TESTING/MATGEN/dlatm6.f(3)                            Library Functions Manual

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

                     N is INTEGER
                     Size of the matrices A and B.

           A

                     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

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

           X

                     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

                     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

                     WX is DOUBLE PRECISION
                     Constant for right eigenvector matrix.

           WY

                     WY is DOUBLE PRECISION
                     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 174 of file dlatm6.f.

Author
       Generated automatically by Doxygen for LAPACK from the source code.

LAPACK                          Version 3.12.0      TESTING/MATGEN/dlatm6.f(3)