mirror of
https://github.com/opencv/opencv.git
synced 2024-12-20 04:28:02 +08:00
287 lines
8.1 KiB
C
287 lines
8.1 KiB
C
#include "clapack.h"
|
|
|
|
/* Table of constant values */
|
|
|
|
static integer c__1 = 1;
|
|
static integer c_n1 = -1;
|
|
|
|
/* Subroutine */ int dorgbr_(char *vect, integer *m, integer *n, integer *k,
|
|
doublereal *a, integer *lda, doublereal *tau, doublereal *work,
|
|
integer *lwork, integer *info)
|
|
{
|
|
/* System generated locals */
|
|
integer a_dim1, a_offset, i__1, i__2, i__3;
|
|
|
|
/* Local variables */
|
|
integer i__, j, nb, mn;
|
|
extern logical lsame_(char *, char *);
|
|
integer iinfo;
|
|
logical wantq;
|
|
extern /* Subroutine */ int xerbla_(char *, integer *);
|
|
extern integer ilaenv_(integer *, char *, char *, integer *, integer *,
|
|
integer *, integer *);
|
|
extern /* Subroutine */ int dorglq_(integer *, integer *, integer *,
|
|
doublereal *, integer *, doublereal *, doublereal *, integer *,
|
|
integer *), dorgqr_(integer *, integer *, integer *, doublereal *,
|
|
integer *, doublereal *, doublereal *, integer *, integer *);
|
|
integer lwkopt;
|
|
logical lquery;
|
|
|
|
|
|
/* -- LAPACK routine (version 3.1) -- */
|
|
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
|
|
/* November 2006 */
|
|
|
|
/* .. Scalar Arguments .. */
|
|
/* .. */
|
|
/* .. Array Arguments .. */
|
|
/* .. */
|
|
|
|
/* Purpose */
|
|
/* ======= */
|
|
|
|
/* DORGBR generates one of the real orthogonal matrices Q or P**T */
|
|
/* determined by DGEBRD when reducing a real matrix A to bidiagonal */
|
|
/* form: A = Q * B * P**T. Q and P**T are defined as products of */
|
|
/* elementary reflectors H(i) or G(i) respectively. */
|
|
|
|
/* If VECT = 'Q', A is assumed to have been an M-by-K matrix, and Q */
|
|
/* is of order M: */
|
|
/* if m >= k, Q = H(1) H(2) . . . H(k) and DORGBR returns the first n */
|
|
/* columns of Q, where m >= n >= k; */
|
|
/* if m < k, Q = H(1) H(2) . . . H(m-1) and DORGBR returns Q as an */
|
|
/* M-by-M matrix. */
|
|
|
|
/* If VECT = 'P', A is assumed to have been a K-by-N matrix, and P**T */
|
|
/* is of order N: */
|
|
/* if k < n, P**T = G(k) . . . G(2) G(1) and DORGBR returns the first m */
|
|
/* rows of P**T, where n >= m >= k; */
|
|
/* if k >= n, P**T = G(n-1) . . . G(2) G(1) and DORGBR returns P**T as */
|
|
/* an N-by-N matrix. */
|
|
|
|
/* Arguments */
|
|
/* ========= */
|
|
|
|
/* VECT (input) CHARACTER*1 */
|
|
/* Specifies whether the matrix Q or the matrix P**T is */
|
|
/* required, as defined in the transformation applied by DGEBRD: */
|
|
/* = 'Q': generate Q; */
|
|
/* = 'P': generate P**T. */
|
|
|
