268 lines
7.2 KiB
C
268 lines
7.2 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__3 = 3;
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static integer c__2 = 2;
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/* Subroutine */ int dorglq_(integer *m, integer *n, integer *k, doublereal *
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a, integer *lda, doublereal *tau, doublereal *work, integer *lwork,
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integer *info)
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{
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/* System generated locals */
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integer a_dim1, a_offset, i__1, i__2, i__3;
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/* Local variables */
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integer i__, j, l, ib, nb, ki, kk, nx, iws, nbmin, iinfo;
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extern /* Subroutine */ int dorgl2_(integer *, integer *, integer *,
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doublereal *, integer *, doublereal *, doublereal *, integer *),
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dlarfb_(char *, char *, char *, char *, integer *, integer *,
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integer *, doublereal *, integer *, doublereal *, integer *,
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doublereal *, integer *, doublereal *, integer *), dlarft_(char *, char *, integer *, integer *,
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doublereal *, 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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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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/* DORGLQ generates an M-by-N real matrix Q with orthonormal rows, */
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/* which is defined as the first M rows of a product of K elementary */
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/* reflectors of order N */
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/* Q = H(k) . . . H(2) H(1) */
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/* as returned by DGELQF. */
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/* Arguments */
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/* ========= */
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/* M (input) INTEGER */
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/* The number of rows of the matrix Q. M >= 0. */
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/* N (input) INTEGER */
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/* The number of columns of the matrix Q. N >= M. */
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/* K (input) INTEGER */
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/* The number of elementary reflectors whose product defines the */
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/* matrix Q. M >= K >= 0. */
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/* A (input/output) DOUBLE PRECISION array, dimension (LDA,N) */
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/* On entry, the i-th row must contain the vector which defines */
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/* the elementary reflector H(i), for i = 1,2,...,k, as returned */
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/* by DGELQF in the first k rows of its array argument A. */
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/* On exit, the M-by-N matrix Q. */
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/* LDA (input) INTEGER */
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/* The first dimension of the array A. LDA >= max(1,M). */
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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 DGELQF. */
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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. LWORK >= max(1,M). */
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/* For optimum performance LWORK >= M*NB, where NB is */
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/* the optimal 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 has 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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/* .. External Subroutines .. */
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/* .. */
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/* .. Intrinsic Functions .. */
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/* .. */
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/* .. External 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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--work;
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/* Function Body */
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*info = 0;
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nb = ilaenv_(&c__1, "DORGLQ", " ", m, n, k, &c_n1);
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lwkopt = max(1,*m) * nb;
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work[1] = (doublereal) lwkopt;
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lquery = *lwork == -1;
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if (*m < 0) {
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*info = -1;
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} else if (*n < *m) {
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*info = -2;
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} else if (*k < 0 || *k > *m) {
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*info = -3;
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} else if (*lda < max(1,*m)) {
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*info = -5;
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} else if (*lwork < max(1,*m) && ! lquery) {
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*info = -8;
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}
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if (*info != 0) {
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i__1 = -(*info);
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xerbla_("DORGLQ", &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) {
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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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nx = 0;
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iws = *m;
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if (nb > 1 && nb < *k) {
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/* Determine when to cross over from blocked to unblocked code. */
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/* Computing MAX */
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i__1 = 0, i__2 = ilaenv_(&c__3, "DORGLQ", " ", m, n, k, &c_n1);
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nx = max(i__1,i__2);
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if (nx < *k) {
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/* Determine if workspace is large enough for blocked code. */
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ldwork = *m;
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iws = ldwork * nb;
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if (*lwork < iws) {
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/* Not enough workspace to use optimal NB: reduce NB and */
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/* determine the minimum value of NB. */
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nb = *lwork / ldwork;
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/* Computing MAX */
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i__1 = 2, i__2 = ilaenv_(&c__2, "DORGLQ", " ", m, n, k, &c_n1);
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nbmin = max(i__1,i__2);
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}
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}
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}
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if (nb >= nbmin && nb < *k && nx < *k) {
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/* Use blocked code after the last block. */
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/* The first kk rows are handled by the block method. */
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ki = (*k - nx - 1) / nb * nb;
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/* Computing MIN */
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i__1 = *k, i__2 = ki + nb;
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kk = min(i__1,i__2);
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/* Set A(kk+1:m,1:kk) to zero. */
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i__1 = kk;
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for (j = 1; j <= i__1; ++j) {
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i__2 = *m;
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for (i__ = kk + 1; i__ <= i__2; ++i__) {
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a[i__ + j * a_dim1] = 0.;
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/* L10: */
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}
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/* L20: */
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}
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} else {
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kk = 0;
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}
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/* Use unblocked code for the last or only block. */
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if (kk < *m) {
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i__1 = *m - kk;
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i__2 = *n - kk;
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i__3 = *k - kk;
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dorgl2_(&i__1, &i__2, &i__3, &a[kk + 1 + (kk + 1) * a_dim1], lda, &
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tau[kk + 1], &work[1], &iinfo);
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}
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if (kk > 0) {
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/* Use blocked code */
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i__1 = -nb;
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for (i__ = ki + 1; i__1 < 0 ? i__ >= 1 : i__ <= 1; i__ += i__1) {
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/* Computing MIN */
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i__2 = nb, i__3 = *k - i__ + 1;
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ib = min(i__2,i__3);
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if (i__ + ib <= *m) {
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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__2 = *n - i__ + 1;
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dlarft_("Forward", "Rowwise", &i__2, &ib, &a[i__ + i__ *
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a_dim1], lda, &tau[i__], &work[1], &ldwork);
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/* Apply H' to A(i+ib:m,i:n) from the right */
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i__2 = *m - i__ - ib + 1;
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i__3 = *n - i__ + 1;
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dlarfb_("Right", "Transpose", "Forward", "Rowwise", &i__2, &
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i__3, &ib, &a[i__ + i__ * a_dim1], lda, &work[1], &
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ldwork, &a[i__ + ib + i__ * a_dim1], lda, &work[ib +
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1], &ldwork);
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}
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/* Apply H' to columns i:n of current block */
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i__2 = *n - i__ + 1;
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dorgl2_(&ib, &i__2, &ib, &a[i__ + i__ * a_dim1], lda, &tau[i__], &
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work[1], &iinfo);
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/* Set columns 1:i-1 of current block to zero */
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i__2 = i__ - 1;
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for (j = 1; j <= i__2; ++j) {
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i__3 = i__ + ib - 1;
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for (l = i__; l <= i__3; ++l) {
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a[l + j * a_dim1] = 0.;
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/* L30: */
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}
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/* L40: */
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}
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/* L50: */
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}
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}
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work[1] = (doublereal) iws;
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return 0;
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/* End of DORGLQ */
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} /* dorglq_ */
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