299 lines
9 KiB
C
299 lines
9 KiB
C
#include "blaswrap.h"
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#ifdef __cplusplus
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extern "C" {
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#endif
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#include "f2c.h"
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/* Subroutine */ int dsbmv_(char *uplo, integer *n, integer *k, doublereal *
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alpha, doublereal *a, integer *lda, doublereal *x, integer *incx,
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doublereal *beta, doublereal *y, integer *incy)
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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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static integer info;
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static doublereal temp1, temp2;
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static integer i__, j, l;
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extern logical lsame_(char *, char *);
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static integer kplus1, ix, iy, jx, jy, kx, ky;
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extern /* Subroutine */ int xerbla_(char *, integer *);
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#define a_ref(a_1,a_2) a[(a_2)*a_dim1 + a_1]
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/* Purpose
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=======
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DSBMV 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 symmetric band matrix, with k super-diagonals.
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Parameters
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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 - DOUBLE PRECISION.
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On entry, ALPHA specifies the scalar alpha.
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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 symmetric 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 symmetric 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 symmetric 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 symmetric 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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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
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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 - DOUBLE PRECISION.
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On entry, BETA specifies the scalar beta.
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Unchanged on exit.
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Y - DOUBLE PRECISION 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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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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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 * 1;
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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") && ! lsame_(uplo, "L")) {
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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_("DSBMV ", &info);
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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 == 0. && *beta == 1.) {
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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 != 1.) {
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if (*incy == 1) {
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if (*beta == 0.) {
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i__1 = *n;
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for (i__ = 1; i__ <= i__1; ++i__) {
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y[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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y[i__] = *beta * y[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 == 0.) {
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i__1 = *n;
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for (i__ = 1; i__ <= i__1; ++i__) {
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y[iy] = 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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y[iy] = *beta * y[iy];
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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 == 0.) {
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return 0;
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}
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if (lsame_(uplo, "U")) {
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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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temp1 = *alpha * x[j];
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temp2 = 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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y[i__] += temp1 * a_ref(l + i__, j);
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temp2 += a_ref(l + i__, j) * x[i__];
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/* L50: */
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}
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y[j] = y[j] + temp1 * a_ref(kplus1, j) + *alpha * temp2;
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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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temp1 = *alpha * x[jx];
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temp2 = 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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y[iy] += temp1 * a_ref(l + i__, j);
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temp2 += a_ref(l + i__, j) * x[ix];
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ix += *incx;
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iy += *incy;
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/* L70: */
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}
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y[jy] = y[jy] + temp1 * a_ref(kplus1, j) + *alpha * temp2;
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jx += *incx;
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jy += *incy;
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if (j > *k) {
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kx += *incx;
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ky += *incy;
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}
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/* L80: */
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}
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}
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} else {
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/* Form y when lower triangle of A is stored. */
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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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temp1 = *alpha * x[j];
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temp2 = 0.;
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y[j] += temp1 * a_ref(1, j);
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l = 1 - j;
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/* Computing MIN */
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i__4 = *n, i__2 = j + *k;
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i__3 = min(i__4,i__2);
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for (i__ = j + 1; i__ <= i__3; ++i__) {
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y[i__] += temp1 * a_ref(l + i__, j);
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temp2 += a_ref(l + i__, j) * x[i__];
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/* L90: */
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}
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y[j] += *alpha * temp2;
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/* L100: */
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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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temp1 = *alpha * x[jx];
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temp2 = 0.;
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y[jy] += temp1 * a_ref(1, j);
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l = 1 - j;
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ix = jx;
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iy = jy;
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/* Computing MIN */
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i__4 = *n, i__2 = j + *k;
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i__3 = min(i__4,i__2);
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for (i__ = j + 1; i__ <= i__3; ++i__) {
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ix += *incx;
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iy += *incy;
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y[iy] += temp1 * a_ref(l + i__, j);
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temp2 += a_ref(l + i__, j) * x[ix];
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/* L110: */
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}
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y[jy] += *alpha * temp2;
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jx += *incx;
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jy += *incy;
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/* L120: */
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}
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}
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}
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return 0;
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/* End of DSBMV . */
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} /* dsbmv_ */
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#undef a_ref
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#ifdef __cplusplus
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}
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#endif
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