301 lines
8.6 KiB
Fortran
301 lines
8.6 KiB
Fortran
*> \brief \b CLATM6
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*
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* =========== DOCUMENTATION ===========
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*
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* Online html documentation available at
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* http://www.netlib.org/lapack/explore-html/
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*
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* Definition:
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* ===========
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*
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* SUBROUTINE CLATM6( TYPE, N, A, LDA, B, X, LDX, Y, LDY, ALPHA,
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* BETA, WX, WY, S, DIF )
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*
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* .. Scalar Arguments ..
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* INTEGER LDA, LDX, LDY, N, TYPE
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* COMPLEX ALPHA, BETA, WX, WY
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* ..
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* .. Array Arguments ..
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* REAL DIF( * ), S( * )
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* COMPLEX A( LDA, * ), B( LDA, * ), X( LDX, * ),
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* $ Y( LDY, * )
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* ..
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*
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*
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*> \par Purpose:
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* =============
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*>
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*> \verbatim
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*>
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*> CLATM6 generates test matrices for the generalized eigenvalue
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*> problem, their corresponding right and left eigenvector matrices,
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*> and also reciprocal condition numbers for all eigenvalues and
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*> the reciprocal condition numbers of eigenvectors corresponding to
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*> the 1th and 5th eigenvalues.
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*>
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*> Test Matrices
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*> =============
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*>
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*> Two kinds of test matrix pairs
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*> (A, B) = inverse(YH) * (Da, Db) * inverse(X)
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*> are used in the tests:
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*>
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*> Type 1:
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*> Da = 1+a 0 0 0 0 Db = 1 0 0 0 0
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*> 0 2+a 0 0 0 0 1 0 0 0
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*> 0 0 3+a 0 0 0 0 1 0 0
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*> 0 0 0 4+a 0 0 0 0 1 0
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*> 0 0 0 0 5+a , 0 0 0 0 1
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*> and Type 2:
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*> Da = 1+i 0 0 0 0 Db = 1 0 0 0 0
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*> 0 1-i 0 0 0 0 1 0 0 0
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*> 0 0 1 0 0 0 0 1 0 0
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*> 0 0 0 (1+a)+(1+b)i 0 0 0 0 1 0
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*> 0 0 0 0 (1+a)-(1+b)i, 0 0 0 0 1 .
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*>
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*> In both cases the same inverse(YH) and inverse(X) are used to compute
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*> (A, B), giving the exact eigenvectors to (A,B) as (YH, X):
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*>
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*> YH: = 1 0 -y y -y X = 1 0 -x -x x
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*> 0 1 -y y -y 0 1 x -x -x
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*> 0 0 1 0 0 0 0 1 0 0
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*> 0 0 0 1 0 0 0 0 1 0
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*> 0 0 0 0 1, 0 0 0 0 1 , where
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*>
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*> a, b, x and y will have all values independently of each other.
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*> \endverbatim
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*
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* Arguments:
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* ==========
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*
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*> \param[in] TYPE
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*> \verbatim
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*> TYPE is INTEGER
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*> Specifies the problem type (see further details).
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*> \endverbatim
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*>
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*> \param[in] N
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*> \verbatim
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*> N is INTEGER
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*> Size of the matrices A and B.
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*> \endverbatim
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*>
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*> \param[out] A
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*> \verbatim
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*> A is COMPLEX array, dimension (LDA, N).
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*> On exit A N-by-N is initialized according to TYPE.
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*> \endverbatim
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*>
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*> \param[in] LDA
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*> \verbatim
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*> LDA is INTEGER
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*> The leading dimension of A and of B.
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*> \endverbatim
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*>
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*> \param[out] B
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*> \verbatim
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*> B is COMPLEX array, dimension (LDA, N).
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*> On exit B N-by-N is initialized according to TYPE.
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*> \endverbatim
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*>
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*> \param[out] X
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*> \verbatim
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*> X is COMPLEX array, dimension (LDX, N).
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*> On exit X is the N-by-N matrix of right eigenvectors.
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*> \endverbatim
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*>
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*> \param[in] LDX
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*> \verbatim
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*> LDX is INTEGER
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*> The leading dimension of X.
