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*> \brief \b CLATM6
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
* Definition:
* ===========
*
* SUBROUTINE CLATM6( TYPE, N, A, LDA, B, X, LDX, Y, LDY, ALPHA,
* BETA, WX, WY, S, DIF )
*
* .. Scalar Arguments ..
* INTEGER LDA, LDX, LDY, N, TYPE
* COMPLEX ALPHA, BETA, WX, WY
* ..
* .. Array Arguments ..
* REAL DIF( * ), S( * )
* COMPLEX A( LDA, * ), B( LDA, * ), X( LDX, * ),
* $ Y( LDY, * )
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> CLATM6 generates test matrices for the generalized eigenvalue
*> problem, their corresponding right and left eigenvector matrices,
*> and also reciprocal condition numbers for all eigenvalues and
*> the reciprocal condition numbers of eigenvectors corresponding to
*> the 1th and 5th eigenvalues.
*>
*> Test Matrices
*> =============
*>
*> Two kinds of test matrix pairs
*> (A, B) = inverse(YH) * (Da, Db) * inverse(X)
*> are used in the tests:
*>
*> Type 1:
*> Da = 1+a 0 0 0 0 Db = 1 0 0 0 0
*> 0 2+a 0 0 0 0 1 0 0 0
*> 0 0 3+a 0 0 0 0 1 0 0
*> 0 0 0 4+a 0 0 0 0 1 0
*> 0 0 0 0 5+a , 0 0 0 0 1
*> and Type 2:
*> Da = 1+i 0 0 0 0 Db = 1 0 0 0 0
*> 0 1-i 0 0 0 0 1 0 0 0
*> 0 0 1 0 0 0 0 1 0 0
*> 0 0 0 (1+a)+(1+b)i 0 0 0 0 1 0
*> 0 0 0 0 (1+a)-(1+b)i, 0 0 0 0 1 .
*>
*> In both cases the same inverse(YH) and inverse(X) are used to compute
*> (A, B), giving the exact eigenvectors to (A,B) as (YH, X):
*>
*> YH: = 1 0 -y y -y X = 1 0 -x -x x
*> 0 1 -y y -y 0 1 x -x -x
*> 0 0 1 0 0 0 0 1 0 0
*> 0 0 0 1 0 0 0 0 1 0
*> 0 0 0 0 1, 0 0 0 0 1 , where
*>
*> a, b, x and y will have all values independently of each other.
*> \endverbatim
*
* Arguments:
* ==========
*
*> \param[in] TYPE
*> \verbatim
*> TYPE is INTEGER
*> Specifies the problem type (see further details).
*> \endverbatim
*>
*> \param[in] N
*> \verbatim
*> N is INTEGER
*> Size of the matrices A and B.
*> \endverbatim
*>
*> \param[out] A
*> \verbatim
*> A is COMPLEX array, dimension (LDA, N).
*> On exit A N-by-N is initialized according to TYPE.
*> \endverbatim
*>
*> \param[in] LDA
*> \verbatim
*> LDA is INTEGER
*> The leading dimension of A and of B.
*> \endverbatim
*>
*> \param[out] B
*> \verbatim
*> B is COMPLEX array, dimension (LDA, N).
*> On exit B N-by-N is initialized according to TYPE.
*> \endverbatim
*>
*> \param[out] X
*> \verbatim
*> X is COMPLEX array, dimension (LDX, N).
*> On exit X is the N-by-N matrix of right eigenvectors.
*> \endverbatim
*>
*> \param[in] LDX
*> \verbatim
*> LDX is INTEGER
*> The leading dimension of X.
*> \endverbatim
*>
*> \param[out] Y
*> \verbatim
*> Y is COMPLEX array, dimension (LDY, N).
*> On exit Y is the N-by-N matrix of left eigenvectors.
*> \endverbatim
*>
*> \param[in] LDY
*> \verbatim
*> LDY is INTEGER
*> The leading dimension of Y.
*> \endverbatim
*>
*> \param[in] ALPHA
*> \verbatim
*> ALPHA is COMPLEX
*> \endverbatim
*>
*> \param[in] BETA
*> \verbatim
*> BETA is COMPLEX
*>
*> Weighting constants for matrix A.
*> \endverbatim
*>
*> \param[in] WX
*> \verbatim
*> WX is COMPLEX
*> Constant for right eigenvector matrix.
*> \endverbatim
*>
*> \param[in] WY
*> \verbatim
*> WY is COMPLEX
*> Constant for left eigenvector matrix.
*> \endverbatim
*>
*> \param[out] S
*> \verbatim
*> S is REAL array, dimension (N)
*> S(i) is the reciprocal condition number for eigenvalue i.
*> \endverbatim
*>
*> \param[out] DIF
*> \verbatim
*> DIF is REAL array, dimension (N)
*> DIF(i) is the reciprocal condition number for eigenvector i.
*> \endverbatim
*
* Authors:
* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \date November 2011
*
*> \ingroup complex_matgen
*
* =====================================================================
SUBROUTINE CLATM6( TYPE, N, A, LDA, B, X, LDX, Y, LDY, ALPHA,
$ BETA, WX, WY, S, DIF )
*
* -- 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, LDX, LDY, N, TYPE
COMPLEX ALPHA, BETA, WX, WY
* ..
* .. Array Arguments ..
REAL DIF( * ), S( * )
COMPLEX A( LDA, * ), B( LDA, * ), X( LDX, * ),
$ Y( LDY, * )
* ..
