950 lines
34 KiB
C++
950 lines
34 KiB
C++
/* fortran/zlarfb.f -- translated by f2c (version 20200916).
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You must link the resulting object file with libf2c:
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on Microsoft Windows system, link with libf2c.lib;
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on Linux or Unix systems, link with .../path/to/libf2c.a -lm
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or, if you install libf2c.a in a standard place, with -lf2c -lm
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-- in that order, at the end of the command line, as in
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cc *.o -lf2c -lm
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Source for libf2c is in /netlib/f2c/libf2c.zip, e.g.,
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http://www.netlib.org/f2c/libf2c.zip
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*/
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#ifdef __cplusplus
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extern "C" {
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#endif
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#include "lmp_f2c.h"
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/* Table of constant values */
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static doublecomplex c_b1 = {1.,0.};
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static integer c__1 = 1;
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/* > \brief \b ZLARFB applies a block reflector or its conjugate-transpose to a general rectangular matrix. */
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/* =========== DOCUMENTATION =========== */
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/* Online html documentation available at */
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/* http://www.netlib.org/lapack/explore-html/ */
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/* > \htmlonly */
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/* > Download ZLARFB + dependencies */
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/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zlarfb.
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f"> */
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/* > [TGZ]</a> */
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/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zlarfb.
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f"> */
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/* > [ZIP]</a> */
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/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zlarfb.
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f"> */
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/* > [TXT]</a> */
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/* > \endhtmlonly */
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/* Definition: */
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/* =========== */
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/* SUBROUTINE ZLARFB( SIDE, TRANS, DIRECT, STOREV, M, N, K, V, LDV, */
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/* T, LDT, C, LDC, WORK, LDWORK ) */
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/* .. Scalar Arguments .. */
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/* CHARACTER DIRECT, SIDE, STOREV, TRANS */
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/* INTEGER K, LDC, LDT, LDV, LDWORK, M, N */
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/* .. */
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/* .. Array Arguments .. */
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/* COMPLEX*16 C( LDC, * ), T( LDT, * ), V( LDV, * ), */
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/* $ WORK( LDWORK, * ) */
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/* .. */
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/* > \par Purpose: */
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/* ============= */
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/* > */
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/* > \verbatim */
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/* > */
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/* > ZLARFB applies a complex block reflector H or its transpose H**H to a */
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/* > complex M-by-N matrix C, from either the left or the right. */
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/* > \endverbatim */
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/* Arguments: */
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/* ========== */
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/* > \param[in] SIDE */
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/* > \verbatim */
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/* > SIDE is CHARACTER*1 */
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/* > = 'L': apply H or H**H from the Left */
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/* > = 'R': apply H or H**H from the Right */
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/* > \endverbatim */
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/* > */
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/* > \param[in] TRANS */
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/* > \verbatim */
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/* > TRANS is CHARACTER*1 */
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/* > = 'N': apply H (No transpose) */
