466 lines
17 KiB
C++
466 lines
17 KiB
C++
/* static/zlarft.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 ZLARFT forms the triangular factor T of a block reflector H = I - vtvH */
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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 ZLARFT + dependencies */
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/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zlarft.
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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/zlarft.
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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/zlarft.
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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 ZLARFT( DIRECT, STOREV, N, K, V, LDV, TAU, T, LDT ) */
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/* .. Scalar Arguments .. */
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/* CHARACTER DIRECT, STOREV */
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/* INTEGER K, LDT, LDV, N */
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/* .. */
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/* .. Array Arguments .. */
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/* COMPLEX*16 T( LDT, * ), TAU( * ), V( LDV, * ) */
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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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/* > ZLARFT forms the triangular factor T of a complex block reflector H */
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/* > of order n, which is defined as a product of k elementary reflectors. */
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/* > */
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/* > If DIRECT = 'F', H = H(1) H(2) . . . H(k) and T is upper triangular; */
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/* > */
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/* > If DIRECT = 'B', H = H(k) . . . H(2) H(1) and T is lower triangular. */
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/* > */
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/* > If STOREV = 'C', the vector which defines the elementary reflector */
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/* > H(i) is stored in the i-th column of the array V, and */
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/* > */
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/* > H = I - V * T * V**H */
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/* > */
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/* > If STOREV = 'R', the vector which defines the elementary reflector */
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/* > H(i) is stored in the i-th row of the array V, and */
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/* > */
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/* > H = I - V**H * T * V */
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/* > \endverbatim */
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/* Arguments: */
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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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/* > Specifies the order in which the elementary reflectors are */
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/* > multiplied to form the block reflector: */
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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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/* > Specifies how the vectors which define the elementary */
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/* > reflectors are stored (see also Further Details): */
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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] N */
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/* > \verbatim */
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/* > N is INTEGER */
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/* > The order of the block reflector H. N >= 0. */
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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 triangular factor T (= the number of */
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/* > elementary reflectors). K >= 1. */
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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,N) if STOREV = 'R' */
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/* > The matrix V. 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', LDV >= max(1,N); if STOREV = 'R', LDV >= K. */
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/* > \endverbatim */
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/* > */
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/* > \param[in] TAU */
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/* > \verbatim */
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/* > TAU is COMPLEX*16 array, dimension (K) */
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/* > TAU(i) must contain the scalar factor of the elementary */
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/* > reflector H(i). */
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/* > \endverbatim */
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/* > */
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/* > \param[out] T */
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/* > \verbatim */
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/* > T is COMPLEX*16 array, dimension (LDT,K) */
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/* > The k by k triangular factor T of the block reflector. */
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/* > If DIRECT = 'F', T is upper triangular; if DIRECT = 'B', T is */
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/* > lower triangular. The rest of the array is not used. */
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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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/* 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. */
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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 zlarft_(char *direct, char *storev, integer *n, integer *
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k, doublecomplex *v, integer *ldv, doublecomplex *tau, doublecomplex *
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t, integer *ldt, ftnlen direct_len, ftnlen storev_len)
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{
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/* System generated locals */
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integer t_dim1, t_offset, v_dim1, v_offset, i__1, i__2, i__3, i__4, i__5;
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doublecomplex z__1, z__2, z__3;
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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, prevlastv;
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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), zgemv_(char *, integer *, integer *,
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doublecomplex *, doublecomplex *, integer *, doublecomplex *,
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integer *, doublecomplex *, doublecomplex *, integer *, ftnlen);
