static void VHmatExtract_f(svdObj_f *svd)
{
vsip_mview_f*B = svd->B;
vsip_index i,j;
vsip_length n = vsip_mgetrowlength_f(B);
vsip_mview_f *Bs=svd->Bs;
vsip_mview_f *V=svd->R;
vsip_mview_f *Vs=svd->Rs;
vsip_vview_f *v;
vsip_scalar_f t;
if(n < 3)
return;
v = row_sv_f(B,svd->bs,0);
for(i=n-3; i>0; i--){
j=i+1;
row_sv_f(msv_f(B,Bs,i,j),v,0);
t=vsip_vget_f(v,0);vsip_vput_f(v,0,1.0);
prodHouse_f(msv_f(V,Vs,j,j),v);
vsip_vput_f(v,0,t);
}
row_sv_f(msv_f(B,Bs,0,1),v,0);
t=vsip_vget_f(v,0);vsip_vput_f(v,0,1.0);
prodHouse_f(msv_f(V,Vs,1,1),v);
vsip_vput_f(v,0,t);
}
/* sign function as defined in http://www.netlib.org/lapack/lawnspdf/lawn148.pdf */
static vsip_scalar_f sign_f(vsip_scalar_f a_in)
{
if(a_in < 0.0)
return -1.0;
else
return 1.0;
} /* same */
static void biDiagPhaseToZero_f( svdObj_f *svd)
{
vsip_mview_f *L = svd->L;
vsip_vview_f *d = svd->d;
vsip_vview_f *f = svd->f;
vsip_mview_f *R = svd->R;
vsip_scalar_f eps0 = svd->eps0;
vsip_length n_d=vsip_vgetlength_f(d);
vsip_length n_f=vsip_vgetlength_f(f);
vsip_index i,j;
vsip_scalar_f ps;
vsip_scalar_f m;
vsip_vview_f *l = svd->ls_one;
vsip_vview_f *r = svd->rs_one;
for(i=0; i<n_d; i++){
ps=vsip_vget_f(d,i);
m = vsip_mag_f(ps);
ps=sign_f(ps);
if(m > eps0){
col_sv_f(L,l,i);vsip_svmul_f(ps,l,l);
vsip_vput_f(d,i,m);
if (i < n_f)
vsip_vput_f(f,i,ps*vsip_vget_f(f,i));
} else {
vsip_vput_f(d,i,0.0);
}
}
svdZeroCheckAndSet_f(eps0,d,f);
for (i=0; i<n_f-1; i++){
j=i+1;
ps = vsip_vget_f(f,i);
m = vsip_mag_f(ps);
ps=sign_f(ps);
col_sv_f(L, l, j);vsip_svmul_f(ps,l,l);
row_sv_f(R,r,j);vsip_svmul_f(ps,r,r);
vsip_vput_f(f,i,m);
vsip_vput_f(f,j,ps * vsip_vget_f(f,j));
}
j=n_f;
i=j-1;
ps=vsip_vget_f(f,i);
m=vsip_mag_f(ps);
ps=sign_f(ps);
vsip_vput_f(f,i,m);
col_sv_f(L, l, j);vsip_svmul_f(ps,l,l);
row_sv_f(R,r,j);vsip_svmul_f(ps,r,r);
}
static void phaseCheck_f(svdObj_f *svd)
{
biDiagPhaseToZero_f(svd);
}
void houseProd_f(vsip_vview_f *v, vsip_mview_f *A)
{
vsip_mattr_f a_atr;
vsip_vview_f *w;
vsip_mview_f *B;
vsip_mgetattrib_f(A,&a_atr);
B=vsip_mcreate_f(a_atr.col_length,a_atr.row_length,VSIP_ROW,VSIP_MEM_NONE);
w = vsip_vcreate_f(a_atr.row_length,VSIP_MEM_NONE);
vsip_scalar_f beta = 2.0/vsip_vdot_f(v,v);
vsip_vmprod_f(v,A,w);
vsip_vouter_f(beta,v,w,B);
vsip_msub_f(A,B,A);
vsip_valldestroy_f(w);
vsip_malldestroy_f(B);
} /* need to remove create */
void prodHouse_f(vsip_mview_f *A, vsip_vview_f *v)
{
vsip_mattr_f a_atr;
vsip_vview_f *w;
vsip_mview_f *B;
vsip_mgetattrib_f(A,&a_atr);
B=vsip_mcreate_f(a_atr.col_length,a_atr.row_length,VSIP_ROW,VSIP_MEM_NONE);
w = vsip_vcreate_f(a_atr.col_length,VSIP_MEM_NONE);
vsip_scalar_f beta = 2.0/vsip_vdot_f(v,v);
vsip_mvprod_f(A,v,w);
vsip_vouter_f(beta,w,v,B);
vsip_msub_f(A,B,A);
vsip_valldestroy_f(w);
vsip_malldestroy_f(B);
} /* need to remove create */
static vsip_vview_f *houseVector_f(vsip_vview_f* x)