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/* > = 'C': apply H**H (Conjugate transpose) */
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/* > \endverbatim */
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/* > */
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/* > \param[in] DIRECT */
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/* > \verbatim */
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/* > DIRECT is CHARACTER*1 */
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/* > Indicates how H is formed from a product of elementary */
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/* > reflectors */
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/* > = 'F': H = H(1) H(2) . . . H(k) (Forward) */
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/* > = 'B': H = H(k) . . . H(2) H(1) (Backward) */
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/* > \endverbatim */
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/* > */
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/* > \param[in] STOREV */
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/* > \verbatim */
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/* > STOREV is CHARACTER*1 */
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/* > Indicates how the vectors which define the elementary */
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/* > reflectors are stored: */
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/* > = 'C': Columnwise */
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/* > = 'R': Rowwise */
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/* > \endverbatim */
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/* > */
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/* > \param[in] M */
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/* > \verbatim */
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/* > M is INTEGER */
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/* > The number of rows of the matrix C. */
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/* > \endverbatim */
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/* > */
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/* > \param[in] N */
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/* > \verbatim */
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/* > N is INTEGER */
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/* > The number of columns of the matrix C. */
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/* > \endverbatim */
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/* > */
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/* > \param[in] K */
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/* > \verbatim */
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/* > K is INTEGER */
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/* > The order of the matrix T (= the number of elementary */
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/* > reflectors whose product defines the block reflector). */
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/* > If SIDE = 'L', M >= K >= 0; */
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/* > if SIDE = 'R', N >= K >= 0. */
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/* > \endverbatim */
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/* > */
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/* > \param[in] V */
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/* > \verbatim */
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/* > V is COMPLEX*16 array, dimension */
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/* > (LDV,K) if STOREV = 'C' */
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/* > (LDV,M) if STOREV = 'R' and SIDE = 'L' */
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/* > (LDV,N) if STOREV = 'R' and SIDE = 'R' */
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/* > See Further Details. */
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/* > \endverbatim */
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/* > */
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/* > \param[in] LDV */
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/* > \verbatim */
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/* > LDV is INTEGER */
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/* > The leading dimension of the array V. */
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/* > If STOREV = 'C' and SIDE = 'L', LDV >= max(1,M); */
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/* > if STOREV = 'C' and SIDE = 'R', LDV >= max(1,N); */
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/* > if STOREV = 'R', LDV >= K. */
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/* > \endverbatim */
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/* > */
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/* > \param[in] T */
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/* > \verbatim */
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/* > T is COMPLEX*16 array, dimension (LDT,K) */
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/* > The triangular K-by-K matrix T in the representation of the */
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/* > block reflector. */
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/* > \endverbatim */
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/* > */
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/* > \param[in] LDT */
