322 lines
10 KiB
Fortran
322 lines
10 KiB
Fortran
*> \brief \b ZLAGTM performs a matrix-matrix product of the form C = αAB+βC, where A is a tridiagonal matrix, B and C are rectangular matrices, and α and β are scalars, which may be 0, 1, or -1.
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*
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* =========== DOCUMENTATION ===========
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*
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* Online html documentation available at
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* http://www.netlib.org/lapack/explore-html/
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*
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*> \htmlonly
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*> Download ZLAGTM + dependencies
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zlagtm.f">
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*> [TGZ]</a>
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zlagtm.f">
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*> [ZIP]</a>
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zlagtm.f">
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*> [TXT]</a>
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*> \endhtmlonly
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*
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* Definition:
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* ===========
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*
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* SUBROUTINE ZLAGTM( TRANS, N, NRHS, ALPHA, DL, D, DU, X, LDX, BETA,
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* B, LDB )
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*
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* .. Scalar Arguments ..
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* CHARACTER TRANS
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* INTEGER LDB, LDX, N, NRHS
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* DOUBLE PRECISION ALPHA, BETA
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* ..
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* .. Array Arguments ..
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* COMPLEX*16 B( LDB, * ), D( * ), DL( * ), DU( * ),
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* $ X( LDX, * )
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* ..
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*
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*
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*> \par Purpose:
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* =============
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*>
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*> \verbatim
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*>
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*> ZLAGTM performs a matrix-vector product of the form
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*>
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*> B := alpha * A * X + beta * B
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*>
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*> where A is a tridiagonal matrix of order N, B and X are N by NRHS
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*> matrices, and alpha and beta are real scalars, each of which may be
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*> 0., 1., or -1.
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*> \endverbatim
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*
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* Arguments:
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* ==========
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*
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*> \param[in] TRANS
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*> \verbatim
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*> TRANS is CHARACTER*1
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*> Specifies the operation applied to A.
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*> = 'N': No transpose, B := alpha * A * X + beta * B
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*> = 'T': Transpose, B := alpha * A**T * X + beta * B
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*> = 'C': Conjugate transpose, B := alpha * A**H * X + beta * B
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*> \endverbatim
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*>
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*> \param[in] N
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*> \verbatim
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*> N is INTEGER
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*> The order of the matrix A. N >= 0.
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*> \endverbatim
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*>
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*> \param[in] NRHS
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*> \verbatim
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*> NRHS is INTEGER
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*> The number of right hand sides, i.e., the number of columns
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*> of the matrices X and B.
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*> \endverbatim
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*>
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*> \param[in] ALPHA
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*> \verbatim
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*> ALPHA is DOUBLE PRECISION
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*> The scalar alpha. ALPHA must be 0., 1., or -1.; otherwise,
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*> it is assumed to be 0.
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*> \endverbatim
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*>
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*> \param[in] DL
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*> \verbatim
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*> DL is COMPLEX*16 array, dimension (N-1)
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*> The (n-1) sub-diagonal elements of T.
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*> \endverbatim
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*>
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*> \param[in] D
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*> \verbatim
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*> D is COMPLEX*16 array, dimension (N)
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*> The diagonal elements of T.
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*> \endverbatim
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*>
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*> \param[in] DU
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*> \verbatim
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*> DU is COMPLEX*16 array, dimension (N-1)
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*> The (n-1) super-diagonal elements of T.
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*> \endverbatim
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*>
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*> \param[in] X
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*> \verbatim
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*> X is COMPLEX*16 array, dimension (LDX,NRHS)
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*> The N by NRHS matrix X.
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*> \endverbatim
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*>
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*> \param[in] LDX
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*> \verbatim
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*> LDX is INTEGER
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*> The leading dimension of the array X. LDX >= max(N,1).
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*> \endverbatim
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*>
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*> \param[in] BETA
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*> \verbatim
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*> BETA is DOUBLE PRECISION
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*> The scalar beta. BETA must be 0., 1., or -1.; otherwise,
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*> it is assumed to be 1.