{
vsip_scalar_f nrm=vnorm2_f(x);
vsip_scalar_f t = vsip_vget_f(x,0);
vsip_scalar_f s = t + sign_f(t) * nrm;
vsip_vput_f(x,0,s);
nrm = vnorm2_f(x);
if (nrm == 0.0)
vsip_vput_f(x,0,1.0);
else
vsip_svmul_f(1.0/nrm,x,x);
return x;
}
void VU_mprodq_f(
vsip_mview_f *C,
vsip_mview_f *H,
vsip_scalar_f *beta)
{
vsip_mattr_f attr_C,attr_C0;
vsip_mattr_f attr_H0;
vsip_vattr_f attr_h,attr_v0;
vsip_vview_f *h = vsip_mcolview_f(H,0);
vsip_length m,n;
vsip_length j;
vsip_stride k;
vsip_vview_f *v, *w;
vsip_mgetattrib_f(C,&attr_C);
vsip_vgetattrib_f(h,&attr_h);
vsip_mgetattrib_f(H,&attr_H0);
attr_C0 = attr_C;
m = attr_C.col_length;
n = attr_C.row_length;
v = vsip_vcreate_f(n,0);
vsip_vgetattrib_f(v,&attr_v0);
w = vsip_vcreate_f(m,0);
for(k= 0; k < attr_H0.row_length; k++){
j = (vsip_length)k;
attr_h.offset = j * attr_H0.row_stride +
j * attr_H0.col_stride + attr_H0.offset;
attr_h.length = attr_H0.col_length - j;
vsip_vputlength_f(v,attr_h.length);
vsip_vputoffset_f(v,n - attr_h.length);
vsip_vputattrib_f(h,&attr_h);
vsip_vcopy_f_f(h,v);
vsip_vput_f(v,0,1);
vsip_vputattrib_f(v,&attr_v0);
VU_smvprod_f(-beta[j],C,v,w);
VU_opu_f(C,w,v);
vsip_vput_f(v,k,0);
}
printf("here 1\n");
vsip_mputattrib_f(C,&attr_C0);
vsip_vdestroy_f(h);
vsip_valldestroy_f(v);
vsip_valldestroy_f(w);
return;
}
static void svdZeroCheckAndSet_f(vsip_scalar_f e, vsip_vview_f *b0, vsip_vview_f *b1)
{
vsip_index i;
vsip_length n = vsip_vgetlength_f(b1);
vsip_scalar_f z = 0.0;
for(i=0; i<n; i++){
vsip_scalar_f b = vsip_mag_f(vsip_vget_f(b1,i));
vsip_scalar_f a = e*(vsip_mag_f(vsip_vget_f(b0,i))
+ vsip_mag_f(vsip_vget_f(b0,i+1)));
if( b < a ) vsip_vput_f(b1,i,z);
}
} /* same */
static void UmatExtract_f(svdObj_f *svd)
{
vsip_mview_f* B=svd->B;
vsip_mview_f *U=svd->L;
vsip_index i;
vsip_length m = vsip_mgetcollength_f(B);
vsip_length n = vsip_mgetrowlength_f(B);
vsip_mview_f *Bs=svd->Bs;
vsip_mview_f *Us=svd->Ls;
vsip_vview_f *v;
vsip_scalar_f t;
v = col_sv_f(B,svd->bs,0);
if (m > n){
i=n-1;
col_sv_f(msv_f(B,Bs,i,i),v,0);
t=vsip_vget_f(v,0); vsip_vput_f(v,0,1.0);
houseProd_f(v,msv_f(U,Us,i,i));
vsip_vput_f(v,0,t);
}
for(i=n-2; i>0; i--){
col_sv_f(msv_f(B,Bs,i,i),v,0);
t=vsip_vget_f(v,0); vsip_vput_f(v,0,1.0);
houseProd_f(v,msv_f(U,Us,i,i));
vsip_vput_f(v,0,t);
}
col_sv_f(msv_f(B,Bs,0,0),v,0);
t=vsip_vget_f(v,0); vsip_vput_f(v,0,1.0);
houseProd_f(v,msv_f(U,Us,0,0));
vsip_vput_f(v,0,t);
}
/* eps0 is a number << maximum singular value */
svd->eps0=mnormFro_f(B)/(vsip_scalar_f)vsip_mgetrowlength_f(B)*1E-10;
bidiag_f(svd);
UmatExtract_f(svd);
VHmatExtract_f(svd);
biDiagPhaseToZero_f(svd);
vsip_vcopy_f_f(diag_sv_f(B,svd->bs,0),svd->d);
vsip_vcopy_f_f(diag_sv_f(B,svd->bs,1),svd->f);
}
static void gtProd_f(vsip_index i, vsip_index j, vsip_scalar_f c,vsip_scalar_f s, svdObj_f* svd)
{
vsip_mview_f* R = svd->Rs;
