slatm6.f - Man Page

subroutine slatm6 (type, n, a, lda, b, x, ldx, y, ldy, alpha, beta, wx, wy, s, dif)
SLATM6

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

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.

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 174 of file slatm6.f.