421 lines
12 KiB
C
421 lines
12 KiB
C
|
|
/* -- translated by f2c (version 19940927).
|
|
You must link the resulting object file with the libraries:
|
|
-lf2c -lm (in that order)
|
|
*/
|
|
|
|
#include "f2c.h"
|
|
|
|
/* Subroutine */ int chemv_(char *uplo, integer *n, complex *alpha, complex *
|
|
a, integer *lda, complex *x, integer *incx, complex *beta, complex *y,
|
|
integer *incy)
|
|
{
|
|
|
|
|
|
/* System generated locals */
|
|
integer a_dim1, a_offset, i__1, i__2, i__3, i__4, i__5;
|
|
doublereal d__1;
|
|
complex q__1, q__2, q__3, q__4;
|
|
|
|
/* Builtin functions */
|
|
void r_cnjg(complex *, complex *);
|
|
|
|
/* Local variables */
|
|
static integer info;
|
|
static complex temp1, temp2;
|
|
static integer i, j;
|
|
extern logical lsame_(char *, char *);
|
|
static integer ix, iy, jx, jy, kx, ky;
|
|
extern /* Subroutine */ int xerbla_(char *, integer *);
|
|
|
|
|
|
/* Purpose
|
|
=======
|
|
|
|
CHEMV 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.
|
|
|
|
Parameters
|
|
==========
|
|
|
|
UPLO - 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.
|
|
|
|
Unchanged on exit.
|
|
|
|
N - INTEGER.
|
|
On entry, N specifies the order of the matrix A.
|
|
N must be at least zero.
|
|
Unchanged on exit.
|
|
|
|
ALPHA - COMPLEX .
|
|
On entry, ALPHA specifies the scalar alpha.
|
|
Unchanged on exit.
|
|
|
|
A - COMPLEX array of 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.
|
|
Unchanged on exit.
|
|
|
|
LDA - 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 ).
|
|
Unchanged on exit.
|
|
|
|
X - COMPLEX array of dimension at least
|
|
( 1 + ( n - 1 )*abs( INCX ) ).
|
|
Before entry, the incremented array X must contain the n
|
|
element vector x.
|
|
Unchanged on exit.
|
|
|
|
INCX - INTEGER.
|
|
On entry, INCX specifies the increment for the elements of
|
|
X. INCX must not be zero.
|
|
Unchanged on exit.
|
|
|
|
BETA - COMPLEX .
|
|
On entry, BETA specifies the scalar beta. When BETA is
|
|
supplied as zero then Y need not be set on input.
|
|
Unchanged on exit.
|
|
|
|
Y - COMPLEX array of 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.
|
|
|
|
INCY - INTEGER.
|
|
On entry, INCY specifies the increment for the elements of
|
|
Y. INCY must not be zero.
|
|
Unchanged on exit.
|
|
|
|
|
|
Level 2 Blas routine.
|
|
|
|
-- 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.
|
|
|
|
|
|
|
|
Test the input parameters.