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/* > \verbatim */
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/* > LDT is INTEGER */
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/* > The leading dimension of the array T. LDT >= K. */
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/* > \endverbatim */
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/* > */
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/* > \param[in,out] C */
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/* > \verbatim */
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/* > C is COMPLEX*16 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 H*C or H**H*C or C*H or C*H**H. */
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/* > \endverbatim */
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/* > */
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/* > \param[in] LDC */
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/* > \verbatim */
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/* > LDC is INTEGER */
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/* > The leading dimension of the array C. LDC >= max(1,M). */
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/* > \endverbatim */
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/* > */
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/* > \param[out] WORK */
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/* > \verbatim */
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/* > WORK is COMPLEX*16 array, dimension (LDWORK,K) */
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/* > \endverbatim */
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/* > */
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/* > \param[in] LDWORK */
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/* > \verbatim */
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/* > LDWORK is INTEGER */
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/* > The leading dimension of the array WORK. */
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/* > If SIDE = 'L', LDWORK >= max(1,N); */
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/* > if SIDE = 'R', LDWORK >= max(1,M). */
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/* > \endverbatim */
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/* Authors: */
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/* ======== */
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/* > \author Univ. of Tennessee */
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/* > \author Univ. of California Berkeley */
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/* > \author Univ. of Colorado Denver */
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/* > \author NAG Ltd. */
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/* > \ingroup complex16OTHERauxiliary */
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/* > \par Further Details: */
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/* ===================== */
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/* > */
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/* > \verbatim */
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/* > */
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/* > The shape of the matrix V and the storage of the vectors which define */
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/* > the H(i) is best illustrated by the following example with n = 5 and */
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/* > k = 3. The elements equal to 1 are not stored; the corresponding */
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/* > array elements are modified but restored on exit. The rest of the */
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/* > array is not used. */
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/* > */
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/* > DIRECT = 'F' and STOREV = 'C': DIRECT = 'F' and STOREV = 'R': */
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/* > */
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/* > V = ( 1 ) V = ( 1 v1 v1 v1 v1 ) */
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/* > ( v1 1 ) ( 1 v2 v2 v2 ) */
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/* > ( v1 v2 1 ) ( 1 v3 v3 ) */
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/* > ( v1 v2 v3 ) */
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/* > ( v1 v2 v3 ) */
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/* > */
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/* > DIRECT = 'B' and STOREV = 'C': DIRECT = 'B' and STOREV = 'R': */
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/* > */
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/* > V = ( v1 v2 v3 ) V = ( v1 v1 1 ) */
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/* > ( v1 v2 v3 ) ( v2 v2 v2 1 ) */
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/* > ( 1 v2 v3 ) ( v3 v3 v3 v3 1 ) */
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/* > ( 1 v3 ) */
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/* > ( 1 ) */
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/* > \endverbatim */
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/* > */
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/* ===================================================================== */
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/* Subroutine */ int zlarfb_(char *side, char *trans, char *direct, char *
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storev, integer *m, integer *n, integer *k, doublecomplex *v, integer
