dlatm6.f3

Usage

Functions/Subroutines

subroutine dlatm6 (type, n, a, lda, b, x, ldx, y, ldy, alpha, beta, wx, wy, s, dif)
DLATM6

Function/Subroutine Documentation

subroutine dlatm6 (integer type, integer n, double precision, dimension( lda, * ) a, integer lda, double precision, dimension( lda, * ) b, double precision, dimension( ldx, * ) x, integer ldx, double precision, dimension( ldy, * ) y, integer ldy, double precision alpha, double precision beta, double precision wx, double precision wy, double precision, dimension( * ) s, double precision, dimension( * ) dif)

DLATM6

Purpose:

!>
!> DLATM6 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 is INTEGER
!>          Size of the matrices A and B.
!>

!>          A is DOUBLE PRECISION 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 is DOUBLE PRECISION array, dimension (LDA, N).
!>          On exit B N-by-N is initialized according to TYPE.
!>

!>          X is DOUBLE PRECISION 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 is DOUBLE PRECISION 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 DOUBLE PRECISION
!>

BETA

!>          BETA is DOUBLE PRECISION
!>
!>          Weighting constants for matrix A.
!>

!>          WX is DOUBLE PRECISION
!>          Constant for right eigenvector matrix.
!>

!>          WY is DOUBLE PRECISION
!>          Constant for left eigenvector matrix.
!>

!>          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 174 of file dlatm6.f.