|
|
|
|
|
|
Parameter adjustments
|
|
Function Body */
|
|
#define X(I) x[(I)-1]
|
|
#define Y(I) y[(I)-1]
|
|
|
|
#define A(I,J) a[(I)-1 + ((J)-1)* ( *lda)]
|
|
|
|
info = 0;
|
|
if (! lsame_(uplo, "U") && ! lsame_(uplo, "L")) {
|
|
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_("CHEMV ", &info);
|
|
return 0;
|
|
}
|
|
|
|
/* Quick return if possible. */
|
|
|
|
if (*n == 0 || alpha->r == 0.f && alpha->i == 0.f && (beta->r == 1.f &&
|
|
beta->i == 0.f)) {
|
|
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.f || beta->i != 0.f) {
|
|
if (*incy == 1) {
|
|
if (beta->r == 0.f && beta->i == 0.f) {
|
|
i__1 = *n;
|
|
for (i = 1; i <= *n; ++i) {
|
|
i__2 = i;
|
|
Y(i).r = 0.f, Y(i).i = 0.f;
|
|
/* L10: */
|
|
}
|
|
} else {
|
|
i__1 = *n;
|
|
for (i = 1; i <= *n; ++i) {
|
|
i__2 = i;
|
|
i__3 = i;
|
|
q__1.r = beta->r * Y(i).r - beta->i * Y(i).i,
|
|
q__1.i = beta->r * Y(i).i + beta->i * Y(i)
|
|
.r;
|
|
Y(i).r = q__1.r, Y(i).i = q__1.i;
|
|
/* L20: */
|
|
}
|
|
}
|
|
} else {
|
|
iy = ky;
|
|
if (beta->r == 0.f && beta->i == 0.f) {
|
|
i__1 = *n;
|
|
for (i = 1; i <= *n; ++i) {
|
|
i__2 = iy;
|
|
Y(iy).r = 0.f, Y(iy).i = 0.f;
|
|
iy += *incy;
|
|
/* L30: */
|
|
}
|
|
} else {
|
|
i__1 = *n;
|
|
for (i = 1; i <= *n; ++i) {
|
|
i__2 = iy;
|
|
i__3 = iy;
|
|
q__1.r = beta->r * Y(iy).r - beta->i * Y(iy).i,
|
|
q__1.i = beta->r * Y(iy).i + beta->i * Y(iy)
|
|
.r;
|
|
Y(iy).r = q__1.r, Y(iy).i = q__1.i;
|
|
iy += *incy;
|
|
/* L40: */
|
|
}
|
|
}
|
|
}
|
|
}
|
|
if (alpha->r == 0.f && alpha->i == 0.f) {
|
|
return 0;
|
|
}
|
|
if (lsame_(uplo, "U")) {
|
|
|
|
/* Form y when A is stored in upper triangle. */
|
|
|
|
if (*incx == 1 && *incy == 1) {
|
|
i__1 = *n;
|
|
for (j = 1; j <= *n; ++j) {
|
|
i__2 = j;
|
|
q__1.r = alpha->r * X(j).r - alpha->i * X(j).i, q__1.i =
|
|
alpha->r * X(j).i + alpha->i * X(j).r;
|
|
temp1.r = q__1.r, temp1.i = q__1.i;
|
|
temp2.r = 0.f, temp2.i = 0.f;
|
|
i__2 = j - 1;
|
|
for (i = 1; i <= j-1; ++i) {
|
|
i__3 = i;
|
|
i__4 = i;
|
|
i__5 = i + j * a_dim1;
|
|
q__2.r = temp1.r * A(i,j).r - temp1.i * A(i,j).i,
|
|
q__2.i = temp1.r * A(i,j).i + temp1.i * A(i,j)
|
|
.r;
|
|
q__1.r = Y(i).r + q__2.r, q__1.i = Y(i).i + q__2.i;
|
|
Y(i).r = q__1.r, Y(i).i = q__1.i;
|
|
r_cnjg(&q__3, &A(i,j));
|
|
i__3 = i;
|
|
q__2.r = q__3.r * X(i).r - q__3.i * X(i).i, q__2.i =
|
|
