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* Revert "restore bli_extern_defs exporting for now" This reverts commit 09fb07c350b2acee17645e8e9e1b8d829c73dca8. * Remove symbols not intended to be public * No need of def file anymore * Fix whitespace * No need of configure option * Remove export macro from definitions * Remove blas export macro from definitions
1635 lines
51 KiB
C
1635 lines
51 KiB
C
/*
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BLIS
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An object-based framework for developing high-performance BLAS-like
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libraries.
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Copyright (C) 2014, The University of Texas at Austin
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Redistribution and use in source and binary forms, with or without
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modification, are permitted provided that the following conditions are
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met:
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- Redistributions of source code must retain the above copyright
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notice, this list of conditions and the following disclaimer.
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- Redistributions in binary form must reproduce the above copyright
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notice, this list of conditions and the following disclaimer in the
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documentation and/or other materials provided with the distribution.
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- Neither the name(s) of the copyright holder(s) nor the names of its
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contributors may be used to endorse or promote products derived
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from this software without specific prior written permission.
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THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
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"AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
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LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
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A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT
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HOLDER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
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SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT
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LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
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DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
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THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
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(INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
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OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
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*/
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#include "blis.h"
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#ifdef BLIS_ENABLE_BLAS
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/* cgbmv.f -- translated by f2c (version 19991025).
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You must link the resulting object file with the libraries:
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-lf2c -lm (in that order)
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*/
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/* Subroutine */ int PASTEF77(c,gbmv)(const bla_character *trans, const bla_integer *m, const bla_integer *n, const bla_integer *kl, const bla_integer *ku, const bla_scomplex *alpha, const bla_scomplex *a, const bla_integer *lda, const bla_scomplex *x, const bla_integer *incx, const bla_scomplex *beta, bla_scomplex *y, const bla_integer *incy)
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{
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/* System generated locals */
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bla_integer a_dim1, a_offset, i__1, i__2, i__3, i__4, i__5, i__6;
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bla_scomplex q__1, q__2, q__3;
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/* Builtin functions */
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//void bla_r_cnjg(bla_scomplex *, bla_scomplex *);
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/* Local variables */
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bla_integer info;
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bla_scomplex temp;
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bla_integer lenx, leny, i__, j, k;
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//extern bla_logical PASTEF770(lsame)(bla_character *, bla_character *, ftnlen, ftnlen);
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bla_integer ix, iy, jx, jy, kx, ky;
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//extern /* Subroutine */ int PASTEF770(xerbla)(bla_character *, bla_integer *, ftnlen);
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bla_logical noconj;
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bla_integer kup1;
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/* .. Scalar Arguments .. */
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/* .. Array Arguments .. */
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/* .. */
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/* Purpose */
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/* ======= */
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/* CGBMV performs one of the matrix-vector operations */
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/* y := alpha*A*x + beta*y, or y := alpha*A'*x + beta*y, or */
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/* y := alpha*conjg( A' )*x + beta*y, */
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/* where alpha and beta are scalars, x and y are vectors and A is an */
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/* m by n band matrix, with kl sub-diagonals and ku super-diagonals. */
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/* Parameters */
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/* ========== */
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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' y := alpha*A*x + beta*y. */
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/* TRANS = 'T' or 't' y := alpha*A'*x + beta*y. */
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/* TRANS = 'C' or 'c' y := alpha*conjg( A' )*x + beta*y. */
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/* Unchanged on exit. */
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/* M - INTEGER. */
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/* On entry, M specifies the number of rows of the matrix A. */
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/* M must be at least zero. */
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/* Unchanged on exit. */
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/* N - INTEGER. */
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/* On entry, N specifies the number of columns 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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/* KL - INTEGER. */
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/* On entry, KL specifies the number of sub-diagonals of the */
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/* matrix A. KL must satisfy 0 .le. KL. */
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/* Unchanged on exit. */
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/* KU - INTEGER. */
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/* On entry, KU specifies the number of super-diagonals of the */
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/* matrix A. KU must satisfy 0 .le. KU. */
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/* Unchanged on exit. */
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/* ALPHA - COMPLEX . */
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/* On entry, ALPHA specifies the scalar alpha. */
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/* Unchanged on exit. */
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/* A - COMPLEX array of DIMENSION ( LDA, n ). */
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/* Before entry, the leading ( kl + ku + 1 ) by n part of the */
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/* array A must contain the matrix of coefficients, supplied */
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/* column by column, with the leading diagonal of the matrix in */
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/* row ( ku + 1 ) of the array, the first super-diagonal */
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/* starting at position 2 in row ku, the first sub-diagonal */
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/* starting at position 1 in row ( ku + 2 ), and so on. */
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/* Elements in the array A that do not correspond to elements */