*
* =====================================================================
*
* .. Parameters ..
REAL RONE, TWO, THREE
PARAMETER ( RONE = 1.0E+0, TWO = 2.0E+0, THREE = 3.0E+0 )
COMPLEX ZERO, ONE
PARAMETER ( ZERO = ( 0.0E+0, 0.0E+0 ),
$ ONE = ( 1.0E+0, 0.0E+0 ) )
* ..
* .. Local Scalars ..
INTEGER I, INFO, J
* ..
* .. Local Arrays ..
REAL RWORK( 50 )
COMPLEX WORK( 26 ), Z( 8, 8 )
* ..
* .. Intrinsic Functions ..
INTRINSIC CABS, CMPLX, CONJG, REAL, SQRT
* ..
* .. External Subroutines ..
EXTERNAL CGESVD, CLACPY, CLAKF2
* ..
* .. Executable Statements ..
*
* Generate test problem ...
* (Da, Db) ...
*
DO 20 I = 1, N
DO 10 J = 1, N
*
IF( I.EQ.J ) THEN
A( I, I ) = CMPLX( I ) + ALPHA
B( I, I ) = ONE
ELSE
A( I, J ) = ZERO
B( I, J ) = ZERO
END IF
*
10 CONTINUE
20 CONTINUE
IF( TYPE.EQ.2 ) THEN
A( 1, 1 ) = CMPLX( RONE, RONE )
A( 2, 2 ) = CONJG( A( 1, 1 ) )
A( 3, 3 ) = ONE
A( 4, 4 ) = CMPLX( REAL( ONE+ALPHA ), REAL( ONE+BETA ) )
A( 5, 5 ) = CONJG( A( 4, 4 ) )
END IF
*
* Form X and Y
*
CALL CLACPY( 'F', N, N, B, LDA, Y, LDY )
Y( 3, 1 ) = -CONJG( WY )
Y( 4, 1 ) = CONJG( WY )
Y( 5, 1 ) = -CONJG( WY )
Y( 3, 2 ) = -CONJG( WY )
Y( 4, 2 ) = CONJG( WY )
Y( 5, 2 ) = -CONJG( WY )
*
CALL CLACPY( 'F', N, N, B, LDA, X, LDX )
X( 1, 3 ) = -WX
X( 1, 4 ) = -WX
X( 1, 5 ) = WX
X( 2, 3 ) = WX
X( 2, 4 ) = -WX
X( 2, 5 ) = -WX
*
* Form (A, B)
*
B( 1, 3 ) = WX + WY
B( 2, 3 ) = -WX + WY
B( 1, 4 ) = WX - WY
B( 2, 4 ) = WX - WY
B( 1, 5 ) = -WX + WY
B( 2, 5 ) = WX + WY
A( 1, 3 ) = WX*A( 1, 1 ) + WY*A( 3, 3 )
A( 2, 3 ) = -WX*A( 2, 2 ) + WY*A( 3, 3 )
A( 1, 4 ) = WX*A( 1, 1 ) - WY*A( 4, 4 )
A( 2, 4 ) = WX*A( 2, 2 ) - WY*A( 4, 4 )
A( 1, 5 ) = -WX*A( 1, 1 ) + WY*A( 5, 5 )
A( 2, 5 ) = WX*A( 2, 2 ) + WY*A( 5, 5 )
*
* Compute condition numbers
*
S( 1 ) = RONE / SQRT( ( RONE+THREE*CABS( WY )*CABS( WY ) ) /
$ ( RONE+CABS( A( 1, 1 ) )*CABS( A( 1, 1 ) ) ) )
S( 2 ) = RONE / SQRT( ( RONE+THREE*CABS( WY )*CABS( WY ) ) /
$ ( RONE+CABS( A( 2, 2 ) )*CABS( A( 2, 2 ) ) ) )
S( 3 ) = RONE / SQRT( ( RONE+TWO*CABS( WX )*CABS( WX ) ) /
$ ( RONE+CABS( A( 3, 3 ) )*CABS( A( 3, 3 ) ) ) )
S( 4 ) = RONE / SQRT( ( RONE+TWO*CABS( WX )*CABS( WX ) ) /
$ ( RONE+CABS( A( 4, 4 ) )*CABS( A( 4, 4 ) ) ) )
S( 5 ) = RONE / SQRT( ( RONE+TWO*CABS( WX )*CABS( WX ) ) /
$ ( RONE+CABS( A( 5, 5 ) )*CABS( A( 5, 5 ) ) ) )
*
CALL CLAKF2( 1, 4, A, LDA, A( 2, 2 ), B, B( 2, 2 ), Z, 8 )
CALL CGESVD( 'N', 'N', 8, 8, Z, 8, RWORK, WORK, 1, WORK( 2 ), 1,
$ WORK( 3 ), 24, RWORK( 9 ), INFO )
DIF( 1 ) = RWORK( 8 )
*
CALL CLAKF2( 4, 1, A, LDA, A( 5, 5 ), B, B( 5, 5 ), Z, 8 )
CALL CGESVD( 'N', 'N', 8, 8, Z, 8, RWORK, WORK, 1, WORK( 2 ), 1,
$ WORK( 3 ), 24, RWORK( 9 ), INFO )
DIF( 5 ) = RWORK( 8 )
*
RETURN
*
* End of CLATM6
*
END
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