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/* zhbmv.f -- translated by f2c (version 20100827).
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
*/
#include "datatypes.h"
/* Subroutine */ int zhbmv_(char *uplo, integer *n, integer *k, 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_cnjg(doublecomplex *, doublecomplex *);
/* Local variables */
integer i__, j, l, ix, iy, jx, jy, kx, ky, info;
doublecomplex temp1, temp2;
extern logical lsame_(char *, char *, ftnlen, ftnlen);
integer kplus1;
extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen);
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* ZHBMV 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 band matrix, with k super-diagonals. */
/* Arguments */
/* ========== */
/* UPLO - CHARACTER*1. */
/* On entry, UPLO specifies whether the upper or lower */
/* triangular part of the band matrix A is being supplied as */
/* follows: */
/* UPLO = 'U' or 'u' The upper triangular part of A is */
/* being supplied. */
/* UPLO = 'L' or 'l' The lower triangular part of A is */
/* being supplied. */
/* Unchanged on exit. */
/* N - INTEGER. */
/* On entry, N specifies the order of the matrix A. */
/* N must be at least zero. */
/* Unchanged on exit. */
/* K - INTEGER. */
/* On entry, K specifies the number of super-diagonals of the */
/* matrix A. K must satisfy 0 .le. K. */
/* Unchanged on exit. */
/* ALPHA - COMPLEX*16 . */
/* On entry, ALPHA specifies the scalar alpha. */
/* Unchanged on exit. */
/* A - COMPLEX*16 array of DIMENSION ( LDA, n ). */
/* Before entry with UPLO = 'U' or 'u', the leading ( k + 1 ) */
/* by n part of the array A must contain the upper triangular */
/* band part of the hermitian matrix, supplied column by */
/* column, with the leading diagonal of the matrix in row */
/* ( k + 1 ) of the array, the first super-diagonal starting at */
/* position 2 in row k, and so on. The top left k by k triangle */
/* of the array A is not referenced. */
/* The following program segment will transfer the upper */
/* triangular part of a hermitian band matrix from conventional */
/* full matrix storage to band storage: */
/* DO 20, J = 1, N */
/* M = K + 1 - J */
/* DO 10, I = MAX( 1, J - K ), J */
/* A( M + I, J ) = matrix( I, J ) */
/* 10 CONTINUE */
/* 20 CONTINUE */
/* Before entry with UPLO = 'L' or 'l', the leading ( k + 1 ) */
/* by n part of the array A must contain the lower triangular */
/* band part of the hermitian matrix, supplied column by */
/* column, with the leading diagonal of the matrix in row 1 of */
/* the array, the first sub-diagonal starting at position 1 in */
/* row 2, and so on. The bottom right k by k triangle of the */
/* array A is not referenced. */
/* The following program segment will transfer the lower */
/* triangular part of a hermitian band matrix from conventional */
/* full matrix storage to band storage: */
/* DO 20, J = 1, N */
/* M = 1 - J */
/* DO 10, I = J, MIN( N, J + K ) */
/* A( M + I, J ) = matrix( I, J ) */
/* 10 CONTINUE */
/* 20 CONTINUE */
/* 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 */
/* ( k + 1 ). */
/* Unchanged on exit. */
/* X - COMPLEX*16 array of DIMENSION at least */
/* ( 1 + ( n - 1 )*abs( INCX ) ). */
/* Before entry, the incremented array X must contain the */
/* 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*16 . */
/* On entry, BETA specifies the scalar beta. */
/* Unchanged on exit. */
/* Y - COMPLEX*16 array of DIMENSION at least */
/* ( 1 + ( n - 1 )*abs( INCY ) ). */
/* Before entry, the incremented array Y must contain the */
/* 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. */
/* Further Details */
/* =============== */
/* 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. */
/* ===================================================================== */
/* .. 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, "U", (ftnlen)1, (ftnlen)1) && ! lsame_(uplo, "L", (
ftnlen)1, (ftnlen)1)) {
info = 1;
} else if (*n < 0) {
info = 2;
} else if (*k < 0) {
info = 3;
} else if (*lda < *k + 1) {
info = 6;
} else if (*incx == 0) {
info = 8;
} else if (*incy == 0) {
info = 11;
}
if (info != 0) {
xerbla_("ZHBMV ", &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 the array A */
/* are accessed sequentially with one pass through 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, "U", (ftnlen)1, (ftnlen)1)) {