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/* in the band matrix (such as the top left ku by ku triangle) */
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/* are not referenced. */
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/* The following program segment will transfer a band matrix */
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/* from conventional full matrix storage to band storage: */
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/* DO 20, J = 1, N */
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/* K = KU + 1 - J */
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/* DO 10, I = MAX( 1, J - KU ), MIN( M, J + KL ) */
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/* A( K + 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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/* ( kl + ku + 1 ). */
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/* Unchanged on exit. */
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/* X - COMPLEX array of DIMENSION at least */
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/* ( 1 + ( n - 1 )*abs( INCX ) ) when TRANS = 'N' or 'n' */
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/* and at least */
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/* ( 1 + ( m - 1 )*abs( INCX ) ) otherwise. */
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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 . */
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/* On entry, BETA specifies the scalar beta. When BETA is */
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/* supplied as zero then Y need not be set on input. */
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/* Unchanged on exit. */
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/* Y - COMPLEX array of DIMENSION at least */
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/* ( 1 + ( m - 1 )*abs( INCY ) ) when TRANS = 'N' or 'n' */
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/* and at least */
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/* ( 1 + ( n - 1 )*abs( INCY ) ) otherwise. */
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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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/* .. Parameters .. */
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/* .. Local Scalars .. */
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/* .. External Functions .. */
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/* .. External Subroutines .. */
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/* .. Intrinsic Functions .. */
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/* .. */
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/* .. Executable Statements .. */
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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 (! PASTEF770(lsame)(trans, "N", (ftnlen)1, (ftnlen)1) && ! PASTEF770(lsame)(trans, "T", (
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ftnlen)1, (ftnlen)1) && ! PASTEF770(lsame)(trans, "C", (ftnlen)1, (ftnlen)1)
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) {
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info = 1;
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} else if (*m < 0) {
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info = 2;
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} else if (*n < 0) {
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info = 3;
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} else if (*kl < 0) {
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info = 4;
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} else if (*ku < 0) {
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info = 5;
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} else if (*lda < *kl + *ku + 1) {
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info = 8;
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} else if (*incx == 0) {
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info = 10;
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} else if (*incy == 0) {
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info = 13;
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}
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if (info != 0) {
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PASTEF770(xerbla)("CGBMV ", &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 (*m == 0 || *n == 0 || (bli_creal(*alpha) == 0.f && bli_cimag(*alpha) == 0.f && (bli_creal(*beta)
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== 1.f && bli_cimag(*beta) == 0.f))) {
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return 0;
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}
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noconj = PASTEF770(lsame)(trans, "T", (ftnlen)1, (ftnlen)1);
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/* Set LENX and LENY, the lengths of the vectors x and y, and set */
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/* up the start points in X and Y. */
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if (PASTEF770(lsame)(trans, "N", (ftnlen)1, (ftnlen)1)) {
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lenx = *n;
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leny = *m;
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} else {
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lenx = *m;
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leny = *n;
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}
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if (*incx > 0) {
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kx = 1;
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} else {
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kx = 1 - (lenx - 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 - (leny - 1) * *incy;
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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 the band part of A. */
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/* First form y := beta*y. */
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if (bli_creal(*beta) != 1.f || bli_cimag(*beta) != 0.f) {
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if (*incy == 1) {
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if (bli_creal(*beta) == 0.f && bli_cimag(*beta) == 0.f) {
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i__1 = leny;
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for (i__ = 1; i__ <= i__1; ++i__) {
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i__2 = i__;
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bli_csets( (0.f), (0.f), y[i__2] );
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/* L10: */
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}
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} else {
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i__1 = leny;
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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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bli_csets( (bli_creal(*beta) * bli_creal(y[i__3]) - bli_cimag(*beta) * bli_cimag(y[i__3])), (bli_creal(*beta) * bli_cimag(y[i__3]) + bli_cimag(*beta) * bli_creal(y[i__3])), q__1 );
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bli_csets( (bli_creal(q__1)), (bli_cimag(q__1)), y[i__2] );
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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 (bli_creal(*beta) == 0.f && bli_cimag(*beta) == 0.f) {
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i__1 = leny;
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for (i__ = 1; i__ <= i__1; ++i__) {
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i__2 = iy;
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bli_csets( (0.f), (0.f), y[i__2] );
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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 = leny;
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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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bli_csets( (bli_creal(*beta) * bli_creal(y[i__3]) - bli_cimag(*beta) * bli_cimag(y[i__3])), (bli_creal(*beta) * bli_cimag(y[i__3]) + bli_cimag(*beta) * bli_creal(y[i__3])), q__1 );
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bli_csets( (bli_creal(q__1)), (bli_cimag(q__1)), y[i__2] );
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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 (bli_creal(*alpha) == 0.f && bli_cimag(*alpha) == 0.f) {
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return 0;
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}
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kup1 = *ku + 1;
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if (PASTEF770(lsame)(trans, "N", (ftnlen)1, (ftnlen)1)) {
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/* Form y := alpha*A*x + y. */
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jx = kx;
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if (*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 = jx;
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if (bli_creal(x[i__2]) != 0.f || bli_cimag(x[i__2]) != 0.f) {
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i__2 = jx;
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bli_csets( (bli_creal(*alpha) * bli_creal(x[i__2]) - bli_cimag(*alpha) * bli_cimag(x[i__2])), (bli_creal(*alpha) * bli_cimag(x[i__2]) + bli_cimag(*alpha) * bli_creal(x[i__2])), q__1 );
