📄 dggsvp.c
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#include "f2c.h"
#include "netlib.h"
/* Table of constant values */
static doublereal c_b12 = 0.;
static doublereal c_b22 = 1.;
/* Subroutine */ void dggsvp_(char *jobu, char *jobv, char *jobq, integer *m,
integer *p, integer *n, doublereal *a, integer *lda, doublereal *b, integer *ldb,
doublereal *tola, doublereal *tolb, integer *k, integer *l, doublereal *u, integer *ldu,
doublereal *v, integer *ldv, doublereal *q, integer *ldq, integer *iwork, doublereal *tau,
doublereal *work, integer *info)
{
/* System generated locals */
integer i__1, i__2;
/* Local variables */
static integer i, j;
static logical wantq, wantu, wantv;
static logical forwrd;
/* -- LAPACK routine (version 2.0) -- */
/* Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd., */
/* Courant Institute, Argonne National Lab, and Rice University */
/* September 30, 1994 */
/* Purpose */
/* ======= */
/* DGGSVP computes orthogonal matrices U, V and Q such that */
/* N-K-L K L */
/* U'*A*Q = K ( 0 A12 A13 ) if M-K-L >= 0; */
/* L ( 0 0 A23 ) */
/* M-K-L ( 0 0 0 ) */
/* N-K-L K L */
/* = K ( 0 A12 A13 ) if M-K-L < 0; */
/* M-K ( 0 0 A23 ) */
/* N-K-L K L */
/* V'*B*Q = L ( 0 0 B13 ) */
/* P-L ( 0 0 0 ) */
/* where the K-by-K matrix A12 and L-by-L matrix B13 are nonsingular */
/* upper triangular; A23 is L-by-L upper triangular if M-K-L >= 0, */
/* otherwise A23 is (M-K)-by-L upper trapezoidal. K+L = the effective */
/* numerical rank of the (M+P)-by-N matrix (A',B')'. Z' denotes the */
/* transpose of Z. */
/* This decomposition is the preprocessing step for computing the */
/* Generalized Singular Value Decomposition (GSVD), see subroutine */
/* DGGSVD. */
/* Arguments */
/* ========= */
/* JOBU (input) CHARACTER*1 */
/* = 'U': Orthogonal matrix U is computed; */
/* = 'N': U is not computed. */
/* JOBV (input) CHARACTER*1 */
/* = 'V': Orthogonal matrix V is computed; */
/* = 'N': V is not computed. */
/* JOBQ (input) CHARACTER*1 */
/* = 'Q': Orthogonal matrix Q is computed; */
/* = 'N': Q is not computed. */
/* M (input) INTEGER */
/* The number of rows of the matrix A. M >= 0. */
/* P (input) INTEGER */
/* The number of rows of the matrix B. P >= 0. */
/* N (input) INTEGER */
/* The number of columns of the matrices A and B. N >= 0. */
/* A (input/output) DOUBLE PRECISION array, dimension (LDA,N) */
/* On entry, the M-by-N matrix A. */
/* On exit, A contains the triangular (or trapezoidal) matrix */
/* described in the Purpose section. */
/* LDA (input) INTEGER */
/* The leading dimension of the array A. LDA >= max(1,M). */
/* B (input/output) DOUBLE PRECISION array, dimension (LDB,N) */
/* On entry, the P-by-N matrix B. */
/* On exit, B contains the triangular matrix described in */
/* the Purpose section. */
/* LDB (input) INTEGER */
/* The leading dimension of the array B. LDB >= max(1,P). */
/* TOLA (input) DOUBLE PRECISION */
/* TOLB (input) DOUBLE PRECISION */
/* TOLA and TOLB are the thresholds to determine the effective */
/* numerical rank of matrix B and a subblock of A. Generally, */
/* they are set to */
/* TOLA = MAX(M,N)*norm(A)*MACHEPS, */
/* TOLB = MAX(P,N)*norm(B)*MACHEPS. */
