/* nag_dorcsd (f08rac) Example Program.
*
* Copyright 2014 Numerical Algorithms Group.
*
* Mark 24, 2013.
*/
#include <stdio.h>
#include <math.h>
#include <nag.h>
#include <nag_stdlib.h>
#include <nagf08.h>
#include <nagf16.h>
#include <nagx04.h>
int main(void)
{
/* Scalars */
Integer exit_status = 0;
Integer pdx, pdu, pdv, pdx11, pdx12, pdx21, pdx22, pdu1, pdu2, pdv1t;
Integer pdv2t, pdw;
Integer i, j, m, p, q, n11, n12, n21, n22, r;
Integer recombine = 1, reprint = 0;
double alpha, beta;
/* Arrays */
double *theta = 0, *u = 0, *u1 = 0, *u2 = 0, *v = 0, *v1t = 0, *w = 0,
*v2t = 0, *x = 0, *x11 = 0, *x12 = 0, *x21 = 0, *x22 = 0;
/* Nag Types */
Nag_OrderType order;
NagError fail;
#ifdef NAG_COLUMN_MAJOR
#define X(I,J) x[(J-1)*pdx + I-1]
#define U(I,J) u[(J-1)*pdu + I-1]
#define V(I,J) v[(J-1)*pdv + I-1]
#define W(I,J) w[(J-1)*pdw + I-1]
#define X11(I,J) x11[(J-1)*pdx11 + I-1]
#define X12(I,J) x12[(J-1)*pdx12 + I-1]
#define X21(I,J) x21[(J-1)*pdx21 + I-1]
#define X22(I,J) x22[(J-1)*pdx22 + I-1]
order = Nag_ColMajor;
#else
#define X(I,J) x[(I-1)*pdx + J-1]
#define U(I,J) u[(I-1)*pdu + J-1]
#define V(I,J) v[(I-1)*pdv + J-1]
#define W(I,J) w[(I-1)*pdw + J-1]
#define X11(I,J) x11[(I-1)*pdx11 + J-1]
#define X12(I,J) x12[(I-1)*pdx12 + J-1]
#define X21(I,J) x21[(I-1)*pdx21 + J-1]
#define X22(I,J) x22[(I-1)*pdx22 + J-1]
order = Nag_RowMajor;
#endif
INIT_FAIL(fail);
printf("nag_dorcsd (f08rac) Example Program Results\n\n");
fflush(stdout);
/* Skip heading in data file*/
scanf("%*[^\n] ");
scanf("%ld%ld%ld%*[^\n] ", &m, &p, &q);
r = MIN(MIN(p,q),MIN(m-p,m-q));
if (!(x = NAG_ALLOC(m*m, double))||
!(u = NAG_ALLOC(m*m, double))||
!(v = NAG_ALLOC(m*m, double))||
!(w = NAG_ALLOC(m*m, double))||
!(theta = NAG_ALLOC(r, double))||
!(x11 = NAG_ALLOC(p*q, double))||
!(x12 = NAG_ALLOC(p*(m-q), double))||
!(x21 = NAG_ALLOC((m-p)*q, double))||
!(x22 = NAG_ALLOC((m-p)*(m-q), double))||
!(u1 = NAG_ALLOC(p*p, double))||
!(u2 = NAG_ALLOC((m-p)*(m-p), double))||
!(v1t = NAG_ALLOC(q*q, double))||
!(v2t = NAG_ALLOC((m-q)*(m-q), double)))
{
printf("Allocation failure\n");
exit_status = -1;
goto END;
}
pdx = m; pdu = m; pdv = m; pdw = m;
pdu1 = p; pdu2 = m-p; pdv1t = q; pdv2t = m-q;
#ifdef NAG_COLUMN_MAJOR
pdx11 = p; pdx12 = p; pdx21 = m-p; pdx22 = m-p;
#else
pdx11 = q; pdx12 = m-q; pdx21 = q; pdx22 = m-q;
#endif
/* Read and print orthogonal X from data file
* (as, say, generated by a generalized singular value decomposition).
