phynexis-deps/lapack
1
0
Fork 0
Code Issues Pull Requests Packages Projects Releases Wiki Activity
Files
introduce-cpp
lapack/TESTING/MATGEN/slatm6.f
T
Julie e18d437924 Making LAPACK's code eternal... no more version and date in source files. 
GitHub is now enabling us to track accurately version and date.
No need for this anymore.
2021-03-25 10:16:58 -07:00

331 lines
9.3 KiB
FortranFixed
Raw Permalink Blame History

*> \brief \b SLATM6
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
* Definition:
* ===========
*
* SUBROUTINE SLATM6( TYPE, N, A, LDA, B, X, LDX, Y, LDY, ALPHA,
* BETA, WX, WY, S, DIF )
*
* .. Scalar Arguments ..
* INTEGER LDA, LDX, LDY, N, TYPE
* REAL ALPHA, BETA, WX, WY
* ..
* .. Array Arguments ..
* REAL A( LDA, * ), B( LDA, * ), DIF( * ), S( * ),
* $ X( LDX, * ), Y( LDY, * )
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> SLATM6 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 -1 0 0 0 Db = 1 0 0 0 0
*> 1 1 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 0 0 0 1 0
*> 0 0 0 -1-b 1+a , 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 REAL 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 REAL array, dimension (LDA, N).
*> On exit B N-by-N is initialized according to TYPE.
*> \endverbatim
*>
*> \param[out] X
*> \verbatim
*> X is REAL 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 REAL 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 REAL
*> \endverbatim
*>
*> \param[in] BETA
*> \verbatim
*> BETA is REAL
*>
*> Weighting constants for matrix A.
*> \endverbatim
*>
*> \param[in] WX
*> \verbatim
*> WX is REAL
*> Constant for right eigenvector matrix.
*> \endverbatim
*>
*> \param[in] WY
*> \verbatim
*> WY is REAL
*> 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.
*
*> \ingroup real_matgen
*
* =====================================================================
SUBROUTINE SLATM6( TYPE, N, A, LDA, B, X, LDX, Y, LDY, ALPHA,
$ BETA, WX, WY, S, DIF )
*
* -- LAPACK computational routine --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*
* .. Scalar Arguments ..
INTEGER LDA, LDX, LDY, N, TYPE
REAL ALPHA, BETA, WX, WY
* ..
* .. Array Arguments ..
REAL A( LDA, * ), B( LDA, * ), DIF( * ), S( * ),
$ X( LDX, * ), Y( LDY, * )
* ..
*
* =====================================================================
*
* .. Parameters ..
REAL ZERO, ONE, TWO, THREE
PARAMETER ( ZERO = 0.0E+0, ONE = 1.0E+0, TWO = 2.0E+0,
$ THREE = 3.0E+0 )
* ..
* .. Local Scalars ..
INTEGER I, INFO, J
* ..
* .. Local Arrays ..
REAL WORK( 100 ), Z( 12, 12 )
* ..
* .. Intrinsic Functions ..
INTRINSIC REAL, SQRT
* ..
* .. External Subroutines ..
EXTERNAL SGESVD, SLACPY, SLAKF2
* ..