vsip_vview_f *a1= row_sv_f(R,svd->rs_one, i);
vsip_vview_f *a2= row_sv_f(R,svd->rs_two, j);
vsip_vview_f *a1c=vclone_f(a1,svd->t);
vsip_svmul_f(c,a1c,a1); vsip_vsma_f(a2,s,a1,a1);
vsip_svmul_f(-s,a1c,a1c); vsip_vsma_f(a2,c,a1c,a2);
}
static void prodG_f(svdObj_f* svd,vsip_index i, vsip_index j,vsip_scalar_f c, vsip_scalar_f s)
{
vsip_mview_f* L = svd->Ls;
vsip_vview_f *a1= col_sv_f(L,svd->ls_one,i);
vsip_vview_f *a2= col_sv_f(L,svd->ls_two,j);
vsip_vview_f *a1c=vclone_f(a1,svd->t);
vsip_svmul_f(c,a1c,a1); vsip_vsma_f(a2,s,a1,a1);
vsip_svmul_f(-s,a1c,a1c);vsip_vsma_f(a2,c,a1c,a2);
}
static givensObj_f givensCoef_f(vsip_scalar_f x1, vsip_scalar_f x2)
{
givensObj_f retval;
vsip_scalar_f t = vsip_hypot_f(x1,x2);
if (x2 == 0.0){
retval.c=1.0;retval.s=0.0;retval.r=x1;
} else if (x1 == 0.0) {
retval.c=0.0;retval.s=sign_f(x2);retval.r=t;
}else{
vsip_scalar_f sn = sign_f(x1);
retval.c=vsip_mag_f(x1)/t;retval.s=sn*x2/t; retval.r=sn*t;
}
return retval;
} /* same */
static void zeroCol_f(svdObj_f *svd)
{
vsip_vview_f *d=svd->ds;
vsip_vview_f *f=svd->fs;
vsip_length n = vsip_vgetlength_f(f);
givensObj_f g;
vsip_scalar_f xd,xf,t;
vsip_index i,j,k;
if (n == 1){
xd=vsip_vget_f(d,0);
xf=vsip_vget_f(f,0);
g=givensCoef_f(xd,xf);
vsip_vput_f(d,0,g.r);
vsip_vput_f(f,0,0.0);
gtProd_f(0,1,g.c,g.s,svd);
}else if (n == 2){
xd=vsip_vget_f(d,1);
xf=vsip_vget_f(f,1);
g=givensCoef_f(xd,xf);
vsip_vput_f(d,1,g.r);
vsip_vput_f(f,1,0.0);
xf=vsip_vget_f(f,0);
t= -xf * g.s; xf *= g.c;
vsip_vput_f(f,0,xf);
gtProd_f(1,2,g.c,g.s,svd);
xd=vsip_vget_f(d,0);
g=givensCoef_f(xd,t);
vsip_vput_f(d,0,g.r);
gtProd_f(0,2,g.c,g.s,svd);
}else{
i=n-1; j=i-1; k=i;
xd=vsip_vget_f(d,i);
xf=vsip_vget_f(f,i);
g=givensCoef_f(xd,xf);
xf=vsip_vget_f(f,j);
vsip_vput_f(f,i,0.0);
vsip_vput_f(d,i,g.r);
t=-xf*g.s; xf*=g.c;
vsip_vput_f(f,j,xf);
gtProd_f(i,k+1,g.c,g.s,svd);
while (i > 1){
i = j; j = i-1;
xd=vsip_vget_f(d,i);
g=givensCoef_f(xd,t);
vsip_vput_f(d,i,g.r);
xf=vsip_vget_f(f,j);
t= -xf * g.s; xf *= g.c;
vsip_vput_f(f,j,xf);
gtProd_f(i,k+1,g.c,g.s,svd);
}
xd=vsip_vget_f(d,0);
g=givensCoef_f(xd,t);
vsip_vput_f(d,0,g.r);
gtProd_f(0,k+1,g.c,g.s,svd);
}
}
static void zeroRow_f(svdObj_f *svd)
{
vsip_vview_f *d = svd->ds;
vsip_vview_f *f = svd->fs;
vsip_length n = vsip_vgetlength_f(d);
givensObj_f g;
vsip_scalar_f xd,xf,t;
vsip_index i;
xd=vsip_vget_f(d,0);
xf=vsip_vget_f(f,0);
g=givensCoef_f(xd,xf);
if (n == 1){
vsip_vput_f(f,0,0.0);
vsip_vput_f(d,0,g.r);
}else{
vsip_vput_f(f,0,0.0);
vsip_vput_f(d,0,g.r);
xf=vsip_vget_f(f,1);
t= -xf * g.s; xf *= g.c;
vsip_vput_f(f,1,xf);
prodG_f(svd,1,0,g.c,g.s);
for(i=1; i<n-1; i++){
xd=vsip_vget_f(d,i);
g=givensCoef_f(xd,t);
prodG_f(svd,i+1,0,g.c,g.s);
vsip_vput_f(d,i,g.r);
xf=vsip_vget_f(f,i+1);
t=-xf * g.s; xf *= g.c;
vsip_vput_f(f,i+1,xf);
}
xd=vsip_vget_f(d,n-1);
g=givensCoef_f(xd,t);
