489 lines
15 KiB
C
489 lines
15 KiB
C
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/* zhbmv.f -- translated by f2c (version 20100827).
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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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#include "datatypes.h"
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/* Subroutine */ int zhbmv_(char *uplo, integer *n, integer *k, doublecomplex
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*alpha, doublecomplex *a, integer *lda, doublecomplex *x, integer *
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incx, doublecomplex *beta, doublecomplex *y, integer *incy, ftnlen
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uplo_len)
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{
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/* System generated locals */
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integer a_dim1, a_offset, i__1, i__2, i__3, i__4, i__5;
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doublereal d__1;
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doublecomplex z__1, z__2, z__3, z__4;
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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, l, ix, iy, jx, jy, kx, ky, info;
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doublecomplex temp1, temp2;
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extern logical lsame_(char *, char *, ftnlen, ftnlen);
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integer kplus1;
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extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen);
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/* .. Scalar Arguments .. */
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/* .. */
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/* .. Array Arguments .. */
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/* .. */
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/* Purpose */
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/* ======= */
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/* ZHBMV performs the matrix-vector operation */
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/* y := alpha*A*x + beta*y, */
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/* where alpha and beta are scalars, x and y are n element vectors and */
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/* A is an n by n hermitian band matrix, with k super-diagonals. */
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/* Arguments */
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/* ========== */
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/* UPLO - CHARACTER*1. */
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/* On entry, UPLO specifies whether the upper or lower */
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/* triangular part of the band matrix A is being supplied as */
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/* follows: */
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/* UPLO = 'U' or 'u' The upper triangular part of A is */
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/* being supplied. */
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/* UPLO = 'L' or 'l' The lower triangular part of A is */
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/* being supplied. */
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/* Unchanged on exit. */
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/* N - 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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/* Unchanged on exit. */
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/* K - INTEGER. */
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/* On entry, K specifies the number of super-diagonals of the */
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/* matrix A. K must satisfy 0 .le. K. */
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/* Unchanged on exit. */
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/* ALPHA - COMPLEX*16 . */
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/* On entry, ALPHA specifies the scalar alpha. */
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/* Unchanged on exit. */
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/* A - COMPLEX*16 array of DIMENSION ( LDA, n ). */
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/* Before entry with UPLO = 'U' or 'u', the leading ( k + 1 ) */
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/* by n part of the array A must contain the upper triangular */
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/* band part of the hermitian matrix, supplied column by */
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/* column, with the leading diagonal of the matrix in row */
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/* ( k + 1 ) of the array, the first super-diagonal starting at */
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/* position 2 in row k, and so on. The top left k by k triangle */
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/* of the array A is not referenced. */
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/* The following program segment will transfer the upper */
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/* triangular part of a hermitian band matrix from conventional */
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/* full matrix storage to band storage: */
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/* DO 20, J = 1, N */
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/* M = K + 1 - J */
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/* DO 10, I = MAX( 1, J - K ), J */
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/* A( M + I, J ) = matrix( I, J ) */
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/* 10 CONTINUE */
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/* 20 CONTINUE */
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/* Before entry with UPLO = 'L' or 'l', the leading ( k + 1 ) */
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/* by n part of the array A must contain the lower triangular */
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/* band part of the hermitian matrix, supplied column by */
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/* column, with the leading diagonal of the matrix in row 1 of */
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/* the array, the first sub-diagonal starting at position 1 in */
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/* row 2, and so on. The bottom right k by k triangle of the */
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/* array A is not referenced. */
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/* The following program segment will transfer the lower */
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/* triangular part of a hermitian band matrix from conventional */
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/* full matrix storage to band storage: */
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/* DO 20, J = 1, N */
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/* M = 1 - J */
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/* DO 10, I = J, MIN( N, J + K ) */
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/* A( M + I, J ) = matrix( I, J ) */
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/* 10 CONTINUE */
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/* 20 CONTINUE */
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/* Note that the imaginary parts of the diagonal elements need */
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/* not be set and are assumed to be zero. */
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/* Unchanged on exit. */
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/* LDA - INTEGER. */
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/* On entry, LDA specifies the first dimension of A as declared */
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/* in the calling (sub) program. LDA must be at least */
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/* ( k + 1 ). */
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/* Unchanged on exit. */
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/* X - COMPLEX*16 array of 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 */
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/* vector x. */
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/* Unchanged on exit. */
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/* INCX - 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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/* Unchanged on exit. */
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/* BETA - COMPLEX*16 . */
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/* On entry, BETA specifies the scalar beta. */
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/* Unchanged on exit. */
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/* Y - COMPLEX*16 array of DIMENSION at least */
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/* ( 1 + ( n - 1 )*abs( INCY ) ). */
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/* Before entry, the incremented array Y must contain the */
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/* vector y. On exit, Y is overwritten by the updated vector y. */
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/* INCY - INTEGER. */
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/* On entry, INCY specifies the increment for the elements of */
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/* Y. INCY must not be zero. */
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/* Unchanged on exit. */
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/* Further Details */
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/* =============== */
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/* Level 2 Blas routine. */
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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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/* ===================================================================== */
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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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a_dim1 = *lda;
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a_offset = 1 + a_dim1;
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a -= a_offset;
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--x;
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--y;
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/* Function Body */
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info = 0;
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if (! lsame_(uplo, "U", (ftnlen)1, (ftnlen)1) && ! lsame_(uplo, "L", (
