648 lines
18 KiB
C
648 lines
18 KiB
C
/* ztbmv.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 ztbmv_(char *uplo, char *trans, char *diag, integer *n,
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integer *k, doublecomplex *a, integer *lda, doublecomplex *x, integer
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*incx, ftnlen uplo_len, ftnlen trans_len, ftnlen diag_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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doublecomplex z__1, z__2, z__3;
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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, jx, kx, info;
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doublecomplex temp;
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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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logical noconj, nounit;
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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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/* ZTBMV performs one of the matrix-vector operations */
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/* x := A*x, or x := A'*x, or x := conjg( A' )*x, */
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/* where x is an n element vector and A is an n by n unit, or non-unit, */
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/* upper or lower triangular band matrix, with ( k + 1 ) 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 matrix is an upper or */
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/* lower triangular matrix as follows: */
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/* UPLO = 'U' or 'u' A is an upper triangular matrix. */
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/* UPLO = 'L' or 'l' A is a lower triangular matrix. */
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/* Unchanged on exit. */
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/* TRANS - CHARACTER*1. */
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/* On entry, TRANS specifies the operation to be performed as */
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/* follows: */
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/* TRANS = 'N' or 'n' x := A*x. */
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/* TRANS = 'T' or 't' x := A'*x. */
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/* TRANS = 'C' or 'c' x := conjg( A' )*x. */
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/* Unchanged on exit. */
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/* DIAG - CHARACTER*1. */
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/* On entry, DIAG specifies whether or not A is unit */
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/* triangular as follows: */
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/* DIAG = 'U' or 'u' A is assumed to be unit triangular. */
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/* DIAG = 'N' or 'n' A is not assumed to be unit */
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/* triangular. */
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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 with UPLO = 'U' or 'u', K specifies the number of */
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/* super-diagonals of the matrix A. */
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/* On entry with UPLO = 'L' or 'l', K specifies the number of */
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/* sub-diagonals of the matrix A. */
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/* K must satisfy 0 .le. K. */
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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 matrix of coefficients, 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 an upper */
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/* triangular band matrix from conventional full matrix storage */
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/* 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 matrix of coefficients, 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 a lower */
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/* triangular band matrix from conventional full matrix storage */
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/* 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 when DIAG = 'U' or 'u' the elements of the array A */
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/* corresponding to the diagonal elements of the matrix are not */
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/* referenced, but are assumed to be unity. */
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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 n */
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/* element vector x. On exit, X is overwritten with the */
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/* transformed vector x. */
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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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/* 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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/* 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 (! lsame_(trans, "N", (ftnlen)1, (ftnlen)1) && ! lsame_(trans,
