/* zggsvp.f -- translated by f2c (version 20061008).
You must link the resulting object file with libf2c:
on Microsoft Windows system, link with libf2c.lib;
on Linux or Unix systems, link with .../path/to/libf2c.a -lm
or, if you install libf2c.a in a standard place, with -lf2c -lm
-- in that order, at the end of the command line, as in
cc *.o -lf2c -lm
Source for libf2c is in /netlib/f2c/libf2c.zip, e.g.,
http://www.netlib.org/f2c/libf2c.zip
*/
#include "f2c.h"
#include "blaswrap.h"
/* Table of constant values */
static doublecomplex c_b1 = {0.,0.};
static doublecomplex c_b2 = {1.,0.};
/* Subroutine */ int zggsvp_(char *jobu, char *jobv, char *jobq, integer *m,
integer *p, integer *n, doublecomplex *a, integer *lda, doublecomplex
*b, integer *ldb, doublereal *tola, doublereal *tolb, integer *k,
integer *l, doublecomplex *u, integer *ldu, doublecomplex *v, integer
*ldv, doublecomplex *q, integer *ldq, integer *iwork, doublereal *
rwork, doublecomplex *tau, doublecomplex *work, integer *info)
{
/* System generated locals */
integer a_dim1, a_offset, b_dim1, b_offset, q_dim1, q_offset, u_dim1,
u_offset, v_dim1, v_offset, i__1, i__2, i__3;
doublereal d__1, d__2;
/* Builtin functions */
double d_imag(doublecomplex *);
/* Local variables */
integer i__, j;
extern logical lsame_(char *, char *);
logical wantq, wantu, wantv;
extern /* Subroutine */ int zgeqr2_(integer *, integer *, doublecomplex *,
integer *, doublecomplex *, doublecomplex *, integer *), zgerq2_(
integer *, integer *, doublecomplex *, integer *, doublecomplex *,
doublecomplex *, integer *), zung2r_(integer *, integer *,
integer *, doublecomplex *, integer *, doublecomplex *,
doublecomplex *, integer *), zunm2r_(char *, char *, integer *,
integer *, integer *, doublecomplex *, integer *, doublecomplex *,
doublecomplex *, integer *, doublecomplex *, integer *), zunmr2_(char *, char *, integer *, integer *, integer *,
doublecomplex *, integer *, doublecomplex *, doublecomplex *,
integer *, doublecomplex *, integer *), xerbla_(
char *, integer *), zgeqpf_(integer *, integer *,
doublecomplex *, integer *, integer *, doublecomplex *,
doublecomplex *, doublereal *, integer *), zlacpy_(char *,
integer *, integer *, doublecomplex *, integer *, doublecomplex *,
integer *);
logical forwrd;
extern /* Subroutine */ int zlaset_(char *, integer *, integer *,
doublecomplex *, doublecomplex *, doublecomplex *, integer *), zlapmt_(logical *, integer *, integer *, doublecomplex *,
integer *, integer *);
/* -- LAPACK routine (version 3.2) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* ZGGSVP computes unitary 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 */
/* conjugate transpose of Z. */
/* This decomposition is the preprocessing step for computing the */
/* Generalized Singular Value Decomposition (GSVD), see subroutine */
/* ZGGSVD. */
/* Arguments */
/* ========= */
/* JOBU (input) CHARACTER*1 */
/* = 'U': Unitary matrix U is computed; */
/* = 'N': U is not computed. */
/* JOBV (input) CHARACTER*1 */
/* = 'V': Unitary matrix V is computed; */
/* = 'N': V is not computed. */
/* JOBQ (input) CHARACTER*1 */
/* = 'Q': Unitary 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) COMPLEX*16 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) COMPLEX*16 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)*MAZHEPS, */