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ftnlen)1, (ftnlen)1)) {
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info = 1;
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} else if (*n < 0) {
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info = 2;
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} else if (*k < 0) {
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info = 3;
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} else if (*lda < *k + 1) {
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info = 6;
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} else if (*incx == 0) {
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info = 8;
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} else if (*incy == 0) {
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info = 11;
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}
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if (info != 0) {
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xerbla_("ZHBMV ", &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 || (alpha->r == 0. && alpha->i == 0. && (beta->r == 1. &&
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beta->i == 0.))) {
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return 0;
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}
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/* Set up the start points in X and Y. */
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if (*incx > 0) {
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kx = 1;
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} else {
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kx = 1 - (*n - 1) * *incx;
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}
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if (*incy > 0) {
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ky = 1;
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} else {
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ky = 1 - (*n - 1) * *incy;
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}
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/* Start the operations. In this version the elements of the array A */
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/* are accessed sequentially with one pass through A. */
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/* First form y := beta*y. */
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if (beta->r != 1. || beta->i != 0.) {
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if (*incy == 1) {
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if (beta->r == 0. && beta->i == 0.) {
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i__1 = *n;
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for (i__ = 1; i__ <= i__1; ++i__) {
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i__2 = i__;
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y[i__2].r = 0., y[i__2].i = 0.;
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/* L10: */
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}
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} else {
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i__1 = *n;
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for (i__ = 1; i__ <= i__1; ++i__) {
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i__2 = i__;
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i__3 = i__;
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z__1.r = beta->r * y[i__3].r - beta->i * y[i__3].i,
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z__1.i = beta->r * y[i__3].i + beta->i * y[i__3]
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.r;
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y[i__2].r = z__1.r, y[i__2].i = z__1.i;
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/* L20: */
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}
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}
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} else {
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iy = ky;
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if (beta->r == 0. && beta->i == 0.) {
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i__1 = *n;
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for (i__ = 1; i__ <= i__1; ++i__) {
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i__2 = iy;
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y[i__2].r = 0., y[i__2].i = 0.;
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iy += *incy;
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/* L30: */
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}
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} else {
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i__1 = *n;
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for (i__ = 1; i__ <= i__1; ++i__) {
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i__2 = iy;
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i__3 = iy;
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z__1.r = beta->r * y[i__3].r - beta->i * y[i__3].i,
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z__1.i = beta->r * y[i__3].i + beta->i * y[i__3]
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.r;
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y[i__2].r = z__1.r, y[i__2].i = z__1.i;
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iy += *incy;
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/* L40: */
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}
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}
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}
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}
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if (alpha->r == 0. && alpha->i == 0.) {
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return 0;
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}
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if (lsame_(uplo, "U", (ftnlen)1, (ftnlen)1)) {
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/* Form y when upper triangle of A is stored. */
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kplus1 = *k + 1;
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if (*incx == 1 && *incy == 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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z__1.r = alpha->r * x[i__2].r - alpha->i * x[i__2].i, z__1.i =
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alpha->r * x[i__2].i + alpha->i * x[i__2].r;
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temp1.r = z__1.r, temp1.i = z__1.i;
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temp2.r = 0., temp2.i = 0.;
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l = kplus1 - j;
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/* Computing MAX */
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i__2 = 1, i__3 = j - *k;
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i__4 = j - 1;
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for (i__ = max(i__2,i__3); i__ <= i__4; ++i__) {
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i__2 = i__;
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i__3 = i__;
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i__5 = l + i__ + j * a_dim1;
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z__2.r = temp1.r * a[i__5].r - temp1.i * a[i__5].i,
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z__2.i = temp1.r * a[i__5].i + temp1.i * a[i__5]
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.r;
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z__1.r = y[i__3].r + z__2.r, z__1.i = y[i__3].i + z__2.i;
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y[i__2].r = z__1.r, y[i__2].i = z__1.i;
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d_cnjg(&z__3, &a[l + i__ + j * a_dim1]);
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i__2 = i__;
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z__2.r = z__3.r * x[i__2].r - z__3.i * x[i__2].i, z__2.i =
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z__3.r * x[i__2].i + z__3.i * x[i__2].r;
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z__1.r = temp2.r + z__2.r, z__1.i = temp2.i + z__2.i;
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temp2.r = z__1.r, temp2.i = z__1.i;
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/* L50: */
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}
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i__4 = j;
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i__2 = j;
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i__3 = kplus1 + j * a_dim1;
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d__1 = a[i__3].r;
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z__3.r = d__1 * temp1.r, z__3.i = d__1 * temp1.i;
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z__2.r = y[i__2].r + z__3.r, z__2.i = y[i__2].i + z__3.i;
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z__4.r = alpha->r * temp2.r - alpha->i * temp2.i, z__4.i =
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alpha->r * temp2.i + alpha->i * temp2.r;
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z__1.r = z__2.r + z__4.r, z__1.i = z__2.i + z__4.i;
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y[i__4].r = z__1.r, y[i__4].i = z__1.i;
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/* L60: */
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}
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} else {
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jx = kx;
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jy = ky;
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i__1 = *n;
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for (j = 1; j <= i__1; ++j) {
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i__4 = jx;
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z__1.r = alpha->r * x[i__4].r - alpha->i * x[i__4].i, z__1.i =
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alpha->r * x[i__4].i + alpha->i * x[i__4].r;
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temp1.r = z__1.r, temp1.i = z__1.i;
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temp2.r = 0., temp2.i = 0.;
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ix = kx;
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iy = ky;
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l = kplus1 - j;
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/* Computing MAX */
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i__4 = 1, i__2 = j - *k;
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i__3 = j - 1;
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for (i__ = max(i__4,i__2); i__ <= i__3; ++i__) {
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i__4 = iy;
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|
|
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_ */
|
||
|
|
|