640 lines
24 KiB
C++
640 lines
24 KiB
C++
/* fortran/ztpmv.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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/* > \brief \b ZTPMV */
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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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/* Definition: */
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/* =========== */
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/* SUBROUTINE ZTPMV(UPLO,TRANS,DIAG,N,AP,X,INCX) */
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/* .. Scalar Arguments .. */
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/* INTEGER INCX,N */
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/* CHARACTER DIAG,TRANS,UPLO */
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/* .. */
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/* .. Array Arguments .. */
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/* COMPLEX*16 AP(*),X(*) */
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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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/* > ZTPMV performs one of the matrix-vector operations */
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/* > */
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/* > x := A*x, or x := A**T*x, or x := A**H*x, */
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/* > */
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/* > where x is an n element vector and A is an n by n unit, or non-unit, */
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/* > upper or lower triangular matrix, supplied in packed form. */
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/* > \endverbatim */
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/* Arguments: */
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/* ========== */
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/* > \param[in] UPLO */
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/* > \verbatim */
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/* > UPLO is CHARACTER*1 */
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/* > On entry, UPLO specifies whether the matrix is an upper or */
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/* > lower triangular matrix as follows: */
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/* > */
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/* > UPLO = 'U' or 'u' A is an upper triangular matrix. */
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/* > */
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/* > UPLO = 'L' or 'l' A is a lower triangular matrix. */
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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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/* > On entry, TRANS specifies the operation to be performed as */
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/* > follows: */
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/* > */
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/* > TRANS = 'N' or 'n' x := A*x. */
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/* > */
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/* > TRANS = 'T' or 't' x := A**T*x. */
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/* > */
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/* > TRANS = 'C' or 'c' x := A**H*x. */
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/* > \endverbatim */
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/* > */
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/* > \param[in] DIAG */
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/* > \verbatim */
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/* > DIAG is CHARACTER*1 */
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/* > On entry, DIAG specifies whether or not A is unit */
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/* > triangular as follows: */
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/* > */
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/* > DIAG = 'U' or 'u' A is assumed to be unit triangular. */
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/* > */
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/* > DIAG = 'N' or 'n' A is not assumed to be unit */
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/* > triangular. */
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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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/* > On entry, N specifies the order of the matrix A. */
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/* > N must be at least zero. */
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/* > \endverbatim */
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/* > */
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/* > \param[in] AP */
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/* > \verbatim */
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/* > AP is COMPLEX*16 array, dimension at least */
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/* > ( ( n*( n + 1 ) )/2 ). */
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/* > Before entry with UPLO = 'U' or 'u', the array AP must */
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/* > contain the upper triangular matrix packed sequentially, */
