265 lines
7.6 KiB
Fortran
265 lines
7.6 KiB
Fortran
*> \brief \b CLAPTM
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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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* Definition:
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* ===========
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*
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* SUBROUTINE CLAPTM( UPLO, N, NRHS, ALPHA, D, E, X, LDX, BETA, B,
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* LDB )
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*
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* .. Scalar Arguments ..
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* CHARACTER UPLO
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* INTEGER LDB, LDX, N, NRHS
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* REAL ALPHA, BETA
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* ..
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* .. Array Arguments ..
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* REAL D( * )
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* COMPLEX B( LDB, * ), E( * ), 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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*> CLAPTM multiplies an N by NRHS matrix X by a Hermitian tridiagonal
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*> matrix A and stores the result in a matrix B. The operation has the
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*> form
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*>
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*> B := alpha * A * X + beta * B
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*>
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*> where alpha may be either 1. or -1. and beta may be 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] UPLO
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*> \verbatim
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*> UPLO is CHARACTER
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*> Specifies whether the superdiagonal or the subdiagonal of the
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*> tridiagonal matrix A is stored.
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*> = 'U': Upper, E is the superdiagonal of A.
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*> = 'L': Lower, E is the subdiagonal of A.
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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 REAL
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*> The scalar alpha. ALPHA must be 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] D
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*> \verbatim
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*> D is REAL array, dimension (N)
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*> The n diagonal elements of the tridiagonal matrix A.
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*> \endverbatim
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*>
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*> \param[in] E
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*> \verbatim
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*> E is COMPLEX array, dimension (N-1)
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*> The (n-1) subdiagonal or superdiagonal elements of A.
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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 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 REAL
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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 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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*> \ingroup complex_lin
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*
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* =====================================================================
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SUBROUTINE CLAPTM( UPLO, N, NRHS, ALPHA, D, E, X, LDX, BETA, B,
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$ LDB )
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*
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* -- LAPACK test routine --
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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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*
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* .. Scalar Arguments ..
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CHARACTER UPLO
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INTEGER LDB, LDX, N, NRHS
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REAL ALPHA, BETA
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* ..
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* .. Array Arguments ..
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REAL D( * )
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COMPLEX B( LDB, * ), E( * ), 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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REAL ONE, ZERO
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PARAMETER ( ONE = 1.0E+0, ZERO = 0.0E+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 CONJG
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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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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( UPLO, 'U' ) ) THEN
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*
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* Compute B := B + A*X, where E is the superdiagonal of A.
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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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$ E( 1 )*X( 2, J )
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B( N, J ) = B( N, J ) + CONJG( E( N-1 ) )*
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$ X( N-1, J ) + 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 ) + CONJG( E( I-1 ) )*
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$ X( I-1, J ) + D( I )*X( I, J ) +
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$ E( 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
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*
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* Compute B := B + A*X, where E is the subdiagonal of A.
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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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$ CONJG( E( 1 ) )*X( 2, J )
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B( N, J ) = B( N, J ) + E( 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 ) + E( I-1 )*X( I-1, J ) +
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$ D( I )*X( I, J ) +
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$ CONJG( E( 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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END IF
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ELSE IF( ALPHA.EQ.-ONE ) THEN
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IF( LSAME( UPLO, 'U' ) ) THEN
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*
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* Compute B := B - A*X, where E is the superdiagonal of A.
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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 ) - 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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$ E( 1 )*X( 2, J )
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B( N, J ) = B( N, J ) - CONJG( E( N-1 ) )*
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$ X( N-1, J ) - 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 ) - CONJG( E( I-1 ) )*
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$ X( I-1, J ) - D( I )*X( I, J ) -
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$ E( I )*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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ELSE
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*
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* Compute B := B - A*X, where E is the subdiagonal of A.
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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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$ CONJG( E( 1 ) )*X( 2, J )
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B( N, J ) = B( N, J ) - E( 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 ) - E( I-1 )*X( I-1, J ) -
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$ D( I )*X( I, J ) -
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$ CONJG( E( 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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END IF
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END IF
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RETURN
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*
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* End of CLAPTM
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*
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END
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