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"T", (ftnlen)1, (ftnlen)1) && ! lsame_(trans, "C", (ftnlen)1, (
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ftnlen)1)) {
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info = 2;
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} else if (! lsame_(diag, "U", (ftnlen)1, (ftnlen)1) && ! lsame_(diag,
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"N", (ftnlen)1, (ftnlen)1)) {
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info = 3;
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} else if (*n < 0) {
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info = 4;
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} else if (*k < 0) {
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info = 5;
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} else if (*lda < *k + 1) {
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info = 7;
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} else if (*incx == 0) {
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info = 9;
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}
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if (info != 0) {
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xerbla_("ZTBMV ", &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) {
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return 0;
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}
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noconj = lsame_(trans, "T", (ftnlen)1, (ftnlen)1);
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nounit = lsame_(diag, "N", (ftnlen)1, (ftnlen)1);
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/* Set up the start point in X if the increment is not unity. This */
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/* will be ( N - 1 )*INCX too small for descending loops. */
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if (*incx <= 0) {
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kx = 1 - (*n - 1) * *incx;
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} else if (*incx != 1) {
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kx = 1;
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}
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/* Start the operations. In this version the elements of A are */
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/* accessed sequentially with one pass through A. */
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if (lsame_(trans, "N", (ftnlen)1, (ftnlen)1)) {
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/* Form x := A*x. */
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if (lsame_(uplo, "U", (ftnlen)1, (ftnlen)1)) {
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kplus1 = *k + 1;
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if (*incx == 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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if (x[i__2].r != 0. || x[i__2].i != 0.) {
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i__2 = j;
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temp.r = x[i__2].r, temp.i = x[i__2].i;
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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 = temp.r * a[i__5].r - temp.i * a[i__5].i,
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z__2.i = temp.r * a[i__5].i + temp.i * a[
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i__5].r;
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z__1.r = x[i__3].r + z__2.r, z__1.i = x[i__3].i +
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z__2.i;
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x[i__2].r = z__1.r, x[i__2].i = z__1.i;
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/* L10: */
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}
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if (nounit) {
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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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z__1.r = x[i__2].r * a[i__3].r - x[i__2].i * a[
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i__3].i, z__1.i = x[i__2].r * a[i__3].i +
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x[i__2].i * a[i__3].r;
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x[i__4].r = z__1.r, x[i__4].i = z__1.i;
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}
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}
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/* L20: */
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}
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} else {
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jx = kx;
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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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if (x[i__4].r != 0. || x[i__4].i != 0.) {
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i__4 = jx;
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temp.r = x[i__4].r, temp.i = x[i__4].i;
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ix = kx;
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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 = ix;
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i__2 = ix;