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/* > column by column, so that AP( 1 ) contains a( 1, 1 ), */
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/* > AP( 2 ) and AP( 3 ) contain a( 1, 2 ) and a( 2, 2 ) */
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/* > respectively, and so on. */
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/* > Before entry with UPLO = 'L' or 'l', the array AP must */
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/* > contain the lower triangular matrix packed sequentially, */
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/* > column by column, so that AP( 1 ) contains a( 1, 1 ), */
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/* > AP( 2 ) and AP( 3 ) contain a( 2, 1 ) and a( 3, 1 ) */
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/* > respectively, and so on. */
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/* > Note that when DIAG = 'U' or 'u', the diagonal elements of */
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/* > A are not referenced, but are assumed to be unity. */
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/* > \endverbatim */
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/* > */
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/* > \param[in,out] X */
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/* > \verbatim */
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/* > X is COMPLEX*16 array, dimension at least */
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/* > ( 1 + ( n - 1 )*abs( INCX ) ). */
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/* > Before entry, the incremented array X must contain the n */
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/* > element vector x. On exit, X is overwritten with the */
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/* > transformed vector x. */
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/* > \endverbatim */
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/* > */
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/* > \param[in] INCX */
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/* > \verbatim */
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/* > INCX is INTEGER */
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/* > On entry, INCX specifies the increment for the elements of */
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/* > X. INCX must not be zero. */
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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 complex16_blas_level2 */
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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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/* > Level 2 Blas routine. */
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/* > The vector and matrix arguments are not referenced when N = 0, or M = 0 */
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/* > */
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/* > -- Written on 22-October-1986. */
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/* > Jack Dongarra, Argonne National Lab. */
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/* > Jeremy Du Croz, Nag Central Office. */
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/* > Sven Hammarling, Nag Central Office. */
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/* > Richard Hanson, Sandia National Labs. */
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/* > \endverbatim */
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/* > */
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/* ===================================================================== */
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/* Subroutine */ int ztpmv_(char *uplo, char *trans, char *diag, integer *n,
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doublecomplex *ap, doublecomplex *x, integer *incx, ftnlen uplo_len,
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ftnlen trans_len, ftnlen diag_len)
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{
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/* System generated locals */
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integer 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, k, kk, ix, jx, kx, info;
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doublecomplex temp;
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extern logical lsame_(char *, char *, ftnlen, ftnlen);
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extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen);
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logical noconj, nounit;
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/* -- Reference BLAS level2 routine -- */
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/* -- Reference BLAS 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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/* Test the input parameters. */
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/* Parameter adjustments */
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--x;
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--ap;
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/* Function Body */
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info = 0;
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if (! lsame_(uplo, (char *)"U", (ftnlen)1, (ftnlen)1) && ! lsame_(uplo, (char *)"L", (
