TESTING/MATGEN/slatm6.f(3)

NAME
TESTING/MATGEN/slatm6.f

SYNOPSIS

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

Function/Subroutine Documentation

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

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.

Author

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