Julie
e18d437924
GitHub is now enabling us to track accurately version and date. No need for this anymore.
265 lines
7.7 KiB
FortranFixed
265 lines
7.7 KiB
FortranFixed
*> \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
|