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ftnlen)1, (ftnlen)1)) {
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info = 1;
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} else if (! lsame_(trans, (char *)"N", (ftnlen)1, (ftnlen)1) && ! lsame_(trans,
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(char *)"T", (ftnlen)1, (ftnlen)1) && ! lsame_(trans, (char *)"C", (ftnlen)1, (
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ftnlen)1)) {
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info = 2;
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} else if (! lsame_(diag, (char *)"U", (ftnlen)1, (ftnlen)1) && ! lsame_(diag,
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(char *)"N", (ftnlen)1, (ftnlen)1)) {
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info = 3;
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} else if (*n < 0) {
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info = 4;
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} else if (*incx == 0) {
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info = 7;
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}
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if (info != 0) {
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xerbla_((char *)"ZTPMV ", &info, (ftnlen)6);
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return 0;
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}
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/* Quick return if possible. */
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if (*n == 0) {
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return 0;
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}
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noconj = lsame_(trans, (char *)"T", (ftnlen)1, (ftnlen)1);
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nounit = lsame_(diag, (char *)"N", (ftnlen)1, (ftnlen)1);
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/* Set up the start point in X if the increment is not unity. This */
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/* will be ( N - 1 )*INCX too small for descending loops. */
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if (*incx <= 0) {
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kx = 1 - (*n - 1) * *incx;
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} else if (*incx != 1) {
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kx = 1;
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}
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/* Start the operations. In this version the elements of AP are */
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/* accessed sequentially with one pass through AP. */
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if (lsame_(trans, (char *)"N", (ftnlen)1, (ftnlen)1)) {
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/* Form x:= A*x. */
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if (lsame_(uplo, (char *)"U", (ftnlen)1, (ftnlen)1)) {
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kk = 1;
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if (*incx == 1) {
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i__1 = *n;
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for (j = 1; j <= i__1; ++j) {
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i__2 = j;
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if (x[i__2].r != 0. || x[i__2].i != 0.) {
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i__2 = j;
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temp.r = x[i__2].r, temp.i = x[i__2].i;
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k = kk;
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i__2 = j - 1;
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for (i__ = 1; i__ <= i__2; ++i__) {
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i__3 = i__;
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i__4 = i__;
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i__5 = k;
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z__2.r = temp.r * ap[i__5].r - temp.i * ap[i__5]
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.i, z__2.i = temp.r * ap[i__5].i + temp.i
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* ap[i__5].r;
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z__1.r = x[i__4].r + z__2.r, z__1.i = x[i__4].i +
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z__2.i;
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x[i__3].r = z__1.r, x[i__3].i = z__1.i;
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++k;
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/* L10: */
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}
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if (nounit) {
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i__2 = j;
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i__3 = j;
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i__4 = kk + j - 1;
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z__1.r = x[i__3].r * ap[i__4].r - x[i__3].i * ap[
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i__4].i, z__1.i = x[i__3].r * ap[i__4].i
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+ x[i__3].i * ap[i__4].r;
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x[i__2].r = z__1.r, x[i__2].i = z__1.i;