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i__5 = l + i__ + j * a_dim1;
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z__2.r = temp.r * a[i__5].r - temp.i * a[i__5].i,
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z__2.i = temp.r * a[i__5].i + temp.i * a[
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i__5].r;
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z__1.r = x[i__2].r + z__2.r, z__1.i = x[i__2].i +
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z__2.i;
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x[i__4].r = z__1.r, x[i__4].i = z__1.i;
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ix += *incx;
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/* L30: */
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}
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if (nounit) {
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i__3 = jx;
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i__4 = jx;
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i__2 = kplus1 + j * a_dim1;
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z__1.r = x[i__4].r * a[i__2].r - x[i__4].i * a[
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i__2].i, z__1.i = x[i__4].r * a[i__2].i +
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x[i__4].i * a[i__2].r;
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x[i__3].r = z__1.r, x[i__3].i = z__1.i;
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}
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}
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jx += *incx;
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if (j > *k) {
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kx += *incx;
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}
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/* L40: */
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}
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}
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} else {
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if (*incx == 1) {
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for (j = *n; j >= 1; --j) {
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i__1 = j;
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if (x[i__1].r != 0. || x[i__1].i != 0.) {
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i__1 = j;
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temp.r = x[i__1].r, temp.i = x[i__1].i;
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l = 1 - j;
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/* Computing MIN */
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i__1 = *n, i__3 = j + *k;
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i__4 = j + 1;
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for (i__ = min(i__1,i__3); i__ >= i__4; --i__) {
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i__1 = i__;
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i__3 = i__;
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i__2 = l + i__ + j * a_dim1;
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z__2.r = temp.r * a[i__2].r - temp.i * a[i__2].i,
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z__2.i = temp.r * a[i__2].i + temp.i * a[
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i__2].r;
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z__1.r = x[i__3].r + z__2.r, z__1.i = x[i__3].i +
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z__2.i;
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x[i__1].r = z__1.r, x[i__1].i = z__1.i;
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/* L50: */
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}
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if (nounit) {
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i__4 = j;
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i__1 = j;
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i__3 = j * a_dim1 + 1;
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z__1.r = x[i__1].r * a[i__3].r - x[i__1].i * a[
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i__3].i, z__1.i = x[i__1].r * a[i__3].i +
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x[i__1].i * a[i__3].r;
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x[i__4].r = z__1.r, x[i__4].i = z__1.i;
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}
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}
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/* L60: */
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}
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} else {
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kx += (*n - 1) * *incx;
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jx = kx;
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for (j = *n; j >= 1; --j) {
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i__4 = jx;
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if (x[i__4].r != 0. || x[i__4].i != 0.) {
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i__4 = jx;
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temp.r = x[i__4].r, temp.i = x[i__4].i;
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ix = kx;
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l = 1 - j;
