*xh+tyn*yh + tzn*zh;
- s=s/4.0;
-#ifdef TS_DOUBLE_DOUBLE
- if(ht>=0.0) {
- vtx->curvature=sqrt(h);
- } else {
- vtx->curvature=-sqrt(h);
- }
-#endif
-#ifdef TS_DOUBLE_FLOAT
- if(ht>=0.0) {
- vtx->curvature=sqrtf(h);
- } else {
- vtx->curvature=-sqrtf(h);
- }
-#endif
-#ifdef TS_DOUBLE_LONGDOUBLE
- if(ht>=0.0) {
- vtx->curvature=sqrtl(h);
- } else {
- vtx->curvature=-sqrtl(h);
- }
-#endif
-// c is forced curvature energy for each vertex. Should be set to zero for
-// normal circumstances.
- vtx->energy=0.5*s*(vtx->curvature/s-vtx->c)*(vtx->curvature/s-vtx->c);
- return TS_SUCCESS;
+ ts_double Se11, Se21, Se22, Se31, Se32, Se33;
+ ts_double Pv11, Pv21, Pv22, Pv31, Pv32, Pv33;
+ ts_double We;
+ ts_double Av, We_Av;
+
+ gsl_matrix *gsl_Sv=gsl_matrix_alloc(3,3);
+ gsl_vector_complex *Sv_eigen=gsl_vector_complex_alloc(3);
+ gsl_eigen_nonsymm_workspace *workspace=gsl_eigen_nonsymm_alloc(3);
+
+ ts_double mprod[7], phi[7], he[7];
+ ts_double Sv[3][3]={{0,0,0},{0,0,0},{0,0,0}};
+ // Here edge vector is calculated
+// fprintf(stderr, "Vertex has neighbours=%d\n", vtx->neigh_no);
+ for(jj=0;jj<vtx->neigh_no;jj++){
+ edge_vector_x[jj]=vtx->neigh[jj]->x-vtx->x;
+ edge_vector_y[jj]=vtx->neigh[jj]->y-vtx->y;
+ edge_vector_z[jj]=vtx->neigh[jj]->z-vtx->z;
+ Av=0;
+ for(i=0; i<vtx->tristar_no; i++){
+ vertex_normal_x=vertex_normal_x + vtx->tristar[i]->xnorm*vtx->tristar[i]->area;
+ vertex_normal_y=vertex_normal_y + vtx->tristar[i]->ynorm*vtx->tristar[i]->area;
+ vertex_normal_z=vertex_normal_z + vtx->tristar[i]->znorm*vtx->tristar[i]->area;
+ Av+=vtx->tristar[i]->area/3;
+ }
+
+ Pv11=1-vertex_normal_x*vertex_normal_x;
+ Pv22=1-vertex_normal_y*vertex_normal_y;
+ Pv33=1-vertex_normal_z*vertex_normal_z;
+ Pv21=vertex_normal_x*vertex_normal_y;
+ Pv31=vertex_normal_x*vertex_normal_z;
+ Pv32=vertex_normal_y*vertex_normal_z;
+
+// printf("(%f %f %f)\n", vertex_normal_x, vertex_normal_y, vertex_normal_z);
+
+
+ it=vtx;
+ k=vtx->neigh[jj];
+ nei=0;
+ for(i=0;i<it->neigh_no;i++){ // Finds the nn of it, that is k
+ if(it->neigh[i]==k){
+ nei=i;
+ break;
+ }
+ }
+ neip=nei+1; // I don't like it.. Smells like I must have it in correct order
+ neim=nei-1;
+ if(neip>=it->neigh_no) neip=0;
+ if((ts_int)neim<0) neim=it->neigh_no-1; /* casting is essential... If not
+there the neim is never <0 !!! */
+ // fprintf(stderr,"The numbers are: %u %u\n",neip, neim);
+ km=it->neigh[neim]; // We located km and kp
+ kp=it->neigh[neip];
+
+ if(km==NULL || kp==NULL){
+ fatal("energy_vertex: cannot determine km and kp!",233);
+ }
+
+ for(i=0;i<it->tristar_no;i++){
+ for(j=0;j<k->tristar_no;j++){
+ if((it->tristar[i] == k->tristar[j])){ //ce gre za skupen trikotnik