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}
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}
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kk += j;
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/* L20: */
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}
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} else {
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jx = kx;
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i__1 = *n;
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for (j = 1; j <= i__1; ++j) {
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i__2 = jx;
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if (x[i__2].r != 0. || x[i__2].i != 0.) {
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i__2 = jx;
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temp.r = x[i__2].r, temp.i = x[i__2].i;
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ix = kx;
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i__2 = kk + j - 2;
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for (k = kk; k <= i__2; ++k) {
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i__3 = ix;
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i__4 = ix;
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i__5 = k;
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z__2.r = temp.r * ap[i__5].r - temp.i * ap[i__5]
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.i, z__2.i = temp.r * ap[i__5].i + temp.i
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* ap[i__5].r;
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z__1.r = x[i__4].r + z__2.r, z__1.i = x[i__4].i +
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z__2.i;
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x[i__3].r = z__1.r, x[i__3].i = z__1.i;
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ix += *incx;
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/* L30: */
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}
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if (nounit) {
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i__2 = jx;
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i__3 = jx;
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i__4 = kk + j - 1;
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z__1.r = x[i__3].r * ap[i__4].r - x[i__3].i * ap[
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i__4].i, z__1.i = x[i__3].r * ap[i__4].i
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+ x[i__3].i * ap[i__4].r;
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x[i__2].r = z__1.r, x[i__2].i = z__1.i;
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}
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}
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jx += *incx;
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kk += j;
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/* L40: */
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}
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}
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} else {
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kk = *n * (*n + 1) / 2;
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if (*incx == 1) {
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for (j = *n; j >= 1; --j) {
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i__1 = j;
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if (x[i__1].r != 0. || x[i__1].i != 0.) {
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i__1 = j;
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temp.r = x[i__1].r, temp.i = x[i__1].i;
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k = kk;
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i__1 = j + 1;
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for (i__ = *n; i__ >= i__1; --i__) {
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i__2 = i__;
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i__3 = i__;
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i__4 = k;
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z__2.r = temp.r * ap[i__4].r - temp.i * ap[i__4]
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.i, z__2.i = temp.r * ap[i__4].i + temp.i
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* ap[i__4].r;
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z__1.r = x[i__3].r + z__2.r, z__1.i = x[i__3].i +
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z__2.i;
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x[i__2].r = z__1.r, x[i__2].i = z__1.i;
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--k;
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/* L50: */
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}
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if (nounit) {
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i__1 = j;
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i__2 = j;
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i__3 = kk - *n + j;
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z__1.r = x[i__2].r * ap[i__3].r - x[i__2].i * ap[
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i__3].i, z__1.i = x[i__2].r * ap[i__3].i
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+ x[i__2].i * ap[i__3].r;
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x[i__1].r = z__1.r, x[i__1].i = z__1.i;
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}