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bli_csets( (bli_creal(q__1)), (bli_cimag(q__1)), temp );
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k = kup1 - j;
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/* Computing MAX */
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i__2 = 1, i__3 = j - *ku;
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/* Computing MIN */
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i__5 = *m, i__6 = j + *kl;
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i__4 = f2c_min(i__5,i__6);
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for (i__ = f2c_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 = k + i__ + j * a_dim1;
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bli_csets( (bli_creal(temp) * bli_creal(a[i__5]) - bli_cimag(temp) * bli_cimag(a[i__5])), (bli_creal(temp) * bli_cimag(a[i__5]) + bli_cimag(temp) * bli_creal(a[i__5])), q__2 );
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bli_csets( (bli_creal(y[i__3]) + bli_creal(q__2)), (bli_cimag(y[i__3]) + bli_cimag(q__2)), q__1 );
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bli_csets( (bli_creal(q__1)), (bli_cimag(q__1)), y[i__2] );
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/* L50: */
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}
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}
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jx += *incx;
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/* L60: */
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}
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} else {
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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 (bli_creal(x[i__4]) != 0.f || bli_cimag(x[i__4]) != 0.f) {
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i__4 = jx;
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bli_csets( (bli_creal(*alpha) * bli_creal(x[i__4]) - bli_cimag(*alpha) * bli_cimag(x[i__4])), (bli_creal(*alpha) * bli_cimag(x[i__4]) + bli_cimag(*alpha) * bli_creal(x[i__4])), q__1 );
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bli_csets( (bli_creal(q__1)), (bli_cimag(q__1)), temp );
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iy = ky;
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k = kup1 - j;
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/* Computing MAX */
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i__4 = 1, i__2 = j - *ku;
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/* Computing MIN */
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i__5 = *m, i__6 = j + *kl;
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i__3 = f2c_min(i__5,i__6);
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for (i__ = f2c_max(i__4,i__2); i__ <= i__3; ++i__) {
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i__4 = iy;
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i__2 = iy;
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i__5 = k + i__ + j * a_dim1;
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bli_csets( (bli_creal(temp) * bli_creal(a[i__5]) - bli_cimag(temp) * bli_cimag(a[i__5])), (bli_creal(temp) * bli_cimag(a[i__5]) + bli_cimag(temp) * bli_creal(a[i__5])), q__2 );
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bli_csets( (bli_creal(y[i__2]) + bli_creal(q__2)), (bli_cimag(y[i__2]) + bli_cimag(q__2)), q__1 );
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bli_csets( (bli_creal(q__1)), (bli_cimag(q__1)), y[i__4] );
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iy += *incy;
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/* L70: */
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}
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}
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jx += *incx;
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if (j > *ku) {
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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 := alpha*A'*x + y or y := alpha*conjg( A' )*x + y. */
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jy = ky;
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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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bli_csets( (0.f), (0.f), temp );
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k = kup1 - j;
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if (noconj) {
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/* Computing MAX */
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i__3 = 1, i__4 = j - *ku;
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/* Computing MIN */
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i__5 = *m, i__6 = j + *kl;
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i__2 = f2c_min(i__5,i__6);
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for (i__ = f2c_max(i__3,i__4); i__ <= i__2; ++i__) {
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i__3 = k + i__ + j * a_dim1;
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i__4 = i__;
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bli_csets( (bli_creal(a[i__3]) * bli_creal(x[i__4]) - bli_cimag(a[i__3]) * bli_cimag(x[i__4])), (bli_creal(a[i__3]) * bli_cimag(x[i__4]) + bli_cimag(a[i__3]) * bli_creal(x[i__4])), q__2 );
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bli_csets( (bli_creal(temp) + bli_creal(q__2)), (bli_cimag(temp) + bli_cimag(q__2)), q__1 );
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bli_csets( (bli_creal(q__1)), (bli_cimag(q__1)), temp );
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/* L90: */
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}
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} else {
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/* Computing MAX */
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i__2 = 1, i__3 = j - *ku;
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/* Computing MIN */
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i__5 = *m, i__6 = j + *kl;
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i__4 = f2c_min(i__5,i__6);
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for (i__ = f2c_max(i__2,i__3); i__ <= i__4; ++i__) {
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bla_r_cnjg(&q__3, &a[k + i__ + j * a_dim1]);
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i__2 = i__;
|
|
bli_csets( (bli_creal(q__3) * bli_creal(x[i__2]) - bli_cimag(q__3) * bli_cimag(x[i__2])), (bli_creal(q__3) * bli_cimag(x[i__2]) + bli_cimag(q__3) * bli_creal(x[i__2])), q__2 );
|
|
bli_csets( (bli_creal(temp) + bli_creal(q__2)), (bli_cimag(temp) + bli_cimag(q__2)), q__1 );
|
|
bli_csets( (bli_creal(q__1)), (bli_cimag(q__1)), temp );
|
|
/* L100: */
|
|
}
|
|
}
|
|
i__4 = jy;
|
|
i__2 = jy;
|
|
bli_csets( (bli_creal(*alpha) * bli_creal(temp) - bli_cimag(*alpha) * bli_cimag(temp)), (bli_creal(*alpha) * bli_cimag(temp) + bli_cimag(*alpha) * bli_creal(temp)), q__2 );
|
|
bli_csets( (bli_creal(y[i__2]) + bli_creal(q__2)), (bli_cimag(y[i__2]) + bli_cimag(q__2)), q__1 );
|
|
bli_csets( (bli_creal(q__1)), (bli_cimag(q__1)), y[i__4] );
|
|
jy += *incy;
|
|
/* L110: */
|
|
}
|
|
} else {
|
|
i__1 = *n;
|
|
for (j = 1; j <= i__1; ++j) {
|
|
bli_csets( (0.f), (0.f), temp );
|
|
ix = kx;
|
|
k = kup1 - j;
|
|
if (noconj) {
|
|
/* Computing MAX */
|
|
i__4 = 1, i__2 = j - *ku;
|
|
/* Computing MIN */
|
|
i__5 = *m, i__6 = j + *kl;
|
|
i__3 = f2c_min(i__5,i__6);
|
|
for (i__ = f2c_max(i__4,i__2); i__ <= i__3; ++i__) {
|
|
i__4 = k + i__ + j * a_dim1;
|
|
i__2 = ix;
|
|
bli_csets( (bli_creal(a[i__4]) * bli_creal(x[i__2]) - bli_cimag(a[i__4]) * bli_cimag(x[i__2])), (bli_creal(a[i__4]) * bli_cimag(x[i__2]) + bli_cimag(a[i__4]) * bli_creal(x[i__2])), q__2 );
|
|
bli_csets( (bli_creal(temp) + bli_creal(q__2)), (bli_cimag(temp) + bli_cimag(q__2)), q__1 );
|
|
bli_csets( (bli_creal(q__1)), (bli_cimag(q__1)), temp );
|
|
ix += *incx;
|
|
/* L120: */
|
|
}
|
|
} else {
|
|
/* Computing MAX */
|
|
i__3 = 1, i__4 = j - *ku;
|
|
/* Computing MIN */
|
|
i__5 = *m, i__6 = j + *kl;
|
|
i__2 = f2c_min(i__5,i__6);
|
|
for (i__ = f2c_max(i__3,i__4); i__ <= i__2; ++i__) {
|
|
bla_r_cnjg(&q__3, &a[k + i__ + j * a_dim1]);
|
|
i__3 = ix;
|
|
bli_csets( (bli_creal(q__3) * bli_creal(x[i__3]) - bli_cimag(q__3) * bli_cimag(x[i__3])), (bli_creal(q__3) * bli_cimag(x[i__3]) + bli_cimag(q__3) * bli_creal(x[i__3])), q__2 );
|
|
bli_csets( (bli_creal(temp) + bli_creal(q__2)), (bli_cimag(temp) + bli_cimag(q__2)), q__1 );
|
|
bli_csets( (bli_creal(q__1)), (bli_cimag(q__1)), temp );
|
|
ix += *incx;
|
|
/* L130: */
|
|
}
|
|
}
|
|
i__2 = jy;
|
|
i__3 = jy;
|
|
bli_csets( (bli_creal(*alpha) * bli_creal(temp) - bli_cimag(*alpha) * bli_cimag(temp)), (bli_creal(*alpha) * bli_cimag(temp) + bli_cimag(*alpha) * bli_creal(temp)), q__2 );
|
|
bli_csets( (bli_creal(y[i__3]) + bli_creal(q__2)), (bli_cimag(y[i__3]) + bli_cimag(q__2)), q__1 );
|
|
bli_csets( (bli_creal(q__1)), (bli_cimag(q__1)), y[i__2] );
|
|
jy += *incy;
|
|
if (j > *ku) {
|
|
kx += *incx;
|
|
}
|
|
/* L140: */
|
|
}
|
|
}
|
|
}
|
|
|
|
return 0;
|
|
|
|
/* End of CGBMV . */
|
|
|
|
} /* cgbmv_ */
|
|
|
|
/* dgbmv.f -- translated by f2c (version 19991025).
|
|
You must link the resulting object file with the libraries:
|
|
-lf2c -lm (in that order)
|
|
*/
|
|
|
|