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integer lastv;
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extern /* Subroutine */ int ztrmv_(char *, char *, char *, integer *,
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doublecomplex *, integer *, doublecomplex *, integer *, ftnlen,
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ftnlen, ftnlen);
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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 Subroutines .. */
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/* .. */
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/* .. External 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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--tau;
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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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/* Function Body */
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if (*n == 0) {
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return 0;
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}
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if (lsame_(direct, (char *)"F", (ftnlen)1, (ftnlen)1)) {
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prevlastv = *n;
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i__1 = *k;
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for (i__ = 1; i__ <= i__1; ++i__) {
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prevlastv = max(prevlastv,i__);
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i__2 = i__;
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if (tau[i__2].r == 0. && tau[i__2].i == 0.) {
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/* H(i) = I */
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i__2 = i__;
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for (j = 1; j <= i__2; ++j) {
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i__3 = j + i__ * t_dim1;
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t[i__3].r = 0., t[i__3].i = 0.;
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}
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} else {
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/* general case */
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if (lsame_(storev, (char *)"C", (ftnlen)1, (ftnlen)1)) {
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/* Skip any trailing zeros. */
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i__2 = i__ + 1;
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for (lastv = *n; lastv >= i__2; --lastv) {
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i__3 = lastv + i__ * v_dim1;
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if (v[i__3].r != 0. || v[i__3].i != 0.) {
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goto L220;
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}
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}
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L220:
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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 = j + i__ * t_dim1;
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i__4 = i__;
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z__2.r = -tau[i__4].r, z__2.i = -tau[i__4].i;
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d_cnjg(&z__3, &v[i__ + j * v_dim1]);
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z__1.r = z__2.r * z__3.r - z__2.i * z__3.i, z__1.i =
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z__2.r * z__3.i + z__2.i * z__3.r;
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t[i__3].r = z__1.r, t[i__3].i = z__1.i;
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}
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j = min(lastv,prevlastv);
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/* T(1:i-1,i) := - tau(i) * V(i:j,1:i-1)**H * V(i:j,i) */
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i__2 = j - i__;
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i__3 = i__ - 1;
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i__4 = i__;
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z__1.r = -tau[i__4].r, z__1.i = -tau[i__4].i;
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zgemv_((char *)"Conjugate transpose", &i__2, &i__3, &z__1, &v[i__
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+ 1 + v_dim1], ldv, &v[i__ + 1 + i__ * v_dim1], &
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c__1, &c_b1, &t[i__ * t_dim1 + 1], &c__1, (ftnlen)
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19);
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} else {
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/* Skip any trailing zeros. */
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i__2 = i__ + 1;
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for (lastv = *n; lastv >= i__2; --lastv) {
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i__3 = i__ + lastv * v_dim1;
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if (v[i__3].r != 0. || v[i__3].i != 0.) {
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goto L236;
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}
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}
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L236:
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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 = j + i__ * t_dim1;
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i__4 = i__;
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z__2.r = -tau[i__4].r, z__2.i = -tau[i__4].i;
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i__5 = j + i__ * v_dim1;
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z__1.r = z__2.r * v[i__5].r - z__2.i * v[i__5].i,
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z__1.i = z__2.r * v[i__5].i + z__2.i * v[i__5]
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.r;
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t[i__3].r = z__1.r, t[i__3].i = z__1.i;
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}
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j = min(lastv,prevlastv);
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/* T(1:i-1,i) := - tau(i) * V(1:i-1,i:j) * V(i,i:j)**H */
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i__2 = i__ - 1;
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i__3 = j - i__;
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i__4 = i__;
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z__1.r = -tau[i__4].r, z__1.i = -tau[i__4].i;
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zgemm_((char *)"N", (char *)"C", &i__2, &c__1, &i__3, &z__1, &v[(i__ + 1)
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* v_dim1 + 1], ldv, &v[i__ + (i__ + 1) * v_dim1],
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ldv, &c_b1, &t[i__ * t_dim1 + 1], ldt, (ftnlen)1,
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(ftnlen)1);
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}
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/* T(1:i-1,i) := T(1:i-1,1:i-1) * T(1:i-1,i) */
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i__2 = i__ - 1;
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ztrmv_((char *)"Upper", (char *)"No transpose", (char *)"Non-unit", &i__2, &t[
