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429 lines
11 KiB
C
429 lines
11 KiB
C
/* dtbmv.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 dtbmv_(char *uplo, char *trans, char *diag, integer *n,
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integer *k, doublereal *a, integer *lda, doublereal *x, integer *incx,
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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;
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/* Local variables */
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integer i__, j, l, ix, jx, kx, info;
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doublereal 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 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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/* DTBMV performs one of the matrix-vector operations */
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/* x := A*x, or x := 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 := 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 - DOUBLE PRECISION 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 - DOUBLE PRECISION 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_("DTBMV ", &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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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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if (x[j] != 0.) {
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temp = x[j];
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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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x[i__] += temp * a[l + i__ + j * a_dim1];
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/* L10: */
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}
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if (nounit) {
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x[j] *= a[kplus1 + j * a_dim1];
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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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if (x[jx] != 0.) {
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temp = x[jx];
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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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x[ix] += temp * a[l + i__ + j * a_dim1];
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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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x[jx] *= a[kplus1 + j * a_dim1];
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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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if (x[j] != 0.) {
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temp = x[j];
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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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x[i__] += temp * a[l + i__ + j * a_dim1];
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/* L50: */
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}
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if (nounit) {
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x[j] *= a[j * a_dim1 + 1];
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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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if (x[jx] != 0.) {
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temp = x[jx];
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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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x[ix] += temp * a[l + i__ + j * a_dim1];
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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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x[jx] *= a[j * a_dim1 + 1];
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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. */
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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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temp = x[j];
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l = kplus1 - j;
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if (nounit) {
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temp *= a[kplus1 + j * a_dim1];
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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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temp += a[l + i__ + j * a_dim1] * x[i__];
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/* L90: */
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}
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x[j] = temp;
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/* L100: */
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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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temp = x[jx];
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kx -= *incx;
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ix = kx;
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l = kplus1 - j;
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if (nounit) {
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temp *= a[kplus1 + j * a_dim1];
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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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temp += a[l + i__ + j * a_dim1] * x[ix];
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ix -= *incx;
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/* L110: */
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}
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x[jx] = temp;
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jx -= *incx;
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/* L120: */
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}
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}
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} else {
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if (*incx == 1) {
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i__3 = *n;
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for (j = 1; j <= i__3; ++j) {
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temp = x[j];
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l = 1 - j;
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if (nounit) {
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temp *= a[j * a_dim1 + 1];
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}
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/* Computing MIN */
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i__1 = *n, i__2 = j + *k;
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i__4 = min(i__1,i__2);
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for (i__ = j + 1; i__ <= i__4; ++i__) {
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temp += a[l + i__ + j * a_dim1] * x[i__];
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/* L130: */
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}
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x[j] = temp;
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/* L140: */
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}
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} else {
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jx = kx;
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i__3 = *n;
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for (j = 1; j <= i__3; ++j) {
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temp = x[jx];
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kx += *incx;
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ix = kx;
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l = 1 - j;
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if (nounit) {
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temp *= a[j * a_dim1 + 1];
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}
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/* Computing MIN */
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i__1 = *n, i__2 = j + *k;
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i__4 = min(i__1,i__2);
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for (i__ = j + 1; i__ <= i__4; ++i__) {
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temp += a[l + i__ + j * a_dim1] * x[ix];
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ix += *incx;
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/* L150: */
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}
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x[jx] = temp;
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jx += *incx;
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/* L160: */
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}
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}
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}
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}
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return 0;
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/* End of DTBMV . */
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} /* dtbmv_ */
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