315 lines
8.6 KiB
C
315 lines
8.6 KiB
C
#include "clapack.h"
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/* Table of constant values */
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static integer c__1 = 1;
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static integer c_n1 = -1;
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static integer c__2 = 2;
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static integer c__65 = 65;
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/* Subroutine */ int dormqr_(char *side, char *trans, integer *m, integer *n,
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integer *k, doublereal *a, integer *lda, doublereal *tau, doublereal *
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c__, integer *ldc, doublereal *work, integer *lwork, integer *info)
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{
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/* System generated locals */
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address a__1[2];
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integer a_dim1, a_offset, c_dim1, c_offset, i__1, i__2, i__3[2], i__4,
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i__5;
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char ch__1[2];
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/* Builtin functions */
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/* Subroutine */ int s_cat(char *, char **, integer *, integer *, ftnlen);
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/* Local variables */
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integer i__;
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doublereal t[4160] /* was [65][64] */;
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integer i1, i2, i3, ib, ic, jc, nb, mi, ni, nq, nw, iws;
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logical left;
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extern logical lsame_(char *, char *);
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integer nbmin, iinfo;
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extern /* Subroutine */ int dorm2r_(char *, char *, integer *, integer *,
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integer *, doublereal *, integer *, doublereal *, doublereal *,
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integer *, doublereal *, integer *), dlarfb_(char
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*, char *, char *, char *, integer *, integer *, integer *,
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doublereal *, integer *, doublereal *, integer *, doublereal *,
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integer *, doublereal *, integer *), dlarft_(char *, char *, integer *, integer *, doublereal
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*, integer *, doublereal *, doublereal *, integer *), xerbla_(char *, integer *);
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extern integer ilaenv_(integer *, char *, char *, integer *, integer *,
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integer *, integer *);
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logical notran;
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integer ldwork, lwkopt;
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logical lquery;
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/* -- LAPACK routine (version 3.1) -- */
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/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
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/* November 2006 */
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/* .. Scalar Arguments .. */
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/* .. */
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/* .. Array Arguments .. */
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/* .. */
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/* Purpose */
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/* ======= */
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/* DORMQR overwrites the general real M-by-N matrix C with */
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/* SIDE = 'L' SIDE = 'R' */
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/* TRANS = 'N': Q * C C * Q */
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/* TRANS = 'T': Q**T * C C * Q**T */
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/* where Q is a real orthogonal matrix defined as the product of k */
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/* elementary reflectors */
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/* Q = H(1) H(2) . . . H(k) */
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/* as returned by DGEQRF. Q is of order M if SIDE = 'L' and of order N */
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/* if SIDE = 'R'. */
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/* Arguments */
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/* ========= */
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/* SIDE (input) CHARACTER*1 */
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/* = 'L': apply Q or Q**T from the Left; */
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/* = 'R': apply Q or Q**T from the Right. */
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/* TRANS (input) CHARACTER*1 */
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/* = 'N': No transpose, apply Q; */
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/* = 'T': Transpose, apply Q**T. */
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/* M (input) INTEGER */
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/* The number of rows of the matrix C. M >= 0. */
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/* N (input) INTEGER */
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/* The number of columns of the matrix C. N >= 0. */
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/* K (input) INTEGER */
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/* The number of elementary reflectors whose product defines */
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/* the matrix Q. */
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/* If SIDE = 'L', M >= K >= 0; */
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/* if SIDE = 'R', N >= K >= 0. */
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/* A (input) DOUBLE PRECISION array, dimension (LDA,K) */
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/* The i-th column must contain the vector which defines the */
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/* elementary reflector H(i), for i = 1,2,...,k, as returned by */
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/* DGEQRF in the first k columns of its array argument A. */
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/* A is modified by the routine but restored on exit. */
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/* LDA (input) INTEGER */
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/* The leading dimension of the array A. */
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/* If SIDE = 'L', LDA >= max(1,M); */
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/* if SIDE = 'R', LDA >= max(1,N). */
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/* TAU (input) DOUBLE PRECISION array, dimension (K) */
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/* TAU(i) must contain the scalar factor of the elementary */
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/* reflector H(i), as returned by DGEQRF. */
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/* C (input/output) DOUBLE PRECISION array, dimension (LDC,N) */
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/* On entry, the M-by-N matrix C. */
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/* On exit, C is overwritten by Q*C or Q**T*C or C*Q**T or C*Q. */
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/* LDC (input) INTEGER */
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/* The leading dimension of the array C. LDC >= max(1,M). */
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/* WORK (workspace/output) DOUBLE PRECISION array, dimension (MAX(1,LWORK)) */
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/* On exit, if INFO = 0, WORK(1) returns the optimal LWORK. */
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/* LWORK (input) INTEGER */
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/* The dimension of the array WORK. */
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/* If SIDE = 'L', LWORK >= max(1,N); */
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/* if SIDE = 'R', LWORK >= max(1,M). */
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/* For optimum performance LWORK >= N*NB if SIDE = 'L', and */
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/* LWORK >= M*NB if SIDE = 'R', where NB is the optimal */
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/* blocksize. */
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/* If LWORK = -1, then a workspace query is assumed; the routine */
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/* only calculates the optimal size of the WORK array, returns */
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/* this value as the first entry of the WORK array, and no error */
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/* message related to LWORK is issued by XERBLA. */
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/* INFO (output) INTEGER */
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/* = 0: successful exit */
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/* < 0: if INFO = -i, the i-th argument had an illegal value */
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/* ===================================================================== */
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/* .. Parameters .. */
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/* .. */
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/* .. Local Scalars .. */
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/* .. */
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/* .. Local Arrays .. */
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/* .. */
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/* .. External Functions .. */
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/* .. */