/* Form y when upper triangle of A is stored. */
kplus1 = *k + 1;
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.;
l = kplus1 - j;
/* Computing MAX */
i__2 = 1, i__3 = j - *k;
i__4 = j - 1;
for (i__ = max(i__2,i__3); i__ <= i__4; ++i__) {
i__2 = i__;
i__3 = i__;
i__5 = l + 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__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;
d_cnjg(&z__3, &a[l + i__ + j * a_dim1]);
i__2 = i__;
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 = 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__4 = j;
i__2 = j;
i__3 = kplus1 + j * a_dim1;
d__1 = a[i__3].r;
z__3.r = d__1 * temp1.r, z__3.i = d__1 * temp1.i;
z__2.r = y[i__2].r + z__3.r, z__2.i = y[i__2].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__4].r = z__1.r, y[i__4].i = z__1.i;
/* L60: */
}
} else {
jx = kx;
jy = ky;
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__4 = jx;
z__1.r = alpha->r * x[i__4].r - alpha->i * x[i__4].i, z__1.i =
alpha->r * x[i__4].i + alpha->i * x[i__4].r;
temp1.r = z__1.r, temp1.i = z__1.i;
temp2.r = 0., temp2.i = 0.;
ix = kx;
iy = ky;
l = kplus1 - j;
/* Computing MAX */
i__4 = 1, i__2 = j - *k;
i__3 = j - 1;
for (i__ = max(i__4,i__2); i__ <= i__3; ++i__) {
i__4 = iy;
i__2 = iy;
i__5 = l + 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__2].r + z__2.r, z__1.i = y[i__2].i + z__2.i;
y[i__4].r = z__1.r, y[i__4].i = z__1.i;
d_cnjg(&z__3, &a[l + i__ + j * a_dim1]);
i__4 = ix;
z__2.r = z__3.r * x[i__4].r - z__3.i * x[i__4].i, z__2.i =
z__3.r * x[i__4].i + z__3.i * x[i__4].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__3 = jy;
i__4 = jy;
i__2 = kplus1 + j * a_dim1;
d__1 = a[i__2].r;
z__3.r = d__1 * temp1.r, z__3.i = d__1 * temp1.i;
z__2.r = y[i__4].r + z__3.r, z__2.i = y[i__4].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__3].r = z__1.r, y[i__3].i = z__1.i;
jx += *incx;
jy += *incy;
if (j > *k) {
kx += *incx;
ky += *incy;
}
/* L80: */
}
}
} else {
/* Form y when lower triangle of A is stored. */
if (*incx == 1 && *incy == 1) {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__3 = j;
z__1.r = alpha->r * x[i__3].r - alpha->i * x[i__3].i, z__1.i =
alpha->r * x[i__3].i + alpha->i * x[i__3].r;
temp1.r = z__1.r, temp1.i = z__1.i;
temp2.r = 0., temp2.i = 0.;
i__3 = j;
i__4 = j;
i__2 = j * a_dim1 + 1;
d__1 = a[i__2].r;
z__2.r = d__1 * temp1.r, z__2.i = d__1 * temp1.i;
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;
l = 1 - j;
/* Computing MIN */
i__4 = *n, i__2 = j + *k;
i__3 = min(i__4,i__2);
for (i__ = j + 1; i__ <= i__3; ++i__) {
i__4 = i__;
i__2 = i__;
i__5 = l + 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__2].r + z__2.r, z__1.i = y[i__2].i + z__2.i;
y[i__4].r = z__1.r, y[i__4].i = z__1.i;
d_cnjg(&z__3, &a[l + i__ + j * a_dim1]);
i__4 = i__;
z__2.r = z__3.r * x[i__4].r - z__3.i * x[i__4].i, z__2.i =
z__3.r * x[i__4].i + z__3.i * x[i__4].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__3 = j;
i__4 = 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__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;
/* L100: */
}
} else {
jx = kx;
jy = ky;
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__3 = jx;
z__1.r = alpha->r * x[i__3].r - alpha->i * x[i__3].i, z__1.i =
alpha->r * x[i__3].i + alpha->i * x[i__3].r;
temp1.r = z__1.r, temp1.i = z__1.i;
temp2.r = 0., temp2.i = 0.;
i__3 = jy;
i__4 = jy;
i__2 = j * a_dim1 + 1;
d__1 = a[i__2].r;
z__2.r = d__1 * temp1.r, z__2.i = d__1 * temp1.i;
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;
l = 1 - j;
ix = jx;
iy = jy;
/* Computing MIN */
i__4 = *n, i__2 = j + *k;
i__3 = min(i__4,i__2);
for (i__ = j + 1; i__ <= i__3; ++i__) {
ix += *incx;
iy += *incy;
i__4 = iy;
i__2 = iy;
i__5 = l + 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__2].r + z__2.r, z__1.i = y[i__2].i + z__2.i;
y[i__4].r = z__1.r, y[i__4].i = z__1.i;
d_cnjg(&z__3, &a[l + i__ + j * a_dim1]);
i__4 = ix;
z__2.r = z__3.r * x[i__4].r - z__3.i * x[i__4].i, z__2.i =
z__3.r * x[i__4].i + z__3.i * x[i__4].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__3 = jy;
i__4 = 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__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;
jx += *incx;
jy += *incy;
/* L120: */
}
}
}
return 0;
/* End of ZHBMV . */
} /* zhbmv_ */
|