/* Subroutine */ int PASTEF77(d,gbmv)(const bla_character *trans, const bla_integer *m, const bla_integer *n, const bla_integer *kl, const bla_integer *ku, const bla_double *alpha, const bla_double *a, const bla_integer *lda, const bla_double *x, const bla_integer *incx, const bla_double *beta, bla_double *y, const bla_integer *incy)
|
|
{
|
|
/* System generated locals */
|
|
bla_integer a_dim1, a_offset, i__1, i__2, i__3, i__4, i__5, i__6;
|
|
|
|
/* Local variables */
|
|
bla_integer info;
|
|
bla_double temp;
|
|
bla_integer lenx, leny, i__, j, k;
|
|
//extern bla_logical PASTEF770(lsame)(bla_character *, bla_character *, ftnlen, ftnlen);
|
|
bla_integer ix, iy, jx, jy, kx, ky;
|
|
//extern /* Subroutine */ int PASTEF770(xerbla)(bla_character *, bla_integer *, ftnlen);
|
|
bla_integer kup1;
|
|
|
|
/* .. Scalar Arguments .. */
|
|
/* .. Array Arguments .. */
|
|
/* .. */
|
|
|
|
/* Purpose */
|
|
/* ======= */
|
|
|
|
/* DGBMV performs one of the matrix-vector operations */
|
|
|
|
/* y := alpha*A*x + beta*y, or y := alpha*A'*x + beta*y, */
|
|
|
|
/* where alpha and beta are scalars, x and y are vectors and A is an */
|
|
/* m by n band matrix, with kl sub-diagonals and ku super-diagonals. */
|
|
|
|
/* Parameters */
|
|
/* ========== */
|
|
|
|
/* TRANS - CHARACTER*1. */
|
|
/* On entry, TRANS specifies the operation to be performed as */
|
|
/* follows: */
|
|
|
|
/* TRANS = 'N' or 'n' y := alpha*A*x + beta*y. */
|
|
|
|
/* TRANS = 'T' or 't' y := alpha*A'*x + beta*y. */
|
|
|
|
/* TRANS = 'C' or 'c' y := alpha*A'*x + beta*y. */
|
|
|
|
/* Unchanged on exit. */
|
|
|
|
/* M - INTEGER. */
|
|
/* On entry, M specifies the number of rows of the matrix A. */
|
|
/* M must be at least zero. */
|
|
/* Unchanged on exit. */
|
|
|
|
/* N - INTEGER. */
|
|
/* On entry, N specifies the number of columns of the matrix A. */
|
|
/* N must be at least zero. */
|
|
/* Unchanged on exit. */
|
|
|
|
/* KL - INTEGER. */
|
|
/* On entry, KL specifies the number of sub-diagonals of the */
|
|
/* matrix A. KL must satisfy 0 .le. KL. */
|
|
/* Unchanged on exit. */
|
|
|
|
/* KU - INTEGER. */
|
|
/* On entry, KU specifies the number of super-diagonals of the */
|
|
/* matrix A. KU must satisfy 0 .le. KU. */
|
|
/* Unchanged on exit. */
|
|
|
|
/* ALPHA - DOUBLE PRECISION. */
|
|
/* On entry, ALPHA specifies the scalar alpha. */
|
|
/* Unchanged on exit. */
|
|
|
|
/* A - DOUBLE PRECISION array of DIMENSION ( LDA, n ). */
|
|
/* Before entry, the leading ( kl + ku + 1 ) by n part of the */
|
|
/* array A must contain the matrix of coefficients, supplied */
|
|
/* column by column, with the leading diagonal of the matrix in */
|
|
/* row ( ku + 1 ) of the array, the first super-diagonal */
|
|
/* starting at position 2 in row ku, the first sub-diagonal */
|
|
/* starting at position 1 in row ( ku + 2 ), and so on. */
|
|
/* Elements in the array A that do not correspond to elements */
|
|
/* in the band matrix (such as the top left ku by ku triangle) */
|
|
/* are not referenced. */
|
|
/* The following program segment will transfer a band matrix */
|
|
/* from conventional full matrix storage to band storage: */
|
|
|
|
/* DO 20, J = 1, N */
|
|
/* K = KU + 1 - J */
|
|
/* DO 10, I = MAX( 1, J - KU ), MIN( M, J + KL ) */
|
|
/* A( K + I, J ) = matrix( I, J ) */
|
|
/* 10 CONTINUE */
|
|
/* 20 CONTINUE */
|
|
|
|
/* Unchanged on exit. */
|
|
|
|
/* LDA - INTEGER. */
|
|
/* On entry, LDA specifies the first dimension of A as declared */
|
|
/* in the calling (sub) program. LDA must be at least */
|
|
/* ( kl + ku + 1 ). */
|
|
/* Unchanged on exit. */
|
|
|
|
/* X - DOUBLE PRECISION array of DIMENSION at least */
|
|
/* ( 1 + ( n - 1 )*abs( INCX ) ) when TRANS = 'N' or 'n' */
|
|
/* and at least */
|
|
/* ( 1 + ( m - 1 )*abs( INCX ) ) otherwise. */
|
|
/* Before entry, the incremented array X must contain the */
|
|
/* vector x. */
|
|
/* Unchanged on exit. */
|
|
|
|
/* INCX - INTEGER. */
|
|
/* On entry, INCX specifies the increment for the elements of */
|
|
/* X. INCX must not be zero. */
|
|
/* Unchanged on exit. */
|
|
|
|
/* BETA - DOUBLE PRECISION. */
|
|
/* On entry, BETA specifies the scalar beta. When BETA is */
|
|
/* supplied as zero then Y need not be set on input. */
|
|
/* Unchanged on exit. */
|
|
|
|
/* Y - DOUBLE PRECISION array of DIMENSION at least */
|
|
/* ( 1 + ( m - 1 )*abs( INCY ) ) when TRANS = 'N' or 'n' */
|
|
/* and at least */
|
|
/* ( 1 + ( n - 1 )*abs( INCY ) ) otherwise. */
|
|
/* Before entry, the incremented array Y must contain the */
|
|
/* vector y. On exit, Y is overwritten by the updated vector y. */
|
|
|
|
/* INCY - INTEGER. */
|
|
/* On entry, INCY specifies the increment for the elements of */
|
|
/* Y. INCY must not be zero. */
|
|
/* Unchanged on exit. */
|
|
|
|
|
|
/* Level 2 Blas routine. */
|
|
|
|
/* -- Written on 22-October-1986. */
|
|
/* Jack Dongarra, Argonne National Lab. */
|
|
/* Jeremy Du Croz, Nag Central Office. */
|
|
/* Sven Hammarling, Nag Central Office. */
|
|
/* Richard Hanson, Sandia National Labs. */
|
|
|
|
/* .. Parameters .. */
|
|
/* .. Local Scalars .. */
|
|
/* .. External Functions .. */
|
|
/* .. External Subroutines .. */
|
|
/* .. Intrinsic Functions .. */
|
|
/* .. */
|
|
/* .. Executable Statements .. */
|
|
|
|
/* Test the input parameters. */
|
|
|
|
/* Parameter adjustments */
|
|
a_dim1 = *lda;
|
|
a_offset = 1 + a_dim1 * 1;
|
|
a -= a_offset;
|
|
--x;
|
|
--y;
|
|
|
|
/* Function Body */
|
|
info = 0;
|
|
if (! PASTEF770(lsame)(trans, "N", (ftnlen)1, (ftnlen)1) && ! PASTEF770(lsame)(trans, "T", (
|
|
ftnlen)1, (ftnlen)1) && ! PASTEF770(lsame)(trans, "C", (ftnlen)1, (ftnlen)1)
|
|
) {
|
|
info = 1;
|
|
} else if (*m < 0) {
|
|
info = 2;
|
|
} else if (*n < 0) {
|
|
info = 3;
|
|
} else if (*kl < 0) {
|
|
info = 4;
|
|
} else if (*ku < 0) {
|
|
info = 5;
|
|
} else if (*lda < *kl + *ku + 1) {
|
|
info = 8;
|
|
} else if (*incx == 0) {
|
|
info = 10;
|
|
} else if (*incy == 0) {
|
|
info = 13;
|
|
}
|
|
if (info != 0) {
|
|
PASTEF770(xerbla)("DGBMV ", &info, (ftnlen)6);
|
|
return 0;
|
|
}
|
|
|
|
/* Quick return if possible. */
|
|
|
|
if (*m == 0 || *n == 0 || (*alpha == 0. && *beta == 1.)) {
|
|
return 0;
|
|
}
|
|
|
|
/* Set LENX and LENY, the lengths of the vectors x and y, and set */
|
|
/* up the start points in X and Y. */
|
|
|
|
if (PASTEF770(lsame)(trans, "N", (ftnlen)1, (ftnlen)1)) {
|
|
lenx = *n;
|
|
leny = *m;
|
|
} else {
|
|
lenx = *m;
|
|
leny = *n;
|
|
}
|
|
if (*incx > 0) {
|
|
kx = 1;
|
|
} else {
|
|
kx = 1 - (lenx - 1) * *incx;
|
|
}
|
|
if (*incy > 0) {
|
|
ky = 1;
|
|
} else {
|
|
ky = 1 - (leny - 1) * *incy;
|
|
}
|
|
|
|
/* Start the operations. In this version the elements of A are */
|
|
/* accessed sequentially with one pass through the band part of A. */
|
|
|
|
/* First form y := beta*y. */
|
|
|
|
if (*beta != 1.) {
|
|
if (*incy == 1) {
|
|
if (*beta == 0.) {
|
|
i__1 = leny;
|
|
for (i__ = 1; i__ <= i__1; ++i__) {
|
|
y[i__] = 0.;
|
|
/* L10: */
|
|
}
|
|
} else {
|
|
i__1 = leny;
|
|
for (i__ = 1; i__ <= i__1; ++i__) {
|
|
y[i__] = *beta * y[i__];
|
|
/* L20: */
|
|
}
|
|
}
|
|
} else {
|
|
iy = ky;
|
|
if (*beta == 0.) {
|
|
i__1 = leny;
|
|
for (i__ = 1; i__ <= i__1; ++i__) {
|
|
y[iy] = 0.;
|
|
iy += *incy;
|
|
/* L30: */
|
|
}
|
|
} else {
|
|
i__1 = leny;
|
|
for (i__ = 1; i__ <= i__1; ++i__) {
|
|
y[iy] = *beta * y[iy];
|
|
iy += *incy;
|
|
/* L40: */
|
|
}
|
|
}
|
|
}
|
|
}
|
|
if (*alpha == 0.) {
|
|
return 0;
|
|
}
|
|
kup1 = *ku + 1;
|
|
if (PASTEF770(lsame)(trans, "N", (ftnlen)1, (ftnlen)1)) {
|
|
|
|
/* Form y := alpha*A*x + y. */
|
|
|
|
jx = kx;
|
|
if (*incy == 1) {
|
|
i__1 = *n;
|
|
for (j = 1; j <= i__1; ++j) {
|
|
if (x[jx] != 0.) {
|
|
temp = *alpha * x[jx];
|
|
k = kup1 - j;
|
|
/* Computing MAX */
|
|
i__2 = 1, i__3 = j - *ku;
|
|
/* Computing MIN */
|
|
i__5 = *m, i__6 = j + *kl;
|
|
i__4 = f2c_min(i__5,i__6);
|
|
for (i__ = f2c_max(i__2,i__3); i__ <= i__4; ++i__) {
|
|
y[i__] += temp * a[k + i__ + j * a_dim1];
|
|
/* L50: */
|
|
}
|
|
}
|
|
jx += *incx;
|
|
/* L60: */
|
|
}
|
|
} else {
|
|
i__1 = *n;
|
|
for (j = 1; j <= i__1; ++j) {
|
|
if (x[jx] != 0.) {
|
|
temp = *alpha * x[jx];
|
|
iy = ky;
|
|
k = kup1 - j;
|
|
/* Computing MAX */
|
|
i__4 = 1, i__2 = j - *ku;
|
|
/* Computing MIN */
|
|
i__5 = *m, i__6 = j + *kl;
|
|
i__3 = f2c_min(i__5,i__6);
|
|
for (i__ = f2c_max(i__4,i__2); i__ <= i__3; ++i__) {
|
|
y[iy] += temp * a[k + i__ + j * a_dim1];
|
|
iy += *incy;
|
|
/* L70: */
|
|
}
|
|
}
|
|
jx += *incx;
|
|
if (j > *ku) {
|
|
ky += *incy;
|
|
}
|
|
/* L80: */
|
|
}
|
|
}
|
|
} else {
|
|
|
|
/* Form y := alpha*A'*x + y. */
|
|
|
|
jy = ky;
|
|
if (*incx == 1) {
|
|
i__1 = *n;
|
|
for (j = 1; j <= i__1; ++j) {
|
|
temp = 0.;
|
|
k = kup1 - j;
|
|
/* Computing MAX */
|
|
i__3 = 1, i__4 = j - *ku;
|
|
/* Computing MIN */
|
|
i__5 = *m, i__6 = j + *kl;
|
|
i__2 = f2c_min(i__5,i__6);
|
|
for (i__ = f2c_max(i__3,i__4); i__ <= i__2; ++i__) {
|
|
temp += a[k + i__ + j * a_dim1] * x[i__];
|
|
/* L90: */
|
|
}
|
|
y[jy] += *alpha * temp;
|
|
jy += *incy;
|
|
/* L100: */
|
|
}
|
|
} else {
|
|
i__1 = *n;
|
|
for (j = 1; j <= i__1; ++j) {
|
|
temp = 0.;
|
|
ix = kx;
|
|
k = kup1 - j;
|
|
/* Computing MAX */
|
|
i__2 = 1, i__3 = j - *ku;
|
|
/* Computing MIN */
|
|
i__5 = *m, i__6 = j + *kl;
|
|
i__4 = f2c_min(i__5,i__6);
|
|
for (i__ = f2c_max(i__2,i__3); i__ <= i__4; ++i__) {
|
|
temp += a[k + i__ + j * a_dim1] * x[ix];
|
|
ix += *incx;
|
|
/* L110: */
|
|
}
|
|
y[jy] += *alpha * temp;
|
|
jy += *incy;
|
|
if (j > *ku) {
|
|
kx += *incx;
|
|
}
|
|
/* L120: */
|
|
}
|
|
}
|
|
}
|
|
|
|
return 0;
|
|
|
|
/* End of DGBMV . */
|
|
|
|
} /* dgbmv_ */
|
|
|
|
/* sgbmv.f -- translated by f2c (version 19991025).