*/
for ( i=1; i<=m; i++)
for (j=1;j<=m; j++)
scanf("%lf", &X(i, j));
/* nag_gen_real_mat_print (x04cac).
*/
nag_gen_real_mat_print(order, Nag_GeneralMatrix, Nag_NonUnitDiag, m, m,
&X(1,1), pdx, " Orthogonal matrix X", 0, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_gen_real_mat_print (x04cac).\n%s\n", fail.message);
exit_status = 1;
goto END;
}
printf("\n");
fflush(stdout);
/* nag_dorcsd (f08rac).
* Compute the complete CS factorization of X:
* X11 is stored in X(1:p, 1:q), X12 is stored in X(1:p, q+1:m)
* X21 is stored in X(p+1:m, 1:q), X22 is stored in X(p+1:m, q+1:m)
* U1 is stored in U(1:p, 1:p), U2 is stored in U(p+1:m, p+1:m)
* V1 is stored in V(1:q, 1:q), V2 is stored in V(q+1:m, q+1:m)
*/
for (j=1;j<=p; j++) {
for (i=1;i<=q; i++) X11(j, i) = X(j, i);
for (i=1;i<=m-q; i++) X12(j, i) = X(j, i + q);
}
for (j=1;j<=m-p; j++) {
for (i=1;i<=q; i++) X21(j, i) = X(j + p, i);
for (i=1;i<=m-q; i++) X22(j, i) = X(j + p, i + q);
}
for ( i=1; i<=m; i++)
for (j=1;j<=m; j++) {
U(i,j) = 0.0;
V(i,j) = 0.0;
}
/* This is how you might pass partitions as sub-matrices */
nag_dorcsd(order, Nag_AllU, Nag_AllU, Nag_AllVT, Nag_AllVT, Nag_UpperMinus,
m, p, q, &X(1,1), pdx, &X(1,q+1), pdx, &X(p+1,1), pdx, &X(p+1,q+1),
pdx, theta, &U(1,1), pdu, &U(p+1,p+1), pdu, &V(1,1), pdv,
&V(q+1,q+1), pdv, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_dorcsd (f08rac).\n%s\n", fail.message);
exit_status = 2;
goto END;
}
/* Print Theta, U1, U2, V1T, V2T
* using matrix printing routine nag_gen_real_mat_print (x04cac).
*/
printf("Components of CS factorization of X:\n");
fflush(stdout);
nag_gen_real_mat_print(Nag_ColMajor, Nag_GeneralMatrix, Nag_NonUnitDiag,
r, 1, theta, r, " Theta", 0, &fail);
printf("\n");
fflush(stdout);
nag_gen_real_mat_print(order, Nag_GeneralMatrix, Nag_NonUnitDiag,
p, p, &U(1,1), pdu, " U1", 0, &fail);
printf("\n");
fflush(stdout);
nag_gen_real_mat_print(order, Nag_GeneralMatrix, Nag_NonUnitDiag,
m-p, m-p, &U(p+1,p+1), pdu, " U2", 0, &fail);
printf("\n");
fflush(stdout);
nag_gen_real_mat_print(order, Nag_GeneralMatrix, Nag_NonUnitDiag,
q, q, &V(1,1), pdv, " V1T", 0, &fail);
printf("\n");
fflush(stdout);
nag_gen_real_mat_print(order, Nag_GeneralMatrix, Nag_NonUnitDiag,
m-q,m-q, &V(q+1,q+1), pdv, " V2T", 0, &fail);
printf("\n");
fflush(stdout);
/* And this is how you might pass partitions as separate matrices. */
nag_dorcsd(order, Nag_AllU, Nag_AllU, Nag_AllVT, Nag_AllVT, Nag_UpperMinus,
m, p, q,
x11, pdx11, x12, pdx12, x21, pdx21, x22, pdx22, theta,
u1, pdu1, u2, pdu2, v1t, pdv1t, v2t, pdv2t, &fail);
if (fail.code != NE_NOERROR) {
printf("Error second from nag_dorcsd (f08rac).\n%s\n", fail.message);
exit_status = 3;
goto END;
}
/* Print Theta, U1, U2, V1T, V2T
* using matrix printing routine nag_gen_real_mat_print (x04cac).
