TESTING/EIG/sget53.f(3)

NAME
TESTING/EIG/sget53.f

SYNOPSIS

  Functions/Subroutines
subroutine sget53 (a, lda, b, ldb, scale, wr, wi, result, info)
SGET53

Function/Subroutine Documentation

  subroutine sget53 (real, dimension( lda, * ) a, integer lda, real, dimension( ldb, * ) b, integer ldb, real scale, real wr, real wi, real result, integer info)

SGET53

Purpose:

    !>
    !> SGET53  checks the generalized eigenvalues computed by SLAG2.
    !>
    !> The basic test for an eigenvalue is:
    !>
    !>                              | det( s A - w B ) |
    !>     RESULT =  ---------------------------------------------------
    !>               ulp max( s norm(A), |w| norm(B) )*norm( s A - w B )
    !>
    !> Two  are performed:
    !>
    !> (1)  ulp*max( s*norm(A), |w|*norm(B) )  must be at least
    !>      safe_minimum.  This insures that the test performed is
    !>      not essentially  det(0*A + 0*B)=0.
    !>
    !> (2)  s*norm(A) + |w|*norm(B) must be less than 1/safe_minimum.
    !>      This insures that  s*A - w*B  will not overflow.
    !>
    !> If these tests are not passed, then  s  and  w  are scaled and
    !> tested anyway, if this is possible.
    !>

Parameters
    A

    !>          A is REAL array, dimension (LDA, 2)
    !>          The 2x2 matrix A.
    !>

    LDA

    !>          LDA is INTEGER
    !>          The leading dimension of A.  It must be at least 2.
    !>

    B

    !>          B is REAL array, dimension (LDB, N)
    !>          The 2x2 upper-triangular matrix B.
    !>

    LDB

    !>          LDB is INTEGER
    !>          The leading dimension of B.  It must be at least 2.
    !>

    SCALE

    !>          SCALE is REAL
    !>          The  s in the formula  s A - w B .  It is
    !>          assumed to be non-negative.
    !>

    WR

    !>          WR is REAL
    !>          The real part of the eigenvalue  w  in the formula
    !>          s A - w B .
    !>

    WI

    !>          WI is REAL
    !>          The imaginary part of the eigenvalue  w  in the formula
    !>          s A - w B .
    !>

    RESULT

    !>          RESULT is REAL
    !>          If INFO is 2 or less, the value computed by the test
    !>             described above.
    !>          If INFO=3, this will just be 1/ulp.
    !>

    INFO

    !>          INFO is INTEGER
    !>          =0:  The input data pass the .
    !>          =1:  s*norm(A) + |w|*norm(B) > 1/safe_minimum.
    !>          =2:  ulp*max( s*norm(A), |w|*norm(B) ) < safe_minimum
    !>          =3:  same as INFO=2, but  s  and  w  could not be scaled so
    !>               as to compute the test.
    !>

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Definition at line 125 of file sget53.f.

Author

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