q__3.r * X(i).i + q__3.i * X(i).r;
|
|
q__1.r = temp2.r + q__2.r, q__1.i = temp2.i + q__2.i;
|
|
temp2.r = q__1.r, temp2.i = q__1.i;
|
|
/* L50: */
|
|
}
|
|
i__2 = j;
|
|
i__3 = j;
|
|
i__4 = j + j * a_dim1;
|
|
d__1 = A(j,j).r;
|
|
q__3.r = d__1 * temp1.r, q__3.i = d__1 * temp1.i;
|
|
q__2.r = Y(j).r + q__3.r, q__2.i = Y(j).i + q__3.i;
|
|
q__4.r = alpha->r * temp2.r - alpha->i * temp2.i, q__4.i =
|
|
alpha->r * temp2.i + alpha->i * temp2.r;
|
|
q__1.r = q__2.r + q__4.r, q__1.i = q__2.i + q__4.i;
|
|
Y(j).r = q__1.r, Y(j).i = q__1.i;
|
|
/* L60: */
|
|
}
|
|
} else {
|
|
jx = kx;
|
|
jy = ky;
|
|
i__1 = *n;
|
|
for (j = 1; j <= *n; ++j) {
|
|
i__2 = jx;
|
|
q__1.r = alpha->r * X(jx).r - alpha->i * X(jx).i, q__1.i =
|
|
alpha->r * X(jx).i + alpha->i * X(jx).r;
|
|
temp1.r = q__1.r, temp1.i = q__1.i;
|
|
temp2.r = 0.f, temp2.i = 0.f;
|
|
ix = kx;
|
|
iy = ky;
|
|
i__2 = j - 1;
|
|
for (i = 1; i <= j-1; ++i) {
|
|
i__3 = iy;
|
|
i__4 = iy;
|
|
i__5 = i + j * a_dim1;
|
|
q__2.r = temp1.r * A(i,j).r - temp1.i * A(i,j).i,
|
|
q__2.i = temp1.r * A(i,j).i + temp1.i * A(i,j)
|
|
.r;
|
|
q__1.r = Y(iy).r + q__2.r, q__1.i = Y(iy).i + q__2.i;
|
|
Y(iy).r = q__1.r, Y(iy).i = q__1.i;
|
|
r_cnjg(&q__3, &A(i,j));
|
|
i__3 = ix;
|
|
q__2.r = q__3.r * X(ix).r - q__3.i * X(ix).i, q__2.i =
|
|
q__3.r * X(ix).i + q__3.i * X(ix).r;
|
|
q__1.r = temp2.r + q__2.r, q__1.i = temp2.i + q__2.i;
|
|
temp2.r = q__1.r, temp2.i = q__1.i;
|
|
ix += *incx;
|
|
iy += *incy;
|
|
/* L70: */
|
|
}
|
|
i__2 = jy;
|
|
i__3 = jy;
|
|
i__4 = j + j * a_dim1;
|
|
d__1 = A(j,j).r;
|
|
q__3.r = d__1 * temp1.r, q__3.i = d__1 * temp1.i;
|
|
q__2.r = Y(jy).r + q__3.r, q__2.i = Y(jy).i + q__3.i;
|
|
q__4.r = alpha->r * temp2.r - alpha->i * temp2.i, q__4.i =
|
|
alpha->r * temp2.i + alpha->i * temp2.r;
|
|
q__1.r = q__2.r + q__4.r, q__1.i = q__2.i + q__4.i;
|
|
Y(jy).r = q__1.r, Y(jy).i = q__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 <= *n; ++j) {
|
|
i__2 = j;
|
|
q__1.r = alpha->r * X(j).r - alpha->i * X(j).i, q__1.i =
|
|
alpha->r * X(j).i + alpha->i * X(j).r;
|
|
temp1.r = q__1.r, temp1.i = q__1.i;
|
|
temp2.r = 0.f, temp2.i = 0.f;
|
|
i__2 = j;
|
|
i__3 = j;
|
|
i__4 = j + j * a_dim1;
|
|
d__1 = A(j,j).r;
|
|
q__2.r = d__1 * temp1.r, q__2.i = d__1 * temp1.i;
|
|
q__1.r = Y(j).r + q__2.r, q__1.i = Y(j).i + q__2.i;
|
|
Y(j).r = q__1.r, Y(j).i = q__1.i;
|
|