*/
if (reprint != 0) {
printf("Components of CS factorization of X:\n");
fflush(stdout);
nag_gen_real_mat_print(Nag_ColMajor, Nag_GeneralMatrix, Nag_NonUnitDiag,
r, 1, theta, r, " Theta", 0, &fail);
nag_gen_real_mat_print(order, Nag_GeneralMatrix, Nag_NonUnitDiag,
p, p, u1, pdu1, " U1", 0, &fail);
nag_gen_real_mat_print(order, Nag_GeneralMatrix, Nag_NonUnitDiag,
m-p, m-p, u2, pdu2, " U2", 0, &fail);
nag_gen_real_mat_print(order, Nag_GeneralMatrix, Nag_NonUnitDiag,
q, q, v1t, pdv1t, " V1T", 0, &fail);
nag_gen_real_mat_print(order, Nag_GeneralMatrix, Nag_NonUnitDiag,
m-q, m-q, v2t, pdv2t, " V2T", 0, &fail);
}
if ( recombine != 0) {
/* Recombining should return the original matrix.
Assemble Sigma_p into X
*/
for ( i=1; i<=m; i++)
for (j=1;j<=m; j++)
X(i,j) = 0.0;
n11 = MIN(p,q)-r;
n12 = MIN(p,m-q)-r;
n21 = MIN(m-p,q)-r;
n22 = MIN(m-p,m-q)-r;
/* top half */
for (j=1; j<=n11; j++) X(j,j) = 1.0;
for (j=1; j<=r; j++) {
X(j+n11,j+n11) = cos(theta[j-1]);
X(j+n11,j+n11+r+n21+n22) = -sin(theta[j-1]);
}
for (j=1; j<=n12; j++) X(j+n11+r,j+n11+r+n21+n22+r) = -1.0;
/* bottom half */
for (j=1; j<=n22; j++) X(p+j,q+j) = 1.0;
for (j=1; j<=r; j++) {
X(p+n22+j,j+n11) = sin(theta[j-1]);
X(p+n22+j,j+r+n21+n22) = cos(theta[j-1]);
}
for (j=1; j<=n21; j++) X(p+n22+r+j,n11+r+j) = 1.0;
alpha = 1.0;
beta = 0.0;
/* multiply U * Sigma_p into w */
nag_dgemm(order, Nag_NoTrans, Nag_NoTrans, m, m, m, alpha,
&U(1,1), pdu, &X(1,1), pdx, beta, &W(1,1), pdw, &fail);
/* form U * Sigma_p * V^T into u */
nag_dgemm(order, Nag_NoTrans, Nag_NoTrans, m, m, m, alpha,
&W(1,1), pdw, &V(1,1), pdv, beta, &U(1,1), pdu, &fail);
nag_gen_real_mat_print(order, Nag_GeneralMatrix, Nag_NonUnitDiag,
m, m, &U(1,1), pdu, " U * Sigma_p * V^T", 0, &fail);
}
END:
NAG_FREE(x);
NAG_FREE(u);
NAG_FREE(v);
NAG_FREE(w);
NAG_FREE(theta);
NAG_FREE(x11);
NAG_FREE(x12);
NAG_FREE(x21);
NAG_FREE(x22);
NAG_FREE(u1);
NAG_FREE(u2);
NAG_FREE(v1t);
NAG_FREE(v2t);
return exit_status;
}