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*ldv, doublecomplex *t, integer *ldt, doublecomplex *c__, integer *
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ldc, doublecomplex *work, integer *ldwork, ftnlen side_len, ftnlen
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trans_len, ftnlen direct_len, ftnlen storev_len)
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{
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/* System generated locals */
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integer c_dim1, c_offset, t_dim1, t_offset, v_dim1, v_offset, work_dim1,
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work_offset, i__1, i__2, i__3, i__4, i__5;
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doublecomplex z__1, z__2;
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/* Builtin functions */
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void d_cnjg(doublecomplex *, doublecomplex *);
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/* Local variables */
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integer i__, j;
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extern logical lsame_(char *, char *, ftnlen, ftnlen);
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extern /* Subroutine */ int zgemm_(char *, char *, integer *, integer *,
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integer *, doublecomplex *, doublecomplex *, integer *,
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doublecomplex *, integer *, doublecomplex *, doublecomplex *,
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integer *, ftnlen, ftnlen), zcopy_(integer *, doublecomplex *,
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integer *, doublecomplex *, integer *), ztrmm_(char *, char *,
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char *, char *, integer *, integer *, doublecomplex *,
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doublecomplex *, integer *, doublecomplex *, integer *, ftnlen,
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ftnlen, ftnlen, ftnlen), zlacgv_(integer *, doublecomplex *,
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integer *);
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char transt[1];
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/* -- LAPACK auxiliary routine -- */
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/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
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/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
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/* .. Scalar Arguments .. */
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/* .. */
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/* .. Array Arguments .. */
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/* .. */
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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 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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/* Quick return if possible */
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/* Parameter adjustments */
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v_dim1 = *ldv;
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v_offset = 1 + v_dim1;
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v -= v_offset;
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t_dim1 = *ldt;
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t_offset = 1 + t_dim1;
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t -= t_offset;
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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_dim1 = *ldwork;
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work_offset = 1 + work_dim1;
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work -= work_offset;
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/* Function Body */
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if (*m <= 0 || *n <= 0) {
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return 0;
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}
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if (lsame_(trans, (char *)"N", (ftnlen)1, (ftnlen)1)) {
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*(unsigned char *)transt = 'C';
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} else {
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*(unsigned char *)transt = 'N';
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}
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if (lsame_(storev, (char *)"C", (ftnlen)1, (ftnlen)1)) {
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if (lsame_(direct, (char *)"F", (ftnlen)1, (ftnlen)1)) {
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/* Let V = ( V1 ) (first K rows) */
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/* ( V2 ) */
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/* where V1 is unit lower triangular. */
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if (lsame_(side, (char *)"L", (ftnlen)1, (ftnlen)1)) {
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/* Form H * C or H**H * C where C = ( C1 ) */
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/* ( C2 ) */
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/* W := C**H * V = (C1**H * V1 + C2**H * V2) (stored in WORK) */
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/* W := C1**H */
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i__1 = *k;
