/* cggqrf.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 integer c__1 = 1;
static integer c_n1 = -1;
/* Subroutine */ int cggqrf_(integer *n, integer *m, integer *p, complex *a,
integer *lda, complex *taua, complex *b, integer *ldb, complex *taub,
complex *work, integer *lwork, integer *info)
{
/* System generated locals */
integer a_dim1, a_offset, b_dim1, b_offset, i__1, i__2, i__3;
/* Local variables */
integer nb, nb1, nb2, nb3, lopt;
extern /* Subroutine */ int cgeqrf_(integer *, integer *, complex *,
integer *, complex *, complex *, integer *, integer *), cgerqf_(
integer *, integer *, complex *, integer *, complex *, complex *,
integer *, integer *), xerbla_(char *, integer *);
extern integer ilaenv_(integer *, char *, char *, integer *, integer *,
integer *, integer *);
extern /* Subroutine */ int cunmqr_(char *, char *, integer *, integer *,
integer *, complex *, integer *, complex *, complex *, integer *,
complex *, integer *, integer *);
integer lwkopt;
logical lquery;
/* -- LAPACK routine (version 3.2) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* CGGQRF computes a generalized QR factorization of an N-by-M matrix A */
/* and an N-by-P matrix B: */
/* A = Q*R, B = Q*T*Z, */
/* where Q is an N-by-N unitary matrix, Z is a P-by-P unitary matrix, */
/* and R and T assume one of the forms: */
/* if N >= M, R = ( R11 ) M , or if N < M, R = ( R11 R12 ) N, */
/* ( 0 ) N-M N M-N */
/* M */
/* where R11 is upper triangular, and */
/* if N <= P, T = ( 0 T12 ) N, or if N > P, T = ( T11 ) N-P, */
/* P-N N ( T21 ) P */
/* P */
/* where T12 or T21 is upper triangular. */
/* In particular, if B is square and nonsingular, the GQR factorization */
/* of A and B implicitly gives the QR factorization of inv(B)*A: */
/* inv(B)*A = Z'*(inv(T)*R) */
/* where inv(B) denotes the inverse of the matrix B, and Z' denotes the */
/* conjugate transpose of matrix Z. */
/* Arguments */
/* ========= */
/* N (input) INTEGER */
/* The number of rows of the matrices A and B. N >= 0. */
/* M (input) INTEGER */
/* The number of columns of the matrix A. M >= 0. */
/* P (input) INTEGER */
/* The number of columns of the matrix B. P >= 0. */
/* A (input/output) COMPLEX array, dimension (LDA,M) */
/* On entry, the N-by-M matrix A. */
/* On exit, the elements on and above the diagonal of the array */
/* contain the min(N,M)-by-M upper trapezoidal matrix R (R is */
/* upper triangular if N >= M); the elements below the diagonal, */
/* with the array TAUA, represent the unitary matrix Q as a */
/* product of min(N,M) elementary reflectors (see Further */
/* Details). */
/* LDA (input) INTEGER */
/* The leading dimension of the array A. LDA >= max(1,N). */
/* TAUA (output) COMPLEX array, dimension (min(N,M)) */
/* The scalar factors of the elementary reflectors which */
/* represent the unitary matrix Q (see Further Details). */
/* B (input/output) COMPLEX array, dimension (LDB,P) */
/* On entry, the N-by-P matrix B. */
/* On exit, if N <= P, the upper triangle of the subarray */
/* B(1:N,P-N+1:P) contains the N-by-N upper triangular matrix T; */
/* if N > P, the elements on and above the (N-P)-th subdiagonal */
/* contain the N-by-P upper trapezoidal matrix T; the remaining */
/* elements, with the array TAUB, represent the unitary */
/* matrix Z as a product of elementary reflectors (see Further */
/* Details). */
/* LDB (input) INTEGER */
/* The leading dimension of the array B. LDB >= max(1,N). */
/* TAUB (output) COMPLEX array, dimension (min(N,P)) */
/* The scalar factors of the elementary reflectors which */
/* represent the unitary matrix Z (see Further Details). */
/* WORK (workspace/output) COMPLEX array, dimension (MAX(1,LWORK)) */
