NAME

TESTING/MATGEN/dlatm6.f

SYNOPSIS

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.

Author

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