int MFTangentLOCA(int n,int k,MFNVector vu,MFNKMatrix mPhi,void *d,
MFErrorHandler err)
{
LOCAData* data = (LOCAData *)d;
LOCANVectorData* u0_data = (LOCANVectorData *) MFNVectorGetData(vu, err);
data->grp->setX(*(u0_data->u_ptr));
data->grp->computePredictor();
const LOCA::MultiContinuation::ExtendedMultiVector& pred =
data->grp->getPredictorTangent();
for (int i=0; i<k; i++) {
Teuchos::RCP<LMCEV> t =
Teuchos::rcp_dynamic_cast<LMCEV>(pred[i].clone());
MFNVector tmp = MFCreateLOCANVectorWithData(t,err);
MFMSetColumn(mPhi, i, tmp, err);
MFFreeNVector(tmp, err);
}
MFGramSchmidt(data->space,mPhi, err);
return 1;
}
void MFGramSchmidtReplace(MFNSpace space,MFNKMatrix A,MFNVector phi0, MFNVector phi1,MFErrorHandler e)
{
static char RoutineName[]={"MFGramSchmidtReplace"};
double *a;
int i,j,n;
int k;
MFNVector u;
MFNVector v;
MFNVector w;
double inner;
int zero;
double *B=NULL;
int sign0,sign1;
int verbose=0;
/* Remove vector phi0 from the basis, and replaces it with the vector phi1 */
if(verbose){printf("%s\n",RoutineName);fflush(stdout);}
n=MFNKMatrixN(A,e);
k=MFNKMatrixK(A,e);
B=(double*)malloc(k*k*sizeof(double));
#ifndef MFNOSAFETYNET
if(B==NULL)
{
sprintf(MFNKMatrixErrorMsg,"Out of memory, trying to allocate %d bytes",k*k*sizeof(double));
MFSetError(e,12,RoutineName,MFNKMatrixErrorMsg,__LINE__,__FILE__);
MFErrorHandlerOutOfMemory(e);
return;
}
#endif
if(verbose)
{
printf("Remove vector phi0 from the basis, and replace it with the vector phi1\n");fflush(stdout);
printf(" phi0=0x%8.8x ",phi0);MFPrintNVector(stdout,phi0,e);printf("\n");fflush(stdout);
printf(" phi1=0x%8.8x ",phi0);MFPrintNVector(stdout,phi1,e);printf("\n");fflush(stdout);
}
for(i=0;i<k;i++)
{
u=MFMColumn(A,i,e);
for(j=0;j<k;j++)
{
v=MFMColumn(A,j,e);
B[i+k*j]=MFNSpaceInner(space,u,v,e);
MFFreeNVector(v,e);
}
MFFreeNVector(u,e);
}
sign0=MFAtlasDet(k,B,e)>0;
u=MFMColumn(A,0,e);
w=MFCloneNVector(u,e);
MFFreeNVector(u,e);
zero=-1;
for(i=-1;i<k;i++)
{
if(i>-1)u=MFMColumn(A,i,e);
else{u=phi0;MFRefNVector(phi0,e);}
inner=MFNSpaceInner(space,u,u,e);
#ifdef MFALLOWVERBOSE
if(verbose){printf("u_%d\n",i);MFPrintNVector(stdout,u,e);printf("\n");fflush(stdout);
printf("<u_%d,u_%d>=%lf\n",i,i,inner);fflush(stdout);}
#endif
if(inner>1.e-7)
{
inner=1./sqrt(inner);
MFNSpaceScale(space,inner,u,u,e);
#ifdef MFALLOWVERBOSE
if(verbose){printf("normalized u_%d\n",i);MFPrintNVector(stdout,u,e);printf("\n");fflush(stdout);}
#endif
}else{
zero=i;
#ifdef MFALLOWVERBOSE
if(verbose){printf("zero vector u_%d\n",i);MFPrintNVector(stdout,u,e);printf("\n");fflush(stdout);}
#endif
}
for(j=i+1;j<k;j++)
{
v=MFMColumn(A,j,e);
#ifdef MFALLOWVERBOSE
if(verbose){printf("v=u_%d\n",j);MFPrintNVector(stdout,v,e);printf("\n");fflush(stdout);}
#endif
inner=MFNSpaceInner(space,u,v,e);
#ifdef MFALLOWVERBOSE
if(verbose){printf("inner=<u_%d,u_%d>=%lf\n",i,j,inner);fflush(stdout);}
#endif
MFNSpaceScale(space,inner,u,w,e);
#ifdef MFALLOWVERBOSE
if(verbose){printf("w=<u_%d,u_%d>u_%d\n",j,i,i);MFPrintNVector(stdout,w,e);printf("\n");fflush(stdout);}
#endif
MFNVDiff(v,w,v,e);
#ifdef MFALLOWVERBOSE
if(verbose){printf("v-w=u_%d-<u_%d,u_%d>u_%d\n",j,j,i,i);MFPrintNVector(stdout,v,e);printf("\n");fflush(stdout);}
#endif
MFFreeNVector(v,e);
}
MFFreeNVector(u,e);
#ifdef MFALLOWVERBOSE
if(verbose){printf("\n");fflush(stdout);}
#endif
}
MFFreeNVector(w,e);
if(verbose){printf("done orthnormalizing, line %d, routine %s\n",__LINE__,RoutineName);fflush(stdout);}