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*> \endverbatim
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*>
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*> \param[in,out] B
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*> \verbatim
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*> B is COMPLEX*16 array, dimension (LDB,NRHS)
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*> On entry, the N by NRHS matrix B.
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*> On exit, B is overwritten by the matrix expression
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*> B := alpha * A * X + beta * B.
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*> \endverbatim
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*>
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*> \param[in] LDB
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*> \verbatim
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*> LDB is INTEGER
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*> The leading dimension of the array B. LDB >= max(N,1).
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*> \endverbatim
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*
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* Authors:
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* ========
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*
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*> \author Univ. of Tennessee
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*> \author Univ. of California Berkeley
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*> \author Univ. of Colorado Denver
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*> \author NAG Ltd.
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*
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*> \date December 2016
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*
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*> \ingroup complex16OTHERauxiliary
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*
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* =====================================================================
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SUBROUTINE ZLAGTM( TRANS, N, NRHS, ALPHA, DL, D, DU, X, LDX, BETA,
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$ B, LDB )
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*
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* -- LAPACK auxiliary routine (version 3.7.0) --
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* -- LAPACK is a software package provided by Univ. of Tennessee, --
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* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
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* December 2016
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*
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* .. Scalar Arguments ..
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CHARACTER TRANS
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INTEGER LDB, LDX, N, NRHS
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DOUBLE PRECISION ALPHA, BETA
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* ..
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* .. Array Arguments ..
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COMPLEX*16 B( LDB, * ), D( * ), DL( * ), DU( * ),
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$ X( LDX, * )
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* ..
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*
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* =====================================================================
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*
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* .. Parameters ..
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DOUBLE PRECISION ONE, ZERO
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PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 )
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* ..
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* .. Local Scalars ..
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INTEGER I, J
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* ..
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* .. External Functions ..
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LOGICAL LSAME
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EXTERNAL LSAME
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* ..
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* .. Intrinsic Functions ..
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INTRINSIC DCONJG
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* ..
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* .. Executable Statements ..
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*
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IF( N.EQ.0 )
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$ RETURN
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*
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* Multiply B by BETA if BETA.NE.1.
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*
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IF( BETA.EQ.ZERO ) THEN
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DO 20 J = 1, NRHS
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DO 10 I = 1, N
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B( I, J ) = ZERO
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10 CONTINUE
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20 CONTINUE
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ELSE IF( BETA.EQ.-ONE ) THEN
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DO 40 J = 1, NRHS
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DO 30 I = 1, N
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B( I, J ) = -B( I, J )
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30 CONTINUE
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40 CONTINUE
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END IF
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*
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IF( ALPHA.EQ.ONE ) THEN
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IF( LSAME( TRANS, 'N' ) ) THEN
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*
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* Compute B := B + A*X
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*
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DO 60 J = 1, NRHS
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IF( N.EQ.1 ) THEN
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B( 1, J ) = B( 1, J ) + D( 1 )*X( 1, J )
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ELSE
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B( 1, J ) = B( 1, J ) + D( 1 )*X( 1, J ) +
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$ DU( 1 )*X( 2, J )
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B( N, J ) = B( N, J ) + DL( N-1 )*X( N-1, J ) +
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$ D( N )*X( N, J )
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DO 50 I = 2, N - 1
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B( I, J ) = B( I, J ) + DL( I-1 )*X( I-1, J ) +
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$ D( I )*X( I, J ) + DU( I )*X( I+1, J )
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50 CONTINUE
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END IF
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60 CONTINUE
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ELSE IF( LSAME( TRANS, 'T' ) ) THEN
