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.

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 REAL 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 REAL array, dimension (LDA, N).


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

X

          X is REAL 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 REAL 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 REAL

BETA

          BETA is REAL


          Weighting constants for matrix A.

WX

          WX is REAL


          Constant for right eigenvector matrix.

WY

          WY is REAL


          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.

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Univ. of California Berkeley

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