|
|
You must link the resulting object file with the libraries:
|
|
-lf2c -lm (in that order)
|
|
*/
|
|
|
|
/* Subroutine */ int PASTEF77(s,gbmv)(const bla_character *trans, const bla_integer *m, const bla_integer *n, const bla_integer *kl, const bla_integer *ku, const bla_real *alpha, const bla_real *a, const bla_integer *lda, const bla_real *x, const bla_integer * incx, const bla_real *beta, bla_real *y, const bla_integer *incy)
|
|
{
|
|
/* System generated locals */
|
|
bla_integer a_dim1, a_offset, i__1, i__2, i__3, i__4, i__5, i__6;
|
|
|
|
/* Local variables */
|
|
bla_integer info;
|
|
bla_real temp;
|
|
bla_integer lenx, leny, i__, j, k;
|
|
//extern bla_logical PASTEF770(lsame)(bla_character *, bla_character *, ftnlen, ftnlen);
|
|
bla_integer ix, iy, jx, jy, kx, ky;
|
|
//extern /* Subroutine */ int PASTEF770(xerbla)(bla_character *, bla_integer *, ftnlen);
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bla_integer kup1;
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/* .. Scalar Arguments .. */
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/* .. Array Arguments .. */
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/* .. */
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/* Purpose */
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/* ======= */
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/* SGBMV performs one of the matrix-vector operations */
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/* y := alpha*A*x + beta*y, or y := alpha*A'*x + beta*y, */
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/* where alpha and beta are scalars, x and y are vectors and A is an */
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/* m by n band matrix, with kl sub-diagonals and ku super-diagonals. */
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/* Parameters */
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/* ========== */
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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' y := alpha*A*x + beta*y. */
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/* TRANS = 'T' or 't' y := alpha*A'*x + beta*y. */
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/* TRANS = 'C' or 'c' y := alpha*A'*x + beta*y. */
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/* Unchanged on exit. */
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/* M - INTEGER. */
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/* On entry, M specifies the number of rows of the matrix A. */
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/* M must be at least zero. */
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/* Unchanged on exit. */
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/* N - INTEGER. */
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/* On entry, N specifies the number of columns 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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/* KL - INTEGER. */
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/* On entry, KL specifies the number of sub-diagonals of the */
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/* matrix A. KL must satisfy 0 .le. KL. */
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/* Unchanged on exit. */
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/* KU - INTEGER. */
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/* On entry, KU specifies the number of super-diagonals of the */
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/* matrix A. KU must satisfy 0 .le. KU. */
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/* Unchanged on exit. */
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/* ALPHA - REAL . */
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/* On entry, ALPHA specifies the scalar alpha. */
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/* Unchanged on exit. */
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/* A - REAL array of DIMENSION ( LDA, n ). */
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/* Before entry, the leading ( kl + ku + 1 ) by n part of the */
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/* array A must contain the matrix of coefficients, supplied */
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/* column by column, with the leading diagonal of the matrix in */
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/* row ( ku + 1 ) of the array, the first super-diagonal */
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/* starting at position 2 in row ku, the first sub-diagonal */
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/* starting at position 1 in row ( ku + 2 ), and so on. */
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/* Elements in the array A that do not correspond to elements */
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/* in the band matrix (such as the top left ku by ku triangle) */
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/* are not referenced. */
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/* The following program segment will transfer a band matrix */
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/* from conventional full matrix storage to band storage: */
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/* DO 20, J = 1, N */
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/* K = KU + 1 - J */
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/* DO 10, I = MAX( 1, J - KU ), MIN( M, J + KL ) */
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/* A( K + 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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/* ( kl + ku + 1 ). */
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/* Unchanged on exit. */
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/* X - REAL array of DIMENSION at least */
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/* ( 1 + ( n - 1 )*abs( INCX ) ) when TRANS = 'N' or 'n' */
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/* and at least */
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/* ( 1 + ( m - 1 )*abs( INCX ) ) otherwise. */
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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 - REAL . */
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/* On entry, BETA specifies the scalar beta. When BETA is */
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/* supplied as zero then Y need not be set on input. */
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/* Unchanged on exit. */
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/* Y - REAL array of DIMENSION at least */
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/* ( 1 + ( m - 1 )*abs( INCY ) ) when TRANS = 'N' or 'n' */
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/* and at least */
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/* ( 1 + ( n - 1 )*abs( INCY ) ) otherwise. */
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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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/* .. Parameters .. */
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/* .. Local Scalars .. */
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/* .. External Functions .. */
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/* .. External Subroutines .. */
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/* .. Intrinsic Functions .. */
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/* .. */
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/* .. Executable Statements .. */
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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 (! PASTEF770(lsame)(trans, "N", (ftnlen)1, (ftnlen)1) && ! PASTEF770(lsame)(trans, "T", (
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ftnlen)1, (ftnlen)1) && ! PASTEF770(lsame)(trans, "C", (ftnlen)1, (ftnlen)1)
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) {
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info = 1;
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} else if (*m < 0) {
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info = 2;
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} else if (*n < 0) {
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info = 3;
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} else if (*kl < 0) {
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info = 4;
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} else if (*ku < 0) {
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info = 5;
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} else if (*lda < *kl + *ku + 1) {
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info = 8;
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} else if (*incx == 0) {
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info = 10;
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} else if (*incy == 0) {
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info = 13;
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}
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if (info != 0) {
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PASTEF770(xerbla)("SGBMV ", &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 (*m == 0 || *n == 0 || (*alpha == 0.f && *beta == 1.f)) {
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return 0;
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}
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/* Set LENX and LENY, the lengths of the vectors x and y, and set */
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/* up the start points in X and Y. */
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if (PASTEF770(lsame)(trans, "N", (ftnlen)1, (ftnlen)1)) {
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lenx = *n;
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leny = *m;
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} else {
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lenx = *m;
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leny = *n;
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}
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if (*incx > 0) {
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kx = 1;
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} else {
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kx = 1 - (lenx - 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 - (leny - 1) * *incy;
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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 the band part of A. */