+ if((it->tristar[i]->vertex[0] == km || it->tristar[i]->vertex[1]
+== km || it->tristar[i]->vertex[2]== km )){
+ lm=it->tristar[i];
+ // lmidx=i;
+ }
+ else
+ {
+ lp=it->tristar[i];
+ // lpidx=i;
+ }
+
+ }
+ }
+ }
+if(lm==NULL || lp==NULL) fatal("energy_vertex: Cannot find triangles lm and lp!",233);
+
+ sumnorm=sqrt( pow((lm->xnorm + lp->xnorm),2) + pow((lm->ynorm + lp->ynorm), 2) + pow((lm->znorm + lp->znorm), 2));
+
+ edge_normal_x[jj]=(lm->xnorm+ lp->xnorm)/sumnorm;
+ edge_normal_y[jj]=(lm->ynorm+ lp->ynorm)/sumnorm;
+ edge_normal_z[jj]=(lm->znorm+ lp->znorm)/sumnorm;
+
+
+ edge_binormal_x[jj]=(edge_normal_y[jj]*edge_vector_z[jj])-(edge_normal_z[jj]*edge_vector_y[jj]);
+ edge_binormal_y[jj]=-(edge_normal_x[jj]*edge_vector_z[jj])+(edge_normal_z[jj]*edge_vector_x[jj]);
+ edge_binormal_z[jj]=(edge_normal_x[jj]*edge_vector_y[jj])-(edge_normal_y[jj]*edge_vector_x[jj]);
+
+
+ mprod[jj]=it->x*(k->y*edge_vector_z[jj]-edge_vector_y[jj]*k->z)-it->y*(k->x*edge_vector_z[jj]-k->z*edge_vector_x[jj])+it->z*(k->x*edge_vector_y[jj]-k->y*edge_vector_x[jj]);
+ phi[jj]=copysign(acos(lm->xnorm*lp->xnorm+lm->ynorm*lp->ynorm+lm->znorm*lp->znorm),mprod[jj])+M_PI;
+ he[jj]=2.0*sqrt( pow((edge_vector_x[jj]*2),2) + pow((edge_vector_y[jj]*2), 2) + pow((edge_vector_z[jj]*2), 2))*cos(phi[jj]/2.0);
+
+
+ Se11=edge_binormal_x[jj]*edge_binormal_x[jj]*he[jj];
+ Se21=edge_binormal_x[jj]*edge_binormal_y[jj]*he[jj];
+ Se22=edge_binormal_y[jj]*edge_binormal_y[jj]*he[jj];
+ Se31=edge_binormal_x[jj]*edge_binormal_z[jj]*he[jj];
+ Se32=edge_binormal_y[jj]*edge_binormal_z[jj]*he[jj];
+ Se33=edge_binormal_z[jj]*edge_binormal_z[jj]*he[jj];
+
+ We=vertex_normal_x*edge_normal_x[jj]+vertex_normal_y*edge_normal_y[jj]+vertex_normal_z*edge_normal_z[jj];
+ We_Av=We/Av;
+
+ Sv[0][0]+=We_Av* ( Pv11*(Pv11*Se11+Pv21*Se21+Pv31*Se31)+Pv21*(Pv11*Se21+Pv21*Se22+Pv31*Se32)+Pv31*(Pv11*Se31+Pv21*Se32+Pv31*Se33) );
+ Sv[0][1]+=We_Av* (Pv21*(Pv11*Se11+Pv21*Se21+Pv31*Se31)+Pv22*(Pv11*Se21+Pv21*Se22+Pv31*Se32)+Pv32*(Pv11*Se31+Pv21*Se32+Pv31*Se33));
+ Sv[0][2]+=We_Av* (Pv31*(Pv11*Se11+Pv21*Se21+Pv31*Se31)+Pv32*(Pv11*Se21+Pv21*Se22+Pv31*Se32)+Pv33*(Pv11*Se31+Pv21*Se32+Pv31*Se33));
+
+ Sv[1][0]+=We_Av* (Pv11*(Pv21*Se11+Pv22*Se21+Pv32*Se31)+Pv21*(Pv21*Se21+Pv22*Se22+Pv32*Se32)+Pv31*(Pv21*Se31+Pv22*Se32+Pv32*Se33));
+ Sv[1][1]+=We_Av* (Pv21*(Pv21*Se11+Pv22*Se21+Pv32*Se31)+Pv22*(Pv21*Se21+Pv22*Se22+Pv32*Se32)+Pv32*(Pv21*Se31+Pv22*Se32+Pv32*Se33));
+ Sv[1][2]+=We_Av* (Pv31*(Pv21*Se11+Pv22*Se21+Pv32*Se31)+Pv32*(Pv21*Se21+Pv22*Se22+Pv32*Se32)+Pv33*(Pv21*Se31+Pv22*Se32+Pv32*Se33));
+
+ Sv[2][0]+=We_Av* (Pv11*(Pv31*Se11+Pv32*Se21+Pv33*Se31)+Pv21*(Pv31*Se21+Pv32*Se22+Pv33*Se32)+Pv31*(Pv31*Se31+Pv32*Se32+Pv33*Se33));