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*
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* Compute B := B + A**T * X
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*
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DO 80 J = 1, NRHS
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IF( N.EQ.1 ) THEN
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B( 1, J ) = B( 1, J ) + D( 1 )*X( 1, J )
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ELSE
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B( 1, J ) = B( 1, J ) + D( 1 )*X( 1, J ) +
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$ DL( 1 )*X( 2, J )
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B( N, J ) = B( N, J ) + DU( N-1 )*X( N-1, J ) +
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$ D( N )*X( N, J )
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DO 70 I = 2, N - 1
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B( I, J ) = B( I, J ) + DU( I-1 )*X( I-1, J ) +
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$ D( I )*X( I, J ) + DL( I )*X( I+1, J )
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70 CONTINUE
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END IF
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80 CONTINUE
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ELSE IF( LSAME( TRANS, 'C' ) ) THEN
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*
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* Compute B := B + A**H * X
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*
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DO 100 J = 1, NRHS
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IF( N.EQ.1 ) THEN
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B( 1, J ) = B( 1, J ) + DCONJG( D( 1 ) )*X( 1, J )
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ELSE
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B( 1, J ) = B( 1, J ) + DCONJG( D( 1 ) )*X( 1, J ) +
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$ DCONJG( DL( 1 ) )*X( 2, J )
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B( N, J ) = B( N, J ) + DCONJG( DU( N-1 ) )*
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$ X( N-1, J ) + DCONJG( D( N ) )*X( N, J )
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DO 90 I = 2, N - 1
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B( I, J ) = B( I, J ) + DCONJG( DU( I-1 ) )*
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$ X( I-1, J ) + DCONJG( D( I ) )*
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$ X( I, J ) + DCONJG( DL( I ) )*
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$ X( I+1, J )
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90 CONTINUE
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END IF
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100 CONTINUE
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END IF
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ELSE IF( ALPHA.EQ.-ONE ) THEN
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IF( LSAME( TRANS, 'N' ) ) THEN
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*
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* Compute B := B - A*X
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*
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DO 120 J = 1, NRHS
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IF( N.EQ.1 ) THEN
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B( 1, J ) = B( 1, J ) - D( 1 )*X( 1, J )
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ELSE
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B( 1, J ) = B( 1, J ) - D( 1 )*X( 1, J ) -
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$ DU( 1 )*X( 2, J )
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B( N, J ) = B( N, J ) - DL( N-1 )*X( N-1, J ) -
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$ D( N )*X( N, J )
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DO 110 I = 2, N - 1
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B( I, J ) = B( I, J ) - DL( I-1 )*X( I-1, J ) -
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$ D( I )*X( I, J ) - DU( I )*X( I+1, J )
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110 CONTINUE
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END IF
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120 CONTINUE
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ELSE IF( LSAME( TRANS, 'T' ) ) THEN
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*
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* Compute B := B - A**T *X
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*
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DO 140 J = 1, NRHS
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IF( N.EQ.1 ) THEN
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B( 1, J ) = B( 1, J ) - D( 1 )*X( 1, J )
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ELSE
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B( 1, J ) = B( 1, J ) - D( 1 )*X( 1, J ) -
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$ DL( 1 )*X( 2, J )
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B( N, J ) = B( N, J ) - DU( N-1 )*X( N-1, J ) -
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$ D( N )*X( N, J )
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DO 130 I = 2, N - 1
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B( I, J ) = B( I, J ) - DU( I-1 )*X( I-1, J ) -
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$ D( I )*X( I, J ) - DL( I )*X( I+1, J )
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130 CONTINUE
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END IF
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140 CONTINUE
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ELSE IF( LSAME( TRANS, 'C' ) ) THEN
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*
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* Compute B := B - A**H *X
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*
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DO 160 J = 1, NRHS
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IF( N.EQ.1 ) THEN
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B( 1, J ) = B( 1, J ) - DCONJG( D( 1 ) )*X( 1, J )
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ELSE
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B( 1, J ) = B( 1, J ) - DCONJG( D( 1 ) )*X( 1, J ) -
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$ DCONJG( DL( 1 ) )*X( 2, J )
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B( N, J ) = B( N, J ) - DCONJG( DU( N-1 ) )*
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$ X( N-1, J ) - DCONJG( D( N ) )*X( N, J )
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DO 150 I = 2, N - 1
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B( I, J ) = B( I, J ) - DCONJG( DU( I-1 ) )*
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$ X( I-1, J ) - DCONJG( D( I ) )*
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$ X( I, J ) - DCONJG( DL( I ) )*
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$ X( I+1, J )
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150 CONTINUE
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END IF
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160 CONTINUE
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END IF
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END IF
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RETURN
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*
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* End of ZLAGTM
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*
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END
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