509 lines
18 KiB
C++
509 lines
18 KiB
C++
/* fortran/zhemv.f -- translated by f2c (version 20200916).
|
|
You must link the resulting object file with libf2c:
|
|
on Microsoft Windows system, link with libf2c.lib;
|
|
on Linux or Unix systems, link with .../path/to/libf2c.a -lm
|
|
or, if you install libf2c.a in a standard place, with -lf2c -lm
|
|
-- in that order, at the end of the command line, as in
|
|
cc *.o -lf2c -lm
|
|
Source for libf2c is in /netlib/f2c/libf2c.zip, e.g.,
|
|
|
|
http://www.netlib.org/f2c/libf2c.zip
|
|
*/
|
|
|
|
#ifdef __cplusplus
|
|
extern "C" {
|
|
#endif
|
|
#include "lmp_f2c.h"
|
|
|
|
/* > \brief \b ZHEMV */
|
|
|
|
/* =========== DOCUMENTATION =========== */
|
|
|
|
/* Online html documentation available at */
|
|
/* http://www.netlib.org/lapack/explore-html/ */
|
|
|
|
/* Definition: */
|
|
/* =========== */
|
|
|
|
/* SUBROUTINE ZHEMV(UPLO,N,ALPHA,A,LDA,X,INCX,BETA,Y,INCY) */
|
|
|
|
/* .. Scalar Arguments .. */
|
|
/* COMPLEX*16 ALPHA,BETA */
|
|
/* INTEGER INCX,INCY,LDA,N */
|
|
/* CHARACTER UPLO */
|
|
/* .. */
|
|
/* .. Array Arguments .. */
|
|
/* COMPLEX*16 A(LDA,*),X(*),Y(*) */
|
|
/* .. */
|
|
|
|
|
|
/* > \par Purpose: */
|
|
/* ============= */
|
|
/* > */
|
|
/* > \verbatim */
|
|
/* > */
|
|
/* > ZHEMV performs the matrix-vector operation */
|
|
/* > */
|
|
/* > y := alpha*A*x + beta*y, */
|
|
/* > */
|
|
/* > where alpha and beta are scalars, x and y are n element vectors and */
|
|
/* > A is an n by n hermitian matrix. */
|
|
/* > \endverbatim */
|
|
|
|
/* Arguments: */
|
|
/* ========== */
|
|
|
|
/* > \param[in] UPLO */
|
|
/* > \verbatim */
|
|
/* > UPLO is CHARACTER*1 */
|
|
/* > On entry, UPLO specifies whether the upper or lower */
|
|
/* > triangular part of the array A is to be referenced as */
|
|
/* > follows: */
|
|
/* > */
|
|
/* > UPLO = 'U' or 'u' Only the upper triangular part of A */
|
|
/* > is to be referenced. */
|
|
/* > */
|
|
/* > UPLO = 'L' or 'l' Only the lower triangular part of A */
|
|
/* > is to be referenced. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] N */
|
|
/* > \verbatim */
|
|
/* > N is INTEGER */
|
|
/* > On entry, N specifies the order of the matrix A. */
|
|
/* > N must be at least zero. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] ALPHA */
|
|
/* > \verbatim */
|
|
/* > ALPHA is COMPLEX*16 */
|
|
/* > On entry, ALPHA specifies the scalar alpha. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] A */
|
|
/* > \verbatim */
|
|
/* > A is COMPLEX*16 array, dimension ( LDA, N ) */
|
|
/* > Before entry with UPLO = 'U' or 'u', the leading n by n */
|
|
/* > upper triangular part of the array A must contain the upper */
|
|
/* > triangular part of the hermitian matrix and the strictly */
|
|
/* > lower triangular part of A is not referenced. */
|
|
/* > Before entry with UPLO = 'L' or 'l', the leading n by n */
|
|
/* > lower triangular part of the array A must contain the lower */
|
|
/* > triangular part of the hermitian matrix and the strictly */