* .. 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 ) = REAL( I ) + ALPHA
B( I, I ) = ONE
ELSE
A( I, J ) = ZERO
B( I, J ) = ZERO
END IF
*
10 CONTINUE
20 CONTINUE
*
* Form X and Y
*
CALL SLACPY( 'F', N, N, B, LDA, Y, LDY )
Y( 3, 1 ) = -WY
Y( 4, 1 ) = WY
Y( 5, 1 ) = -WY
Y( 3, 2 ) = -WY
Y( 4, 2 ) = WY
Y( 5, 2 ) = -WY
*
CALL SLACPY( '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
IF( TYPE.EQ.1 ) THEN
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 )
ELSE IF( TYPE.EQ.2 ) THEN
A( 1, 3 ) = TWO*WX + WY
A( 2, 3 ) = WY
A( 1, 4 ) = -WY*( TWO+ALPHA+BETA )
A( 2, 4 ) = TWO*WX - WY*( TWO+ALPHA+BETA )
A( 1, 5 ) = -TWO*WX + WY*( ALPHA-BETA )
A( 2, 5 ) = WY*( ALPHA-BETA )
A( 1, 1 ) = ONE
A( 1, 2 ) = -ONE
A( 2, 1 ) = ONE
A( 2, 2 ) = A( 1, 1 )
A( 3, 3 ) = ONE
A( 4, 4 ) = ONE + ALPHA
A( 4, 5 ) = ONE + BETA
A( 5, 4 ) = -A( 4, 5 )
A( 5, 5 ) = A( 4, 4 )
END IF
*
* Compute condition numbers
*
IF( TYPE.EQ.1 ) THEN
*
S( 1 ) = ONE / SQRT( ( ONE+THREE*WY*WY ) /
$ ( ONE+A( 1, 1 )*A( 1, 1 ) ) )
S( 2 ) = ONE / SQRT( ( ONE+THREE*WY*WY ) /
$ ( ONE+A( 2, 2 )*A( 2, 2 ) ) )
S( 3 ) = ONE / SQRT( ( ONE+TWO*WX*WX ) /
$ ( ONE+A( 3, 3 )*A( 3, 3 ) ) )
S( 4 ) = ONE / SQRT( ( ONE+TWO*WX*WX ) /
$ ( ONE+A( 4, 4 )*A( 4, 4 ) ) )
S( 5 ) = ONE / SQRT( ( ONE+TWO*WX*WX ) /
$ ( ONE+A( 5, 5 )*A( 5, 5 ) ) )
*
CALL SLAKF2( 1, 4, A, LDA, A( 2, 2 ), B, B( 2, 2 ), Z, 12 )
CALL SGESVD( 'N', 'N', 8, 8, Z, 12, WORK, WORK( 9 ), 1,
$ WORK( 10 ), 1, WORK( 11 ), 40, INFO )
DIF( 1 ) = WORK( 8 )
*
CALL SLAKF2( 4, 1, A, LDA, A( 5, 5 ), B, B( 5, 5 ), Z, 12 )
CALL SGESVD( 'N', 'N', 8, 8, Z, 12, WORK, WORK( 9 ), 1,
$ WORK( 10 ), 1, WORK( 11 ), 40, INFO )
DIF( 5 ) = WORK( 8 )
*
ELSE IF( TYPE.EQ.2 ) THEN
*
S( 1 ) = ONE / SQRT( ONE / THREE+WY*WY )
S( 2 ) = S( 1 )
S( 3 ) = ONE / SQRT( ONE / TWO+WX*WX )
S( 4 ) = ONE / SQRT( ( ONE+TWO*WX*WX ) /
$ ( ONE+( ONE+ALPHA )*( ONE+ALPHA )+( ONE+BETA )*( ONE+
$ BETA ) ) )
S( 5 ) = S( 4 )
*
CALL SLAKF2( 2, 3, A, LDA, A( 3, 3 ), B, B( 3, 3 ), Z, 12 )
CALL SGESVD( 'N', 'N', 12, 12, Z, 12, WORK, WORK( 13 ), 1,
$ WORK( 14 ), 1, WORK( 15 ), 60, INFO )
DIF( 1 ) = WORK( 12 )
*
CALL SLAKF2( 3, 2, A, LDA, A( 4, 4 ), B, B( 4, 4 ), Z, 12 )
CALL SGESVD( 'N', 'N', 12, 12, Z, 12, WORK, WORK( 13 ), 1,
$ WORK( 14 ), 1, WORK( 15 ), 60, INFO )
DIF( 5 ) = WORK( 12 )
*
END IF
*
RETURN
*
* End of SLATM6
*
END
Reference in New Issue View Git Blame Copy Permalink