added lapack 3.7.0 with latest patches from git
This commit is contained in:
Werner Saar
321
lapack-netlib/SRC/zlagtm.f
Normal file
321
lapack-netlib/SRC/zlagtm.f
Normal file
@@ -0,0 +1,321 @@
|
||||
*> \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
|
||||
Reference in New Issue
Block a user