/* build orthonormal basis matrix
Q = Y;
for j=1:k
vj = Q(:,j);
for i=1:(j-1)
vi = Q(:,i);
vj = vj - project_vec(vj,vi);
end
vj = vj/norm(vj);
Q(:,j) = vj;
end
*/
void build_orthonormal_basis_from_mat(mat *A, mat *Q){
int m,n,i,j,ind,num_ortos=2;
double vec_norm;
vec *vi,*vj,*p;
m = A->nrows;
n = A->ncols;
vi = vector_new(m);
vj = vector_new(m);
p = vector_new(m);
matrix_copy(Q, A);
for(ind=0; ind<num_ortos; ind++){
for(j=0; j<n; j++){
matrix_get_col(Q, j, vj);
for(i=0; i<j; i++){
matrix_get_col(Q, i, vi);
project_vector(vj, vi, p);
vector_sub(vj, p);
}
vec_norm = vector_get2norm(vj);
vector_scale(vj, 1.0/vec_norm);
matrix_set_col(Q, j, vj);
}
}
vector_delete(vi);
vector_delete(vj);
vector_delete(p);
}
static void ProjectAmplitude (
BeadParams *p,
const float *observed,
const float *const *model_trace,
const float *em_vector,
int npts,
float negative_amplitude_limit ,
float positive_amplitude_limit,
int flow_block_size
)
{
static int numWarnings = 0;
for ( int fnum=0; fnum<flow_block_size; fnum++ )
{
float tmp_mult= project_vector ( & ( observed[npts*fnum] ),model_trace[fnum],em_vector,npts );
p->Ampl[fnum] *=tmp_mult;
// Some limited warnings
if ( p->Ampl[fnum]!=p->Ampl[fnum] && numWarnings++ < 10 )
{
printf ( "BSA: tmp_mult:\t%f\n",tmp_mult );
printf ( "BSA: em\t" );
for ( int ix=0; ix<npts; ix++ )
printf ( "%f\t",em_vector[ix] );
printf ( "\n" );
printf ( "BSA: obser\t" );
for ( int ix=0; ix<npts; ix++ )
printf ( "%f\t",observed[npts*fnum+ix] );
printf ( "\n" );
printf ( "BSA: model\t" );
for ( int ix=0; ix<npts; ix++ )
printf ( "%f\t",model_trace[fnum][ix] );
printf ( "\n" );
}
// Not sure why 1.0f but this is how I found it...
if ( p->Ampl[fnum]!=p->Ampl[fnum] )
{
p->Ampl[fnum]=1.0f;
}
// bounds check
if ( p->Ampl[fnum]<negative_amplitude_limit )
p->Ampl[fnum] = negative_amplitude_limit; // Projection onto zero returns potentially large number, but we may want negative values here
if ( p->Ampl[fnum]>positive_amplitude_limit )
p->Ampl[fnum]=positive_amplitude_limit; // we limit this everywhere else, so keep from explosion
}
}
/* build orthonormal basis matrix
Q = Y;
for j=1:k
vj = Q(:,j);
for i=1:(j-1)
vi = Q(:,i);
vj = vj - project_vec(vj,vi);
end
vj = vj/norm(vj);
Q(:,j) = vj;
end
*/
void build_orthonormal_basis_from_mat(gsl_matrix *A, gsl_matrix *Q){
int m,n,i,j,ind,num_ortos=2;
double vec_norm;
gsl_vector *vi,*vj,*p;
m = A->size1;
n = A->size2;
vi = gsl_vector_calloc(m);
vj = gsl_vector_calloc(m);
p = gsl_vector_calloc(m);
gsl_matrix_memcpy(Q, A);
for(ind=0; ind<num_ortos; ind++){
for(j=0; j<n; j++){
gsl_matrix_get_col(vj, Q, j);
for(i=0; i<j; i++){
gsl_matrix_get_col(vi, Q, i);
project_vector(vj, vi, p);
gsl_vector_sub(vj, p);
}
vec_norm = gsl_blas_dnrm2(vj);
gsl_vector_scale(vj, 1.0/vec_norm);
gsl_matrix_set_col (Q, j, vj);
}
}
}
void estimate_rank_and_buildQ(mat *M, double frac_of_max_rank, double TOL, mat **Q, int *good_rank){
int m,n,i,j,ind,maxdim;
double vec_norm;
