You can not select more than 25 topics
Topics must start with a letter or number, can include dashes ('-') and can be up to 35 characters long.
189 lines
4.1 KiB
189 lines
4.1 KiB
2 years ago
|
*> \brief \b SLAKF2
|
||
|
|
*
|
||
|
|
* =========== DOCUMENTATION ===========
|
||
|
|
*
|
||
|
|
* Online html documentation available at
|
||
|
|
* http://www.netlib.org/lapack/explore-html/
|
||
|
|
*
|
||
|
|
* Definition:
|
||
|
|
* ===========
|
||
|
|
*
|
||
|
|
* SUBROUTINE SLAKF2( M, N, A, LDA, B, D, E, Z, LDZ )
|
||
|
|
*
|
||
|
|
* .. Scalar Arguments ..
|
||
|
|
* INTEGER LDA, LDZ, M, N
|
||
|
|
* ..
|
||
|
|
* .. Array Arguments ..
|
||
|
|
* REAL A( LDA, * ), B( LDA, * ), D( LDA, * ),
|
||
|
|
* $ E( LDA, * ), Z( LDZ, * )
|
||
|
|
* ..
|
||
|
|
*
|
||
|
|
*
|
||
|
|
*> \par Purpose:
|
||
|
|
* =============
|
||
|
|
*>
|
||
|
|
*> \verbatim
|
||
|
|
*>
|
||
|
|
*> Form the 2*M*N by 2*M*N matrix
|
||
|
|
*>
|
||
|
|
*> Z = [ kron(In, A) -kron(B', Im) ]
|
||
|
|
*> [ kron(In, D) -kron(E', Im) ],
|
||
|
|
*>
|
||
|
|
*> where In is the identity matrix of size n and X' is the transpose
|
||
|
|
*> of X. kron(X, Y) is the Kronecker product between the matrices X
|
||
|
|
*> and Y.
|
||
|
|
*> \endverbatim
|
||
|
|
*
|
||
|
|
* Arguments:
|
||
|
|
* ==========
|
||
|
|
*
|
||
|
|
*> \param[in] M
|
||
|
|
*> \verbatim
|
||
|
|
*> M is INTEGER
|
||
|
|
*> Size of matrix, must be >= 1.
|
||
|
|
*> \endverbatim
|
||
|
|
*>
|
||
|
|
*> \param[in] N
|
||
|
|
*> \verbatim
|
||
|
|
*> N is INTEGER
|
||
|
|
*> Size of matrix, must be >= 1.
|
||
|
|
*> \endverbatim
|
||
|
|
*>
|
||
|
|
*> \param[in] A
|
||
|
|
*> \verbatim
|
||
|
|
*> A is REAL, dimension ( LDA, M )
|
||
|
|
*> The matrix A in the output matrix Z.
|
||
|
|
*> \endverbatim
|
||
|
|
*>
|
||
|
|
*> \param[in] LDA
|
||
|
|
*> \verbatim
|
||
|
|
*> LDA is INTEGER
|
||
|
|
*> The leading dimension of A, B, D, and E. ( LDA >= M+N )
|
||
|
|
*> \endverbatim
|
||
|
|
*>
|
||
|
|
*> \param[in] B
|
||
|
|
*> \verbatim
|
||
|
|
*> B is REAL, dimension ( LDA, N )
|
||
|
|
*> \endverbatim
|
||
|
|
*>
|
||
|
|
*> \param[in] D
|
||
|
|
*> \verbatim
|
||
|
|
*> D is REAL, dimension ( LDA, M )
|
||
|
|
*> \endverbatim
|
||
|
|
*>
|
||
|
|
*> \param[in] E
|
||
|
|
*> \verbatim
|
||
|
|
*> E is REAL, dimension ( LDA, N )
|
||
|
|
*>
|
||
|
|
*> The matrices used in forming the output matrix Z.
|
||
|
|
*> \endverbatim
|
||
|
|
*>
|
||
|
|
*> \param[out] Z
|
||
|
|
*> \verbatim
|
||
|
|
*> Z is REAL, dimension ( LDZ, 2*M*N )
|
||
|
|
*> The resultant Kronecker M*N*2 by M*N*2 matrix (see above.)