+ Sv[2][1]+=We_Av* (Pv21*(Pv31*Se11+Pv32*Se21+Pv33*Se31)+Pv22*(Pv31*Se21+Pv32*Se22+Pv33*Se32)+Pv32*(Pv31*Se31+Pv32*Se32+Pv33*Se33));
+ Sv[2][2]+=We_Av* (Pv31*(Pv31*Se11+Pv32*Se21+Pv33*Se31)+Pv32*(Pv31*Se21+Pv32*Se22+Pv33*Se32)+Pv33*(Pv31*Se31+Pv32*Se32+Pv33*Se33));
+// printf("(%f %f %f); (%f %f %f); (%f %f %f)\n", edge_vector_x[jj], edge_vector_y[jj], edge_vector_z[jj], edge_normal_x[jj], edge_normal_y[jj], edge_normal_z[jj], edge_binormal_x[jj], edge_binormal_y[jj], edge_binormal_z[jj]);
+
+ }
+
+ gsl_matrix_set(gsl_Sv, 0,0, Sv[0][0]);
+ gsl_matrix_set(gsl_Sv, 0,1, Sv[0][1]);
+ gsl_matrix_set(gsl_Sv, 0,2, Sv[0][2]);
+ gsl_matrix_set(gsl_Sv, 1,0, Sv[1][0]);
+ gsl_matrix_set(gsl_Sv, 1,1, Sv[1][1]);
+ gsl_matrix_set(gsl_Sv, 1,2, Sv[1][2]);
+ gsl_matrix_set(gsl_Sv, 2,0, Sv[2][0]);
+ gsl_matrix_set(gsl_Sv, 2,1, Sv[2][1]);
+ gsl_matrix_set(gsl_Sv, 2,2, Sv[2][2]);
+
+ gsl_eigen_nonsymm_params(0, 1, workspace);
+ gsl_eigen_nonsymm(gsl_Sv, Sv_eigen, workspace);
+
+ printf("Eigenvalues: %f+ i%f, %f+i%f, %f+i%f\n",
+ GSL_REAL(gsl_vector_complex_get(Sv_eigen, 0)), GSL_IMAG(gsl_vector_complex_get(Sv_eigen, 0)),
+ GSL_REAL(gsl_vector_complex_get(Sv_eigen, 1)), GSL_IMAG(gsl_vector_complex_get(Sv_eigen, 1)),
+ GSL_REAL(gsl_vector_complex_get(Sv_eigen, 2)), GSL_IMAG(gsl_vector_complex_get(Sv_eigen, 2))
+ );
+ vtx->energy=0.0;
+
+ gsl_matrix_free(gsl_Sv);
+ gsl_vector_complex_free(Sv_eigen);
+ gsl_eigen_nonsymm_free(workspace);
+ return TS_SUCCESS;
}
-
-
ts_bool sweep_attraction_bond_energy(ts_vesicle *vesicle){
int i;
@@ -216,11 +282,11 @@
ts_double norml,ddp=0.0;
ts_uint i;
ts_double xnorm=0.0,ynorm=0.0,znorm=0.0;
- /*find normal of the vertex as average normal of all the triangles surrounding it. */
+ /*find normal of the vertex as sum of all the normals of the triangles surrounding it. */
for(i=0;i<vtx->tristar_no;i++){
- xnorm=vtx->tristar[i]->xnorm;
- ynorm=vtx->tristar[i]->ynorm;
- znorm=vtx->tristar[i]->znorm;
+ xnorm+=vtx->tristar[i]->xnorm;
+ ynorm+=vtx->tristar[i]->ynorm;
+ znorm+=vtx->tristar[i]->znorm;
}
/*normalize*/
norml=sqrt(xnorm*xnorm+ynorm*ynorm+znorm*znorm);
@@ -228,9 +294,13 @@
ynorm/=norml;
znorm/=norml;
/*calculate ddp, perpendicular displacement*/
- ddp=xnorm*(vtx->x-vtx_old->x)+xnorm*(vtx->y-vtx_old->y)+znorm*(vtx->z-vtx_old->z);
+ ddp=xnorm*(vtx->x-vtx_old->x)+ynorm*(vtx->y-vtx_old->y)+znorm*(vtx->z-vtx_old->z);
/*calculate dE*/
// printf("ddp=%e",ddp);
return vesicle->tape->F*ddp;
}
+
+void stretchenergy(ts_vesicle *vesicle, ts_triangle *triangle){
+ triangle->energy=vesicle->tape->xkA0/2.0*pow((triangle->area/vesicle->tlist->a0-1.0),2);
+}
--
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