vsip_vput_f(d,n-1,g.r);
prodG_f(svd,n,0,g.c,g.s);
}
}
static vsip_scalar_f svdMu_f(vsip_scalar_f d2,vsip_scalar_f f1,vsip_scalar_f d3,vsip_scalar_f f2)
{
vsip_scalar_f mu;
vsip_scalar_f cu=d2 * d2 + f1 * f1;
vsip_scalar_f cl=d3 * d3 + f2 * f2;
vsip_scalar_f cd = d2 * f2;
vsip_scalar_f D = (cu * cl - cd * cd);
vsip_scalar_f T = (cu + cl);
vsip_scalar_f root = vsip_sqrt_f(T*T - 4 * D);
vsip_scalar_f lambda1 = (T + root)/(2.);
vsip_scalar_f lambda2 = (T - root)/(2.);
if(vsip_mag_f(lambda1 - cl) < vsip_mag_f(lambda2 - cl))
mu = lambda1;
else
mu = lambda2;
return mu;
} /* same */
static vsip_index zeroFind_f(vsip_vview_f* d, vsip_scalar_f eps0)
{
vsip_index j = vsip_vgetlength_f(d);
vsip_scalar_f xd=vsip_vget_f(d,j-1);
while(xd > eps0){
if (j > 1){
j -= 1;
xd=vsip_vget_f(d,j-1);
}else{
break;
}
}
if(xd <= eps0)
vsip_vput_f(d,j-1,0.0);
if (j == 1)
j=0;
return j;
} /* same */
void VU_qprodm_f(
vsip_mview_f *C,
vsip_mview_f *H,
vsip_scalar_f *beta)
{
vsip_mattr_f attr_C,attr_C0;
vsip_mattr_f attr_H0;
vsip_vattr_f attr_h,attr_v0;
vsip_vview_f *h = vsip_mcolview_f(H,0);
vsip_length m,n;
vsip_length j;
vsip_stride k;
vsip_vview_f *v, *w;
vsip_mgetattrib_f(C,&attr_C);
vsip_vgetattrib_f(h,&attr_h);
vsip_mgetattrib_f(H,&attr_H0);
attr_C0 = attr_C;
m = attr_C.col_length;
n = attr_C.row_length;
v = vsip_vcreate_f(m,0);
vsip_vgetattrib_f(v,&attr_v0);
w = vsip_vcreate_f(n,0);
vsip_vfill_f(0,v);
for(k= attr_H0.row_length - 1; k >= 0; k--){
j = (vsip_length)k;
attr_h.offset = j * attr_H0.row_stride +
j * attr_H0.col_stride + attr_H0.offset;
attr_h.length = attr_H0.col_length -j;
vsip_vputlength_f(v,attr_h.length);
vsip_vputoffset_f(v,m - attr_h.length);
vsip_vputattrib_f(h,&attr_h);
vsip_vcopy_f_f(h,v);
vsip_vput_f(v,0,1);
vsip_vputattrib_f(v,&attr_v0);
VU_svmprod_f(-beta[j],v,C,w);
VU_opu_f(C,v,w);
}
vsip_mputattrib_f(C,&attr_C0);
vsip_vdestroy_f(h);
vsip_valldestroy_f(v);
vsip_valldestroy_f(w);
return;
}
/* sign function as defined in http://www.netlib.org/lapack/lawnspdf/lawn148.pdf */
static vsip_scalar_f sign_f(vsip_scalar_f a_in)
{
if(a_in < 0.0)
return -1.0;
else
return 1.0;
} /* same */
static void biDiagPhaseToZero_f( svdObj_f *svd)
{
vsip_mview_f *L = svd->L;
vsip_vview_f *d = svd->d;
vsip_vview_f *f = svd->f;
vsip_mview_f *R = svd->R;
vsip_scalar_f eps0 = svd->eps0;
vsip_length n_d=vsip_vgetlength_f(d);
vsip_length n_f=vsip_vgetlength_f(f);
vsip_index i,j;
vsip_scalar_f ps;
vsip_scalar_f m;
vsip_vview_f *l = svd->ls_one;
vsip_vview_f *r = svd->rs_one;
for(i=0; i<n_d; i++){
ps=vsip_vget_f(d,i);
m = vsip_mag_f(ps);
ps=sign_f(ps);
if(m > eps0){
col_sv_f(L,l,i);vsip_svmul_f(ps,l,l);
vsip_vput_f(d,i,m);
if (i < n_f)
vsip_vput_f(f,i,ps*vsip_vget_f(f,i));
} else {
vsip_vput_f(d,i,0.0);
}
}
svdZeroCheckAndSet_f(eps0,d,f);
for (i=0; i<n_f-1; i++){
j=i+1;
ps = vsip_vget_f(f,i);