|
|
/* > upper triangular part of A is not referenced. */
|
|
/* > Note that the imaginary parts of the diagonal elements need */
|
|
/* > not be set and are assumed to be zero. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] LDA */
|
|
/* > \verbatim */
|
|
/* > LDA is INTEGER */
|
|
/* > On entry, LDA specifies the first dimension of A as declared */
|
|
/* > in the calling (sub) program. LDA must be at least */
|
|
/* > max( 1, n ). */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] X */
|
|
/* > \verbatim */
|
|
/* > X is COMPLEX*16 array, dimension at least */
|
|
/* > ( 1 + ( n - 1 )*abs( INCX ) ). */
|
|
/* > Before entry, the incremented array X must contain the n */
|
|
/* > element vector x. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] INCX */
|
|
/* > \verbatim */
|
|
/* > INCX is INTEGER */
|
|
/* > On entry, INCX specifies the increment for the elements of */
|
|
/* > X. INCX must not be zero. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] BETA */
|
|
/* > \verbatim */
|
|
/* > BETA is COMPLEX*16 */
|
|
/* > On entry, BETA specifies the scalar beta. When BETA is */
|
|
/* > supplied as zero then Y need not be set on input. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in,out] Y */
|
|
/* > \verbatim */
|
|
/* > Y is COMPLEX*16 array, dimension at least */
|
|
/* > ( 1 + ( n - 1 )*abs( INCY ) ). */
|
|
/* > Before entry, the incremented array Y must contain the n */
|
|
/* > element vector y. On exit, Y is overwritten by the updated */
|
|
/* > vector y. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* > \param[in] INCY */
|
|
/* > \verbatim */
|
|
/* > INCY is INTEGER */
|
|
/* > On entry, INCY specifies the increment for the elements of */
|
|
/* > Y. INCY must not be zero. */
|
|
/* > \endverbatim */
|
|
|
|
/* Authors: */
|
|
/* ======== */
|
|
|
|
/* > \author Univ. of Tennessee */
|
|
/* > \author Univ. of California Berkeley */
|
|
/* > \author Univ. of Colorado Denver */
|
|
/* > \author NAG Ltd. */
|
|
|
|
/* > \ingroup complex16_blas_level2 */
|
|
|
|
/* > \par Further Details: */
|
|
/* ===================== */
|
|
/* > */
|
|
/* > \verbatim */
|
|
/* > */
|
|
/* > Level 2 Blas routine. */
|
|
/* > The vector and matrix arguments are not referenced when N = 0, or M = 0 */
|
|
/* > */
|
|
/* > -- Written on 22-October-1986. */
|
|
/* > Jack Dongarra, Argonne National Lab. */
|
|
/* > Jeremy Du Croz, Nag Central Office. */
|
|
/* > Sven Hammarling, Nag Central Office. */
|
|
/* > Richard Hanson, Sandia National Labs. */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* ===================================================================== */
|
|
/* Subroutine */ int zhemv_(char *uplo, integer *n, doublecomplex *alpha,
|
|
doublecomplex *a, integer *lda, doublecomplex *x, integer *incx,
|
|
doublecomplex *beta, doublecomplex *y, integer *incy, ftnlen uplo_len)
|
|
{
|
|
/* System generated locals */
|
|
integer a_dim1, a_offset, i__1, i__2, i__3, i__4, i__5;
|
|
doublereal d__1;