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for (j = 1; j <= i__1; ++j) {
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zcopy_(n, &c__[j + c_dim1], ldc, &work[j * work_dim1 + 1],
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&c__1);
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zlacgv_(n, &work[j * work_dim1 + 1], &c__1);
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/* L10: */
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}
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/* W := W * V1 */
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ztrmm_((char *)"Right", (char *)"Lower", (char *)"No transpose", (char *)"Unit", n, k, &c_b1,
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&v[v_offset], ldv, &work[work_offset], ldwork, (
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ftnlen)5, (ftnlen)5, (ftnlen)12, (ftnlen)4);
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if (*m > *k) {
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/* W := W + C2**H * V2 */
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i__1 = *m - *k;
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zgemm_((char *)"Conjugate transpose", (char *)"No transpose", n, k, &i__1,
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&c_b1, &c__[*k + 1 + c_dim1], ldc, &v[*k + 1 +
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v_dim1], ldv, &c_b1, &work[work_offset], ldwork, (
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ftnlen)19, (ftnlen)12);
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}
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/* W := W * T**H or W * T */
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ztrmm_((char *)"Right", (char *)"Upper", transt, (char *)"Non-unit", n, k, &c_b1, &t[
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t_offset], ldt, &work[work_offset], ldwork, (ftnlen)5,
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(ftnlen)5, (ftnlen)1, (ftnlen)8);
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/* C := C - V * W**H */
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if (*m > *k) {
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/* C2 := C2 - V2 * W**H */
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i__1 = *m - *k;
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z__1.r = -1., z__1.i = -0.;
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zgemm_((char *)"No transpose", (char *)"Conjugate transpose", &i__1, n, k,
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&z__1, &v[*k + 1 + v_dim1], ldv, &work[
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work_offset], ldwork, &c_b1, &c__[*k + 1 + c_dim1]
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, ldc, (ftnlen)12, (ftnlen)19);
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}
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/* W := W * V1**H */
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ztrmm_((char *)"Right", (char *)"Lower", (char *)"Conjugate transpose", (char *)"Unit", n, k,
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&c_b1, &v[v_offset], ldv, &work[work_offset], ldwork,
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(ftnlen)5, (ftnlen)5, (ftnlen)19, (ftnlen)4);
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/* C1 := C1 - W**H */
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i__1 = *k;
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for (j = 1; j <= i__1; ++j) {
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i__2 = *n;
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for (i__ = 1; i__ <= i__2; ++i__) {
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i__3 = j + i__ * c_dim1;
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i__4 = j + i__ * c_dim1;
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d_cnjg(&z__2, &work[i__ + j * work_dim1]);
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z__1.r = c__[i__4].r - z__2.r, z__1.i = c__[i__4].i -
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z__2.i;
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c__[i__3].r = z__1.r, c__[i__3].i = z__1.i;
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/* L20: */
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}
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/* L30: */
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}
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} else if (lsame_(side, (char *)"R", (ftnlen)1, (ftnlen)1)) {
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/* Form C * H or C * H**H where C = ( C1 C2 ) */
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/* W := C * V = (C1*V1 + C2*V2) (stored in WORK) */
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/* W := C1 */
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i__1 = *k;
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for (j = 1; j <= i__1; ++j) {
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zcopy_(m, &c__[j * c_dim1 + 1], &c__1, &work[j *
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work_dim1 + 1], &c__1);
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/* L40: */
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}
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/* W := W * V1 */
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ztrmm_((char *)"Right", (char *)"Lower", (char *)"No transpose", (char *)"Unit", m, k, &c_b1,
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&v[v_offset], ldv, &work[work_offset], ldwork, (
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ftnlen)5, (ftnlen)5, (ftnlen)12, (ftnlen)4);
