You can not select more than 25 topics
Topics must start with a letter or number, can include dashes ('-') and can be up to 35 characters long.
367 lines
9.9 KiB
367 lines
9.9 KiB
/* dsbmv.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 dsbmv_(char *uplo, integer *n, integer *k, doublereal *
|
|
alpha, doublereal *a, integer *lda, doublereal *x, integer *incx,
|
|
doublereal *beta, doublereal *y, integer *incy, ftnlen uplo_len)
|
|
{
|
|
/* System generated locals */
|
|
integer a_dim1, a_offset, i__1, i__2, i__3, i__4;
|
|
|
|
/* Local variables */
|
|
integer i__, j, l, ix, iy, jx, jy, kx, ky, info;
|
|
doublereal temp1, temp2;
|
|
extern logical lsame_(char *, char *, ftnlen, ftnlen);
|
|
integer kplus1;
|
|
extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen);
|
|
|
|
/* .. Scalar Arguments .. */
|
|
/* .. */
|
|
/* .. Array Arguments .. */
|
|
/* .. */
|
|
|
|
/* Purpose */
|
|
/* ======= */
|
|
|
|
/* DSBMV 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 symmetric 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 - DOUBLE PRECISION. */
|
|
/* On entry, ALPHA specifies the scalar alpha. */
|
|
/* Unchanged on exit. */
|
|
|
|
/* A - DOUBLE PRECISION 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 symmetric 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 symmetric 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 symmetric 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 symmetric 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 */
|
|
|
|
/* 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 - DOUBLE PRECISION 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 - DOUBLE PRECISION. */
|
|
/* On entry, BETA specifies the scalar beta. */
|
|
/* Unchanged on exit. */
|
|
|
|
/* Y - DOUBLE PRECISION 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. */
|
|
|
|
|
|
/* 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_("DSBMV ", &info, (ftnlen)6);
|
|
return 0;
|
|
}
|
|
|
|
/* Quick return if possible. */
|
|
|
|
if (*n == 0 || (*alpha == 0. && *beta == 1.)) {
|
|
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 != 1.) {
|
|
if (*incy == 1) {
|
|
if (*beta == 0.) {
|
|
i__1 = *n;
|
|
for (i__ = 1; i__ <= i__1; ++i__) {
|
|
y[i__] = 0.;
|
|
/* L10: */
|
|
}
|
|
} else {
|
|
i__1 = *n;
|
|
for (i__ = 1; i__ <= i__1; ++i__) {
|
|
y[i__] = *beta * y[i__];
|
|
/* L20: */
|
|
}
|
|
}
|
|
} else {
|
|
iy = ky;
|
|
if (*beta == 0.) {
|
|
i__1 = *n;
|
|
for (i__ = 1; i__ <= i__1; ++i__) {
|
|
y[iy] = 0.;
|
|
iy += *incy;
|
|
/* L30: */
|
|
}
|
|
} else {
|
|
i__1 = *n;
|
|
for (i__ = 1; i__ <= i__1; ++i__) {
|
|
y[iy] = *beta * y[iy];
|
|
iy += *incy;
|
|
/* L40: */
|
|
}
|
|
}
|
|
}
|
|
}
|
|
if (*alpha == 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) {
|
|
temp1 = *alpha * x[j];
|
|
temp2 = 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__) {
|
|
y[i__] += temp1 * a[l + i__ + j * a_dim1];
|
|
temp2 += a[l + i__ + j * a_dim1] * x[i__];
|
|
/* L50: */
|
|
}
|
|
y[j] = y[j] + temp1 * a[kplus1 + j * a_dim1] + *alpha * temp2;
|
|
/* L60: */
|
|
}
|
|
} else {
|
|
jx = kx;
|
|
jy = ky;
|
|
i__1 = *n;
|
|
for (j = 1; j <= i__1; ++j) {
|
|
temp1 = *alpha * x[jx];
|
|
temp2 = 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__) {
|
|
y[iy] += temp1 * a[l + i__ + j * a_dim1];
|
|
temp2 += a[l + i__ + j * a_dim1] * x[ix];
|
|
ix += *incx;
|
|
iy += *incy;
|
|
/* L70: */
|
|
}
|
|
y[jy] = y[jy] + temp1 * a[kplus1 + j * a_dim1] + *alpha *
|
|
temp2;
|
|
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) {
|
|
temp1 = *alpha * x[j];
|
|
temp2 = 0.;
|
|
y[j] += temp1 * a[j * a_dim1 + 1];
|
|
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__) {
|
|
y[i__] += temp1 * a[l + i__ + j * a_dim1];
|
|
temp2 += a[l + i__ + j * a_dim1] * x[i__];
|
|
/* L90: */
|
|
}
|
|
y[j] += *alpha * temp2;
|
|
/* L100: */
|
|
}
|
|
} else {
|
|
jx = kx;
|
|
jy = ky;
|
|
i__1 = *n;
|
|
for (j = 1; j <= i__1; ++j) {
|
|
temp1 = *alpha * x[jx];
|
|
temp2 = 0.;
|
|
y[jy] += temp1 * a[j * a_dim1 + 1];
|
|
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;
|
|
y[iy] += temp1 * a[l + i__ + j * a_dim1];
|
|
temp2 += a[l + i__ + j * a_dim1] * x[ix];
|
|
/* L110: */
|
|
}
|
|
y[jy] += *alpha * temp2;
|
|
jx += *incx;
|
|
jy += *incy;
|
|
/* L120: */
|
|
}
|
|
}
|
|
}
|
|
|
|
return 0;
|
|
|
|
/* End of DSBMV . */
|
|
|
|
} /* dsbmv_ */
|
|
|