/* On exit, if INFO = 0, WORK(1) returns the optimal LWORK. */
/* LWORK (input) INTEGER */
/* The dimension of the array WORK. LWORK >= max(1,N,M,P). */
/* For optimum performance LWORK >= max(N,M,P)*max(NB1,NB2,NB3), */
/* where NB1 is the optimal blocksize for the QR factorization */
/* of an N-by-M matrix, NB2 is the optimal blocksize for the */
/* RQ factorization of an N-by-P matrix, and NB3 is the optimal */
/* blocksize for a call of CUNMQR. */
/* If LWORK = -1, then a workspace query is assumed; the routine */
/* only calculates the optimal size of the WORK array, returns */
/* this value as the first entry of the WORK array, and no error */
/* message related to LWORK is issued by XERBLA. */
/* INFO (output) INTEGER */
/* = 0: successful exit */
/* < 0: if INFO = -i, the i-th argument had an illegal value. */
/* Further Details */
/* =============== */
/* The matrix Q is represented as a product of elementary reflectors */
/* Q = H(1) H(2) . . . H(k), where k = min(n,m). */
/* Each H(i) has the form */
/* H(i) = I - taua * v * v' */
/* where taua is a complex scalar, and v is a complex vector with */
/* v(1:i-1) = 0 and v(i) = 1; v(i+1:n) is stored on exit in A(i+1:n,i), */
/* and taua in TAUA(i). */
/* To form Q explicitly, use LAPACK subroutine CUNGQR. */
/* To use Q to update another matrix, use LAPACK subroutine CUNMQR. */
/* The matrix Z is represented as a product of elementary reflectors */
/* Z = H(1) H(2) . . . H(k), where k = min(n,p). */
/* Each H(i) has the form */
/* H(i) = I - taub * v * v' */
/* where taub is a complex scalar, and v is a complex vector with */
/* v(p-k+i+1:p) = 0 and v(p-k+i) = 1; v(1:p-k+i-1) is stored on exit in */
/* B(n-k+i,1:p-k+i-1), and taub in TAUB(i). */
/* To form Z explicitly, use LAPACK subroutine CUNGRQ. */
/* To use Z to update another matrix, use LAPACK subroutine CUNMRQ. */
/* ===================================================================== */
/* .. Local Scalars .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. Executable Statements .. */
/* Test the input parameters */
/* Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1;
a -= a_offset;
--taua;
b_dim1 = *ldb;
b_offset = 1 + b_dim1;
b -= b_offset;
--taub;
--work;
/* Function Body */
*info = 0;
nb1 = ilaenv_(&c__1, "CGEQRF", " ", n, m, &c_n1, &c_n1);
nb2 = ilaenv_(&c__1, "CGERQF", " ", n, p, &c_n1, &c_n1);
nb3 = ilaenv_(&c__1, "CUNMQR", " ", n, m, p, &c_n1);
/* Computing MAX */
i__1 = max(nb1,nb2);
nb = max(i__1,nb3);
/* Computing MAX */
i__1 = max(*n,*m);
lwkopt = max(i__1,*p) * nb;
work[1].r = (real) lwkopt, work[1].i = 0.f;
lquery = *lwork == -1;
if (*n < 0) {
*info = -1;
} else if (*m < 0) {
*info = -2;
} else if (*p < 0) {
*info = -3;
} else if (*lda < max(1,*n)) {
*info = -5;
} else if (*ldb < max(1,*n)) {
*info = -8;
} else /* if(complicated condition) */ {
/* Computing MAX */
i__1 = max(1,*n), i__1 = max(i__1,*m);
if (*lwork < max(i__1,*p) && ! lquery) {
*info = -11;
}
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("CGGQRF", &i__1);
return 0;
} else if (lquery) {
return 0;
}
/* QR factorization of N-by-M matrix A: A = Q*R */
cgeqrf_(n, m, &a[a_offset], lda, &taua[1], &work[1], lwork, info);
lopt = work[1].r;
/* Update B := Q'*B. */
i__1 = min(*n,*m);
cunmqr_("Left", "Conjugate Transpose", n, p, &i__1, &a[a_offset], lda, &
taua[1], &b[b_offset], ldb, &work[1], lwork, info);
/* Computing MAX */
i__1 = lopt, i__2 = (integer) work[1].r;
lopt = max(i__1,i__2);
/* RQ factorization of N-by-P matrix B: B = T*Z. */
cgerqf_(n, p, &b[b_offset], ldb, &taub[1], &work[1], lwork, info);
/* Computing MAX */
i__2 = lopt, i__3 = (integer) work[1].r;
i__1 = max(i__2,i__3);
work[1].r = (real) i__1, work[1].i = 0.f;
return 0;
/* End of CGGQRF */
} /* cggqrf_ */