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/* First form y := beta*y. */
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if (*beta != 1.f) {
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if (*incy == 1) {
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if (*beta == 0.f) {
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i__1 = leny;
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for (i__ = 1; i__ <= i__1; ++i__) {
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y[i__] = 0.f;
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/* L10: */
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}
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} else {
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i__1 = leny;
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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.f) {
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i__1 = leny;
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for (i__ = 1; i__ <= i__1; ++i__) {
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y[iy] = 0.f;
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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 = leny;
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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.f) {
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return 0;
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}
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kup1 = *ku + 1;
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if (PASTEF770(lsame)(trans, "N", (ftnlen)1, (ftnlen)1)) {
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/* Form y := alpha*A*x + y. */
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jx = kx;
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if (*incy == 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[jx] != 0.f) {
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temp = *alpha * x[jx];
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k = kup1 - j;
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/* Computing MAX */
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i__2 = 1, i__3 = j - *ku;
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/* Computing MIN */
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i__5 = *m, i__6 = j + *kl;
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i__4 = f2c_min(i__5,i__6);
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for (i__ = f2c_max(i__2,i__3); i__ <= i__4; ++i__) {
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y[i__] += temp * a[k + i__ + j * a_dim1];
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/* L50: */
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}
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}
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jx += *incx;
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/* L60: */
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}
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} else {
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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.f) {
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temp = *alpha * x[jx];
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iy = ky;
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k = kup1 - j;
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/* Computing MAX */
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i__4 = 1, i__2 = j - *ku;
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/* Computing MIN */
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i__5 = *m, i__6 = j + *kl;
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i__3 = f2c_min(i__5,i__6);
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for (i__ = f2c_max(i__4,i__2); i__ <= i__3; ++i__) {
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y[iy] += temp * a[k + i__ + j * a_dim1];
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iy += *incy;
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/* L70: */
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}
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}
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jx += *incx;
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if (j > *ku) {
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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 := alpha*A'*x + y. */
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jy = ky;
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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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temp = 0.f;
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k = kup1 - j;
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/* Computing MAX */
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|
i__3 = 1, i__4 = j - *ku;
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|
/* Computing MIN */
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|
i__5 = *m, i__6 = j + *kl;
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i__2 = f2c_min(i__5,i__6);
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for (i__ = f2c_max(i__3,i__4); i__ <= i__2; ++i__) {
|
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temp += a[k + i__ + j * a_dim1] * x[i__];
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|
/* L90: */
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|
}
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y[jy] += *alpha * temp;
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jy += *incy;
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|
/* L100: */
|
|
}
|
|
} else {
|
|
i__1 = *n;
|
|
for (j = 1; j <= i__1; ++j) {
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|
temp = 0.f;
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|
ix = kx;
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|
k = kup1 - j;
|
|
/* Computing MAX */
|
|
i__2 = 1, i__3 = j - *ku;
|
|
/* Computing MIN */
|
|
i__5 = *m, i__6 = j + *kl;
|
|
i__4 = f2c_min(i__5,i__6);
|
|
for (i__ = f2c_max(i__2,i__3); i__ <= i__4; ++i__) {
|
|
temp += a[k + i__ + j * a_dim1] * x[ix];
|
|
ix += *incx;
|
|
/* L110: */
|
|
}
|
|
y[jy] += *alpha * temp;
|
|
jy += *incy;
|
|
if (j > *ku) {
|
|
kx += *incx;
|
|
}
|
|
/* L120: */
|
|
}
|
|
}
|
|
}
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|
|
return 0;
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|
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/* End of SGBMV . */
|
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|
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} /* sgbmv_ */
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|
|
/* zgbmv.f -- translated by f2c (version 19991025).
|
|
You must link the resulting object file with the libraries:
|
|
-lf2c -lm (in that order)
|
|
*/
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|
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/* Subroutine */ int PASTEF77(z,gbmv)(const bla_character *trans, const bla_integer *m, const bla_integer *n, const bla_integer *kl, const bla_integer *ku, const bla_dcomplex *alpha, const bla_dcomplex *a, const bla_integer *lda, const bla_dcomplex *x, const bla_integer *incx, const bla_dcomplex *beta, bla_dcomplex * y, const bla_integer *incy)
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|
{
|
|
/* System generated locals */
|
|
bla_integer a_dim1, a_offset, i__1, i__2, i__3, i__4, i__5, i__6;
|
|
bla_dcomplex z__1, z__2, z__3;
|
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|
|
/* Builtin functions */
|
|
//void bla_d_cnjg(bla_dcomplex *, bla_dcomplex *);
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|
|
/* Local variables */
|
|
bla_integer info;
|
|
bla_dcomplex temp;
|
|
bla_integer lenx, leny, i__, j, k;
|
|
//extern bla_logical PASTEF770(lsame)(bla_character *, bla_character *, ftnlen, ftnlen);
|
|
bla_integer ix, iy, jx, jy, kx, ky;
|
|
//extern /* Subroutine */ int PASTEF770(xerbla)(bla_character *, bla_integer *, ftnlen);
|
|
bla_logical noconj;
|
|
bla_integer kup1;
|
|
|
|
/* .. Scalar Arguments .. */
|
|
/* .. Array Arguments .. */
|
|
/* .. */
|
|
|
|
/* Purpose */
|
|
/* ======= */
|
|
|
|
/* ZGBMV performs one of the matrix-vector operations */
|
|
|
|
/* y := alpha*A*x + beta*y, or y := alpha*A'*x + beta*y, or */
|
|
|
|
/* y := alpha*conjg( A' )*x + beta*y, */
|
|
|
|
/* where alpha and beta are scalars, x and y are vectors and A is an */
|
|
/* m by n band matrix, with kl sub-diagonals and ku super-diagonals. */
|
|
|
|
/* Parameters */
|
|
/* ========== */
|
|
|
|
/* TRANS - CHARACTER*1. */
|
|
/* On entry, TRANS specifies the operation to be performed as */
|
|
/* follows: */
|
|
|
|
/* TRANS = 'N' or 'n' y := alpha*A*x + beta*y. */
|
|
|
|
/* TRANS = 'T' or 't' y := alpha*A'*x + beta*y. */
|
|
|
|
/* TRANS = 'C' or 'c' y := alpha*conjg( A' )*x + beta*y. */
|
|
|
|
/* Unchanged on exit. */
|
|
|
|
/* M - INTEGER. */
|
|
/* On entry, M specifies the number of rows of the matrix A. */
|
|
/* M must be at least zero. */
|
|
/* Unchanged on exit. */
|
|
|
|
/* N - INTEGER. */
|
|
/* On entry, N specifies the number of columns of the matrix A. */
|
|
/* N must be at least zero. */
|
|
/* Unchanged on exit. */
|
|
|
|
/* KL - INTEGER. */
|
|
/* On entry, KL specifies the number of sub-diagonals of the */
|
|
/* matrix A. KL must satisfy 0 .le. KL. */
|
|
/* Unchanged on exit. */
|
|
|
|
/* KU - INTEGER. */
|
|
/* On entry, KU specifies the number of super-diagonals of the */
|
|
/* matrix A. KU must satisfy 0 .le. KU. */
|
|
/* Unchanged on exit. */
|
|
|
|
/* ALPHA - COMPLEX*16 . */
|
|
/* On entry, ALPHA specifies the scalar alpha. */
|
|
/* Unchanged on exit. */
|
|
|
|
/* A - COMPLEX*16 array of DIMENSION ( LDA, n ). */
|
|
/* Before entry, the leading ( kl + ku + 1 ) by n part of the */
|
|
/* array A must contain the matrix of coefficients, supplied */
|
|
/* column by column, with the leading diagonal of the matrix in */
|
|
/* row ( ku + 1 ) of the array, the first super-diagonal */
|
|
/* starting at position 2 in row ku, the first sub-diagonal */
|
|
/* starting at position 1 in row ( ku + 2 ), and so on. */
|
|
/* Elements in the array A that do not correspond to elements */
|
|
/* in the band matrix (such as the top left ku by ku triangle) */
|
|
/* are not referenced. */
|
|
/* The following program segment will transfer a band matrix */
|
|
/* from conventional full matrix storage to band storage: */
|
|
|
|
/* DO 20, J = 1, N */
|
|
/* K = KU + 1 - J */
|
|
/* DO 10, I = MAX( 1, J - KU ), MIN( M, J + KL ) */
|
|
/* A( K + I, J ) = matrix( I, J ) */
|
|