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}
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kk -= *n - j + 1;
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/* L60: */
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}
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} else {
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kx += (*n - 1) * *incx;
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jx = kx;
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for (j = *n; j >= 1; --j) {
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i__1 = jx;
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if (x[i__1].r != 0. || x[i__1].i != 0.) {
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i__1 = jx;
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temp.r = x[i__1].r, temp.i = x[i__1].i;
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ix = kx;
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i__1 = kk - (*n - (j + 1));
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for (k = kk; k >= i__1; --k) {
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i__2 = ix;
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i__3 = ix;
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i__4 = k;
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z__2.r = temp.r * ap[i__4].r - temp.i * ap[i__4]
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.i, z__2.i = temp.r * ap[i__4].i + temp.i
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* ap[i__4].r;
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z__1.r = x[i__3].r + z__2.r, z__1.i = x[i__3].i +
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z__2.i;
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x[i__2].r = z__1.r, x[i__2].i = z__1.i;
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ix -= *incx;
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/* L70: */
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}
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if (nounit) {
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i__1 = jx;
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i__2 = jx;
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i__3 = kk - *n + j;
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z__1.r = x[i__2].r * ap[i__3].r - x[i__2].i * ap[
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i__3].i, z__1.i = x[i__2].r * ap[i__3].i
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+ x[i__2].i * ap[i__3].r;
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x[i__1].r = z__1.r, x[i__1].i = z__1.i;
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}
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}
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jx -= *incx;
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kk -= *n - j + 1;
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/* L80: */
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}
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}
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}
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} else {
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/* Form x := A**T*x or x := A**H*x. */
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if (lsame_(uplo, (char *)"U", (ftnlen)1, (ftnlen)1)) {
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kk = *n * (*n + 1) / 2;
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if (*incx == 1) {
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for (j = *n; j >= 1; --j) {
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i__1 = j;
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temp.r = x[i__1].r, temp.i = x[i__1].i;
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k = kk - 1;
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if (noconj) {
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if (nounit) {
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i__1 = kk;
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z__1.r = temp.r * ap[i__1].r - temp.i * ap[i__1]
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.i, z__1.i = temp.r * ap[i__1].i + temp.i
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* ap[i__1].r;
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temp.r = z__1.r, temp.i = z__1.i;
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}
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for (i__ = j - 1; i__ >= 1; --i__) {
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i__1 = k;
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i__2 = i__;
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z__2.r = ap[i__1].r * x[i__2].r - ap[i__1].i * x[
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i__2].i, z__2.i = ap[i__1].r * x[i__2].i
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+ ap[i__1].i * x[i__2].r;
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z__1.r = temp.r + z__2.r, z__1.i = temp.i +
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z__2.i;
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temp.r = z__1.r, temp.i = z__1.i;
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--k;
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/* L90: */
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}
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} else {
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if (nounit) {