|
||
|
|
*> \endverbatim
|
||
|
|
*>
|
||
|
|
*> \param[in] LDZ
|
||
|
|
*> \verbatim
|
||
|
|
*> LDZ is INTEGER
|
||
|
|
*> The leading dimension of Z. ( LDZ >= 2*M*N )
|
||
|
|
*> \endverbatim
|
||
|
|
*
|
||
|
|
* Authors:
|
||
|
|
* ========
|
||
|
|
*
|
||
|
|
*> \author Univ. of Tennessee
|
||
|
|
*> \author Univ. of California Berkeley
|
||
|
|
*> \author Univ. of Colorado Denver
|
||
|
|
*> \author NAG Ltd.
|
||
|
|
*
|
||
|
|
*> \ingroup real_matgen
|
||
|
|
*
|
||
|
|
* =====================================================================
|
||
|
|
SUBROUTINE SLAKF2( M, N, A, LDA, B, D, E, Z, LDZ )
|
||
|
|
*
|
||
|
|
* -- LAPACK computational routine --
|
||
|
|
* -- LAPACK is a software package provided by Univ. of Tennessee, --
|
||
|
|
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
|
||
|
|
*
|
||
|
|
* .. Scalar Arguments ..
|
||
|
|
INTEGER LDA, LDZ, M, N
|
||
|
|
* ..
|
||
|
|
* .. Array Arguments ..
|
||
|
|
REAL A( LDA, * ), B( LDA, * ), D( LDA, * ),
|
||
|
|
$ E( LDA, * ), Z( LDZ, * )
|
||
|
|
* ..
|
||
|
|
*
|
||
|
|
* ====================================================================
|
||
|
|
*
|
||
|
|
* .. Parameters ..
|
||
|
|
REAL ZERO
|
||
|
|
PARAMETER ( ZERO = 0.0E+0 )
|
||
|
|
* ..
|
||
|
|
* .. Local Scalars ..
|
||
|
|
INTEGER I, IK, J, JK, L, MN, MN2
|
||
|
|
* ..
|
||
|
|
* .. External Subroutines ..
|
||
|
|
EXTERNAL SLASET
|
||
|
|
* ..
|
||
|
|
* .. Executable Statements ..
|
||
|
|
*
|
||
|
|
* Initialize Z
|
||
|
|
*
|
||
|
|
MN = M*N
|
||
|
|
MN2 = 2*MN
|
||
|
|
CALL SLASET( 'Full', MN2, MN2, ZERO, ZERO, Z, LDZ )
|
||
|
|
*
|
||
|
|
IK = 1
|
||
|
|
DO 50 L = 1, N
|
||
|
|
*
|
||
|
|
* form kron(In, A)
|
||
|
|
*
|
||
|
|
DO 20 I = 1, M
|
||
|
|
DO 10 J = 1, M
|
||
|
|
Z( IK+I-1, IK+J-1 ) = A( I, J )
|
||
|
|
10 CONTINUE
|
||
|
|
20 CONTINUE
|
||
|
|
*
|
||
|
|
* form kron(In, D)
|
||
|
|
*
|
||
|
|
DO 40 I = 1, M
|
||
|
|
DO 30 J = 1, M
|
||
|
|
Z( IK+MN+I-1, IK+J-1 ) = D( I, J )
|
||
|
|
30 CONTINUE
|
||
|
|
40 CONTINUE
|
||
|
|
*
|
||
|
|
IK = IK + M
|
||
|
|
50 CONTINUE
|
||
|
|
*
|
||
|
|
IK = 1
|
||
|
|
DO 90 L = 1, N
|
||
|
|
JK = MN + 1
|
||
|
|
*
|
||
|
|
DO 80 J = 1, N
|
||
|
|
*
|
||
|
|
* form -kron(B', Im)
|
||
|
|
*
|
||
|
|
DO 60 I = 1, M
|
||
|
|
Z( IK+I-1, JK+I-1 ) = -B( J, L )
|
||
|
|
60 CONTINUE
|
||
|
|
*
|
||
|
|
* form -kron(E', Im)
|
||
|
|
*
|
||
|
|
DO 70 I = 1, M
|
||
|
|
Z( IK+MN+I-1, JK+I-1 ) = -E( J, L )
|
||
|
|
70 CONTINUE
|
||
|
|
*
|
||
|
|
JK = JK + M
|
||
|
|
80 CONTINUE
|
||
|
|
*
|
||
|
|
IK = IK + M
|
||
|
|
90 CONTINUE
|
||
|
|
*
|
||
|
|
RETURN
|
||
|
|
*
|
||
|
|
* End of SLAKF2
|
||
|
|
*
|
||
|
|
END
|