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*> \endverbatim
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*>
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*> \param[out] Y
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*> \verbatim
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*> Y is COMPLEX array, dimension (LDY, N).
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*> On exit Y is the N-by-N matrix of left eigenvectors.
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*> \endverbatim
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*>
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*> \param[in] LDY
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*> \verbatim
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*> LDY is INTEGER
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*> The leading dimension of Y.
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*> \endverbatim
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*>
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*> \param[in] ALPHA
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*> \verbatim
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*> ALPHA is COMPLEX
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*> \endverbatim
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*>
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*> \param[in] BETA
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*> \verbatim
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*> BETA is COMPLEX
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*>
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*> Weighting constants for matrix A.
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*> \endverbatim
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*>
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*> \param[in] WX
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*> \verbatim
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*> WX is COMPLEX
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*> Constant for right eigenvector matrix.
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*> \endverbatim
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*>
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*> \param[in] WY
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*> \verbatim
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*> WY is COMPLEX
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*> Constant for left eigenvector matrix.
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*> \endverbatim
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*>
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*> \param[out] S
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*> \verbatim
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*> S is REAL array, dimension (N)
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*> S(i) is the reciprocal condition number for eigenvalue i.
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*> \endverbatim
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*>
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*> \param[out] DIF
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*> \verbatim
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*> DIF is REAL array, dimension (N)
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*> DIF(i) is the reciprocal condition number for eigenvector i.
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*> \endverbatim
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*
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* Authors:
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* ========
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*
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*> \author Univ. of Tennessee
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*> \author Univ. of California Berkeley
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*> \author Univ. of Colorado Denver
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*> \author NAG Ltd.
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*
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*> \date December 2016
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*
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*> \ingroup complex_matgen
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*
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* =====================================================================
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SUBROUTINE CLATM6( TYPE, N, A, LDA, B, X, LDX, Y, LDY, ALPHA,
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$ BETA, WX, WY, S, DIF )
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*
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* -- LAPACK computational routine (version 3.7.0) --
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* -- LAPACK is a software package provided by Univ. of Tennessee, --
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* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
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* December 2016
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*
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* .. Scalar Arguments ..
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INTEGER LDA, LDX, LDY, N, TYPE
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COMPLEX ALPHA, BETA, WX, WY
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* ..
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* .. Array Arguments ..
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REAL DIF( * ), S( * )
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COMPLEX A( LDA, * ), B( LDA, * ), X( LDX, * ),
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$ Y( LDY, * )
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* ..
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*
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* =====================================================================
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*
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* .. Parameters ..
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REAL RONE, TWO, THREE
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PARAMETER ( RONE = 1.0E+0, TWO = 2.0E+0, THREE = 3.0E+0 )
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COMPLEX ZERO, ONE
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PARAMETER ( ZERO = ( 0.0E+0, 0.0E+0 ),
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$ ONE = ( 1.0E+0, 0.0E+0 ) )
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* ..
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* .. Local Scalars ..
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INTEGER I, INFO, J
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* ..
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* .. Local Arrays ..
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REAL RWORK( 50 )
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COMPLEX WORK( 26 ), Z( 8, 8 )
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* ..
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* .. Intrinsic Functions ..
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INTRINSIC CABS, CMPLX, CONJG, REAL, SQRT
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* ..
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* .. External Subroutines ..
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EXTERNAL CGESVD, CLACPY, CLAKF2
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* ..
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* .. Executable Statements ..
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*
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* Generate test problem ...
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* (Da, Db) ...