|
|
doublecomplex z__1, z__2, z__3, z__4;
|
|
|
|
/* Builtin functions */
|
|
void d_lmp_cnjg(doublecomplex *, doublecomplex *);
|
|
|
|
/* Local variables */
|
|
integer i__, j, ix, iy, jx, jy, kx, ky, info;
|
|
doublecomplex temp1, temp2;
|
|
extern logical lsame_(char *, char *, ftnlen, ftnlen);
|
|
extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen);
|
|
|
|
|
|
/* -- Reference BLAS level2 routine -- */
|
|
/* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- */
|
|
/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
|
|
|
|
/* .. Scalar Arguments .. */
|
|
/* .. */
|
|
/* .. Array Arguments .. */
|
|
/* .. */
|
|
|
|
/* ===================================================================== */
|
|
|
|
/* .. Parameters .. */
|
|
/* .. */
|
|
/* .. Local Scalars .. */
|
|
/* .. */
|
|
/* .. External Functions .. */
|
|
/* .. */
|
|
/* .. External Subroutines .. */
|
|
/* .. */
|
|
/* .. Intrinsic Functions .. */
|
|
/* .. */
|
|
|
|
/* Test the input parameters. */
|
|
|
|
/* Parameter adjustments */
|
|
a_dim1 = *lda;
|
|
a_offset = 1 + a_dim1;
|
|
a -= a_offset;
|
|
--x;
|
|
--y;
|
|
|
|
/* Function Body */
|
|
info = 0;
|
|
if (! lsame_(uplo, (char *)"U", (ftnlen)1, (ftnlen)1) && ! lsame_(uplo, (char *)"L", (
|
|
ftnlen)1, (ftnlen)1)) {
|
|
info = 1;
|
|
} else if (*n < 0) {
|
|
info = 2;
|
|
} else if (*lda < max(1,*n)) {
|
|
info = 5;
|
|
} else if (*incx == 0) {
|
|
info = 7;
|
|
} else if (*incy == 0) {
|
|
info = 10;
|
|
}
|
|
if (info != 0) {
|
|
xerbla_((char *)"ZHEMV ", &info, (ftnlen)6);
|
|
return 0;
|
|
}
|
|
|
|
/* Quick return if possible. */
|
|
|
|
if (*n == 0 || alpha->r == 0. && alpha->i == 0. && (beta->r == 1. &&
|
|
beta->i == 0.)) {
|
|
return 0;
|
|
}
|
|
|
|
/* Set up the start points in X and Y. */
|
|
|
|
if (*incx > 0) {
|
|
kx = 1;
|
|
} else {
|
|
kx = 1 - (*n - 1) * *incx;
|
|
}
|
|
if (*incy > 0) {
|
|
ky = 1;
|
|
} else {
|
|
ky = 1 - (*n - 1) * *incy;
|
|
}
|
|
|
|
/* Start the operations. In this version the elements of A are */
|
|
/* accessed sequentially with one pass through the triangular part */
|
|
/* of A. */
|
|
|
|
/* First form y := beta*y. */
|
|
|
|
if (beta->r != 1. || beta->i != 0.) {
|
|
if (*incy == 1) {
|
|
if (beta->r == 0. && beta->i == 0.) {
|
|
i__1 = *n;
|
|
for (i__ = 1; i__ <= i__1; ++i__) {
|
|
i__2 = i__;
|
|
y[i__2].r = 0., y[i__2].i = 0.;
|
|
/* L10: */
|
|
}
|
|
} else {
|
|
i__1 = *n;
|
|
for (i__ = 1; i__ <= i__1; ++i__) {
|
|
i__2 = i__;
|
|
i__3 = i__;
|
|
z__1.r = beta->r * y[i__3].r - beta->i * y[i__3].i,
|
|
z__1.i = beta->r * y[i__3].i + beta->i * y[i__3]
|
|
.r;
|
|
y[i__2].r = z__1.r, y[i__2].i = z__1.i;
|
|
/* L20: */
|
|
}
|
|
}
|
|
} else {
|
|
iy = ky;
|
|
if (beta->r == 0. && beta->i == 0.) {
|
|
i__1 = *n;
|
|
for (i__ = 1; i__ <= i__1; ++i__) {
|
|
i__2 = iy;
|
|
y[i__2].r = 0., y[i__2].i = 0.;
|
|
iy += *incy;
|
|
/* L30: */
|
|
}
|
|
} else {
|
|
i__1 = *n;
|
|
for (i__ = 1; i__ <= i__1; ++i__) {
|
|
i__2 = iy;
|
|
i__3 = iy;
|
|