/* The size of TOLA and TOLB may affect the size of backward */
/* errors of the decomposition. */
/* K (output) INTEGER */
/* L (output) INTEGER */
/* On exit, K and L specify the dimension of the subblocks */
/* described in Purpose. */
/* K + L = effective numerical rank of (A',B')'. */
/* U (output) DOUBLE PRECISION array, dimension (LDU,M) */
/* If JOBU = 'U', U contains the orthogonal matrix U. */
/* If JOBU = 'N', U is not referenced. */
/* LDU (input) INTEGER */
/* The leading dimension of the array U. LDU >= max(1,M) if */
/* JOBU = 'U'; LDU >= 1 otherwise. */
/* V (output) DOUBLE PRECISION array, dimension (LDV,M) */
/* If JOBV = 'V', V contains the orthogonal matrix V. */
/* If JOBV = 'N', V is not referenced. */
/* LDV (input) INTEGER */
/* The leading dimension of the array V. LDV >= max(1,P) if */
/* JOBV = 'V'; LDV >= 1 otherwise. */
/* Q (output) DOUBLE PRECISION array, dimension (LDQ,N) */
/* If JOBQ = 'Q', Q contains the orthogonal matrix Q. */
/* If JOBQ = 'N', Q is not referenced. */
/* LDQ (input) INTEGER */
/* The leading dimension of the array Q. LDQ >= max(1,N) if */
/* JOBQ = 'Q'; LDQ >= 1 otherwise. */
/* IWORK (workspace) INTEGER array, dimension (N) */
/* TAU (workspace) DOUBLE PRECISION array, dimension (N) */
/* WORK (workspace) DOUBLE PRECISION array, dimension (max(3*N,M,P)) */
/* INFO (output) INTEGER */
/* = 0: successful exit */
/* < 0: if INFO = -i, the i-th argument had an illegal value. */
/* Further Details */
/* =============== */
/* The subroutine uses LAPACK subroutine DGEQPF for the QR factorization */
/* with column pivoting to detect the effective numerical rank of the */
/* a matrix. It may be replaced by a better rank determination strategy. */
/* ===================================================================== */
/* Test the input parameters */
wantu = lsame_(jobu, "U");
wantv = lsame_(jobv, "V");
wantq = lsame_(jobq, "Q");
forwrd = TRUE_;
*info = 0;
if (! (wantu || lsame_(jobu, "N"))) {
*info = -1;
} else if (! (wantv || lsame_(jobv, "N"))) {
*info = -2;
} else if (! (wantq || lsame_(jobq, "N"))) {
*info = -3;
} else if (*m < 0) {
*info = -4;
} else if (*p < 0) {
*info = -5;
} else if (*n < 0) {
*info = -6;
} else if (*lda < max(1,*m)) {
*info = -8;
} else if (*ldb < max(1,*p)) {
*info = -10;
} else if (*ldu < 1 || (wantu && *ldu < *m) ) {
*info = -16;
} else if (*ldv < 1 || (wantv && *ldv < *p) ) {
*info = -18;
} else if (*ldq < 1 || (wantq && *ldq < *n) ) {
*info = -20;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("DGGSVP", &i__1);
return;
}
/* QR with column pivoting of B: B*P = V*( S11 S12 ) */
/* ( 0 0 ) */
for (i = 0; i < *n; ++i) {
iwork[i] = 0;
}
dgeqpf_(p, n, b, ldb, iwork, tau, work, info);
/* Update A := A*P */
dlapmt_(&forwrd, m, n, a, lda, iwork);
/* Determine the effective rank of matrix B. */
*l = 0;
for (i = 0; i < *p && i < *n; ++i) {
if (abs(b[i + i * *ldb]) > *tolb) {
++(*l);
}
}
if (wantv) {
/* Copy the details of V, and form V. */
dlaset_("Full", p, p, &c_b12, &c_b12, v, ldv);
if (*p > 1) {
i__1 = *p - 1;
dlacpy_("Lower", &i__1, n, &b[1], ldb, &v[1], ldv);
}
i__1 = min(*p,*n);
dorg2r_(p, p, &i__1, v, ldv, tau, work, info);
}
