MRI_IMAGE * DES_get_psinv( int ntim , int nref , float **ref )
{
MRI_IMAGE *refim , *psinv ; float *refar , *jar ; int ii , jj ;
refim = mri_new(ntim,nref,MRI_float) ;
refar = MRI_FLOAT_PTR(refim) ;
for( jj=0 ; jj < nref ; jj++ ){
jar = refar + jj*ntim ;
for( ii=0 ; ii < ntim ; ii++ ) jar[ii] = ref[jj][ii] ;
}
mri_matrix_psinv_svd(1) ;
psinv = mri_matrix_psinv(refim,NULL,0.0f) ;
mri_free(refim) ;
return psinv ;
}
MRI_IMAGE * LSS_setup( MRI_IMAGE *ima , MRI_IMAGE *imc )
{
int nn, mm, nc, ii, jj, ic , nwarn=0 ;
float *cc, *pp, *qq, *qj, *vv, *ss, *pv , cj, cvdot, pc ;
MRI_IMAGE *ims , *imp , *imq ;
MRI_IMARR *imar ;
ENTRY("LSS_setup") ;
if( ima == NULL || imc == NULL ){ /* bad user */
ERROR_message("LSS_setup: NULL input image?!") ;
RETURN(NULL) ;
}
/* [A] is nn X mm ; [C] is nn x nc */
nn = ima->nx ; mm = ima->ny ; nc = imc->ny ; cc = MRI_FLOAT_PTR(imc) ;
if( imc->nx != nn || nn <= mm+2 ){ /* stoopid user */
ERROR_message("LSS_setup: ima->nx=%d does not equal imc->nx=%d :-(" ,
ima->nx,imc->nx) ;
RETURN(NULL) ;
}
/* get imp = [P] = psinv of [A] = mm X nn matrix
imq = [Q] = ortproj onto column null space of [A] = nn X nn matrix */
mri_matrix_psinv_svd(1) ;
imar = mri_matrix_psinv_ortproj( ima , 1 ) ;
if( imar == NULL ){ /* should not happen */
ERROR_message("LSS_setup: cannot compute pseudo-inverse :-(") ;
RETURN(NULL) ;
}
imp = IMARR_SUBIM(imar,0) ; pp = MRI_FLOAT_PTR(imp) ;
imq = IMARR_SUBIM(imar,1) ; qq = MRI_FLOAT_PTR(imq) ;
/* create output image = [S] = nn X nc
Each column of [S] is the vector that we
dot into a data vector [z] to get the estimate of
gamma+delta for the corresponding column from [C] */
ims = mri_new(nn,nc,MRI_float) ; ss = MRI_FLOAT_PTR(ims) ;
/* workspace vectors */
vv = (float *)malloc(sizeof(float)*nn) ; /* will be [Q] [c] */
pv = (float *)malloc(sizeof(float)*nn) ; /* last row of [P] */
for( ii=0 ; ii < nn ; ii++ ) pv[ii] = pp[ mm-1 + ii*mm ] ;
/* loop over columns of [C] (and [S]) */
for( ic=0 ; ic < nc ; ic++,cc+=nn,ss+=nn ){
/* compute [v] = [Q] [c] */
for( ii=0 ; ii < nn ; ii++ ) vv[ii] = 0.0f ; /* initialize [v] to 0 */
for( jj=0 ; jj < nn ; jj++ ){ /* loop over columns of Q */
qj = qq + jj*nn ; /* ptr to jj-th column of Q */
cj = cc[jj] ; /* jj-th value of [c] */
for( ii=0 ; ii < nn ; ii++ ) vv[ii] += qj[ii] * cj ; /* sum into [v] */
}
/* compute cvdot = [c] *dot* [v]
cj = [c] *dot* [c]
pc = [c] *dot* {last row of [P] = pv} */
for( pc=cj=cvdot=ii=0 ; ii < nn ; ii++ ){
cvdot += cc[ii]*vv[ii] ; cj += cc[ii]*cc[ii] ; pc += pv[ii]*cc[ii] ;
}
/* initialize [s] = last row of [P] */
for( ii=0 ; ii < nn ; ii++ ) ss[ii] = pv[ii] ;
/* If cvdot is zero(ish), this means that the extra column [c]
is collinear(ish) with the columns of [A], and we skip the next step.
Note that since [Q] is an orthogonal matrix,
we are guaranteed that L2norm([Q][c]) == L2norm([c]),
which implies that abs(cvdot) <= abs(cj), by the triangle inequality. */
if( fabsf(cvdot) >= 1.e-5*cj ){
/* add the proper fraction of [v] into [s] */
pc = (1.0f - pc) / cvdot ;
for( ii=0 ; ii < nn ; ii++ ) ss[ii] += pc * vv[ii] ;
} else {
nwarn++ ;
}
} /* end of loop over columns of [C] */
if( verb && nwarn > 0 )
INFO_message("%d (out of %d) LSS individual estimators were collinear",
nwarn , nc ) ;
/* toss the trash and return the output set of columns */
free(pv) ; free(vv) ; DESTROY_IMARR(imar) ; RETURN(ims) ;
}