/* TOLB = MAX(P,N)*norm(B)*MAZHEPS. */
/* 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 section. */
/* K + L = effective numerical rank of (A',B')'. */
/* U (output) COMPLEX*16 array, dimension (LDU,M) */
/* If JOBU = 'U', U contains the unitary 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) COMPLEX*16 array, dimension (LDV,P) */
/* If JOBV = 'V', V contains the unitary 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) COMPLEX*16 array, dimension (LDQ,N) */
/* If JOBQ = 'Q', Q contains the unitary 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) */
/* RWORK (workspace) DOUBLE PRECISION array, dimension (2*N) */
/* TAU (workspace) COMPLEX*16 array, dimension (N) */
/* WORK (workspace) COMPLEX*16 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 ZGEQPF 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. */
/* ===================================================================== */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. Statement Functions .. */
/* .. */
/* .. Statement Function definitions .. */
/* .. */
/* .. Executable Statements .. */
/* Test the input parameters */
/* Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1;
a -= a_offset;
b_dim1 = *ldb;
b_offset = 1 + b_dim1;
b -= b_offset;
u_dim1 = *ldu;
u_offset = 1 + u_dim1;
u -= u_offset;
v_dim1 = *ldv;
v_offset = 1 + v_dim1;
v -= v_offset;
q_dim1 = *ldq;
q_offset = 1 + q_dim1;
q -= q_offset;
--iwork;
--rwork;
--tau;
--work;
/* Function Body */
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_("ZGGSVP", &i__1);
return 0;
}
/* QR with column pivoting of B: B*P = V*( S11 S12 ) */
/* ( 0 0 ) */
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
iwork[i__] = 0;
/* L10: */
}
zgeqpf_(p, n, &b[b_offset], ldb, &iwork[1], &tau[1], &work[1], &rwork[1],
info);
/* Update A := A*P */
zlapmt_(&forwrd, m, n, &a[a_offset], lda, &iwork[1]);
/* Determine the effective rank of matrix B. */
*l = 0;
i__1 = min(*p,*n);
for (i__ = 1; i__ <= i__1; ++i__) {
i__2 = i__ + i__ * b_dim1;
if ((d__1 = b[i__2].r, abs(d__1)) + (d__2 = d_imag(&b[i__ + i__ *
b_dim1]), abs(d__2)) > *tolb) {
++(*l);
}
/* L20: */
}
if (wantv) {
/* Copy the details of V, and form V. */
zlaset_("Full", p, p, &c_b1, &c_b1, &v[v_offset], ldv);
if (*p > 1) {
i__1 = *p - 1;
zlacpy_("Lower", &i__1, n, &b[b_dim1 + 2], ldb, &v[v_dim1 + 2],
ldv);
}
i__1 = min(*p,*n);
zung2r_(p, p, &i__1, &v[v_offset], ldv, &tau[1], &work[1], info);
}
/* Clean up B */
i__1 = *l - 1;
for (j = 1; j <= i__1; ++j) {
i__2 = *l;
for (i__ = j + 1; i__ <= i__2; ++i__) {
i__3 = i__ + j * b_dim1;
b[i__3].r = 0., b[i__3].i = 0.;
/* L30: */
}
/* L40: */
}
if (*p > *l) {
i__1 = *p - *l;
zlaset_("Full", &i__1, n, &c_b1, &c_b1, &b[*l + 1 + b_dim1], ldb);
}
if (wantq) {
/* Set Q = I and Update Q := Q*P */
zlaset_("Full", n, n, &c_b1, &c_b2, &q[q_offset], ldq);
zlapmt_(&forwrd, n, n, &q[q_offset], ldq, &iwork[1]);
}
if (*p >= *l && *n != *l) {
/* RQ factorization of ( S11 S12 ) = ( 0 S12 )*Z */
zgerq2_(l, n, &b[b_offset], ldb, &tau[1], &work[1], info);
/* Update A := A*Z' */
zunmr2_("Right", "Conjugate transpose", m, n, l, &b[b_offset], ldb, &
tau[1], &a[a_offset], lda, &work[1], info);
if (wantq) {
/* Update Q := Q*Z' */
zunmr2_("Right", "Conjugate transpose", n, n, l, &b[b_offset],
ldb, &tau[1], &q[q_offset], ldq, &work[1], info);
}
/* Clean up B */