/* 10 CONTINUE */
|
|
/* 20 CONTINUE */
|
|
|
|
/* Unchanged on exit. */
|
|
|
|
/* LDA - INTEGER. */
|
|
/* On entry, LDA specifies the first dimension of A as declared */
|
|
/* in the calling (sub) program. LDA must be at least */
|
|
/* ( kl + ku + 1 ). */
|
|
/* Unchanged on exit. */
|
|
|
|
/* X - COMPLEX*16 array of DIMENSION at least */
|
|
/* ( 1 + ( n - 1 )*abs( INCX ) ) when TRANS = 'N' or 'n' */
|
|
/* and at least */
|
|
/* ( 1 + ( m - 1 )*abs( INCX ) ) otherwise. */
|
|
/* Before entry, the incremented array X must contain the */
|
|
/* vector x. */
|
|
/* Unchanged on exit. */
|
|
|
|
/* INCX - INTEGER. */
|
|
/* On entry, INCX specifies the increment for the elements of */
|
|
/* X. INCX must not be zero. */
|
|
/* Unchanged on exit. */
|
|
|
|
/* BETA - COMPLEX*16 . */
|
|
/* On entry, BETA specifies the scalar beta. When BETA is */
|
|
/* supplied as zero then Y need not be set on input. */
|
|
/* Unchanged on exit. */
|
|
|
|
/* Y - COMPLEX*16 array of DIMENSION at least */
|
|
/* ( 1 + ( m - 1 )*abs( INCY ) ) when TRANS = 'N' or 'n' */
|
|
/* and at least */
|
|
/* ( 1 + ( n - 1 )*abs( INCY ) ) otherwise. */
|
|
/* Before entry, the incremented array Y must contain the */
|
|
/* vector y. On exit, Y is overwritten by the updated vector y. */
|
|
|
|
|
|
/* INCY - INTEGER. */
|
|
/* On entry, INCY specifies the increment for the elements of */
|
|
/* Y. INCY must not be zero. */
|
|
/* Unchanged on exit. */
|
|
|
|
|
|
/* Level 2 Blas routine. */
|
|
|
|
/* -- Written on 22-October-1986. */
|
|
/* Jack Dongarra, Argonne National Lab. */
|
|
/* Jeremy Du Croz, Nag Central Office. */
|
|
/* Sven Hammarling, Nag Central Office. */
|
|
/* Richard Hanson, Sandia National Labs. */
|
|
|
|
|
|
/* .. Parameters .. */
|
|
/* .. Local Scalars .. */
|
|
/* .. External Functions .. */
|
|
/* .. External Subroutines .. */
|
|
/* .. Intrinsic Functions .. */
|
|
/* .. */
|
|
/* .. Executable Statements .. */
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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 (! PASTEF770(lsame)(trans, "N", (ftnlen)1, (ftnlen)1) && ! PASTEF770(lsame)(trans, "T", (
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ftnlen)1, (ftnlen)1) && ! PASTEF770(lsame)(trans, "C", (ftnlen)1, (ftnlen)1)
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) {
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info = 1;
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} else if (*m < 0) {
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info = 2;
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} else if (*n < 0) {
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info = 3;
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} else if (*kl < 0) {
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info = 4;
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} else if (*ku < 0) {
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info = 5;
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} else if (*lda < *kl + *ku + 1) {
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info = 8;
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} else if (*incx == 0) {
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info = 10;
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} else if (*incy == 0) {
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info = 13;
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}
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if (info != 0) {
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PASTEF770(xerbla)("ZGBMV ", &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 (*m == 0 || *n == 0 || (bli_zreal(*alpha) == 0. && bli_zimag(*alpha) == 0. && (bli_zreal(*beta) ==
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1. && bli_zimag(*beta) == 0.))) {
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return 0;
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}
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noconj = PASTEF770(lsame)(trans, "T", (ftnlen)1, (ftnlen)1);
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/* Set LENX and LENY, the lengths of the vectors x and y, and set */
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/* up the start points in X and Y. */
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if (PASTEF770(lsame)(trans, "N", (ftnlen)1, (ftnlen)1)) {
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lenx = *n;
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leny = *m;
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} else {
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lenx = *m;
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leny = *n;
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}
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if (*incx > 0) {
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kx = 1;
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} else {
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kx = 1 - (lenx - 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 - (leny - 1) * *incy;
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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 the band part of A. */
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/* First form y := beta*y. */
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if (bli_zreal(*beta) != 1. || bli_zimag(*beta) != 0.) {
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if (*incy == 1) {
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if (bli_zreal(*beta) == 0. && bli_zimag(*beta) == 0.) {
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i__1 = leny;
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for (i__ = 1; i__ <= i__1; ++i__) {
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i__2 = i__;
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bli_zsets( (0.), (0.), y[i__2] );
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/* L10: */
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}
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} else {
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i__1 = leny;
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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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bli_zsets( (bli_zreal(*beta) * bli_zreal(y[i__3]) - bli_zimag(*beta) * bli_zimag(y[i__3])), (bli_zreal(*beta) * bli_zimag(y[i__3]) + bli_zimag(*beta) * bli_zreal(y[i__3])), z__1 );
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bli_zsets( (bli_zreal(z__1)), (bli_zimag(z__1)), y[i__2] );
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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 (bli_zreal(*beta) == 0. && bli_zimag(*beta) == 0.) {
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i__1 = leny;
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for (i__ = 1; i__ <= i__1; ++i__) {
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i__2 = iy;
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bli_zsets( (0.), (0.), y[i__2] );
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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 = leny;
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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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bli_zsets( (bli_zreal(*beta) * bli_zreal(y[i__3]) - bli_zimag(*beta) * bli_zimag(y[i__3])), (bli_zreal(*beta) * bli_zimag(y[i__3]) + bli_zimag(*beta) * bli_zreal(y[i__3])), z__1 );
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bli_zsets( (bli_zreal(z__1)), (bli_zimag(z__1)), y[i__2] );
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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 (bli_zreal(*alpha) == 0. && bli_zimag(*alpha) == 0.) {
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return 0;
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}
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kup1 = *ku + 1;
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if (PASTEF770(lsame)(trans, "N", (ftnlen)1, (ftnlen)1)) {
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/* Form y := alpha*A*x + y. */
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jx = kx;
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if (*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 = jx;
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if (bli_zreal(x[i__2]) != 0. || bli_zimag(x[i__2]) != 0.) {
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i__2 = jx;
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bli_zsets( (bli_zreal(*alpha) * bli_zreal(x[i__2]) - bli_zimag(*alpha) * bli_zimag(x[i__2])), (bli_zreal(*alpha) * bli_zimag(x[i__2]) + bli_zimag(*alpha) * bli_zreal(x[i__2])), z__1 );
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bli_zsets( (bli_zreal(z__1)), (bli_zimag(z__1)), temp );
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k = kup1 - j;
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/* Computing MAX */
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i__2 = 1, i__3 = j - *ku;
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/* Computing MIN */
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i__5 = *m, i__6 = j + *kl;
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i__4 = f2c_min(i__5,i__6);
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for (i__ = f2c_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 = k + i__ + j * a_dim1;
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bli_zsets( (bli_zreal(temp) * bli_zreal(a[i__5]) - bli_zimag(temp) * bli_zimag(a[i__5])), (bli_zreal(temp) * bli_zimag(a[i__5]) + bli_zimag(temp) * bli_zreal(a[i__5])), z__2 );
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bli_zsets( (bli_zreal(y[i__3]) + bli_zreal(z__2)), (bli_zimag(y[i__3]) + bli_zimag(z__2)), z__1 );
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bli_zsets( (bli_zreal(z__1)), (bli_zimag(z__1)), y[i__2] );
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/* L50: */
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}
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}
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jx += *incx;
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/* L60: */
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}
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} else {
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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 (bli_zreal(x[i__4]) != 0. || bli_zimag(x[i__4]) != 0.) {
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i__4 = jx;