if(verbose){printf("Delete the zero column (move it to the first position) zero=%d, line %d, routine %s\n",zero,__LINE__,RoutineName);fflush(stdout);}
if(zero>1)
{
for(i=zero;i>-1;i--)
{
u=MFMColumn(A,i-1,e);
v=MFMColumn(A,i,e);
MFMSetColumn(A,i,u,e);
MFFreeNVector(u,e);
MFFreeNVector(v,e);
}
if(verbose){printf("done removing the zero column line %d, routine %s\n",__LINE__,RoutineName);fflush(stdout);}
}
/* Replace the zero column with phi1 */
u=MFMColumn(A,0,e);
MFFreeNVector(u,e);
MFMSetColumn(A,0,phi1,e);
if(verbose){printf("Gram-Schmidt on new basis line %d, routine %s\n",__LINE__,RoutineName);fflush(stdout);}
MFGramSchmidt(space,A,e);
if(verbose){printf("done Gram-Schmidt on new basis line %d, routine %s\n",__LINE__,RoutineName);fflush(stdout);}
for(i=0;i<k;i++)
{
u=MFMColumn(A,i,e);
for(j=0;j<k;j++)
{
v=MFMColumn(A,j,e);
B[i+k*j]=MFNSpaceInner(space,u,v,e);
MFFreeNVector(v,e);
}
MFFreeNVector(u,e);
}
sign1=MFAtlasDet(k,B,e)>0;
if(verbose){printf("make Det the same line %d, routine %s\n",__LINE__,RoutineName);fflush(stdout);}
if(sign0&&!sign1||sign1&&!sign0)
{
u=MFMColumn(A,0,e);
MFNSpaceScale(space,-1.,u,u,e);
MFFreeNVector(u,e);
}
free(B);
if(verbose){printf("done %s\n",RoutineName);fflush(stdout);}
return;
}
void MFNKMProjectTangentForBranchSwitch(MFNSpace space, MFNKMatrix A,MFNVector phi,MFNKMatrix Phi,MFErrorHandler e)
{
static char RoutineName[]={"MFNKMProjectTangentForBranchSwitch"};
int i,j;
int k,m;
MFNVector u,w;
double *p;
double pmax;
MFNVector pi,pj;
int verbose=0;
#ifdef MFALLOWVERBOSE
if(verbose){printf("%s\n",RoutineName);fflush(stdout);
printf(" A=");MFPrintNKMatrix(stdout,A,e);fflush(stdout);
printf(" phi=");MFPrintNVector(stdout,phi,e);printf("\n");fflush(stdout);}
#endif
k=MFNKMatrixK(A,e);
p=(double*)malloc(k*sizeof(double));
#ifndef MFNOSAFETYNET
if(p==NULL)
{
sprintf(MFNKMatrixErrorMsg,"Out of memory, trying to allocate %d bytes",k*sizeof(double));
MFSetError(e,12,RoutineName,MFNKMatrixErrorMsg,__LINE__,__FILE__);
MFErrorHandlerOutOfMemory(e);
return;
}
#endif
j=0;
pmax=0.;
for(i=0;i<k;i++)
{
u=MFMColumn(A,i,e);
p[i]=MFNSpaceInner(space,phi,u,e);
if(fabs(p[i])>pmax){pmax=fabs(p[i]);j=i;}
MFFreeNVector(u,e);
#ifdef MFALLOWVERBOSE
if(verbose){printf("phi^* A_[%d]=%lf\n",i,p[i]);fflush(stdout);}
#endif
}
#ifdef MFALLOWVERBOSE
if(verbose){printf("max of phi^* A_j is for j=%d, =%lf\n",j,pmax);fflush(stdout);}
#endif
m=0;
u=MFMColumn(Phi,m,e);
w=MFCloneNVector(u,e);
MFNSpaceScale(space,1.,phi,u,e);
#ifdef MFALLOWVERBOSE
if(verbose){printf("column 0 of Phi is phi ");MFPrintNVector(stdout,u,e);printf("\n");(stdout);}
#endif
if(Phi->type==DENSE)MFMSetColumn(Phi,m,u,e);
MFFreeNVector(u,e);
m++;
pj=MFMColumn(A,j,e);
for(i=0;i<k;i++)
{
if(i!=j)
{
pi=MFMColumn(A,i,e);
u=MFMColumn(Phi,m,e);
MFNSpaceScale(space, p[i],pj,u,e);
MFNSpaceScale(space,-p[j],pi,w,e);
MFNSpaceAdd(space,u,w,u,e);
#ifdef MFALLOWVERBOSE
if(verbose){printf("column %d of Phi is %lf A_%d - %lf A_%d ",m,p[i],j,p[j],i);MFPrintNVector(stdout,u,e);printf("\n");(stdout);}
#endif
if(Phi->type==DENSE)MFMSetColumn(Phi,m,u,e);
m++;
MFFreeNVector(u,e);
MFFreeNVector(pi,e);
}
}
MFFreeNVector(pj,e);
free(p);
#ifdef MFALLOWVERBOSE
if(verbose){printf("Before G-S:\n");MFPrintNKMatrix(stdout,Phi,e);fflush(stdout);}
#endif
MFGramSchmidt(space,Phi,e);
#ifdef MFALLOWVERBOSE
if(verbose){printf("After G-S:\n");MFPrintNKMatrix(stdout,Phi,e);fflush(stdout);
printf("done %s\n",RoutineName);fflush(stdout);}
#endif
return;
}
