*> \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 November 2011 * *> \ingroup real_matgen * * ===================================================================== SUBROUTINE SLAKF2( M, N, A, LDA, B, D, E, Z, LDZ ) * * -- LAPACK computational routine (version 3.4.0) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * November 2011 * * .. 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