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d_cnjg(&z__2, &ap[kk]);
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z__1.r = temp.r * z__2.r - temp.i * z__2.i,
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z__1.i = temp.r * z__2.i + temp.i *
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z__2.r;
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temp.r = z__1.r, temp.i = z__1.i;
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}
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for (i__ = j - 1; i__ >= 1; --i__) {
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d_cnjg(&z__3, &ap[k]);
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i__1 = i__;
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z__2.r = z__3.r * x[i__1].r - z__3.i * x[i__1].i,
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z__2.i = z__3.r * x[i__1].i + z__3.i * x[
|
|
i__1].r;
|
|
z__1.r = temp.r + z__2.r, z__1.i = temp.i +
|
|
z__2.i;
|
|
temp.r = z__1.r, temp.i = z__1.i;
|
|
--k;
|
|
/* L100: */
|
|
}
|
|
}
|
|
i__1 = j;
|
|
x[i__1].r = temp.r, x[i__1].i = temp.i;
|
|
kk -= j;
|
|
/* L110: */
|
|
}
|
|
} else {
|
|
jx = kx + (*n - 1) * *incx;
|
|
for (j = *n; j >= 1; --j) {
|
|
i__1 = jx;
|
|
temp.r = x[i__1].r, temp.i = x[i__1].i;
|
|
ix = jx;
|
|
if (noconj) {
|
|
if (nounit) {
|
|
i__1 = kk;
|
|
z__1.r = temp.r * ap[i__1].r - temp.i * ap[i__1]
|
|
.i, z__1.i = temp.r * ap[i__1].i + temp.i
|
|
* ap[i__1].r;
|
|
temp.r = z__1.r, temp.i = z__1.i;
|
|
}
|
|
i__1 = kk - j + 1;
|
|
for (k = kk - 1; k >= i__1; --k) {
|
|
ix -= *incx;
|
|
i__2 = k;
|
|
i__3 = ix;
|
|
z__2.r = ap[i__2].r * x[i__3].r - ap[i__2].i * x[
|
|
i__3].i, z__2.i = ap[i__2].r * x[i__3].i
|
|
+ ap[i__2].i * x[i__3].r;
|
|
z__1.r = temp.r + z__2.r, z__1.i = temp.i +
|
|
z__2.i;
|
|
temp.r = z__1.r, temp.i = z__1.i;
|
|
/* L120: */
|
|
}
|
|
} else {
|
|
if (nounit) {
|
|
d_cnjg(&z__2, &ap[kk]);
|
|
z__1.r = temp.r * z__2.r - temp.i * z__2.i,
|
|
z__1.i = temp.r * z__2.i + temp.i *
|
|
z__2.r;
|
|
temp.r = z__1.r, temp.i = z__1.i;
|
|
}
|
|
i__1 = kk - j + 1;
|
|
for (k = kk - 1; k >= i__1; --k) {
|
|
ix -= *incx;
|
|
d_cnjg(&z__3, &ap[k]);
|
|
i__2 = ix;
|
|
z__2.r = z__3.r * x[i__2].r - z__3.i * x[i__2].i,
|
|
z__2.i = z__3.r * x[i__2].i + z__3.i * x[
|
|
i__2].r;
|
|
z__1.r = temp.r + z__2.r, z__1.i = temp.i +
|
|
z__2.i;
|
|
temp.r = z__1.r, temp.i = z__1.i;
|
|
/* L130: */
|
|
}
|
|
}
|
|
i__1 = jx;
|
|
x[i__1].r = temp.r, x[i__1].i = temp.i;
|
|
jx -= *incx;
|
|
kk -= j;
|
|
/* L140: */
|
|
}
|
|
}
|
|
} else {
|
|
kk = 1;
|
|
if (*incx == 1) {
|
|
i__1 = *n;
|
|
for (j = 1; j <= i__1; ++j) {
|
|
i__2 = j;
|
|
temp.r = x[i__2].r, temp.i = x[i__2].i;
|
|
k = kk + 1;
|
|
if (noconj) {
|
|
if (nounit) {
|
|
i__2 = kk;
|
|
z__1.r = temp.r * ap[i__2].r - temp.i * ap[i__2]
|
|
.i, z__1.i = temp.r * ap[i__2].i + temp.i
|
|
* ap[i__2].r;
|
|
temp.r = z__1.r, temp.i = z__1.i;
|
|
}
|
|
i__2 = *n;
|
|
for (i__ = j + 1; i__ <= i__2; ++i__) {
|
|
i__3 = k;
|
|
i__4 = i__;
|
|
z__2.r = ap[i__3].r * x[i__4].r - ap[i__3].i * x[
|
|
i__4].i, z__2.i = ap[i__3].r * x[i__4].i
|
|
+ ap[i__3].i * x[i__4].r;
|
|
z__1.r = temp.r + z__2.r, z__1.i = temp.i +
|
|
z__2.i;
|
|
temp.r = z__1.r, temp.i = z__1.i;
|
|
++k;
|
|
/* L150: */
|
|
}
|
|
} else {
|
|
if (nounit) {
|
|
d_cnjg(&z__2, &ap[kk]);
|
|
z__1.r = temp.r * z__2.r - temp.i * z__2.i,
|
|
z__1.i = temp.r * z__2.i + temp.i *
|
|
z__2.r;
|
|
temp.r = z__1.r, temp.i = z__1.i;
|
|
}
|
|
i__2 = *n;
|
|
for (i__ = j + 1; i__ <= i__2; ++i__) {
|
|
d_cnjg(&z__3, &ap[k]);
|
|
i__3 = i__;
|
|
z__2.r = z__3.r * x[i__3].r - z__3.i * x[i__3].i,
|
|
z__2.i = z__3.r * x[i__3].i + z__3.i * x[
|
|
i__3].r;
|
|
z__1.r = temp.r + z__2.r, z__1.i = temp.i +
|
|
z__2.i;
|
|
temp.r = z__1.r, temp.i = z__1.i;
|
|
++k;
|
|
/* L160: */
|
|
}
|
|
}
|
|
i__2 = j;
|
|
x[i__2].r = temp.r, x[i__2].i = temp.i;
|
|
kk += *n - j + 1;
|
|
/* L170: */
|
|
}
|
|
} else {
|
|
jx = kx;
|
|
i__1 = *n;
|
|
for (j = 1; j <= i__1; ++j) {
|
|
i__2 = jx;
|
|
temp.r = x[i__2].r, temp.i = x[i__2].i;
|
|
ix = jx;
|
|
if (noconj) {
|
|
if (nounit) {
|
|
i__2 = kk;
|
|
z__1.r = temp.r * ap[i__2].r - temp.i * ap[i__2]
|
|
.i, z__1.i = temp.r * ap[i__2].i + temp.i
|
|
* ap[i__2].r;
|
|
temp.r = z__1.r, temp.i = z__1.i;
|
|
}
|
|
i__2 = kk + *n - j;
|
|
for (k = kk + 1; k <= i__2; ++k) {
|
|
ix += *incx;
|
|
i__3 = k;
|
|
i__4 = ix;
|
|
z__2.r = ap[i__3].r * x[i__4].r - ap[i__3].i * x[
|
|
i__4].i, z__2.i = ap[i__3].r * x[i__4].i
|
|
+ ap[i__3].i * x[i__4].r;
|
|
z__1.r = temp.r + z__2.r, z__1.i = temp.i +
|
|
z__2.i;
|
|
temp.r = z__1.r, temp.i = z__1.i;
|
|
/* L180: */
|
|
}
|
|
} else {
|
|
if (nounit) {
|
|
d_cnjg(&z__2, &ap[kk]);
|
|
z__1.r = temp.r * z__2.r - temp.i * z__2.i,
|
|
z__1.i = temp.r * z__2.i + temp.i *
|
|
z__2.r;
|
|
temp.r = z__1.r, temp.i = z__1.i;
|
|
}
|
|
i__2 = kk + *n - j;
|
|
for (k = kk + 1; k <= i__2; ++k) {
|
|
ix += *incx;
|
|
d_cnjg(&z__3, &ap[k]);
|
|
i__3 = ix;
|
|
z__2.r = z__3.r * x[i__3].r - z__3.i * x[i__3].i,
|
|
z__2.i = z__3.r * x[i__3].i + z__3.i * x[
|
|
i__3].r;
|
|
z__1.r = temp.r + z__2.r, z__1.i = temp.i +
|
|
z__2.i;
|
|
temp.r = z__1.r, temp.i = z__1.i;
|
|
/* L190: */
|
|
}
|
|
}
|
|
i__2 = jx;
|
|
x[i__2].r = temp.r, x[i__2].i = temp.i;
|
|
jx += *incx;
|
|
kk += *n - j + 1;
|
|
/* L200: */
|
|
}
|
|
}
|
|
}
|
|
}
|
|
|
|
return 0;
|
|
|
|
/* End of ZTPMV */
|
|
|
|
} /* ztpmv_ */
|
|
|
|
#ifdef __cplusplus
|
|
}
|
|
#endif
|