TESTING/MATGEN/slatm6.f(3)                            Library Functions Manual

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
       Generated automatically by Doxygen for LAPACK from the source code.

LAPACK                          Version 3.12.0      TESTING/MATGEN/slatm6.f(3)