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bli_zsets( (bli_zreal(*alpha) * bli_zreal(x[i__4]) - bli_zimag(*alpha) * bli_zimag(x[i__4])), (bli_zreal(*alpha) * bli_zimag(x[i__4]) + bli_zimag(*alpha) * bli_zreal(x[i__4])), z__1 );
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bli_zsets( (bli_zreal(z__1)), (bli_zimag(z__1)), temp );
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iy = ky;
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k = kup1 - j;
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/* Computing MAX */
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i__4 = 1, i__2 = j - *ku;
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/* Computing MIN */
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i__5 = *m, i__6 = j + *kl;
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i__3 = f2c_min(i__5,i__6);
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for (i__ = f2c_max(i__4,i__2); i__ <= i__3; ++i__) {
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i__4 = iy;
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i__2 = iy;
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i__5 = k + i__ + j * a_dim1;
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bli_zsets( (bli_zreal(temp) * bli_zreal(a[i__5]) - bli_zimag(temp) * bli_zimag(a[i__5])), (bli_zreal(temp) * bli_zimag(a[i__5]) + bli_zimag(temp) * bli_zreal(a[i__5])), z__2 );
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bli_zsets( (bli_zreal(y[i__2]) + bli_zreal(z__2)), (bli_zimag(y[i__2]) + bli_zimag(z__2)), z__1 );
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bli_zsets( (bli_zreal(z__1)), (bli_zimag(z__1)), y[i__4] );
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iy += *incy;
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/* L70: */
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}
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}
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jx += *incx;
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if (j > *ku) {
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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 := alpha*A'*x + y or y := alpha*conjg( A' )*x + y. */
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jy = ky;
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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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bli_zsets( (0.), (0.), temp );
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k = kup1 - j;
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if (noconj) {
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/* Computing MAX */
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i__3 = 1, i__4 = j - *ku;
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/* Computing MIN */
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i__5 = *m, i__6 = j + *kl;
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i__2 = f2c_min(i__5,i__6);
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for (i__ = f2c_max(i__3,i__4); i__ <= i__2; ++i__) {
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i__3 = k + i__ + j * a_dim1;
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i__4 = i__;
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bli_zsets( (bli_zreal(a[i__3]) * bli_zreal(x[i__4]) - bli_zimag(a[i__3]) * bli_zimag(x[i__4])), (bli_zreal(a[i__3]) * bli_zimag(x[i__4]) + bli_zimag(a[i__3]) * bli_zreal(x[i__4])), z__2 );
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bli_zsets( (bli_zreal(temp) + bli_zreal(z__2)), (bli_zimag(temp) + bli_zimag(z__2)), z__1 );
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bli_zsets( (bli_zreal(z__1)), (bli_zimag(z__1)), temp );
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/* L90: */
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}
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} else {
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/* Computing MAX */
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i__2 = 1, i__3 = j - *ku;
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/* Computing MIN */
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i__5 = *m, i__6 = j + *kl;
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i__4 = f2c_min(i__5,i__6);
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for (i__ = f2c_max(i__2,i__3); i__ <= i__4; ++i__) {
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bla_d_cnjg(&z__3, &a[k + i__ + j * a_dim1]);
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i__2 = i__;
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bli_zsets( (bli_zreal(z__3) * bli_zreal(x[i__2]) - bli_zimag(z__3) * bli_zimag(x[i__2])), (bli_zreal(z__3) * bli_zimag(x[i__2]) + bli_zimag(z__3) * bli_zreal(x[i__2])), z__2 );
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bli_zsets( (bli_zreal(temp) + bli_zreal(z__2)), (bli_zimag(temp) + bli_zimag(z__2)), z__1 );
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bli_zsets( (bli_zreal(z__1)), (bli_zimag(z__1)), temp );
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/* L100: */
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}
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}
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i__4 = jy;
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i__2 = jy;
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bli_zsets( (bli_zreal(*alpha) * bli_zreal(temp) - bli_zimag(*alpha) * bli_zimag(temp)), (bli_zreal(*alpha) * bli_zimag(temp) + bli_zimag(*alpha) * bli_zreal(temp)), z__2 );
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bli_zsets( (bli_zreal(y[i__2]) + bli_zreal(z__2)), (bli_zimag(y[i__2]) + bli_zimag(z__2)), z__1 );
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bli_zsets( (bli_zreal(z__1)), (bli_zimag(z__1)), y[i__4] );
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jy += *incy;
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/* L110: */
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}
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} else {
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i__1 = *n;
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for (j = 1; j <= i__1; ++j) {
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bli_zsets( (0.), (0.), temp );
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ix = kx;
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k = kup1 - j;
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if (noconj) {
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/* Computing MAX */
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i__4 = 1, i__2 = j - *ku;
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/* Computing MIN */
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i__5 = *m, i__6 = j + *kl;
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i__3 = f2c_min(i__5,i__6);
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for (i__ = f2c_max(i__4,i__2); i__ <= i__3; ++i__) {
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i__4 = k + i__ + j * a_dim1;
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i__2 = ix;
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bli_zsets( (bli_zreal(a[i__4]) * bli_zreal(x[i__2]) - bli_zimag(a[i__4]) * bli_zimag(x[i__2])), (bli_zreal(a[i__4]) * bli_zimag(x[i__2]) + bli_zimag(a[i__4]) * bli_zreal(x[i__2])), z__2 );
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bli_zsets( (bli_zreal(temp) + bli_zreal(z__2)), (bli_zimag(temp) + bli_zimag(z__2)), z__1 );
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bli_zsets( (bli_zreal(z__1)), (bli_zimag(z__1)), temp );
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ix += *incx;
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/* L120: */
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}
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} else {
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/* Computing MAX */
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i__3 = 1, i__4 = j - *ku;
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/* Computing MIN */
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i__5 = *m, i__6 = j + *kl;
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i__2 = f2c_min(i__5,i__6);
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for (i__ = f2c_max(i__3,i__4); i__ <= i__2; ++i__) {
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bla_d_cnjg(&z__3, &a[k + i__ + j * a_dim1]);
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i__3 = ix;
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bli_zsets( (bli_zreal(z__3) * bli_zreal(x[i__3]) - bli_zimag(z__3) * bli_zimag(x[i__3])), (bli_zreal(z__3) * bli_zimag(x[i__3]) + bli_zimag(z__3) * bli_zreal(x[i__3])), z__2 );
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bli_zsets( (bli_zreal(temp) + bli_zreal(z__2)), (bli_zimag(temp) + bli_zimag(z__2)), z__1 );
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bli_zsets( (bli_zreal(z__1)), (bli_zimag(z__1)), temp );
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ix += *incx;
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/* L130: */
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}
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}
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i__2 = jy;
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i__3 = jy;
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bli_zsets( (bli_zreal(*alpha) * bli_zreal(temp) - bli_zimag(*alpha) * bli_zimag(temp)), (bli_zreal(*alpha) * bli_zimag(temp) + bli_zimag(*alpha) * bli_zreal(temp)), z__2 );
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bli_zsets( (bli_zreal(y[i__3]) + bli_zreal(z__2)), (bli_zimag(y[i__3]) + bli_zimag(z__2)), z__1 );
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bli_zsets( (bli_zreal(z__1)), (bli_zimag(z__1)), y[i__2] );
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jy += *incy;
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if (j > *ku) {
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kx += *incx;
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}
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/* L140: */
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}
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}
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}
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return 0;
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/* End of ZGBMV . */
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} /* zgbmv_ */
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#endif
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