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330 lines
9.4 KiB
330 lines
9.4 KiB
*> \brief \b DLATM6
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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 DLATM6( 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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* DOUBLE PRECISION ALPHA, BETA, WX, WY
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* ..
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* .. Array Arguments ..
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* DOUBLE PRECISION A( LDA, * ), B( LDA, * ), DIF( * ), S( * ),
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* $ X( LDX, * ), 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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*> DLATM6 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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*>
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*> (A, B) = inverse(YH) * (Da, Db) * inverse(X)
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*>
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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 , and
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*>
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*> Type 2:
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*> Da = 1 -1 0 0 0 Db = 1 0 0 0 0
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*> 1 1 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 0 0 0 1 0
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*> 0 0 0 -1-b 1+a , 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 ,
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*>
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*> where 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 DOUBLE PRECISION 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 DOUBLE PRECISION 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 DOUBLE PRECISION 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 DOUBLE PRECISION 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 DOUBLE PRECISION
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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 DOUBLE PRECISION
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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 DOUBLE PRECISION
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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 DOUBLE PRECISION
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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 DOUBLE PRECISION 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 DOUBLE PRECISION 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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*> \ingroup double_matgen
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*
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* =====================================================================
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SUBROUTINE DLATM6( 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 --
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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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*
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* .. Scalar Arguments ..
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INTEGER LDA, LDX, LDY, N, TYPE
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DOUBLE PRECISION ALPHA, BETA, WX, WY
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* ..
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* .. Array Arguments ..
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DOUBLE PRECISION A( LDA, * ), B( LDA, * ), DIF( * ), S( * ),
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$ X( LDX, * ), 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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DOUBLE PRECISION ZERO, ONE, TWO, THREE
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PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0, TWO = 2.0D+0,
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$ THREE = 3.0D+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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DOUBLE PRECISION WORK( 100 ), Z( 12, 12 )
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* ..
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* .. Intrinsic Functions ..
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INTRINSIC DBLE, SQRT
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* ..
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* .. External Subroutines ..
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EXTERNAL DGESVD, DLACPY, DLAKF2
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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 ) = DBLE( 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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*
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* Form X and Y
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*
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CALL DLACPY( 'F', N, N, B, LDA, Y, LDY )
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Y( 3, 1 ) = -WY
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Y( 4, 1 ) = WY
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Y( 5, 1 ) = -WY
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Y( 3, 2 ) = -WY
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Y( 4, 2 ) = WY
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Y( 5, 2 ) = -WY
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*
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CALL DLACPY( '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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IF( TYPE.EQ.1 ) THEN
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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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ELSE IF( TYPE.EQ.2 ) THEN
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A( 1, 3 ) = TWO*WX + WY
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A( 2, 3 ) = WY
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A( 1, 4 ) = -WY*( TWO+ALPHA+BETA )
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A( 2, 4 ) = TWO*WX - WY*( TWO+ALPHA+BETA )
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A( 1, 5 ) = -TWO*WX + WY*( ALPHA-BETA )
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A( 2, 5 ) = WY*( ALPHA-BETA )
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A( 1, 1 ) = ONE
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A( 1, 2 ) = -ONE
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A( 2, 1 ) = ONE
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A( 2, 2 ) = A( 1, 1 )
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A( 3, 3 ) = ONE
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A( 4, 4 ) = ONE + ALPHA
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A( 4, 5 ) = ONE + BETA
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A( 5, 4 ) = -A( 4, 5 )
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A( 5, 5 ) = A( 4, 4 )
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END IF
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*
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* Compute condition numbers
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*
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IF( TYPE.EQ.1 ) THEN
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*
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S( 1 ) = ONE / SQRT( ( ONE+THREE*WY*WY ) /
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$ ( ONE+A( 1, 1 )*A( 1, 1 ) ) )
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S( 2 ) = ONE / SQRT( ( ONE+THREE*WY*WY ) /
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$ ( ONE+A( 2, 2 )*A( 2, 2 ) ) )
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S( 3 ) = ONE / SQRT( ( ONE+TWO*WX*WX ) /
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$ ( ONE+A( 3, 3 )*A( 3, 3 ) ) )
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S( 4 ) = ONE / SQRT( ( ONE+TWO*WX*WX ) /
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$ ( ONE+A( 4, 4 )*A( 4, 4 ) ) )
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S( 5 ) = ONE / SQRT( ( ONE+TWO*WX*WX ) /
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$ ( ONE+A( 5, 5 )*A( 5, 5 ) ) )
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*
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CALL DLAKF2( 1, 4, A, LDA, A( 2, 2 ), B, B( 2, 2 ), Z, 12 )
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CALL DGESVD( 'N', 'N', 8, 8, Z, 12, WORK, WORK( 9 ), 1,
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$ WORK( 10 ), 1, WORK( 11 ), 40, INFO )
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DIF( 1 ) = WORK( 8 )
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*
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CALL DLAKF2( 4, 1, A, LDA, A( 5, 5 ), B, B( 5, 5 ), Z, 12 )
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CALL DGESVD( 'N', 'N', 8, 8, Z, 12, WORK, WORK( 9 ), 1,
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$ WORK( 10 ), 1, WORK( 11 ), 40, INFO )
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DIF( 5 ) = WORK( 8 )
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*
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ELSE IF( TYPE.EQ.2 ) THEN
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*
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S( 1 ) = ONE / SQRT( ONE / THREE+WY*WY )
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S( 2 ) = S( 1 )
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S( 3 ) = ONE / SQRT( ONE / TWO+WX*WX )
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S( 4 ) = ONE / SQRT( ( ONE+TWO*WX*WX ) /
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$ ( ONE+( ONE+ALPHA )*( ONE+ALPHA )+( ONE+BETA )*( ONE+
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$ BETA ) ) )
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S( 5 ) = S( 4 )
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*
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CALL DLAKF2( 2, 3, A, LDA, A( 3, 3 ), B, B( 3, 3 ), Z, 12 )
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CALL DGESVD( 'N', 'N', 12, 12, Z, 12, WORK, WORK( 13 ), 1,
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$ WORK( 14 ), 1, WORK( 15 ), 60, INFO )
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DIF( 1 ) = WORK( 12 )
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*
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CALL DLAKF2( 3, 2, A, LDA, A( 4, 4 ), B, B( 4, 4 ), Z, 12 )
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CALL DGESVD( 'N', 'N', 12, 12, Z, 12, WORK, WORK( 13 ), 1,
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$ WORK( 14 ), 1, WORK( 15 ), 60, INFO )
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DIF( 5 ) = WORK( 12 )
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*
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END IF
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*
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RETURN
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*
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* End of DLATM6
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*
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END
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