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if (*n > *k) {
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/* W := W + C2 * V2 */
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i__1 = *n - *k;
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zgemm_((char *)"No transpose", (char *)"No transpose", m, k, &i__1, &c_b1,
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&c__[(*k + 1) * c_dim1 + 1], ldc, &v[*k + 1 +
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v_dim1], ldv, &c_b1, &work[work_offset], ldwork, (
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ftnlen)12, (ftnlen)12);
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}
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/* W := W * T or W * T**H */
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ztrmm_((char *)"Right", (char *)"Upper", trans, (char *)"Non-unit", m, k, &c_b1, &t[
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t_offset], ldt, &work[work_offset], ldwork, (ftnlen)5,
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(ftnlen)5, (ftnlen)1, (ftnlen)8);
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/* C := C - W * V**H */
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if (*n > *k) {
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/* C2 := C2 - W * V2**H */
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i__1 = *n - *k;
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z__1.r = -1., z__1.i = -0.;
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zgemm_((char *)"No transpose", (char *)"Conjugate transpose", m, &i__1, k,
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&z__1, &work[work_offset], ldwork, &v[*k + 1 +
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v_dim1], ldv, &c_b1, &c__[(*k + 1) * c_dim1 + 1],
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ldc, (ftnlen)12, (ftnlen)19);
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}
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/* W := W * V1**H */
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ztrmm_((char *)"Right", (char *)"Lower", (char *)"Conjugate transpose", (char *)"Unit", m, k,
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&c_b1, &v[v_offset], ldv, &work[work_offset], ldwork,
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(ftnlen)5, (ftnlen)5, (ftnlen)19, (ftnlen)4);
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/* C1 := C1 - W */
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i__1 = *k;
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for (j = 1; j <= i__1; ++j) {
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i__2 = *m;
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for (i__ = 1; i__ <= i__2; ++i__) {
|
|
i__3 = i__ + j * c_dim1;
|
|
i__4 = i__ + j * c_dim1;
|
|
i__5 = i__ + j * work_dim1;
|
|
z__1.r = c__[i__4].r - work[i__5].r, z__1.i = c__[
|
|
i__4].i - work[i__5].i;
|
|
c__[i__3].r = z__1.r, c__[i__3].i = z__1.i;
|
|
/* L50: */
|
|
}
|
|
/* L60: */
|
|
}
|
|
}
|
|
|
|
} else {
|
|
|
|
/* Let V = ( V1 ) */
|
|
/* ( V2 ) (last K rows) */
|
|
/* where V2 is unit upper triangular. */
|
|
|
|
if (lsame_(side, (char *)"L", (ftnlen)1, (ftnlen)1)) {
|
|
|
|
/* Form H * C or H**H * C where C = ( C1 ) */
|
|
/* ( C2 ) */
|
|
|
|
/* W := C**H * V = (C1**H * V1 + C2**H * V2) (stored in WORK) */
|
|
|
|
/* W := C2**H */
|
|
|
|
i__1 = *k;
|
|
for (j = 1; j <= i__1; ++j) {
|
|
zcopy_(n, &c__[*m - *k + j + c_dim1], ldc, &work[j *
|
|
work_dim1 + 1], &c__1);
|
|
zlacgv_(n, &work[j * work_dim1 + 1], &c__1);
|
|
/* L70: */
|
|
}
|
|
|
|
/* W := W * V2 */
|
|
|
|
ztrmm_((char *)"Right", (char *)"Upper", (char *)"No transpose", (char *)"Unit", n, k, &c_b1,
|
|
&v[*m - *k + 1 + v_dim1], ldv, &work[work_offset],
|
|
ldwork, (ftnlen)5, (ftnlen)5, (ftnlen)12, (ftnlen)4);
|
|
if (*m > *k) {
|
|
|
|
/* W := W + C1**H * V1 */
|
|
|
|
i__1 = *m - *k;
|
|
zgemm_((char *)"Conjugate transpose", (char *)"No transpose", n, k, &i__1,
|
|
&c_b1, &c__[c_offset], ldc, &v[v_offset], ldv, &
|
|
c_b1, &work[work_offset], ldwork, (ftnlen)19, (
|
|
ftnlen)12);
|
|
}
|
|
|
|
/* W := W * T**H or W * T */
|
|
|
|
ztrmm_((char *)"Right", (char *)"Lower", transt, (char *)"Non-unit", n, k, &c_b1, &t[
|
|
t_offset], ldt, &work[work_offset], ldwork, (ftnlen)5,
|
|
(ftnlen)5, (ftnlen)1, (ftnlen)8);
|
|
|
|
/* C := C - V * W**H */
|
|
|
|
if (*m > *k) {
|
|
|
|
/* C1 := C1 - V1 * W**H */
|
|
|
|
i__1 = *m - *k;
|
|
z__1.r = -1., z__1.i = -0.;
|
|
zgemm_((char *)"No transpose", (char *)"Conjugate transpose", &i__1, n, k,
|
|
&z__1, &v[v_offset], ldv, &work[work_offset],
|
|
ldwork, &c_b1, &c__[c_offset], ldc, (ftnlen)12, (
|
|
ftnlen)19);
|
|
}
|
|
|
|
/* W := W * V2**H */
|
|
|
|
ztrmm_((char *)"Right", (char *)"Upper", (char *)"Conjugate transpose", (char *)"Unit", n, k,
|
|
&c_b1, &v[*m - *k + 1 + v_dim1], ldv, &work[
|
|
work_offset], ldwork, (ftnlen)5, (ftnlen)5, (ftnlen)
|
|
19, (ftnlen)4);
|
|
|
|
/* C2 := C2 - W**H */
|
|
|
|
i__1 = *k;
|
|
for (j = 1; j <= i__1; ++j) {
|
|
i__2 = *n;
|
|
for (i__ = 1; i__ <= i__2; ++i__) {
|
|
i__3 = *m - *k + j + i__ * c_dim1;
|
|
i__4 = *m - *k + j + i__ * c_dim1;
|
|
d_cnjg(&z__2, &work[i__ + j * work_dim1]);
|
|
z__1.r = c__[i__4].r - z__2.r, z__1.i = c__[i__4].i -
|
|
z__2.i;
|
|
c__[i__3].r = z__1.r, c__[i__3].i = z__1.i;
|
|
/* L80: */
|
|
}
|
|
/* L90: */
|
|
}
|
|
|
|
} else if (lsame_(side, (char *)"R", (ftnlen)1, (ftnlen)1)) {
|
|
|
|
/* Form C * H or C * H**H where C = ( C1 C2 ) */
|
|
|
|
/* W := C * V = (C1*V1 + C2*V2) (stored in WORK) */
|
|
|
|
/* W := C2 */
|
|
|
|
i__1 = *k;
|
|
for (j = 1; j <= i__1; ++j) {
|
|
