dlatm6()

subroutine dlatm6	(	integer	TYPE,
		integer	N,
		double precision, dimension( lda, * )	A,
		integer	LDA,
		double precision, dimension( lda, * )	B,
		double precision, dimension( ldx, * )	X,
		integer	LDX,
		double precision, dimension( ldy, * )	Y,
		integer	LDY,
		double precision	ALPHA,
		double precision	BETA,
		double precision	WX,
		double precision	WY,
		double precision, dimension( * )	S,
		double precision, dimension( * )	DIF
	)

DLATM6

Purpose:

 DLATM6 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 DOUBLE PRECISION 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 DOUBLE PRECISION array, dimension (LDA, N). On exit B N-by-N is initialized according to TYPE.
[out]	X	X is DOUBLE PRECISION 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 DOUBLE PRECISION 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 DOUBLE PRECISION
[in]	BETA	BETA is DOUBLE PRECISION Weighting constants for matrix A.
[in]	WX	WX is DOUBLE PRECISION Constant for right eigenvector matrix.
[in]	WY	WY is DOUBLE PRECISION Constant for left eigenvector matrix.
[out]	S	S is DOUBLE PRECISION array, dimension (N) S(i) is the reciprocal condition number for eigenvalue i.
[out]	DIF	DIF is DOUBLE PRECISION 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.