i__2 = *n;
|
|
for (i = j + 1; i <= *n; ++i) {
|
|
i__3 = i;
|
|
i__4 = i;
|
|
i__5 = i + j * a_dim1;
|
|
q__2.r = temp1.r * A(i,j).r - temp1.i * A(i,j).i,
|
|
q__2.i = temp1.r * A(i,j).i + temp1.i * A(i,j)
|
|
.r;
|
|
q__1.r = Y(i).r + q__2.r, q__1.i = Y(i).i + q__2.i;
|
|
Y(i).r = q__1.r, Y(i).i = q__1.i;
|
|
r_cnjg(&q__3, &A(i,j));
|
|
i__3 = i;
|
|
q__2.r = q__3.r * X(i).r - q__3.i * X(i).i, q__2.i =
|
|
q__3.r * X(i).i + q__3.i * X(i).r;
|
|
q__1.r = temp2.r + q__2.r, q__1.i = temp2.i + q__2.i;
|
|
temp2.r = q__1.r, temp2.i = q__1.i;
|
|
/* L90: */
|
|
}
|
|
i__2 = j;
|
|
i__3 = j;
|
|
q__2.r = alpha->r * temp2.r - alpha->i * temp2.i, q__2.i =
|
|
alpha->r * temp2.i + alpha->i * temp2.r;
|
|
q__1.r = Y(j).r + q__2.r, q__1.i = Y(j).i + q__2.i;
|
|
Y(j).r = q__1.r, Y(j).i = q__1.i;
|
|
/* L100: */
|
|
}
|
|
} else {
|
|
jx = kx;
|
|
jy = ky;
|
|
i__1 = *n;
|
|
for (j = 1; j <= *n; ++j) {
|
|
i__2 = jx;
|
|
q__1.r = alpha->r * X(jx).r - alpha->i * X(jx).i, q__1.i =
|
|
alpha->r * X(jx).i + alpha->i * X(jx).r;
|
|
temp1.r = q__1.r, temp1.i = q__1.i;
|
|
temp2.r = 0.f, temp2.i = 0.f;
|
|
i__2 = jy;
|
|
i__3 = jy;
|
|
i__4 = j + j * a_dim1;
|
|
d__1 = A(j,j).r;
|
|
q__2.r = d__1 * temp1.r, q__2.i = d__1 * temp1.i;
|
|
q__1.r = Y(jy).r + q__2.r, q__1.i = Y(jy).i + q__2.i;
|
|
Y(jy).r = q__1.r, Y(jy).i = q__1.i;
|
|
ix = jx;
|
|
iy = jy;
|
|
i__2 = *n;
|
|
for (i = j + 1; i <= *n; ++i) {
|
|
ix += *incx;
|
|
iy += *incy;
|
|
i__3 = iy;
|
|
i__4 = iy;
|
|
i__5 = i + j * a_dim1;
|
|
q__2.r = temp1.r * A(i,j).r - temp1.i * A(i,j).i,
|
|
q__2.i = temp1.r * A(i,j).i + temp1.i * A(i,j)
|
|
.r;
|
|
q__1.r = Y(iy).r + q__2.r, q__1.i = Y(iy).i + q__2.i;
|
|
Y(iy).r = q__1.r, Y(iy).i = q__1.i;
|
|
r_cnjg(&q__3, &A(i,j));
|
|
i__3 = ix;
|
|
q__2.r = q__3.r * X(ix).r - q__3.i * X(ix).i, q__2.i =
|
|
q__3.r * X(ix).i + q__3.i * X(ix).r;
|
|
q__1.r = temp2.r + q__2.r, q__1.i = temp2.i + q__2.i;
|
|
temp2.r = q__1.r, temp2.i = q__1.i;
|
|
/* L110: */
|
|
}
|
|
i__2 = jy;
|
|
i__3 = jy;
|
|
q__2.r = alpha->r * temp2.r - alpha->i * temp2.i, q__2.i =
|
|
alpha->r * temp2.i + alpha->i * temp2.r;
|
|
q__1.r = Y(jy).r + q__2.r, q__1.i = Y(jy).i + q__2.i;
|
|
Y(jy).r = q__1.r, Y(jy).i = q__1.i;
|
|
jx += *incx;
|
|
jy += *incy;
|
|
/* L120: */
|
|
}
|
|
}
|
|
}
|
|
|
|
return 0;
|
|
|
|
/* End of CHEMV . */
|
|
|
|
} /* chemv_ */
|
|
|