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.

TYPE

          TYPE is INTEGER


          Specifies the problem type (see further details).

N

          N is INTEGER


          Size of the matrices A and B.

A

          A is COMPLEX array, dimension (LDA, N).


          On exit A N-by-N is initialized according to TYPE.

LDA

          LDA is INTEGER


          The leading dimension of A and of B.

B

          B is COMPLEX array, dimension (LDA, N).


          On exit B N-by-N is initialized according to TYPE.

X

          X is COMPLEX array, dimension (LDX, N).


          On exit X is the N-by-N matrix of right eigenvectors.

LDX

          LDX is INTEGER


          The leading dimension of X.

Y

          Y is COMPLEX array, dimension (LDY, N).


          On exit Y is the N-by-N matrix of left eigenvectors.

LDY

          LDY is INTEGER


          The leading dimension of Y.

ALPHA

          ALPHA is COMPLEX

BETA

          BETA is COMPLEX


          Weighting constants for matrix A.

WX

          WX is COMPLEX


          Constant for right eigenvector matrix.

WY

          WY is COMPLEX


          Constant for left eigenvector matrix.

S

          S is REAL array, dimension (N)


          S(i) is the reciprocal condition number for eigenvalue i.

DIF

          DIF is REAL array, dimension (N)


          DIF(i) is the reciprocal condition number for eigenvector i.

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.