TESTING/MATGEN/zlatm6.f(3)

NAME
TESTING/MATGEN/zlatm6.f

SYNOPSIS

  Functions/Subroutines
subroutine zlatm6 (type, n, a, lda, b, x, ldx, y, ldy, alpha, beta, wx, wy, s, dif)
ZLATM6

Function/Subroutine Documentation

  subroutine zlatm6 (integer type, integer n, complex*16, dimension( lda, * ) a, integer lda, complex*16, dimension( lda, * ) b, complex*16, dimension( ldx, * ) x, integer ldx, complex*16, dimension( ldy, * ) y, integer ldy, complex*16 alpha, complex*16 beta, complex*16 wx, complex*16 wy, double precision, dimension( * ) s, double precision, dimension( * ) dif)

ZLATM6

Purpose:

     ZLATM6 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
    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*16 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*16 array, dimension (LDA, N).
              On exit B N-by-N is initialized according to TYPE.

    X

              X is COMPLEX*16 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*16 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*16

    BETA

              BETA is COMPLEX*16
     \verbatim
              Weighting constants for matrix A.

    WX

              WX is COMPLEX*16
              Constant for right eigenvector matrix.

    WY

              WY is COMPLEX*16
              Constant for left eigenvector matrix.

    S

              S is DOUBLE PRECISION array, dimension (N)
              S(i) is the reciprocal condition number for eigenvalue i.

    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.

Definition at line 172 of file zlatm6.f.

Author

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