i__1 = *n - *l;
zlaset_("Full", l, &i__1, &c_b1, &c_b1, &b[b_offset], ldb);
i__1 = *n;
for (j = *n - *l + 1; j <= i__1; ++j) {
i__2 = *l;
for (i__ = j - *n + *l + 1; i__ <= i__2; ++i__) {
i__3 = i__ + j * b_dim1;
b[i__3].r = 0., b[i__3].i = 0.;
/* L50: */
}
/* L60: */
}
}
/* 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 ) */
i__1 = *n - *l;
for (i__ = 1; i__ <= i__1; ++i__) {
iwork[i__] = 0;
/* L70: */
}
i__1 = *n - *l;
zgeqpf_(m, &i__1, &a[a_offset], lda, &iwork[1], &tau[1], &work[1], &rwork[
1], info);
/* Determine the effective rank of A11 */
*k = 0;
/* Computing MIN */
i__2 = *m, i__3 = *n - *l;
i__1 = min(i__2,i__3);
for (i__ = 1; i__ <= i__1; ++i__) {
i__2 = i__ + i__ * a_dim1;
if ((d__1 = a[i__2].r, abs(d__1)) + (d__2 = d_imag(&a[i__ + i__ *
a_dim1]), abs(d__2)) > *tola) {
++(*k);
}
/* L80: */
}
/* Update A12 := U'*A12, where A12 = A( 1:M, N-L+1:N ) */
/* Computing MIN */
i__2 = *m, i__3 = *n - *l;
i__1 = min(i__2,i__3);
zunm2r_("Left", "Conjugate transpose", m, l, &i__1, &a[a_offset], lda, &
tau[1], &a[(*n - *l + 1) * a_dim1 + 1], lda, &work[1], info);
if (wantu) {
/* Copy the details of U, and form U */
zlaset_("Full", m, m, &c_b1, &c_b1, &u[u_offset], ldu);
if (*m > 1) {
i__1 = *m - 1;
i__2 = *n - *l;
zlacpy_("Lower", &i__1, &i__2, &a[a_dim1 + 2], lda, &u[u_dim1 + 2]
, ldu);
}
/* Computing MIN */
i__2 = *m, i__3 = *n - *l;
i__1 = min(i__2,i__3);
zung2r_(m, m, &i__1, &u[u_offset], ldu, &tau[1], &work[1], info);
}
if (wantq) {
/* Update Q( 1:N, 1:N-L ) = Q( 1:N, 1:N-L )*P1 */
i__1 = *n - *l;
zlapmt_(&forwrd, n, &i__1, &q[q_offset], ldq, &iwork[1]);
}
/* 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. */
i__1 = *k - 1;
for (j = 1; j <= i__1; ++j) {
i__2 = *k;
for (i__ = j + 1; i__ <= i__2; ++i__) {
i__3 = i__ + j * a_dim1;
a[i__3].r = 0., a[i__3].i = 0.;
/* L90: */
}
/* L100: */
}
if (*m > *k) {
i__1 = *m - *k;
i__2 = *n - *l;
zlaset_("Full", &i__1, &i__2, &c_b1, &c_b1, &a[*k + 1 + a_dim1], lda);
}
if (*n - *l > *k) {
/* RQ factorization of ( T11 T12 ) = ( 0 T12 )*Z1 */
i__1 = *n - *l;
zgerq2_(k, &i__1, &a[a_offset], lda, &tau[1], &work[1], info);
if (wantq) {
/* Update Q( 1:N,1:N-L ) = Q( 1:N,1:N-L )*Z1' */
i__1 = *n - *l;
zunmr2_("Right", "Conjugate transpose", n, &i__1, k, &a[a_offset],
lda, &tau[1], &q[q_offset], ldq, &work[1], info);
}
/* Clean up A */
i__1 = *n - *l - *k;
zlaset_("Full", k, &i__1, &c_b1, &c_b1, &a[a_offset], lda);
i__1 = *n - *l;
for (j = *n - *l - *k + 1; j <= i__1; ++j) {
i__2 = *k;
for (i__ = j - *n + *l + *k + 1; i__ <= i__2; ++i__) {
i__3 = i__ + j * a_dim1;
a[i__3].r = 0., a[i__3].i = 0.;
/* L110: */
}
/* L120: */
}
}
if (*m > *k) {
/* QR factorization of A( K+1:M,N-L+1:N ) */
i__1 = *m - *k;
zgeqr2_(&i__1, l, &a[*k + 1 + (*n - *l + 1) * a_dim1], lda, &tau[1], &
work[1], info);
if (wantu) {
/* Update U(:,K+1:M) := U(:,K+1:M)*U1 */
i__1 = *m - *k;
/* Computing MIN */
i__3 = *m - *k;
i__2 = min(i__3,*l);
zunm2r_("Right", "No transpose", m, &i__1, &i__2, &a[*k + 1 + (*n
- *l + 1) * a_dim1], lda, &tau[1], &u[(*k + 1) * u_dim1 +
1], ldu, &work[1], info);
}
/* Clean up */
i__1 = *n;
for (j = *n - *l + 1; j <= i__1; ++j) {
i__2 = *m;
for (i__ = j - *n + *k + *l + 1; i__ <= i__2; ++i__) {
i__3 = i__ + j * a_dim1;
a[i__3].r = 0., a[i__3].i = 0.;
/* L130: */
}
/* L140: */
}
}
return 0;
/* End of ZGGSVP */
} /* zggsvp_ */