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/* Computing MIN */
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i__4 = *n, i__1 = j + *k;
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i__3 = j + 1;
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for (i__ = min(i__4,i__1); i__ >= i__3; --i__) {
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i__4 = ix;
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i__1 = ix;
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i__2 = l + i__ + j * a_dim1;
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z__2.r = temp.r * a[i__2].r - temp.i * a[i__2].i,
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z__2.i = temp.r * a[i__2].i + temp.i * a[
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i__2].r;
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z__1.r = x[i__1].r + z__2.r, z__1.i = x[i__1].i +
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z__2.i;
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x[i__4].r = z__1.r, x[i__4].i = z__1.i;
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ix -= *incx;
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/* L70: */
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}
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if (nounit) {
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i__3 = jx;
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i__4 = jx;
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i__1 = j * a_dim1 + 1;
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z__1.r = x[i__4].r * a[i__1].r - x[i__4].i * a[
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i__1].i, z__1.i = x[i__4].r * a[i__1].i +
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x[i__4].i * a[i__1].r;
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x[i__3].r = z__1.r, x[i__3].i = z__1.i;
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}
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}
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jx -= *incx;
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if (*n - j >= *k) {
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kx -= *incx;
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}
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/* L80: */
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}
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}
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}
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} else {
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/* Form x := A'*x or x := conjg( A' )*x. */
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if (lsame_(uplo, "U", (ftnlen)1, (ftnlen)1)) {
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kplus1 = *k + 1;
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if (*incx == 1) {
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for (j = *n; j >= 1; --j) {
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i__3 = j;
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temp.r = x[i__3].r, temp.i = x[i__3].i;
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l = kplus1 - j;
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if (noconj) {
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if (nounit) {
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i__3 = kplus1 + j * a_dim1;
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z__1.r = temp.r * a[i__3].r - temp.i * a[i__3].i,
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z__1.i = temp.r * a[i__3].i + temp.i * a[
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i__3].r;
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temp.r = z__1.r, temp.i = z__1.i;
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}
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/* Computing MAX */
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i__4 = 1, i__1 = j - *k;
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i__3 = max(i__4,i__1);
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for (i__ = j - 1; i__ >= i__3; --i__) {
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i__4 = l + i__ + j * a_dim1;
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i__1 = i__;
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z__2.r = a[i__4].r * x[i__1].r - a[i__4].i * x[
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i__1].i, z__2.i = a[i__4].r * x[i__1].i +
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a[i__4].i * x[i__1].r;
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z__1.r = temp.r + z__2.r, z__1.i = temp.i +
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z__2.i;
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temp.r = z__1.r, temp.i = z__1.i;
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/* L90: */
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}
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} else {
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if (nounit) {
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d_cnjg(&z__2, &a[kplus1 + j * a_dim1]);
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z__1.r = temp.r * z__2.r - temp.i * z__2.i,
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z__1.i = temp.r * z__2.i + temp.i *
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z__2.r;
