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*> \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.
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
*> \htmlonly
*> Download ZLAGTM + dependencies
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zlagtm.f">
*> [TGZ]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zlagtm.f">
*> [ZIP]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zlagtm.f">
*> [TXT]</a>
*> \endhtmlonly
*
* Definition:
* ===========
*
* SUBROUTINE ZLAGTM( TRANS, N, NRHS, ALPHA, DL, D, DU, X, LDX, BETA,
* B, LDB )
*
* .. Scalar Arguments ..
* CHARACTER TRANS
* INTEGER LDB, LDX, N, NRHS
* DOUBLE PRECISION ALPHA, BETA
* ..
* .. Array Arguments ..
* COMPLEX*16 B( LDB, * ), D( * ), DL( * ), DU( * ),
* $ X( LDX, * )
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> ZLAGTM performs a matrix-vector product of the form
*>
*> B := alpha * A * X + beta * B
*>
*> where A is a tridiagonal matrix of order N, B and X are N by NRHS
*> matrices, and alpha and beta are real scalars, each of which may be
*> 0., 1., or -1.
*> \endverbatim
*
* Arguments:
* ==========
*
*> \param[in] TRANS
*> \verbatim
*> TRANS is CHARACTER*1
*> Specifies the operation applied to A.
*> = 'N': No transpose, B := alpha * A * X + beta * B
*> = 'T': Transpose, B := alpha * A**T * X + beta * B
*> = 'C': Conjugate transpose, B := alpha * A**H * X + beta * B
*> \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 0., 1., or -1.; otherwise,
*> it is assumed to be 0.
*> \endverbatim
*>
*> \param[in] DL
*> \verbatim
*> DL is COMPLEX*16 array, dimension (N-1)
*> The (n-1) sub-diagonal elements of T.
*> \endverbatim
*>
*> \param[in] D
*> \verbatim
*> D is COMPLEX*16 array, dimension (N)
*> The diagonal elements of T.
*> \endverbatim
*>
*> \param[in] DU
*> \verbatim
*> DU is COMPLEX*16 array, dimension (N-1)
*> The (n-1) super-diagonal elements of T.
*> \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.
*
*> \date December 2016
*
*> \ingroup complex16OTHERauxiliary
*
* =====================================================================
SUBROUTINE ZLAGTM( TRANS, N, NRHS, ALPHA, DL, D, DU, X, LDX, BETA,
$ B, LDB )
*
* -- LAPACK auxiliary routine (version 3.7.0) --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
* December 2016
*
* .. Scalar Arguments ..
CHARACTER TRANS
INTEGER LDB, LDX, N, NRHS
DOUBLE PRECISION ALPHA, BETA
* ..
* .. Array Arguments ..
COMPLEX*16 B( LDB, * ), D( * ), DL( * ), DU( * ),
$ 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
*
* Multiply B by BETA if BETA.NE.1.
*
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( TRANS, 'N' ) ) THEN
*
* Compute B := B + A*X
*
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 ) +
$ DU( 1 )*X( 2, J )
B( N, J ) = B( N, J ) + DL( N-1 )*X( N-1, J ) +
$ D( N )*X( N, J )
DO 50 I = 2, N - 1
B( I, J ) = B( I, J ) + DL( I-1 )*X( I-1, J ) +
$ D( I )*X( I, J ) + DU( I )*X( I+1, J )
50 CONTINUE
END IF
60 CONTINUE
ELSE IF( LSAME( TRANS, 'T' ) ) THEN
*
* Compute B := B + A**T * X
*
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 ) +
$ DL( 1 )*X( 2, J )
B( N, J ) = B( N, J ) + DU( N-1 )*X( N-1, J ) +
$ D( N )*X( N, J )
DO 70 I = 2, N - 1
B( I, J ) = B( I, J ) + DU( I-1 )*X( I-1, J ) +
$ D( I )*X( I, J ) + DL( I )*X( I+1, J )
70 CONTINUE
END IF
80 CONTINUE
ELSE IF( LSAME( TRANS, 'C' ) ) THEN
*
* Compute B := B + A**H * X
*
DO 100 J = 1, NRHS
IF( N.EQ.1 ) THEN
B( 1, J ) = B( 1, J ) + DCONJG( D( 1 ) )*X( 1, J )
ELSE
B( 1, J ) = B( 1, J ) + DCONJG( D( 1 ) )*X( 1, J ) +
$ DCONJG( DL( 1 ) )*X( 2, J )
B( N, J ) = B( N, J ) + DCONJG( DU( N-1 ) )*
$ X( N-1, J ) + DCONJG( D( N ) )*X( N, J )
DO 90 I = 2, N - 1
B( I, J ) = B( I, J ) + DCONJG( DU( I-1 ) )*
$ X( I-1, J ) + DCONJG( D( I ) )*
$ X( I, J ) + DCONJG( DL( I ) )*
$ X( I+1, J )
90 CONTINUE
END IF
100 CONTINUE
END IF
ELSE IF( ALPHA.EQ.-ONE ) THEN
IF( LSAME( TRANS, 'N' ) ) THEN
*
* Compute B := B - A*X
*
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 ) -
$ DU( 1 )*X( 2, J )
B( N, J ) = B( N, J ) - DL( N-1 )*X( N-1, J ) -
$ D( N )*X( N, J )
DO 110 I = 2, N - 1
B( I, J ) = B( I, J ) - DL( I-1 )*X( I-1, J ) -
$ D( I )*X( I, J ) - DU( I )*X( I+1, J )
110 CONTINUE
END IF
120 CONTINUE
ELSE IF( LSAME( TRANS, 'T' ) ) THEN
*
* Compute B := B - A**T *X
*
DO 140 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 ) -
$ DL( 1 )*X( 2, J )
B( N, J ) = B( N, J ) - DU( N-1 )*X( N-1, J ) -
$ D( N )*X( N, J )
DO 130 I = 2, N - 1
B( I, J ) = B( I, J ) - DU( I-1 )*X( I-1, J ) -
$ D( I )*X( I, J ) - DL( I )*X( I+1, J )
130 CONTINUE
END IF
140 CONTINUE
ELSE IF( LSAME( TRANS, 'C' ) ) THEN
*
* Compute B := B - A**H *X
*
DO 160 J = 1, NRHS
IF( N.EQ.1 ) THEN
B( 1, J ) = B( 1, J ) - DCONJG( D( 1 ) )*X( 1, J )
ELSE
B( 1, J ) = B( 1, J ) - DCONJG( D( 1 ) )*X( 1, J ) -
$ DCONJG( DL( 1 ) )*X( 2, J )
B( N, J ) = B( N, J ) - DCONJG( DU( N-1 ) )*
$ X( N-1, J ) - DCONJG( D( N ) )*X( N, J )
DO 150 I = 2, N - 1
B( I, J ) = B( I, J ) - DCONJG( DU( I-1 ) )*
$ X( I-1, J ) - DCONJG( D( I ) )*
$ X( I, J ) - DCONJG( DL( I ) )*
$ X( I+1, J )
150 CONTINUE
END IF
160 CONTINUE
END IF
END IF
RETURN
*
* End of ZLAGTM
*
END
|
