clatm6()

subroutine clatm6	(	integer	TYPE,
		integer	N,
		complex, dimension( lda, * )	A,
		integer	LDA,
		complex, dimension( lda, * )	B,
		complex, dimension( ldx, * )	X,
		integer	LDX,
		complex, dimension( ldy, * )	Y,
		integer	LDY,
		complex	ALPHA,
		complex	BETA,
		complex	WX,
		complex	WY,
		real, dimension( * )	S,
		real, dimension( * )	DIF
	)

CLATM6

Purpose:

 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.

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 COMPLEX 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 COMPLEX array, dimension (LDA, N). On exit B N-by-N is initialized according to TYPE.
[out]	X	X is COMPLEX 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 COMPLEX 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 COMPLEX
[in]	BETA	BETA is COMPLEX Weighting constants for matrix A.
[in]	WX	WX is COMPLEX Constant for right eigenvector matrix.
[in]	WY	WY is COMPLEX 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.