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*> \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.
*
*> \date December 2016
*
*> \ingroup real_matgen
*
* =====================================================================
SUBROUTINE SLAKF2( M, N, A, LDA, B, D, E, Z, LDZ )
*
* -- LAPACK computational 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 ..
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
|