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temp.r = z__1.r, temp.i = z__1.i;
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}
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/* Computing MAX */
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i__4 = 1, i__1 = j - *k;
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i__3 = max(i__4,i__1);
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for (i__ = j - 1; i__ >= i__3; --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 = temp.r + z__2.r, z__1.i = temp.i +
|
|
z__2.i;
|
|
temp.r = z__1.r, temp.i = z__1.i;
|
|
/* L100: */
|
|
}
|
|
}
|
|
i__3 = j;
|
|
x[i__3].r = temp.r, x[i__3].i = temp.i;
|
|
/* L110: */
|
|
}
|
|
} else {
|
|
kx += (*n - 1) * *incx;
|
|
jx = kx;
|
|
for (j = *n; j >= 1; --j) {
|
|
i__3 = jx;
|
|
temp.r = x[i__3].r, temp.i = x[i__3].i;
|
|
kx -= *incx;
|
|
ix = kx;
|
|
l = kplus1 - j;
|
|
if (noconj) {
|
|
if (nounit) {
|
|
i__3 = kplus1 + j * a_dim1;
|
|
z__1.r = temp.r * a[i__3].r - temp.i * a[i__3].i,
|
|
z__1.i = temp.r * a[i__3].i + temp.i * a[
|
|
i__3].r;
|
|
temp.r = z__1.r, temp.i = z__1.i;
|
|
}
|
|
/* Computing MAX */
|
|
i__4 = 1, i__1 = j - *k;
|
|
i__3 = max(i__4,i__1);
|
|
for (i__ = j - 1; i__ >= i__3; --i__) {
|
|
i__4 = l + i__ + j * a_dim1;
|
|
i__1 = ix;
|
|
z__2.r = a[i__4].r * x[i__1].r - a[i__4].i * x[
|
|
i__1].i, z__2.i = a[i__4].r * x[i__1].i +
|
|
a[i__4].i * x[i__1].r;
|
|
z__1.r = temp.r + z__2.r, z__1.i = temp.i +
|
|
z__2.i;
|
|
temp.r = z__1.r, temp.i = z__1.i;
|
|
ix -= *incx;
|
|
/* L120: */
|
|
}
|
|
} else {
|
|
if (nounit) {
|
|
d_cnjg(&z__2, &a[kplus1 + j * a_dim1]);
|
|
z__1.r = temp.r * z__2.r - temp.i * z__2.i,
|
|
z__1.i = temp.r * z__2.i + temp.i *
|
|
z__2.r;
|
|
temp.r = z__1.r, temp.i = z__1.i;
|
|
}
|
|
/* Computing MAX */
|
|
i__4 = 1, i__1 = j - *k;
|
|
i__3 = max(i__4,i__1);
|
|
for (i__ = j - 1; i__ >= i__3; --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 = temp.r + z__2.r, z__1.i = temp.i +
|
|
z__2.i;
|
|
temp.r = z__1.r, temp.i = z__1.i;
|
|
ix -= *incx;
|
|
/* L130: */
|
|
}
|
|
}
|
|
i__3 = jx;
|
|
x[i__3].r = temp.r, x[i__3].i = temp.i;
|
|
jx -= *incx;
|
|
/* L140: */
|
|
}
|
|
}
|
|
} else {
|
|
if (*incx == 1) {
|
|
i__3 = *n;
|
|
for (j = 1; j <= i__3; ++j) {
|
|
i__4 = j;
|
|
temp.r = x[i__4].r, temp.i = x[i__4].i;
|
|
l = 1 - j;
|
|
if (noconj) {
|
|
if (nounit) {
|
|
i__4 = j * a_dim1 + 1;
|
|
z__1.r = temp.r * a[i__4].r - temp.i * a[i__4].i,
|
|
z__1.i = temp.r * a[i__4].i + temp.i * a[
|
|
i__4].r;
|
|
temp.r = z__1.r, temp.i = z__1.i;
|
|
}
|
|
/* Computing MIN */
|
|
i__1 = *n, i__2 = j + *k;
|
|
i__4 = min(i__1,i__2);
|
|
for (i__ = j + 1; i__ <= i__4; ++i__) {
|
|
i__1 = l + i__ + j * a_dim1;
|
|
i__2 = i__;
|
|
z__2.r = a[i__1].r * x[i__2].r - a[i__1].i * x[
|
|
i__2].i, z__2.i = a[i__1].r * x[i__2].i +
|
|
a[i__1].i * x[i__2].r;
|
|
z__1.r = temp.r + z__2.r, z__1.i = temp.i +
|
|
z__2.i;
|
|
temp.r = z__1.r, temp.i = z__1.i;
|
|
/* L150: */
|
|
}
|
|
} else {
|
|
if (nounit) {
|
|
d_cnjg(&z__2, &a[j * a_dim1 + 1]);
|
|
z__1.r = temp.r * z__2.r - temp.i * z__2.i,
|
|
z__1.i = temp.r * z__2.i + temp.i *
|
|
z__2.r;
|
|
temp.r = z__1.r, temp.i = z__1.i;
|
|
}
|
|
/* Computing MIN */
|
|
i__1 = *n, i__2 = j + *k;
|
|
i__4 = min(i__1,i__2);
|
|
for (i__ = j + 1; i__ <= i__4; ++i__) {
|
|
d_cnjg(&z__3, &a[l + i__ + j * a_dim1]);
|
|
i__1 = i__;
|
|
z__2.r = z__3.r * x[i__1].r - z__3.i * x[i__1].i,
|
|
z__2.i = z__3.r * x[i__1].i + z__3.i * x[
|
|
i__1].r;
|
|
z__1.r = temp.r + z__2.r, z__1.i = temp.i +
|
|
z__2.i;
|
|
temp.r = z__1.r, temp.i = z__1.i;
|
|
/* L160: */
|
|
}
|
|
}
|
|
i__4 = j;
|
|
x[i__4].r = temp.r, x[i__4].i = temp.i;
|
|
/* L170: */
|
|
}
|
|
} else {
|
|
jx = kx;
|
|
i__3 = *n;
|
|
for (j = 1; j <= i__3; ++j) {
|
|
i__4 = jx;
|
|
temp.r = x[i__4].r, temp.i = x[i__4].i;
|
|
kx += *incx;
|
|
ix = kx;
|
|
l = 1 - j;
|
|
if (noconj) {
|
|
if (nounit) {
|
|
i__4 = j * a_dim1 + 1;
|
|
z__1.r = temp.r * a[i__4].r - temp.i * a[i__4].i,
|
|
z__1.i = temp.r * a[i__4].i + temp.i * a[
|
|
i__4].r;
|
|
temp.r = z__1.r, temp.i = z__1.i;
|
|
}
|
|
/* Computing MIN */
|
|
i__1 = *n, i__2 = j + *k;
|
|
i__4 = min(i__1,i__2);
|
|
for (i__ = j + 1; i__ <= i__4; ++i__) {
|
|
i__1 = l + i__ + j * a_dim1;
|
|
i__2 = ix;
|
|
z__2.r = a[i__1].r * x[i__2].r - a[i__1].i * x[
|
|
i__2].i, z__2.i = a[i__1].r * x[i__2].i +
|
|
a[i__1].i * x[i__2].r;
|
|
z__1.r = temp.r + z__2.r, z__1.i = temp.i +
|
|
z__2.i;
|
|
temp.r = z__1.r, temp.i = z__1.i;
|
|
ix += *incx;
|
|
/* L180: */
|
|
}
|
|
} else {
|
|
if (nounit) {
|
|
d_cnjg(&z__2, &a[j * a_dim1 + 1]);
|
|
z__1.r = temp.r * z__2.r - temp.i * z__2.i,
|
|
z__1.i = temp.r * z__2.i + temp.i *
|
|
z__2.r;
|
|
temp.r = z__1.r, temp.i = z__1.i;
|
|
}
|
|
/* Computing MIN */
|
|
i__1 = *n, i__2 = j + *k;
|
|
i__4 = min(i__1,i__2);
|
|
for (i__ = j + 1; i__ <= i__4; ++i__) {
|
|
d_cnjg(&z__3, &a[l + i__ + j * a_dim1]);
|
|
i__1 = ix;
|
|
z__2.r = z__3.r * x[i__1].r - z__3.i * x[i__1].i,
|
|
z__2.i = z__3.r * x[i__1].i + z__3.i * x[
|
|
i__1].r;
|
|
z__1.r = temp.r + z__2.r, z__1.i = temp.i +
|
|
z__2.i;
|
|
temp.r = z__1.r, temp.i = z__1.i;
|
|
ix += *incx;
|
|
/* L190: */
|
|
}
|
|
}
|
|
i__4 = jx;
|
|
x[i__4].r = temp.r, x[i__4].i = temp.i;
|
|
jx += *incx;
|
|
/* L200: */
|
|
}
|
|
}
|
|
}
|
|
}
|
|
|
|
return 0;
|
|
|
|
/* End of ZTBMV . */
|
|
|
|
} /* ztbmv_ */
|
|
|