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t_offset], ldt, &t[i__ * t_dim1 + 1], &c__1, (ftnlen)
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5, (ftnlen)12, (ftnlen)8);
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i__2 = i__ + i__ * t_dim1;
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i__3 = i__;
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t[i__2].r = tau[i__3].r, t[i__2].i = tau[i__3].i;
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if (i__ > 1) {
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prevlastv = max(prevlastv,lastv);
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} else {
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prevlastv = lastv;
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}
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}
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}
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} else {
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prevlastv = 1;
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for (i__ = *k; i__ >= 1; --i__) {
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i__1 = i__;
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if (tau[i__1].r == 0. && tau[i__1].i == 0.) {
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/* H(i) = I */
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i__1 = *k;
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for (j = i__; j <= i__1; ++j) {
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i__2 = j + i__ * t_dim1;
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t[i__2].r = 0., t[i__2].i = 0.;
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}
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} else {
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/* general case */
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if (i__ < *k) {
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if (lsame_(storev, (char *)"C", (ftnlen)1, (ftnlen)1)) {
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/* Skip any leading zeros. */
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i__1 = i__ - 1;
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for (lastv = 1; lastv <= i__1; ++lastv) {
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i__2 = lastv + i__ * v_dim1;
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if (v[i__2].r != 0. || v[i__2].i != 0.) {
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goto L281;
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}
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}
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L281:
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i__1 = *k;
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for (j = i__ + 1; j <= i__1; ++j) {
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i__2 = j + i__ * t_dim1;
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i__3 = i__;
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z__2.r = -tau[i__3].r, z__2.i = -tau[i__3].i;
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d_cnjg(&z__3, &v[*n - *k + i__ + j * v_dim1]);
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z__1.r = z__2.r * z__3.r - z__2.i * z__3.i,
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z__1.i = z__2.r * z__3.i + z__2.i *
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z__3.r;
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t[i__2].r = z__1.r, t[i__2].i = z__1.i;
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}
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j = max(lastv,prevlastv);
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/* T(i+1:k,i) = -tau(i) * V(j:n-k+i,i+1:k)**H * V(j:n-k+i,i) */
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i__1 = *n - *k + i__ - j;
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i__2 = *k - i__;
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i__3 = i__;
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z__1.r = -tau[i__3].r, z__1.i = -tau[i__3].i;
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zgemv_((char *)"Conjugate transpose", &i__1, &i__2, &z__1, &v[
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j + (i__ + 1) * v_dim1], ldv, &v[j + i__ *
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v_dim1], &c__1, &c_b1, &t[i__ + 1 + i__ *
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t_dim1], &c__1, (ftnlen)19);
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} else {
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/* Skip any leading zeros. */
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i__1 = i__ - 1;
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for (lastv = 1; lastv <= i__1; ++lastv) {
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i__2 = i__ + lastv * v_dim1;
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if (v[i__2].r != 0. || v[i__2].i != 0.) {
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goto L297;
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}
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}
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L297:
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i__1 = *k;
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for (j = i__ + 1; j <= i__1; ++j) {
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i__2 = j + i__ * t_dim1;
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i__3 = i__;
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z__2.r = -tau[i__3].r, z__2.i = -tau[i__3].i;
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i__4 = j + (*n - *k + i__) * v_dim1;
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z__1.r = z__2.r * v[i__4].r - z__2.i * v[i__4].i,
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z__1.i = z__2.r * v[i__4].i + z__2.i * v[
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i__4].r;
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t[i__2].r = z__1.r, t[i__2].i = z__1.i;
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}
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j = max(lastv,prevlastv);
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/* T(i+1:k,i) = -tau(i) * V(i+1:k,j:n-k+i) * V(i,j:n-k+i)**H */
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i__1 = *k - i__;
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i__2 = *n - *k + i__ - j;
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i__3 = i__;
|
|
z__1.r = -tau[i__3].r, z__1.i = -tau[i__3].i;
|
|
zgemm_((char *)"N", (char *)"C", &i__1, &c__1, &i__2, &z__1, &v[i__ +
|
|
1 + j * v_dim1], ldv, &v[i__ + j * v_dim1],
|
|
ldv, &c_b1, &t[i__ + 1 + i__ * t_dim1], ldt, (
|
|
ftnlen)1, (ftnlen)1);
|
|
}
|
|
|
|
/* T(i+1:k,i) := T(i+1:k,i+1:k) * T(i+1:k,i) */
|
|
|
|
i__1 = *k - i__;
|
|
ztrmv_((char *)"Lower", (char *)"No transpose", (char *)"Non-unit", &i__1, &t[i__
|
|
+ 1 + (i__ + 1) * t_dim1], ldt, &t[i__ + 1 + i__ *
|
|
t_dim1], &c__1, (ftnlen)5, (ftnlen)12, (ftnlen)8)
|
|
;
|
|
if (i__ > 1) {
|
|
prevlastv = min(prevlastv,lastv);
|
|
} else {
|
|
prevlastv = lastv;
|
|
}
|
|
}
|
|
i__1 = i__ + i__ * t_dim1;
|
|
i__2 = i__;
|
|
t[i__1].r = tau[i__2].r, t[i__1].i = tau[i__2].i;
|
|
}
|
|
}
|
|
}
|
|
return 0;
|
|
|
|
/* End of ZLARFT */
|
|
|
|
} /* zlarft_ */
|
|
|
|
#ifdef __cplusplus
|
|
}
|
|
#endif
|