zcopy_(m, &c__[(*n - *k + j) * c_dim1 + 1], &c__1, &work[
|
|
j * work_dim1 + 1], &c__1);
|
|
/* L100: */
|
|
}
|
|
|
|
/* W := W * V2 */
|
|
|
|
ztrmm_((char *)"Right", (char *)"Upper", (char *)"No transpose", (char *)"Unit", m, k, &c_b1,
|
|
&v[*n - *k + 1 + v_dim1], ldv, &work[work_offset],
|
|
ldwork, (ftnlen)5, (ftnlen)5, (ftnlen)12, (ftnlen)4);
|
|
if (*n > *k) {
|
|
|
|
/* W := W + C1 * V1 */
|
|
|
|
i__1 = *n - *k;
|
|
zgemm_((char *)"No transpose", (char *)"No transpose", m, k, &i__1, &c_b1,
|
|
&c__[c_offset], ldc, &v[v_offset], ldv, &c_b1, &
|
|
work[work_offset], ldwork, (ftnlen)12, (ftnlen)12)
|
|
;
|
|
}
|
|
|
|
/* W := W * T or W * T**H */
|
|
|
|
ztrmm_((char *)"Right", (char *)"Lower", trans, (char *)"Non-unit", m, k, &c_b1, &t[
|
|
t_offset], ldt, &work[work_offset], ldwork, (ftnlen)5,
|
|
(ftnlen)5, (ftnlen)1, (ftnlen)8);
|
|
|
|
/* C := C - W * V**H */
|
|
|
|
if (*n > *k) {
|
|
|
|
/* C1 := C1 - W * V1**H */
|
|
|
|
i__1 = *n - *k;
|
|
z__1.r = -1., z__1.i = -0.;
|
|
zgemm_((char *)"No transpose", (char *)"Conjugate transpose", m, &i__1, k,
|
|
&z__1, &work[work_offset], ldwork, &v[v_offset],
|
|
ldv, &c_b1, &c__[c_offset], ldc, (ftnlen)12, (
|
|
ftnlen)19);
|
|
}
|
|
|
|
/* W := W * V2**H */
|
|
|
|
ztrmm_((char *)"Right", (char *)"Upper", (char *)"Conjugate transpose", (char *)"Unit", m, k,
|
|
&c_b1, &v[*n - *k + 1 + v_dim1], ldv, &work[
|
|
work_offset], ldwork, (ftnlen)5, (ftnlen)5, (ftnlen)
|
|
19, (ftnlen)4);
|
|
|
|
/* C2 := C2 - W */
|
|
|
|
i__1 = *k;
|
|
for (j = 1; j <= i__1; ++j) {
|
|
i__2 = *m;
|
|
for (i__ = 1; i__ <= i__2; ++i__) {
|
|
i__3 = i__ + (*n - *k + j) * c_dim1;
|
|
i__4 = i__ + (*n - *k + j) * c_dim1;
|
|
i__5 = i__ + j * work_dim1;
|
|
z__1.r = c__[i__4].r - work[i__5].r, z__1.i = c__[
|
|
i__4].i - work[i__5].i;
|
|
c__[i__3].r = z__1.r, c__[i__3].i = z__1.i;
|
|
/* L110: */
|
|
}
|
|
/* L120: */
|
|
}
|
|
}
|
|
}
|
|
|
|
} else if (lsame_(storev, (char *)"R", (ftnlen)1, (ftnlen)1)) {
|
|
|
|
if (lsame_(direct, (char *)"F", (ftnlen)1, (ftnlen)1)) {
|
|
|
|
/* Let V = ( V1 V2 ) (V1: first K columns) */
|
|
/* where V1 is unit upper triangular. */
|
|
|
|
if (lsame_(side, (char *)"L", (ftnlen)1, (ftnlen)1)) {
|
|
|
|
/* Form H * C or H**H * C where C = ( C1 ) */
|
|
/* ( C2 ) */
|
|
|
|
/* W := C**H * V**H = (C1**H * V1**H + C2**H * V2**H) (stored in WORK) */
|
|
|
|
/* W := C1**H */
|
|
|
|
i__1 = *k;
|
|
for (j = 1; j <= i__1; ++j) {
|
|
zcopy_(n, &c__[j + c_dim1], ldc, &work[j * work_dim1 + 1],
|
|
&c__1);
|
|
zlacgv_(n, &work[j * work_dim1 + 1], &c__1);
|
|
/* L130: */
|
|
}
|
|
|
|
/* W := W * V1**H */
|
|
|
|
ztrmm_((char *)"Right", (char *)"Upper", (char *)"Conjugate transpose", (char *)"Unit", n, k,
|
|
&c_b1, &v[v_offset], ldv, &work[work_offset], ldwork,
|
|
(ftnlen)5, (ftnlen)5, (ftnlen)19, (ftnlen)4);
|
|
if (*m > *k) {
|
|
|
|
/* W := W + C2**H * V2**H */
|
|
|
|
i__1 = *m - *k;
|
|
zgemm_((char *)"Conjugate transpose", (char *)"Conjugate transpose", n, k,
|
|
&i__1, &c_b1, &c__[*k + 1 + c_dim1], ldc, &v[(*k
|
|
+ 1) * v_dim1 + 1], ldv, &c_b1, &work[work_offset]
|
|
, ldwork, (ftnlen)19, (ftnlen)19);
|
|
}
|
|
|
|
/* W := W * T**H or W * T */
|
|
|
|
ztrmm_((char *)"Right", (char *)"Upper", transt, (char *)"Non-unit", n, k, &c_b1, &t[
|
|
t_offset], ldt, &work[work_offset], ldwork, (ftnlen)5,
|
|
(ftnlen)5, (ftnlen)1, (ftnlen)8);
|
|
|
|
/* C := C - V**H * W**H */
|
|
|
|
if (*m > *k) {
|
|
|
|
/* C2 := C2 - V2**H * W**H */
|
|
|
|
i__1 = *m - *k;
|
|
z__1.r = -1., z__1.i = -0.;
|
|
zgemm_((char *)"Conjugate transpose", (char *)"Conjugate transpose", &
|
|
i__1, n, k, &z__1, &v[(*k + 1) * v_dim1 + 1], ldv,
|
|
&work[work_offset], ldwork, &c_b1, &c__[*k + 1 +
|
|
c_dim1], ldc, (ftnlen)19, (ftnlen)19);
|
|
}
|
|
|
|
/* W := W * V1 */
|
|
|
|
ztrmm_((char *)"Right", (char *)"Upper", (char *)"No transpose", (char *)"Unit", n, k, &c_b1,
|
|
&v[v_offset], ldv, &work[work_offset], ldwork, (
|
|
ftnlen)5, (ftnlen)5, (ftnlen)12, (ftnlen)4);
|
|
|
|
/* C1 := C1 - W**H */
|
|
|
|
i__1 = *k;
|
|
for (j = 1; j <= i__1; ++j) {
|
|
i__2 = *n;
|
|
for (i__ = 1; i__ <= i__2; ++i__) {
|
|
i__3 = j + i__ * c_dim1;
|
|
i__4 = j + i__ * c_dim1;
|
|
d_cnjg(&z__2, &work[i__ + j * work_dim1]);
|
|
z__1.r = c__[i__4].r - z__2.r, z__1.i = c__[i__4].i -
|
|
z__2.i;
|
|
c__[i__3].r = z__1.r, c__[i__3].i = z__1.i;
|
|
/* L140: */
|
|
}
|
|
/* L150: */
|
|
}
|
|
|
|
} else if (lsame_(side, (char *)"R", (ftnlen)1, (ftnlen)1)) {
|
|
|
|
/* Form C * H or C * H**H where C = ( C1 C2 ) */
|
|
|
|
/* W := C * V**H = (C1*V1**H + C2*V2**H) (stored in WORK) */
|
|
|
|
/* W := C1 */
|
|
|
|
i__1 = *k;
|
|
for (j = 1; j <= i__1; ++j) {
|
|
zcopy_(m, &c__[j * c_dim1 + 1], &c__1, &work[j *
|
|
work_dim1 + 1], &c__1);
|
|
/* L160: */
|
|
}
|
|
|
|
/* W := W * V1**H */
|
|
|
|
ztrmm_((char *)"Right", (char *)"Upper", (char *)"Conjugate transpose", (char *)"Unit", m, k,
|
|
&c_b1, &v[v_offset], ldv, &work[work_offset], ldwork,
|
|
(ftnlen)5, (ftnlen)5, (ftnlen)19, (ftnlen)4);
|
|
if (*n > *k) {
|
|
|
|
/* W := W + C2 * V2**H */
|
|
|
|
i__1 = *n - *k;
|
|
zgemm_((char *)"No transpose", (char *)"Conjugate transpose", m, k, &i__1,
|
|
&c_b1, &c__[(*k + 1) * c_dim1 + 1], ldc, &v[(*k
|
|
+ 1) * v_dim1 + 1], ldv, &c_b1, &work[work_offset]
|
|
, ldwork, (ftnlen)12, (ftnlen)19);
|
|
}
|
|
|
|
/* W := W * T or W * T**H */
|
|
|
|
ztrmm_((char *)"Right", (char *)"Upper", trans, (char *)"Non-unit", m, k, &c_b1, &t[
|
|
t_offset], ldt, &work[work_offset], ldwork, (ftnlen)5,
|
|
(ftnlen)5, (ftnlen)1, (ftnlen)8);
|
|
|
|
/* C := C - W * V */
|
|
|
|
if (*n > *k) {
|
|
|
|
/* C2 := C2 - W * V2 */
|
|
|
|