z__1.r = beta->r * y[i__3].r - beta->i * y[i__3].i,
|
|
z__1.i = beta->r * y[i__3].i + beta->i * y[i__3]
|
|
.r;
|
|
y[i__2].r = z__1.r, y[i__2].i = z__1.i;
|
|
iy += *incy;
|
|
/* L40: */
|
|
}
|
|
}
|
|
}
|
|
}
|
|
if (alpha->r == 0. && alpha->i == 0.) {
|
|
return 0;
|
|
}
|
|
if (lsame_(uplo, (char *)"U", (ftnlen)1, (ftnlen)1)) {
|
|
|
|
/* Form y when A is stored in upper triangle. */
|
|
|
|
if (*incx == 1 && *incy == 1) {
|
|
i__1 = *n;
|
|
for (j = 1; j <= i__1; ++j) {
|
|
i__2 = j;
|
|
z__1.r = alpha->r * x[i__2].r - alpha->i * x[i__2].i, z__1.i =
|
|
alpha->r * x[i__2].i + alpha->i * x[i__2].r;
|
|
temp1.r = z__1.r, temp1.i = z__1.i;
|
|
temp2.r = 0., temp2.i = 0.;
|
|
i__2 = j - 1;
|
|
for (i__ = 1; i__ <= i__2; ++i__) {
|
|
i__3 = i__;
|
|
i__4 = i__;
|
|
i__5 = i__ + j * a_dim1;
|
|
z__2.r = temp1.r * a[i__5].r - temp1.i * a[i__5].i,
|
|
z__2.i = temp1.r * a[i__5].i + temp1.i * a[i__5]
|
|
.r;
|
|
z__1.r = y[i__4].r + z__2.r, z__1.i = y[i__4].i + z__2.i;
|
|
y[i__3].r = z__1.r, y[i__3].i = z__1.i;
|
|
d_lmp_cnjg(&z__3, &a[i__ + j * a_dim1]);
|
|
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 = temp2.r + z__2.r, z__1.i = temp2.i + z__2.i;
|
|
temp2.r = z__1.r, temp2.i = z__1.i;
|
|
/* L50: */
|
|
}
|
|
i__2 = j;
|
|
i__3 = j;
|
|
i__4 = j + j * a_dim1;
|
|
d__1 = a[i__4].r;
|
|
z__3.r = d__1 * temp1.r, z__3.i = d__1 * temp1.i;
|
|
z__2.r = y[i__3].r + z__3.r, z__2.i = y[i__3].i + z__3.i;
|
|
z__4.r = alpha->r * temp2.r - alpha->i * temp2.i, z__4.i =
|
|
alpha->r * temp2.i + alpha->i * temp2.r;
|
|
z__1.r = z__2.r + z__4.r, z__1.i = z__2.i + z__4.i;
|
|
y[i__2].r = z__1.r, y[i__2].i = z__1.i;
|
|
/* L60: */
|
|
}
|
|
} else {
|
|
jx = kx;
|
|
jy = ky;
|
|
i__1 = *n;
|
|
for (j = 1; j <= i__1; ++j) {
|
|
i__2 = jx;
|
|
z__1.r = alpha->r * x[i__2].r - alpha->i * x[i__2].i, z__1.i =
|
|
alpha->r * x[i__2].i + alpha->i * x[i__2].r;
|
|
temp1.r = z__1.r, temp1.i = z__1.i;
|
|
temp2.r = 0., temp2.i = 0.;
|
|
ix = kx;
|
|
iy = ky;
|
|
i__2 = j - 1;
|
|
for (i__ = 1; i__ <= i__2; ++i__) {
|
|
i__3 = iy;
|
|
i__4 = iy;
|
|
i__5 = i__ + j * a_dim1;
|
|
z__2.r = temp1.r * a[i__5].r - temp1.i * a[i__5].i,
|
|
z__2.i = temp1.r * a[i__5].i + temp1.i * a[i__5]
|
|
.r;
|
|
z__1.r = y[i__4].r + z__2.r, z__1.i = y[i__4].i + z__2.i;
|
|
y[i__3].r = z__1.r, y[i__3].i = z__1.i;
|
|
d_lmp_cnjg(&z__3, &a[i__ + j * a_dim1]);
|
|
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 = temp2.r + z__2.r, z__1.i = temp2.i + z__2.i;
|
|
temp2.r = z__1.r, temp2.i = z__1.i;
|
|
ix += *incx;
|
|
iy += *incy;
|
|
/* L70: */
|
|
}
|
|
i__2 = jy;
|
|
i__3 = jy;
|
|
i__4 = j + j * a_dim1;
|
|
d__1 = a[i__4].r;
|
|
z__3.r = d__1 * temp1.r, z__3.i = d__1 * temp1.i;
|
|
z__2.r = y[i__3].r + z__3.r, z__2.i = y[i__3].i + z__3.i;
|
|
z__4.r = alpha->r * temp2.r - alpha->i * temp2.i, z__4.i =
|
|
alpha->r * temp2.i + alpha->i * temp2.r;
|
|
z__1.r = z__2.r + z__4.r, z__1.i = z__2.i + z__4.i;
|
|
y[i__2].r = z__1.r, y[i__2].i = z__1.i;
|
|
jx += *incx;
|
|
jy += *incy;
|
|
/* L80: */
