*> \brief \b ZLAPTM * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * * Definition: * =========== * * SUBROUTINE ZLAPTM( UPLO, N, NRHS, ALPHA, D, E, X, LDX, BETA, B, * LDB ) * * .. Scalar Arguments .. * CHARACTER UPLO * INTEGER LDB, LDX, N, NRHS * DOUBLE PRECISION ALPHA, BETA * .. * .. Array Arguments .. * DOUBLE PRECISION D( * ) * COMPLEX*16 B( LDB, * ), E( * ), X( LDX, * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> ZLAPTM multiplies an N by NRHS matrix X by a Hermitian tridiagonal *> matrix A and stores the result in a matrix B. The operation has the *> form *> *> B := alpha * A * X + beta * B *> *> where alpha may be either 1. or -1. and beta may be 0., 1., or -1. *> \endverbatim * * Arguments: * ========== * *> \param[in] UPLO *> \verbatim *> UPLO is CHARACTER *> Specifies whether the superdiagonal or the subdiagonal of the *> tridiagonal matrix A is stored. *> = 'U': Upper, E is the superdiagonal of A. *> = 'L': Lower, E is the subdiagonal of A. *> \endverbatim *> *> \param[in] N *> \verbatim *> N is INTEGER *> The order of the matrix A. N >= 0. *> \endverbatim *> *> \param[in] NRHS *> \verbatim *> NRHS is INTEGER *> The number of right hand sides, i.e., the number of columns *> of the matrices X and B. *> \endverbatim *> *> \param[in] ALPHA *> \verbatim *> ALPHA is DOUBLE PRECISION *> The scalar alpha. ALPHA must be 1. or -1.; otherwise, *> it is assumed to be 0. *> \endverbatim *> *> \param[in] D *> \verbatim *> D is DOUBLE PRECISION array, dimension (N) *> The n diagonal elements of the tridiagonal matrix A. *> \endverbatim *> *> \param[in] E *> \verbatim *> E is COMPLEX*16 array, dimension (N-1) *> The (n-1) subdiagonal or superdiagonal elements of A. *> \endverbatim *> *> \param[in] X *> \verbatim *> X is COMPLEX*16 array, dimension (LDX,NRHS) *> The N by NRHS matrix X. *> \endverbatim *> *> \param[in] LDX *> \verbatim *> LDX is INTEGER *> The leading dimension of the array X. LDX >= max(N,1). *> \endverbatim *> *> \param[in] BETA *> \verbatim *> BETA is DOUBLE PRECISION *> The scalar beta. BETA must be 0., 1., or -1.; otherwise, *> it is assumed to be 1. *> \endverbatim *> *> \param[in,out] B *> \verbatim *> B is COMPLEX*16 array, dimension (LDB,NRHS) *> On entry, the N by NRHS matrix B. *> On exit, B is overwritten by the matrix expression *> B := alpha * A * X + beta * B. *> \endverbatim *> *> \param[in] LDB *> \verbatim *> LDB is INTEGER *> The leading dimension of the array B. LDB >= max(N,1). *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \ingroup complex16_lin * * ===================================================================== SUBROUTINE ZLAPTM( UPLO, N, NRHS, ALPHA, D, E, X, LDX, BETA, B, $ LDB ) * * -- LAPACK test routine -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * * .. Scalar Arguments .. CHARACTER UPLO INTEGER LDB, LDX, N, NRHS DOUBLE PRECISION ALPHA, BETA * .. * .. Array Arguments .. DOUBLE PRECISION D( * ) COMPLEX*16 B( LDB, * ), E( * ), X( LDX, * ) * .. * * ===================================================================== * * .. Parameters .. DOUBLE PRECISION ONE, ZERO PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 ) * .. * .. Local Scalars .. INTEGER I, J * .. * .. External Functions .. LOGICAL LSAME EXTERNAL LSAME * .. * .. Intrinsic Functions .. INTRINSIC DCONJG * .. * .. Executable Statements .. * IF( N.EQ.0 ) $ RETURN * IF( BETA.EQ.ZERO ) THEN DO 20 J = 1, NRHS DO 10 I = 1, N B( I, J ) = ZERO 10 CONTINUE 20 CONTINUE ELSE IF( BETA.EQ.-ONE ) THEN DO 40 J = 1, NRHS DO 30 I = 1, N B( I, J ) = -B( I, J ) 30 CONTINUE 40 CONTINUE END IF * IF( ALPHA.EQ.ONE ) THEN IF( LSAME( UPLO, 'U' ) ) THEN * * Compute B := B + A*X, where E is the superdiagonal of A. * DO 60 J = 1, NRHS IF( N.EQ.1 ) THEN B( 1, J ) = B( 1, J ) + D( 1 )*X( 1, J ) ELSE B( 1, J ) = B( 1, J ) + D( 1 )*X( 1, J ) + $ E( 1 )*X( 2, J ) B( N, J ) = B( N, J ) + DCONJG( E( N-1 ) )* $ X( N-1, J ) + D( N )*X( N, J ) DO 50 I = 2, N - 1 B( I, J ) = B( I, J ) + DCONJG( E( I-1 ) )* $ X( I-1, J ) + D( I )*X( I, J ) + $ E( I )*X( I+1, J ) 50 CONTINUE END IF 60 CONTINUE ELSE * * Compute B := B + A*X, where E is the subdiagonal of A. * DO 80 J = 1, NRHS IF( N.EQ.1 ) THEN B( 1, J ) = B( 1, J ) + D( 1 )*X( 1, J ) ELSE B( 1, J ) = B( 1, J ) + D( 1 )*X( 1, J ) + $ DCONJG( E( 1 ) )*X( 2, J ) B( N, J ) = B( N, J ) + E( N-1 )*X( N-1, J ) + $ D( N )*X( N, J ) DO 70 I = 2, N - 1 B( I, J ) = B( I, J ) + E( I-1 )*X( I-1, J ) + $ D( I )*X( I, J ) + $ DCONJG( E( I ) )*X( I+1, J ) 70 CONTINUE END IF 80 CONTINUE END IF ELSE IF( ALPHA.EQ.-ONE ) THEN IF( LSAME( UPLO, 'U' ) ) THEN * * Compute B := B - A*X, where E is the superdiagonal of A. * DO 100 J = 1, NRHS IF( N.EQ.1 ) THEN B( 1, J ) = B( 1, J ) - D( 1 )*X( 1, J ) ELSE B( 1, J ) = B( 1, J ) - D( 1 )*X( 1, J ) - $ E( 1 )*X( 2, J ) B( N, J ) = B( N, J ) - DCONJG( E( N-1 ) )* $ X( N-1, J ) - D( N )*X( N, J ) DO 90 I = 2, N - 1 B( I, J ) = B( I, J ) - DCONJG( E( I-1 ) )* $ X( I-1, J ) - D( I )*X( I, J ) - $ E( I )*X( I+1, J ) 90 CONTINUE END IF 100 CONTINUE ELSE * * Compute B := B - A*X, where E is the subdiagonal of A. * DO 120 J = 1, NRHS IF( N.EQ.1 ) THEN B( 1, J ) = B( 1, J ) - D( 1 )*X( 1, J ) ELSE B( 1, J ) = B( 1, J ) - D( 1 )*X( 1, J ) - $ DCONJG( E( 1 ) )*X( 2, J ) B( N, J ) = B( N, J ) - E( N-1 )*X( N-1, J ) - $ D( N )*X( N, J ) DO 110 I = 2, N - 1 B( I, J ) = B( I, J ) - E( I-1 )*X( I-1, J ) - $ D( I )*X( I, J ) - $ DCONJG( E( I ) )*X( I+1, J ) 110 CONTINUE END IF 120 CONTINUE END IF END IF RETURN * * End of ZLAPTM * END