mat *RN,*Y,*Qbig,*Qsmall;
vec *vi,*vj,*p,*p1;
m = M->nrows;
n = M->ncols;
maxdim = round(min(m,n)*frac_of_max_rank);
vi = vector_new(m);
vj = vector_new(m);
p = vector_new(m);
p1 = vector_new(m);
// build random matrix
printf("form RN..\n");
RN = matrix_new(n, maxdim);
initialize_random_matrix(RN);
// multiply to get matrix of random samples Y
printf("form Y: %d x %d..\n",m,maxdim);
Y = matrix_new(m, maxdim);
matrix_matrix_mult(M, RN, Y);
// estimate rank k and build Q from Y
printf("form Qbig..\n");
Qbig = matrix_new(m, maxdim);
matrix_copy(Qbig, Y);
printf("estimate rank with TOL = %f..\n", TOL);
*good_rank = maxdim;
int forbreak = 0;
for(j=0; !forbreak && j<maxdim; j++){
matrix_get_col(Qbig, j, vj);
for(i=0; i<j; i++){
matrix_get_col(Qbig, i, vi);
project_vector(vj, vi, p);
vector_sub(vj, p);
if(vector_get2norm(p) < TOL && vector_get2norm(p1) < TOL){
*good_rank = j;
forbreak = 1;
break;
}
vector_copy(p1,p);
}
vec_norm = vector_get2norm(vj);
vector_scale(vj, 1.0/vec_norm);
matrix_set_col(Qbig, j, vj);
}
printf("estimated rank = %d\n", *good_rank);
Qsmall = matrix_new(m, *good_rank);
*Q = matrix_new(m, *good_rank);
matrix_copy_first_columns(Qsmall, Qbig);
QR_factorization_getQ(Qsmall, *Q);
matrix_delete(RN);
matrix_delete(Y);
matrix_delete(Qsmall);
matrix_delete(Qbig);
}
void estimate_rank_and_buildQ(gsl_matrix *M, double frac_of_max_rank, double TOL, gsl_matrix **Q, int *good_rank){
int m,n,i,j,ind,maxdim;
double vec_norm;
gsl_matrix *RN,*Y,*Qbig,*Qsmall;
gsl_vector *vi,*vj,*p,*p1;
m = M->size1;
n = M->size2;
maxdim = round(min(m,n)*frac_of_max_rank);
vi = gsl_vector_calloc(m);
vj = gsl_vector_calloc(m);
p = gsl_vector_calloc(m);
p1 = gsl_vector_calloc(m);
// build random matrix
printf("form RN..\n");
RN = gsl_matrix_calloc(n, maxdim);
initialize_random_matrix(RN);
// multiply to get matrix of random samples Y
printf("form Y: %d x %d..\n",m,maxdim);
Y = gsl_matrix_calloc(m, maxdim);
matrix_matrix_mult(M, RN, Y);
// estimate rank k and build Q from Y
printf("form Qbig..\n");
Qbig = gsl_matrix_calloc(m, maxdim);
gsl_matrix_memcpy(Qbig, Y);
printf("estimate rank with TOL = %f..\n", TOL);
*good_rank = maxdim;
int forbreak = 0;
for(j=0; !forbreak && j<maxdim; j++){
gsl_matrix_get_col(vj, Qbig, j);
for(i=0; i<j; i++){
gsl_matrix_get_col(vi, Qbig, i);
project_vector(vj, vi, p);
gsl_vector_sub(vj, p);
if(gsl_blas_dnrm2(p) < TOL && gsl_blas_dnrm2(p1) < TOL){
*good_rank = j;
forbreak = 1;
break;
}
gsl_vector_memcpy(p1,p);
}
vec_norm = gsl_blas_dnrm2(vj);
gsl_vector_scale(vj, 1.0/vec_norm);
gsl_matrix_set_col(Qbig, j, vj);
}
printf("estimated rank = %d\n", *good_rank);
Qsmall = gsl_matrix_calloc(m, *good_rank);
*Q = gsl_matrix_calloc(m, *good_rank);
matrix_copy_first_columns(Qsmall, Qbig);
QR_factorization_getQ(Qsmall, *Q);
gsl_matrix_free(RN);
gsl_matrix_free(Y);
gsl_matrix_free(Qbig);
gsl_matrix_free(Qsmall);
gsl_vector_free(p);
gsl_vector_free(p1);
gsl_vector_free(vi);
gsl_vector_free(vj);
}