m = vsip_mag_f(ps);
ps=sign_f(ps);
col_sv_f(L, l, j);vsip_svmul_f(ps,l,l);
row_sv_f(R,r,j);vsip_svmul_f(ps,r,r);
vsip_vput_f(f,i,m);
vsip_vput_f(f,j,ps * vsip_vget_f(f,j));
}
j=n_f;
i=j-1;
ps=vsip_vget_f(f,i);
m=vsip_mag_f(ps);
ps=sign_f(ps);
vsip_vput_f(f,i,m);
col_sv_f(L, l, j);vsip_svmul_f(ps,l,l);
row_sv_f(R,r,j);vsip_svmul_f(ps,r,r);
}
static void zeroRow_f(svdObj_f *svd)
{
vsip_vview_f *d = svd->ds;
vsip_vview_f *f = svd->fs;
vsip_length n = vsip_vgetlength_f(d);
givensObj_f g;
vsip_scalar_f xd,xf,t;
vsip_index i;
xd=vsip_vget_f(d,0);
xf=vsip_vget_f(f,0);
g=givensCoef_f(xd,xf);
if (n == 1){
vsip_vput_f(f,0,0.0);
vsip_vput_f(d,0,g.r);
}else{
vsip_vput_f(f,0,0.0);
vsip_vput_f(d,0,g.r);
xf=vsip_vget_f(f,1);
t= -xf * g.s; xf *= g.c;
vsip_vput_f(f,1,xf);
prodG_f(svd,1,0,g.c,g.s);
for(i=1; i<n-1; i++){
xd=vsip_vget_f(d,i);
g=givensCoef_f(xd,t);
prodG_f(svd,i+1,0,g.c,g.s);
vsip_vput_f(d,i,g.r);
xf=vsip_vget_f(f,i+1);
t=-xf * g.s; xf *= g.c;
vsip_vput_f(f,i+1,xf);
}
xd=vsip_vget_f(d,n-1);
g=givensCoef_f(xd,t);
vsip_vput_f(d,n-1,g.r);
prodG_f(svd,n,0,g.c,g.s);
}
}
int main(){vsip_init((void*)0);
{
int solretval=0;
vsip_scalar_vi i,j;
vsip_mview_f *A = vsip_mcreate_f(M, N,VSIP_COL,0);
vsip_mview_f *X = vsip_mcreate_f(M,NB,VSIP_ROW,0);
/* Nullify the data-space */
for (i=0; i < vsip_mgetcollength_f(A); i++)
for(j=0; j < vsip_mgetrowlength_f(A); j++)
vsip_mput_f(A,i,j,(double)0);
for (i=0; i < vsip_mgetcollength_f(X); i++)
for(j=0; j < vsip_mgetrowlength_f(X); j++)
vsip_mput_f(X,i,j,(double)0);
/* Initialise matrix A */
for (i=0; i<M; i++)
for (j = 0; j < N; j++)
if(i == j)
vsip_mput_f(A,i,j, (double)(M+1));
else
vsip_mput_f(A,i,j, -1.0);
{ /* store data */
/* vsip_mput_f(A,0,0,1); vsip_mput_f(A,0,1,2); vsip_mput_f(A,0,2,1); */
/* vsip_mput_f(A,1,0,3); vsip_mput_f(A,1,1,-1); vsip_mput_f(A,1,2,0); */
/* vsip_mput_f(A,2,0,2); vsip_mput_f(A,2,1,1); vsip_mput_f(A,2,2,-1); */
/* vsip_mput_f(A,3,0,1); vsip_mput_f(A,3,1,2); vsip_mput_f(A,3,2,2); */
/* vsip_mput_f(X,0,0,1); */
/* vsip_mput_f(X,1,0,2); */
/* vsip_mput_f(X,2,0,2); */
/* vsip_mput_f(X,3,0,1); */
}
{int i,j;
printf("matrix\n A = [\n");
for(i=0; i<M; i++)
{
for(j=0; j< N; j++)
printf("%9.2f%s",vsip_mget_f(A,i,j),(j == N-1) ? "":",");
(i==M-1) ? printf(";]\n") : printf(";\n") ;
}
}
{ int j, k;
vsip_vview_f *y = NULL;
vsip_vview_f *x;
vsip_length L = NB;
vsip_length p = M;
for(k=0; k<L; k++)
{
x = vsip_mcolview_f(X,k);
for (j=0; j<p; j++)
{
y = vsip_mrowview_f(A,j);
vsip_vput_f(x,j,(double)(k+1)*(vsip_vsumval_f(y)));
/* vsip_vput_f(x,j,(vsip_vsumval_f(y)));*/
vsip_vdestroy_f(y);
}
vsip_vdestroy_f(x);
}
}
{int i,j;
printf("rhs matrix\n B = [\n");
for(i=0; i<NN; i++)
{
for(j=0; j<NB; j++)
printf("%9.2f%s",vsip_mget_f(X,i,j),(j == NB-1) ? "":",");
(i==NN-1) ? printf(";]\n") : printf(";\n") ;
}
}