|
/* M (input) INTEGER */
|
|
/* The number of rows of the matrix Q or P**T to be returned. */
|
|
/* M >= 0. */
|
|
|
|
/* N (input) INTEGER */
|
|
/* The number of columns of the matrix Q or P**T to be returned. */
|
|
/* N >= 0. */
|
|
/* If VECT = 'Q', M >= N >= min(M,K); */
|
|
/* if VECT = 'P', N >= M >= min(N,K). */
|
|
|
|
/* K (input) INTEGER */
|
|
/* If VECT = 'Q', the number of columns in the original M-by-K */
|
|
/* matrix reduced by DGEBRD. */
|
|
/* If VECT = 'P', the number of rows in the original K-by-N */
|
|
/* matrix reduced by DGEBRD. */
|
|
/* K >= 0. */
|
|
|
|
/* A (input/output) DOUBLE PRECISION array, dimension (LDA,N) */
|
|
/* On entry, the vectors which define the elementary reflectors, */
|
|
/* as returned by DGEBRD. */
|
|
/* On exit, the M-by-N matrix Q or P**T. */
|
|
|
|
/* LDA (input) INTEGER */
|
|
/* The leading dimension of the array A. LDA >= max(1,M). */
|
|
|
|
/* TAU (input) DOUBLE PRECISION array, dimension */
|
|
/* (min(M,K)) if VECT = 'Q' */
|
|
/* (min(N,K)) if VECT = 'P' */
|
|
/* TAU(i) must contain the scalar factor of the elementary */
|
|
/* reflector H(i) or G(i), which determines Q or P**T, as */
|
|
/* returned by DGEBRD in its array argument TAUQ or TAUP. */
|
|
|
|
/* WORK (workspace/output) DOUBLE PRECISION 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,min(M,N)). */
|
|
/* For optimum performance LWORK >= min(M,N)*NB, where NB */
|
|
/* is the optimal blocksize. */
|
|
|
|
/* 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 */
|
|
|
|
/* ===================================================================== */
|
|
|
|
/* .. Parameters .. */
|
|
/* .. */
|
|
/* .. Local Scalars .. */
|
|
/* .. */
|
|
/* .. External Functions .. */
|
|
/* .. */
|
|
/* .. External Subroutines .. */
|
|
/* .. */
|
|
/* .. Intrinsic Functions .. */
|
|
/* .. */
|
|
/* .. Executable Statements .. */
|
|
|
|
/* Test the input arguments */
|
|
|
|
/* Parameter adjustments */
|
|
a_dim1 = *lda;
|
|
a_offset = 1 + a_dim1;
|
|
a -= a_offset;
|
|
--tau;
|
|
--work;
|
|
|
|
/* Function Body */
|
|
*info = 0;
|
|
wantq = lsame_(vect, "Q");
|
|
mn = min(*m,*n);
|
|
lquery = *lwork == -1;
|
|
if (! wantq && ! lsame_(vect, "P")) {
|
|
*info = -1;
|
|
} else if (*m < 0) {
|
|
*info = -2;
|
|
} else if (*n < 0 || wantq && (*n > *m || *n < min(*m,*k)) || ! wantq && (
|
|
*m > *n || *m < min(*n,*k))) {
|
|
*info = -3;
|
|
} else if (*k < 0) {
|
|
*info = -4;
|
|
} else if (*lda < max(1,*m)) {
|
|
*info = -6;
|
|
} else if (*lwork < max(1,mn) && ! lquery) {
|
|
*info = -9;
|
|
}
|
|
|
|
if (*info == 0) {
|
|
if (wantq) {
|
|
nb = ilaenv_(&c__1, "DORGQR", " ", m, n, k, &c_n1);
