slatm6()

subroutine slatm6	(	integer	TYPE,
		integer	N,
		real, dimension( lda, * )	A,
		integer	LDA,
		real, dimension( lda, * )	B,
		real, dimension( ldx, * )	X,
		integer	LDX,
		real, dimension( ldy, * )	Y,
		integer	LDY,
		real	ALPHA,
		real	BETA,
		real	WX,
		real	WY,
		real, dimension( * )	S,
		real, dimension( * )	DIF
	)

SLATM6

Purpose:

 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.

Parameters

[in]	TYPE	TYPE is INTEGER Specifies the problem type (see further details).
[in]	N	N is INTEGER Size of the matrices A and B.
[out]	A	A is REAL array, dimension (LDA, N). On exit A N-by-N is initialized according to TYPE.
[in]	LDA	LDA is INTEGER The leading dimension of A and of B.
[out]	B	B is REAL array, dimension (LDA, N). On exit B N-by-N is initialized according to TYPE.
[out]	X	X is REAL array, dimension (LDX, N). On exit X is the N-by-N matrix of right eigenvectors.
[in]	LDX	LDX is INTEGER The leading dimension of X.
[out]	Y	Y is REAL array, dimension (LDY, N). On exit Y is the N-by-N matrix of left eigenvectors.
[in]	LDY	LDY is INTEGER The leading dimension of Y.
[in]	ALPHA	ALPHA is REAL
[in]	BETA	BETA is REAL Weighting constants for matrix A.
[in]	WX	WX is REAL Constant for right eigenvector matrix.
[in]	WY	WY is REAL Constant for left eigenvector matrix.
[out]	S	S is REAL array, dimension (N) S(i) is the reciprocal condition number for eigenvalue i.
[out]	DIF	DIF is REAL array, dimension (N) DIF(i) is the reciprocal condition number for eigenvector i.

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.