{vsip_qr_f* qrAop = vsip_qrd_create_f(M,N, QOPT);
if(qrAop == NULL) exit(1);
{int i,j;
if(QOPT == VSIP_QRD_SAVEQ1)
{
printf("qrd returns %i\n",vsip_qrd_f(qrAop,A));
printf("matrix A after factorisation: skinny Q explicitly\n Q1 = [\n");
for(i= 0; i< M ; i++)
{
for(j=0; j< N; j++)
printf("%8.4f %s",vsip_mget_f(A,i,j),(j == N-1) ? "":",");
(i == M - 1) ? printf("]\n") : printf(";\n");
}
} else if(QOPT == VSIP_QRD_SAVEQ || QOPT == VSIP_QRD_NOSAVEQ)
{
printf("qrd returns %i\n",vsip_qrd_f(qrAop,A));
printf("matrix A after fact.: R and ");
(QOPT == VSIP_QRD_SAVEQ) ? printf("full Q implicitly\n Q/R = [\n") :
printf("Q not saved -- ignore LT portion. \n R = [\n");
for(i= 0; i<M ; i++)
{
for(j=0; j< N; j++)
printf("%9.5f %s",vsip_mget_f(A,i,j),(j == N-1) ? "":",");
(i == M - 1) ? printf("]\n") : printf(";\n");
}
}
}
if( QPROB == VSIP_LLS)
{
if (QOPT == VSIP_QRD_SAVEQ1 || QOPT == VSIP_QRD_SAVEQ)
{
if((solretval=vsip_qrsol_f(qrAop, QPROB, X)))
{
printf("Warning -- Least Squares soln returns %i -- Check\n",
solretval);
printf("Upper triang. mat. R, possibly singular\n");
}
else
printf("Least Squares soln returns %i\n", solretval);
}
else
{
printf("Least Squares systems cannot be solved by the NOSAVEQ option --exiting\n");
exit(1);
}
}
else
{
if((solretval=vsip_qrsol_f(qrAop,QPROB, X)))
{
printf("Warning -- Covariance soln returns %i -- Check\n",solretval);
printf("Upper triang. mat. R, possibly singular\n");
}
else
printf("Covariance soln returns %i\n",solretval);
}
vsip_qrd_destroy_f(qrAop);
}
{int i,j;
printf("Soln Matrix\n");
for(i=0; i<N; i++)
{
for(j=0; j<NB; j++)
printf("%9.5f%s",vsip_mget_f(X,i,j),(j == NB-1) ? "":",");
printf(";\n");
}
}
vsip_malldestroy_f(X);
vsip_malldestroy_f(A);
} vsip_finalize((void*)0); return 1;
}
int main() {
vsip_init((void*)0);
{
int i,j;
vsip_mview_f *A = vsip_mcreate_f(M,N,VSIP_COL,0);
vsip_mview_f *X = vsip_mcreate_f(
(NN>= M)?NN:M,
(NB>=M)?NB:M,
VSIP_ROW,0);
/* put the appropriate row, col lengths of X */
X = vsip_mputcollength_f(X,NN);
X = vsip_mputrowlength_f(X,NB);
/* Initialise matrix A */
for (i=0; i<M; i++)
for (j = 0; j < N; j++)
if(i == j)
vsip_mput_f(A,i,j, (double)(M+1));
else
vsip_mput_f(A,i,j, -1.0);
{ int i,j;
printf("matrix\n A = [\n");
for(i=0; i<M; i++)
{
for(j=0; j< N; j++)
printf("%9.2f%s",vsip_mget_f(A,i,j),(j == N-1) ? "":",");
(i == M-1)? printf("]\n") : printf(";\n");
}
}
{ int j, k;
vsip_vview_f *y = NULL;
vsip_vview_f *x;
vsip_length L = NB;
for(k=0; k<L; k++)
{
x = vsip_mcolview_f(X,k);
for (j=0; j<vsip_vgetlength_f(x); j++)
{
y = vsip_mrowview_f(A,j);
vsip_vput_f(x,j,(double)(k+1)*(vsip_vsumval_f(y)));
vsip_vdestroy_f(y);
}
vsip_vdestroy_f(x);
}
}
{ int i,j;
printf("rhs matrix\n C = [\n");
for(i=0; i<NN; i++)
{
for(j=0; j<NB; j++)
printf("%9.2f%s",vsip_mget_f(X,i,j),(j == NB-1) ? "":",");
(i == NN - 1) ? printf("]\n") : printf(";\n");