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/* .. External Subroutines .. */
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/* .. */
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/* .. Intrinsic Functions .. */
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/* .. */
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/* .. Executable Statements .. */
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/* Test the input arguments */
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/* Parameter adjustments */
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a_dim1 = *lda;
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a_offset = 1 + a_dim1;
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a -= a_offset;
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--tau;
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c_dim1 = *ldc;
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c_offset = 1 + c_dim1;
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c__ -= c_offset;
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--work;
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/* Function Body */
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*info = 0;
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left = lsame_(side, "L");
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notran = lsame_(trans, "N");
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lquery = *lwork == -1;
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/* NQ is the order of Q and NW is the minimum dimension of WORK */
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if (left) {
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nq = *m;
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nw = *n;
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} else {
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nq = *n;
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nw = *m;
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}
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if (! left && ! lsame_(side, "R")) {
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*info = -1;
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} else if (! notran && ! lsame_(trans, "T")) {
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*info = -2;
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} else if (*m < 0) {
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*info = -3;
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} else if (*n < 0) {
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*info = -4;
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} else if (*k < 0 || *k > nq) {
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*info = -5;
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} else if (*lda < max(1,nq)) {
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*info = -7;
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} else if (*ldc < max(1,*m)) {
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*info = -10;
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} else if (*lwork < max(1,nw) && ! lquery) {
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*info = -12;
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}
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if (*info == 0) {
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/* Determine the block size. NB may be at most NBMAX, where NBMAX */
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/* is used to define the local array T. */
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/* Computing MIN */
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/* Writing concatenation */
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i__3[0] = 1, a__1[0] = side;
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i__3[1] = 1, a__1[1] = trans;
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s_cat(ch__1, a__1, i__3, &c__2, (ftnlen)2);
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i__1 = 64, i__2 = ilaenv_(&c__1, "DORMQR", ch__1, m, n, k, &c_n1);
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nb = min(i__1,i__2);
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lwkopt = max(1,nw) * nb;
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work[1] = (doublereal) lwkopt;
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}
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if (*info != 0) {
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i__1 = -(*info);
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xerbla_("DORMQR", &i__1);
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return 0;
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} else if (lquery) {
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return 0;
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}
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/* Quick return if possible */
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if (*m == 0 || *n == 0 || *k == 0) {
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work[1] = 1.;
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return 0;
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}
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nbmin = 2;
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ldwork = nw;
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if (nb > 1 && nb < *k) {
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iws = nw * nb;
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if (*lwork < iws) {
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nb = *lwork / ldwork;
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/* Computing MAX */
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/* Writing concatenation */
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i__3[0] = 1, a__1[0] = side;
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i__3[1] = 1, a__1[1] = trans;
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s_cat(ch__1, a__1, i__3, &c__2, (ftnlen)2);
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i__1 = 2, i__2 = ilaenv_(&c__2, "DORMQR", ch__1, m, n, k, &c_n1);
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nbmin = max(i__1,i__2);
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}
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} else {
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iws = nw;
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}
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if (nb < nbmin || nb >= *k) {
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/* Use unblocked code */
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dorm2r_(side, trans, m, n, k, &a[a_offset], lda, &tau[1], &c__[
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c_offset], ldc, &work[1], &iinfo);
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} else {
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/* Use blocked code */
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if (left && ! notran || ! left && notran) {
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i1 = 1;
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i2 = *k;
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i3 = nb;
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} else {
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i1 = (*k - 1) / nb * nb + 1;
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i2 = 1;
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i3 = -nb;
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}
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if (left) {
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ni = *n;
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jc = 1;
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} else {
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mi = *m;
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ic = 1;
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}
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i__1 = i2;
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i__2 = i3;
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for (i__ = i1; i__2 < 0 ? i__ >= i__1 : i__ <= i__1; i__ += i__2) {
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/* Computing MIN */
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i__4 = nb, i__5 = *k - i__ + 1;
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ib = min(i__4,i__5);
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/* Form the triangular factor of the block reflector */
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/* H = H(i) H(i+1) . . . H(i+ib-1) */
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i__4 = nq - i__ + 1;
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dlarft_("Forward", "Columnwise", &i__4, &ib, &a[i__ + i__ *
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a_dim1], lda, &tau[i__], t, &c__65)
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;
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if (left) {
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/* H or H' is applied to C(i:m,1:n) */
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mi = *m - i__ + 1;
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ic = i__;
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} else {
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/* H or H' is applied to C(1:m,i:n) */
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ni = *n - i__ + 1;
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jc = i__;
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}
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/* Apply H or H' */
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dlarfb_(side, trans, "Forward", "Columnwise", &mi, &ni, &ib, &a[
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i__ + i__ * a_dim1], lda, t, &c__65, &c__[ic + jc *
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c_dim1], ldc, &work[1], &ldwork);
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/* L10: */
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}
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}
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work[1] = (doublereal) lwkopt;
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return 0;
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/* End of DORMQR */
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} /* dormqr_ */
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