|
|
}
|
|
}
|
|
} else {
|
|
|
|
/* Form y when A is stored in lower triangle. */
|
|
|
|
if (*incx == 1 && *incy == 1) {
|
|
i__1 = *n;
|
|
for (j = 1; j <= i__1; ++j) {
|
|
i__2 = j;
|
|
z__1.r = alpha->r * x[i__2].r - alpha->i * x[i__2].i, z__1.i =
|
|
alpha->r * x[i__2].i + alpha->i * x[i__2].r;
|
|
temp1.r = z__1.r, temp1.i = z__1.i;
|
|
temp2.r = 0., temp2.i = 0.;
|
|
i__2 = j;
|
|
i__3 = j;
|
|
i__4 = j + j * a_dim1;
|
|
d__1 = a[i__4].r;
|
|
z__2.r = d__1 * temp1.r, z__2.i = d__1 * temp1.i;
|
|
z__1.r = y[i__3].r + z__2.r, z__1.i = y[i__3].i + z__2.i;
|
|
y[i__2].r = z__1.r, y[i__2].i = z__1.i;
|
|
i__2 = *n;
|
|
for (i__ = j + 1; i__ <= i__2; ++i__) {
|
|
i__3 = i__;
|
|
i__4 = i__;
|
|
i__5 = i__ + j * a_dim1;
|
|
z__2.r = temp1.r * a[i__5].r - temp1.i * a[i__5].i,
|
|
z__2.i = temp1.r * a[i__5].i + temp1.i * a[i__5]
|
|
.r;
|
|
z__1.r = y[i__4].r + z__2.r, z__1.i = y[i__4].i + z__2.i;
|
|
y[i__3].r = z__1.r, y[i__3].i = z__1.i;
|
|
d_lmp_cnjg(&z__3, &a[i__ + j * a_dim1]);
|
|
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 = temp2.r + z__2.r, z__1.i = temp2.i + z__2.i;
|
|
temp2.r = z__1.r, temp2.i = z__1.i;
|
|
/* L90: */
|
|
}
|
|
i__2 = j;
|
|
i__3 = j;
|
|
z__2.r = alpha->r * temp2.r - alpha->i * temp2.i, z__2.i =
|
|
alpha->r * temp2.i + alpha->i * temp2.r;
|
|
z__1.r = y[i__3].r + z__2.r, z__1.i = y[i__3].i + z__2.i;
|
|
y[i__2].r = z__1.r, y[i__2].i = z__1.i;
|
|
/* L100: */
|
|
}
|
|
} else {
|
|
jx = kx;
|
|
jy = ky;
|
|
i__1 = *n;
|
|
for (j = 1; j <= i__1; ++j) {
|
|
i__2 = jx;
|
|
z__1.r = alpha->r * x[i__2].r - alpha->i * x[i__2].i, z__1.i =
|
|
alpha->r * x[i__2].i + alpha->i * x[i__2].r;
|
|
temp1.r = z__1.r, temp1.i = z__1.i;
|
|
temp2.r = 0., temp2.i = 0.;
|
|
i__2 = jy;
|
|
i__3 = jy;
|
|
i__4 = j + j * a_dim1;
|
|
d__1 = a[i__4].r;
|
|
z__2.r = d__1 * temp1.r, z__2.i = d__1 * temp1.i;
|
|
z__1.r = y[i__3].r + z__2.r, z__1.i = y[i__3].i + z__2.i;
|
|
y[i__2].r = z__1.r, y[i__2].i = z__1.i;
|
|
ix = jx;
|
|
iy = jy;
|
|
i__2 = *n;
|
|
for (i__ = j + 1; i__ <= i__2; ++i__) {
|
|
ix += *incx;
|
|
iy += *incy;
|
|
i__3 = iy;
|
|
i__4 = iy;
|
|
i__5 = i__ + j * a_dim1;
|
|
z__2.r = temp1.r * a[i__5].r - temp1.i * a[i__5].i,
|
|
z__2.i = temp1.r * a[i__5].i + temp1.i * a[i__5]
|
|
.r;
|
|
z__1.r = y[i__4].r + z__2.r, z__1.i = y[i__4].i + z__2.i;
|
|
y[i__3].r = z__1.r, y[i__3].i = z__1.i;
|
|
d_lmp_cnjg(&z__3, &a[i__ + j * a_dim1]);
|
|
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 = temp2.r + z__2.r, z__1.i = temp2.i + z__2.i;
|
|
temp2.r = z__1.r, temp2.i = z__1.i;
|
|
/* L110: */
|
|
}
|
|
i__2 = jy;
|
|
i__3 = jy;
|
|
z__2.r = alpha->r * temp2.r - alpha->i * temp2.i, z__2.i =
|
|
alpha->r * temp2.i + alpha->i * temp2.r;
|
|
z__1.r = y[i__3].r + z__2.r, z__1.i = y[i__3].i + z__2.i;
|
|
y[i__2].r = z__1.r, y[i__2].i = z__1.i;
|
|
jx += *incx;
|
|
jy += *incy;
|
|
/* L120: */
|
|
}
|
|
}
|
|
}
|
|
|
|
return 0;
|
|
|
|
/* End of ZHEMV */
|
|
|
|
} /* zhemv_ */
|
|
|
|
#ifdef __cplusplus
|
|
}
|
|
#endif
|