}
}
{ vsip_qr_f* qrAop = vsip_qrd_create_f(M,N, QOPT);
if(qrAop == NULL) exit(1);
{ int i,j;
if(QOPT == VSIP_QRD_SAVEQ1)
{
printf("qrd returns %i\n",vsip_qrd_f(qrAop,A));
printf("matrix A after factorisation: skinny Q explicitly\n Q1 = [\n");
for(i= 0; i< M ; i++)
{
for(j=0; j< N; j++)
printf("%9.5f%s",vsip_mget_f(A,i,j),(j == N-1) ? "":",");
(i == M - 1) ? printf("]\n") : printf(";\n");
}
} else if(QOPT == VSIP_QRD_SAVEQ)
{
printf("qrd returns %i\n",vsip_qrd_f(qrAop,A));
printf("matrix A after factorisation: R + full Q implicitly\n Q/R = [\n");
for(i= 0; i<M ; i++)
{
for(j=0; j< N; j++)
printf("%9.2f%s",vsip_mget_f(A,i,j),(j == N-1) ? "":",");
(i == M-1)? printf("]\n") : printf(";\n");
}
} else if(QOPT == VSIP_QRD_NOSAVEQ)
{
printf("Q is not saved with this option. \n");
printf("Product with Q is invalid, exiting\n");
vsip_qrd_destroy_f(qrAop);
vsip_malldestroy_f(X);
vsip_malldestroy_f(A);
exit(1);
}
if (opQ == VSIP_MAT_TRANS || opQ == VSIP_MAT_HERM)
{
if(apQ == VSIP_MAT_RSIDE) /* C * Q^t */
{
printf(" This is a product of type C <- C * Q^t \n");
if(vsip_qrdprodq_f(qrAop,opQ,apQ,X))
{
printf("Size not conformal or invalid operation by Q: -- exiting\n");
vsip_qrd_destroy_f(qrAop);
vsip_malldestroy_f(X);
vsip_malldestroy_f(A);
exit(1);
}
else
{
X = vsip_mputrowlength_f(X,M);
}
}
else if(apQ == VSIP_MAT_LSIDE) /* Q^t * C */
{
if(QOPT == 1)
printf(" This is a product of type C <- Q^t * C \n");
if(QOPT == 2)
printf(" This is a product of type C <- Q_1^t * C \n");
if(vsip_qrdprodq_f(qrAop,opQ,apQ,X))
{
printf("Size not conformal or invalid operation by Q: -- exiting\n");
vsip_qrd_destroy_f(qrAop);
vsip_malldestroy_f(X);
vsip_malldestroy_f(A);
exit(1);
}
else
{
if(QOPT == 2)
X = vsip_mputcollength_f(X,N);
}
}
}
else if (opQ == VSIP_MAT_NTRANS)
{
if(apQ == VSIP_MAT_RSIDE) /* C * Q */
{
printf(" This is a product of type C <- C * Q \n");
if(vsip_qrdprodq_f(qrAop,opQ,apQ,X))
{
printf("Size not conformal or invalid operation by Q: -- exiting\n");
vsip_qrd_destroy_f(qrAop);
vsip_malldestroy_f(X);
vsip_malldestroy_f(A);
exit(1);
}
else
{
X = vsip_mputrowlength_f(X,N);
}
}
else if(apQ == VSIP_MAT_LSIDE) /* Q * C */
{
if(QOPT == 1)
printf(" This is a product of type C <- Q * C \n");
if(QOPT == 2)
printf(" This is a product of type C <- Q_1 * C \n");
if(vsip_qrdprodq_f(qrAop,opQ,apQ,X))
{
printf("Size not conformal or invalid operation by Q: -- exiting\n");
vsip_qrd_destroy_f(qrAop);
vsip_malldestroy_f(X);
vsip_malldestroy_f(A);
exit(1);
}
else
{
X = vsip_mputcollength_f(X,M);
}
}
}
}
vsip_qrd_destroy_f(qrAop);
}
{ int i,j;
printf("Soln Matrix\n C = [\n");
for(i=0; i< vsip_mgetcollength_f(X); i++)
{
for(j=0; j< vsip_mgetrowlength_f(X); j++)
printf("%8.4f%s",vsip_mget_f(X,i,j),
(j == vsip_mgetrowlength_f(X)-1) ? "":",");
(i == vsip_mgetcollength_f(X)-1) ?