i__1 = *n - *k;
|
|
z__1.r = -1., z__1.i = -0.;
|
|
zgemm_((char *)"No transpose", (char *)"No transpose", m, &i__1, k, &z__1,
|
|
&work[work_offset], ldwork, &v[(*k + 1) * v_dim1
|
|
+ 1], ldv, &c_b1, &c__[(*k + 1) * c_dim1 + 1],
|
|
ldc, (ftnlen)12, (ftnlen)12);
|
|
}
|
|
|
|
/* W := W * V1 */
|
|
|
|
ztrmm_((char *)"Right", (char *)"Upper", (char *)"No transpose", (char *)"Unit", m, k, &c_b1,
|
|
&v[v_offset], ldv, &work[work_offset], ldwork, (
|
|
ftnlen)5, (ftnlen)5, (ftnlen)12, (ftnlen)4);
|
|
|
|
/* C1 := C1 - W */
|
|
|
|
i__1 = *k;
|
|
for (j = 1; j <= i__1; ++j) {
|
|
i__2 = *m;
|
|
for (i__ = 1; i__ <= i__2; ++i__) {
|
|
i__3 = i__ + j * c_dim1;
|
|
i__4 = i__ + j * c_dim1;
|
|
i__5 = i__ + j * work_dim1;
|
|
z__1.r = c__[i__4].r - work[i__5].r, z__1.i = c__[
|
|
i__4].i - work[i__5].i;
|
|
c__[i__3].r = z__1.r, c__[i__3].i = z__1.i;
|
|
/* L170: */
|
|
}
|
|
/* L180: */
|
|
}
|
|
|
|
}
|
|
|
|
} else {
|
|
|
|
/* Let V = ( V1 V2 ) (V2: last K columns) */
|
|
/* where V2 is unit lower triangular. */
|
|
|
|
if (lsame_(side, (char *)"L", (ftnlen)1, (ftnlen)1)) {
|
|
|
|
/* Form H * C or H**H * C where C = ( C1 ) */
|
|
/* ( C2 ) */
|
|
|
|
/* W := C**H * V**H = (C1**H * V1**H + C2**H * V2**H) (stored in WORK) */
|
|
|
|
/* W := C2**H */
|
|
|
|
i__1 = *k;
|
|
for (j = 1; j <= i__1; ++j) {
|
|
zcopy_(n, &c__[*m - *k + j + c_dim1], ldc, &work[j *
|
|
work_dim1 + 1], &c__1);
|
|
zlacgv_(n, &work[j * work_dim1 + 1], &c__1);
|
|
/* L190: */
|
|
}
|
|
|
|
/* W := W * V2**H */
|
|
|
|
ztrmm_((char *)"Right", (char *)"Lower", (char *)"Conjugate transpose", (char *)"Unit", n, k,
|
|
&c_b1, &v[(*m - *k + 1) * v_dim1 + 1], ldv, &work[
|
|
work_offset], ldwork, (ftnlen)5, (ftnlen)5, (ftnlen)
|
|
19, (ftnlen)4);
|
|
if (*m > *k) {
|
|
|
|
/* W := W + C1**H * V1**H */
|
|
|
|
i__1 = *m - *k;
|
|
zgemm_((char *)"Conjugate transpose", (char *)"Conjugate transpose", n, k,
|
|
&i__1, &c_b1, &c__[c_offset], ldc, &v[v_offset],
|
|
ldv, &c_b1, &work[work_offset], ldwork, (ftnlen)
|
|
19, (ftnlen)19);
|
|
}
|
|
|
|
/* W := W * T**H or W * T */
|
|
|
|
ztrmm_((char *)"Right", (char *)"Lower", transt, (char *)"Non-unit", n, k, &c_b1, &t[
|
|
t_offset], ldt, &work[work_offset], ldwork, (ftnlen)5,
|
|
(ftnlen)5, (ftnlen)1, (ftnlen)8);
|
|
|
|
/* C := C - V**H * W**H */
|
|
|
|
if (*m > *k) {
|
|
|
|
/* C1 := C1 - V1**H * W**H */
|
|
|
|
i__1 = *m - *k;
|
|
z__1.r = -1., z__1.i = -0.;
|
|
zgemm_((char *)"Conjugate transpose", (char *)"Conjugate transpose", &
|
|
i__1, n, k, &z__1, &v[v_offset], ldv, &work[
|
|
work_offset], ldwork, &c_b1, &c__[c_offset], ldc,
|
|
(ftnlen)19, (ftnlen)19);
|
|
}
|
|
|
|
/* W := W * V2 */
|
|
|
|
ztrmm_((char *)"Right", (char *)"Lower", (char *)"No transpose", (char *)"Unit", n, k, &c_b1,
|
|
&v[(*m - *k + 1) * v_dim1 + 1], ldv, &work[
|
|
work_offset], ldwork, (ftnlen)5, (ftnlen)5, (ftnlen)
|
|
12, (ftnlen)4);
|
|
|
|
/* C2 := C2 - W**H */
|
|
|
|
i__1 = *k;
|
|
for (j = 1; j <= i__1; ++j) {
|
|
i__2 = *n;
|
|
for (i__ = 1; i__ <= i__2; ++i__) {
|
|
i__3 = *m - *k + j + i__ * c_dim1;
|
|
i__4 = *m - *k + j + i__ * c_dim1;
|
|
d_cnjg(&z__2, &work[i__ + j * work_dim1]);
|
|
z__1.r = c__[i__4].r - z__2.r, z__1.i = c__[i__4].i -
|
|
z__2.i;
|
|
c__[i__3].r = z__1.r, c__[i__3].i = z__1.i;
|
|
/* L200: */
|
|
}
|
|
/* L210: */
|
|
}
|
|
|
|
} else if (lsame_(side, (char *)"R", (ftnlen)1, (ftnlen)1)) {
|
|
|
|
/* Form C * H or C * H**H where C = ( C1 C2 ) */
|
|
|
|
/* W := C * V**H = (C1*V1**H + C2*V2**H) (stored in WORK) */
|
|
|
|
/* W := C2 */
|
|
|
|
i__1 = *k;
|
|
for (j = 1; j <= i__1; ++j) {
|
|
zcopy_(m, &c__[(*n - *k + j) * c_dim1 + 1], &c__1, &work[
|
|
j * work_dim1 + 1], &c__1);
|
|
/* L220: */
|
|
}
|
|
|
|
/* W := W * V2**H */
|
|
|
|
ztrmm_((char *)"Right", (char *)"Lower", (char *)"Conjugate transpose", (char *)"Unit", m, k,
|
|
&c_b1, &v[(*n - *k + 1) * v_dim1 + 1], ldv, &work[
|
|
work_offset], ldwork, (ftnlen)5, (ftnlen)5, (ftnlen)
|
|
19, (ftnlen)4);
|
|
if (*n > *k) {
|
|
|
|
/* W := W + C1 * V1**H */
|
|
|
|
i__1 = *n - *k;
|
|
zgemm_((char *)"No transpose", (char *)"Conjugate transpose", m, k, &i__1,
|
|
&c_b1, &c__[c_offset], ldc, &v[v_offset], ldv, &
|
|
c_b1, &work[work_offset], ldwork, (ftnlen)12, (
|
|
ftnlen)19);
|
|
}
|
|
|
|
/* W := W * T or W * T**H */
|
|
|
|
ztrmm_((char *)"Right", (char *)"Lower", trans, (char *)"Non-unit", m, k, &c_b1, &t[
|
|
t_offset], ldt, &work[work_offset], ldwork, (ftnlen)5,
|
|
(ftnlen)5, (ftnlen)1, (ftnlen)8);
|
|
|
|
/* C := C - W * V */
|
|
|
|
if (*n > *k) {
|
|
|
|
/* C1 := C1 - W * V1 */
|
|
|
|
i__1 = *n - *k;
|
|
z__1.r = -1., z__1.i = -0.;
|
|
zgemm_((char *)"No transpose", (char *)"No transpose", m, &i__1, k, &z__1,
|
|
&work[work_offset], ldwork, &v[v_offset], ldv, &
|
|
c_b1, &c__[c_offset], ldc, (ftnlen)12, (ftnlen)12)
|
|
;
|
|
}
|
|
|
|
/* W := W * V2 */
|
|
|
|
ztrmm_((char *)"Right", (char *)"Lower", (char *)"No transpose", (char *)"Unit", m, k, &c_b1,
|
|
&v[(*n - *k + 1) * v_dim1 + 1], ldv, &work[
|
|
work_offset], ldwork, (ftnlen)5, (ftnlen)5, (ftnlen)
|
|
12, (ftnlen)4);
|
|
|
|
/* C1 := C1 - W */
|
|
|
|
i__1 = *k;
|
|
for (j = 1; j <= i__1; ++j) {
|
|
i__2 = *m;
|
|
for (i__ = 1; i__ <= i__2; ++i__) {
|
|
i__3 = i__ + (*n - *k + j) * c_dim1;
|
|
i__4 = i__ + (*n - *k + j) * c_dim1;
|
|
i__5 = i__ + j * work_dim1;
|
|
z__1.r = c__[i__4].r - work[i__5].r, z__1.i = c__[
|
|
i__4].i - work[i__5].i;
|
|
c__[i__3].r = z__1.r, c__[i__3].i = z__1.i;
|
|
/* L230: */
|
|
}
|
|
/* L240: */
|
|
}
|
|
|
|
}
|
|
|
|
}
|
|
}
|
|
|
|
return 0;
|
|
|
|
/* End of ZLARFB */
|
|
|
|
} /* zlarfb_ */
|
|
|
|
#ifdef __cplusplus
|
|
}
|
|
#endif
|