/* Clean up B */
for (j = 0; j < *l; ++j) {
for (i = j + 1; i < *l; ++i) {
b[i + j * *ldb] = 0.;
}
}
if (*p > *l) {
i__1 = *p - *l;
dlaset_("Full", &i__1, n, &c_b12, &c_b12, &b[*l], ldb);
}
if (wantq) {
/* Set Q = I and Update Q := Q*P */
dlaset_("Full", n, n, &c_b12, &c_b22, q, ldq);
dlapmt_(&forwrd, n, n, q, ldq, iwork);
}
if (*p >= *l && *n != *l) {
/* RQ factorization of (S11 S12): ( S11 S12 ) = ( 0 S12 )*Z */
dgerq2_(l, n, b, ldb, tau, work, info);
/* Update A := A*Z' */
dormr2_("Right", "Transpose", m, n, l, b, ldb, tau, a, lda, work, info);
if (wantq) {
/* Update Q := Q*Z' */
dormr2_("Right", "Transpose", n, n, l, b, ldb, tau, q, ldq, work, info);
}
/* Clean up B */
i__1 = *n - *l;
dlaset_("Full", l, &i__1, &c_b12, &c_b12, b, ldb);
for (j = *n - *l; j < *n; ++j) {
for (i = j - *n + *l + 1; i < *l; ++i) {
b[i + j * *ldb] = 0.;
}
}
}
/* Let N-L L */
/* A = ( A11 A12 ) M, */
/* then the following does the complete QR decomposition of A11: */
/* A11 = U*( 0 T12 )*P1' */
/* ( 0 0 ) */
for (i = 0; i < *n - *l; ++i) {
iwork[i] = 0;
}
i__1 = *n - *l;
dgeqpf_(m, &i__1, a, lda, iwork, tau, work, info);
/* Determine the effective rank of A11 */
*k = 0;
for (i = 0; i < *m && i < *n - *l; ++i) {
if (abs(a[i + i * *lda]) > *tola) {
++(*k);
}
}
/* Update A12 := U'*A12, where A12 = A( 1:M, N-L+1:N ) */
i__1 = min(*m,*n - *l);
dorm2r_("Left", "Transpose", m, l, &i__1, a, lda, tau, &a[(*n - *l) * *lda], lda, work, info);
if (wantu) {
/* Copy the details of U, and form U */
dlaset_("Full", m, m, &c_b12, &c_b12, u, ldu);
if (*m > 1) {
i__1 = *m - 1;
i__2 = *n - *l;
dlacpy_("Lower", &i__1, &i__2, &a[1], lda, &u[1], ldu);
}
i__1 = min(*m,*n - *l);
dorg2r_(m, m, &i__1, u, ldu, tau, work, info);
}
if (wantq) {
/* Update Q( 1:N, 1:N-L ) = Q( 1:N, 1:N-L )*P1 */
i__1 = *n - *l;
dlapmt_(&forwrd, n, &i__1, q, ldq, iwork);
}
/* Clean up A: set the strictly lower triangular part of */
/* A(1:K, 1:K) = 0, and A( K+1:M, 1:N-L ) = 0. */
for (j = 0; j < *k; ++j) {
for (i = j + 1; i < *k; ++i) {
a[i + j * *lda] = 0.;
}
}
if (*m > *k) {
i__1 = *m - *k;
i__2 = *n - *l;
dlaset_("Full", &i__1, &i__2, &c_b12, &c_b12, &a[*k], lda);
}
if (*n - *l > *k) {
/* RQ factorization of ( T11 T12 ) = ( 0 T12 )*Z1 */
i__1 = *n - *l;
dgerq2_(k, &i__1, a, lda, tau, work, info);
if (wantq) {
/* Update Q( 1:N,1:N-L ) = Q( 1:N,1:N-L )*Z1' */
i__1 = *n - *l;
dormr2_("Right", "Transpose", n, &i__1, k, a, lda, tau, q, ldq, work, info);
}
/* Clean up A */
i__1 = *n - *l - *k;
dlaset_("Full", k, &i__1, &c_b12, &c_b12, a, lda);
for (j = *n - *l - *k; j < *n - *l; ++j) {
for (i = j - *n + *l + *k + 1; i < *k; ++i) {
a[i + j * *lda] = 0.;
}
}
}
if (*m > *k) {
/* QR factorization of A( K+1:M,N-L+1:N ) */
i__1 = *m - *k;
dgeqr2_(&i__1, l, &a[*k + (*n - *l) * *lda], lda, tau, work, info);
if (wantu) {
/* Update U(:,K+1:M) := U(:,K+1:M)*U1 */
i__1 = *m - *k;
i__2 = min(i__1,*l);
dorm2r_("Right", "No transpose", m, &i__1, &i__2,
&a[*k + (*n - *l) * *lda], lda, tau,
&u[*k * *ldu], ldu, work, info);
}
/* Clean up */
for (j = *n - *l; j < *n; ++j) {
for (i = j - *n + *k + *l + 1; i < *m; ++i) {
a[i + j * *lda] = 0.;
}
}
}
} /* dggsvp_ */
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