printf("]\n") : printf(";\n");
}
}
vsip_malldestroy_f(X);
vsip_malldestroy_f(A);
}
vsip_finalize((void*)0);
return 1;
}
static void svdStep_f(svdObj_f *svd)
{
vsip_vview_f *d = svd->ds;
vsip_vview_f *f = svd->fs;
givensObj_f g;
vsip_length n = vsip_vgetlength_f(d);
vsip_scalar_f mu=0.0, x1=0.0, x2=0.0;
vsip_scalar_f t=0.0;
vsip_index i,j,k;
vsip_scalar_f d2,f1,d3,f2;
if(n >= 3){
d2=vsip_vget_f(d,n-2);f1= vsip_vget_f(f,n-3);d3 = vsip_vget_f(d,n-1);f2= vsip_vget_f(f,n-2);
} else if(n == 2){
d2=vsip_vget_f(d,0);f1= 0.0;d3 = vsip_vget_f(d,1);f2= vsip_vget_f(f,0);
} else {
d2=vsip_vget_f(d,0);f1 = 0.0;d3 = 0.0;f2 = 0.0;
}
mu = svdMu_f(d2,f1,d3,f2);
x1=vsip_vget_f(d,0);
x2 = x1 * vsip_vget_f(f,0);
x1 *= x1; x1 -= mu;
g=givensCoef_f(x1,x2);
x1=vsip_vget_f(d,0);x2=vsip_vget_f(f,0);
vsip_vput_f(f,0,g.c * x2 - g.s * x1);
vsip_vput_f(d,0,x1 * g.c + x2 * g.s);
t=vsip_vget_f(d,1); vsip_vput_f(d,1,t*g.c);
t*=g.s;
gtProd_f(0,1,g.c,g.s,svd);
for(i=0; i<n-2; i++){
j=i+1; k=i+2;
g = givensCoef_f(vsip_vget_f(d,i),t);
vsip_vput_f(d,i,g.r);
x1=vsip_vget_f(d,j)*g.c;
x2=vsip_vget_f(f,i)*g.s;
t= x1 - x2;
x1=vsip_vget_f(f,i) * g.c;
x2=vsip_vget_f(d,j) * g.s ;
vsip_vput_f(f,i,x1+x2);
vsip_vput_f(d,j,t);
x1=vsip_vget_f(f,j);
t=g.s * x1;
vsip_vput_f(f,j, x1*g.c);
prodG_f(svd,i, j, g.c, g.s);
g=givensCoef_f(vsip_vget_f(f,i),t);
vsip_vput_f(f,i,g.r);
x1=vsip_vget_f(d,j); x2=vsip_vget_f(f,j);
vsip_vput_f(d,j,g.c * x1 + g.s * x2); vsip_vput_f(f,j,g.c * x2 - g.s * x1);
x1=vsip_vget_f(d,k);
t=g.s * x1; vsip_vput_f(d,k,x1*g.c);
gtProd_f(j,k, g.c, g.s,svd);
}
i=n-2; j=n-1;
g = givensCoef_f(vsip_vget_f(d,i),t);
vsip_vput_f(d,i,g.r);
x1=vsip_vget_f(d,j)*g.c; x2=vsip_vget_f(f,i)*g.s;
t=x1 - x2;
x1 = vsip_vget_f(f,i) * g.c; x2=vsip_vget_f(d,j) * g.s;
vsip_vput_f(f,i,x1+x2);
vsip_vput_f(d,j,t);
prodG_f(svd,i, j, g.c, g.s);
}
static void zeroCol_f(svdObj_f *svd)
{
vsip_vview_f *d=svd->ds;
vsip_vview_f *f=svd->fs;
vsip_length n = vsip_vgetlength_f(f);
givensObj_f g;
vsip_scalar_f xd,xf,t;
vsip_index i,j,k;
if (n == 1){
xd=vsip_vget_f(d,0);
xf=vsip_vget_f(f,0);
g=givensCoef_f(xd,xf);
vsip_vput_f(d,0,g.r);
vsip_vput_f(f,0,0.0);
gtProd_f(0,1,g.c,g.s,svd);
}else if (n == 2){
xd=vsip_vget_f(d,1);
xf=vsip_vget_f(f,1);
g=givensCoef_f(xd,xf);
vsip_vput_f(d,1,g.r);
vsip_vput_f(f,1,0.0);
xf=vsip_vget_f(f,0);
t= -xf * g.s; xf *= g.c;
vsip_vput_f(f,0,xf);
gtProd_f(1,2,g.c,g.s,svd);
xd=vsip_vget_f(d,0);
g=givensCoef_f(xd,t);
vsip_vput_f(d,0,g.r);
gtProd_f(0,2,g.c,g.s,svd);
}else{
i=n-1; j=i-1; k=i;
xd=vsip_vget_f(d,i);
xf=vsip_vget_f(f,i);
g=givensCoef_f(xd,xf);
xf=vsip_vget_f(f,j);
vsip_vput_f(f,i,0.0);
vsip_vput_f(d,i,g.r);
t=-xf*g.s; xf*=g.c;
vsip_vput_f(f,j,xf);
gtProd_f(i,k+1,g.c,g.s,svd);
while (i > 1){
i = j; j = i-1;
xd=vsip_vget_f(d,i);
g=givensCoef_f(xd,t);
vsip_vput_f(d,i,g.r);
xf=vsip_vget_f(f,j);
t= -xf * g.s; xf *= g.c;
vsip_vput_f(f,j,xf);
gtProd_f(i,k+1,g.c,g.s,svd);
}
xd=vsip_vget_f(d,0);
g=givensCoef_f(xd,t);
vsip_vput_f(d,0,g.r);
gtProd_f(0,k+1,g.c,g.s,svd);
}
}