|
|
} else {
|
|
nb = ilaenv_(&c__1, "DORGLQ", " ", m, n, k, &c_n1);
|
|
}
|
|
lwkopt = max(1,mn) * nb;
|
|
work[1] = (doublereal) lwkopt;
|
|
}
|
|
|
|
if (*info != 0) {
|
|
i__1 = -(*info);
|
|
xerbla_("DORGBR", &i__1);
|
|
return 0;
|
|
} else if (lquery) {
|
|
return 0;
|
|
}
|
|
|
|
/* Quick return if possible */
|
|
|
|
if (*m == 0 || *n == 0) {
|
|
work[1] = 1.;
|
|
return 0;
|
|
}
|
|
|
|
if (wantq) {
|
|
|
|
/* Form Q, determined by a call to DGEBRD to reduce an m-by-k */
|
|
/* matrix */
|
|
|
|
if (*m >= *k) {
|
|
|
|
/* If m >= k, assume m >= n >= k */
|
|
|
|
dorgqr_(m, n, k, &a[a_offset], lda, &tau[1], &work[1], lwork, &
|
|
iinfo);
|
|
|
|
} else {
|
|
|
|
/* If m < k, assume m = n */
|
|
|
|
/* Shift the vectors which define the elementary reflectors one */
|
|
/* column to the right, and set the first row and column of Q */
|
|
/* to those of the unit matrix */
|
|
|
|
for (j = *m; j >= 2; --j) {
|
|
a[j * a_dim1 + 1] = 0.;
|
|
i__1 = *m;
|
|
for (i__ = j + 1; i__ <= i__1; ++i__) {
|
|
a[i__ + j * a_dim1] = a[i__ + (j - 1) * a_dim1];
|
|
/* L10: */
|
|
}
|
|
/* L20: */
|
|
}
|
|
a[a_dim1 + 1] = 1.;
|
|
i__1 = *m;
|
|
for (i__ = 2; i__ <= i__1; ++i__) {
|
|
a[i__ + a_dim1] = 0.;
|
|
/* L30: */
|
|
}
|
|
if (*m > 1) {
|
|
|
|
/* Form Q(2:m,2:m) */
|
|
|
|
i__1 = *m - 1;
|
|
i__2 = *m - 1;
|
|
i__3 = *m - 1;
|
|
dorgqr_(&i__1, &i__2, &i__3, &a[(a_dim1 << 1) + 2], lda, &tau[
|
|
1], &work[1], lwork, &iinfo);
|
|
}
|
|
}
|
|
} else {
|
|
|
|
/* Form P', determined by a call to DGEBRD to reduce a k-by-n */
|
|
/* matrix */
|
|
|
|
if (*k < *n) {
|
|
|
|
/* If k < n, assume k <= m <= n */
|
|
|
|
dorglq_(m, n, k, &a[a_offset], lda, &tau[1], &work[1], lwork, &
|
|
iinfo);
|
|
|
|
} else {
|
|
|
|
/* If k >= n, assume m = n */
|
|
|
|
/* Shift the vectors which define the elementary reflectors one */
|
|
/* row downward, and set the first row and column of P' to */
|
|
/* those of the unit matrix */
|
|
|
|
a[a_dim1 + 1] = 1.;
|
|
i__1 = *n;
|
|
for (i__ = 2; i__ <= i__1; ++i__) {
|
|
a[i__ + a_dim1] = 0.;
|
|
/* L40: */
|
|
}
|
|
i__1 = *n;
|
|
for (j = 2; j <= i__1; ++j) {
|
|
for (i__ = j - 1; i__ >= 2; --i__) {
|
|
a[i__ + j * a_dim1] = a[i__ - 1 + j * a_dim1];
|
|
/* L50: */
|
|
}
|
|
a[j * a_dim1 + 1] = 0.;
|
|
/* L60: */
|
|
}
|
|
if (*n > 1) {
|
|
|
|
/* Form P'(2:n,2:n) */
|
|
|
|
i__1 = *n - 1;
|
|
i__2 = *n - 1;
|
|
i__3 = *n - 1;
|
|
dorglq_(&i__1, &i__2, &i__3, &a[(a_dim1 << 1) + 2], lda, &tau[
|
|
1], &work[1], lwork, &iinfo);
|
|
}
|
|
}
|
|
}
|
|
work[1] = (doublereal) lwkopt;
|
|
return 0;
|
|
|
|
/* End of DORGBR */
|
|
|
|
} /* dorgbr_ */
|