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*
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DO 20 I = 1, N
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DO 10 J = 1, N
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*
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IF( I.EQ.J ) THEN
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A( I, I ) = CMPLX( I ) + ALPHA
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B( I, I ) = ONE
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ELSE
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A( I, J ) = ZERO
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B( I, J ) = ZERO
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END IF
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*
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10 CONTINUE
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20 CONTINUE
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IF( TYPE.EQ.2 ) THEN
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A( 1, 1 ) = CMPLX( RONE, RONE )
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A( 2, 2 ) = CONJG( A( 1, 1 ) )
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A( 3, 3 ) = ONE
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A( 4, 4 ) = CMPLX( REAL( ONE+ALPHA ), REAL( ONE+BETA ) )
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A( 5, 5 ) = CONJG( A( 4, 4 ) )
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END IF
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*
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* Form X and Y
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*
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CALL CLACPY( 'F', N, N, B, LDA, Y, LDY )
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Y( 3, 1 ) = -CONJG( WY )
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Y( 4, 1 ) = CONJG( WY )
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Y( 5, 1 ) = -CONJG( WY )
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Y( 3, 2 ) = -CONJG( WY )
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Y( 4, 2 ) = CONJG( WY )
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Y( 5, 2 ) = -CONJG( WY )
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*
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CALL CLACPY( 'F', N, N, B, LDA, X, LDX )
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X( 1, 3 ) = -WX
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X( 1, 4 ) = -WX
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X( 1, 5 ) = WX
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X( 2, 3 ) = WX
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X( 2, 4 ) = -WX
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X( 2, 5 ) = -WX
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*
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* Form (A, B)
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*
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B( 1, 3 ) = WX + WY
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B( 2, 3 ) = -WX + WY
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B( 1, 4 ) = WX - WY
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B( 2, 4 ) = WX - WY
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B( 1, 5 ) = -WX + WY
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B( 2, 5 ) = WX + WY
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A( 1, 3 ) = WX*A( 1, 1 ) + WY*A( 3, 3 )
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A( 2, 3 ) = -WX*A( 2, 2 ) + WY*A( 3, 3 )
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A( 1, 4 ) = WX*A( 1, 1 ) - WY*A( 4, 4 )
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A( 2, 4 ) = WX*A( 2, 2 ) - WY*A( 4, 4 )
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A( 1, 5 ) = -WX*A( 1, 1 ) + WY*A( 5, 5 )
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A( 2, 5 ) = WX*A( 2, 2 ) + WY*A( 5, 5 )
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*
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* Compute condition numbers
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*
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S( 1 ) = RONE / SQRT( ( RONE+THREE*CABS( WY )*CABS( WY ) ) /
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$ ( RONE+CABS( A( 1, 1 ) )*CABS( A( 1, 1 ) ) ) )
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S( 2 ) = RONE / SQRT( ( RONE+THREE*CABS( WY )*CABS( WY ) ) /
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$ ( RONE+CABS( A( 2, 2 ) )*CABS( A( 2, 2 ) ) ) )
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S( 3 ) = RONE / SQRT( ( RONE+TWO*CABS( WX )*CABS( WX ) ) /
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$ ( RONE+CABS( A( 3, 3 ) )*CABS( A( 3, 3 ) ) ) )
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S( 4 ) = RONE / SQRT( ( RONE+TWO*CABS( WX )*CABS( WX ) ) /
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$ ( RONE+CABS( A( 4, 4 ) )*CABS( A( 4, 4 ) ) ) )
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S( 5 ) = RONE / SQRT( ( RONE+TWO*CABS( WX )*CABS( WX ) ) /
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$ ( RONE+CABS( A( 5, 5 ) )*CABS( A( 5, 5 ) ) ) )
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*
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CALL CLAKF2( 1, 4, A, LDA, A( 2, 2 ), B, B( 2, 2 ), Z, 8 )
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CALL CGESVD( 'N', 'N', 8, 8, Z, 8, RWORK, WORK, 1, WORK( 2 ), 1,
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$ WORK( 3 ), 24, RWORK( 9 ), INFO )
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DIF( 1 ) = RWORK( 8 )
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*
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CALL CLAKF2( 4, 1, A, LDA, A( 5, 5 ), B, B( 5, 5 ), Z, 8 )
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CALL CGESVD( 'N', 'N', 8, 8, Z, 8, RWORK, WORK, 1, WORK( 2 ), 1,
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$ WORK( 3 ), 24, RWORK( 9 ), INFO )
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DIF( 5 ) = RWORK( 8 )
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*
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RETURN
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*
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* End of CLATM6
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*
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END
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