disna(3)

NAME
disna - disna: eig condition numbers

SYNOPSIS

  Functions

subroutine ddisna (job, m, n, d, sep, info)
DDISNA
subroutine sdisna (job, m, n, d, sep, info)
SDISNA

Detailed Description

Function Documentation

  subroutine ddisna (character job, integer m, integer n, double precision, dimension( * ) d, double precision, dimension( * ) sep, integer info)

DDISNA

Purpose:

    !>
    !> DDISNA computes the reciprocal condition numbers for the eigenvectors
    !> of a real symmetric or complex Hermitian matrix or for the left or
    !> right singular vectors of a general m-by-n matrix. The reciprocal
    !> condition number is the 'gap' between the corresponding eigenvalue or
    !> singular value and the nearest other one.
    !>
    !> The bound on the error, measured by angle in radians, in the I-th
    !> computed vector is given by
    !>
    !>        DLAMCH( 'E' ) * ( ANORM / SEP( I ) )
    !>
    !> where ANORM = 2-norm(A) = max( abs( D(j) ) ).  SEP(I) is not allowed
    !> to be smaller than DLAMCH( 'E' )*ANORM in order to limit the size of
    !> the error bound.
    !>
    !> DDISNA may also be used to compute error bounds for eigenvectors of
    !> the generalized symmetric definite eigenproblem.
    !>

Parameters
    JOB

    !>          JOB is CHARACTER*1
    !>          Specifies for which problem the reciprocal condition numbers
    !>          should be computed:
    !>          = 'E':  the eigenvectors of a symmetric/Hermitian matrix;
    !>          = 'L':  the left singular vectors of a general matrix;
    !>          = 'R':  the right singular vectors of a general matrix.
    !>

    M

    !>          M is INTEGER
    !>          The number of rows of the matrix. M >= 0.
    !>

    N

    !>          N is INTEGER
    !>          If JOB = 'L' or 'R', the number of columns of the matrix,
    !>          in which case N >= 0. Ignored if JOB = 'E'.
    !>

    D

    !>          D is DOUBLE PRECISION array, dimension (M) if JOB = 'E'
    !>                              dimension (min(M,N)) if JOB = 'L' or 'R'
    !>          The eigenvalues (if JOB = 'E') or singular values (if JOB =
    !>          'L' or 'R') of the matrix, in either increasing or decreasing
    !>          order. If singular values, they must be non-negative.
    !>

    SEP

    !>          SEP is DOUBLE PRECISION array, dimension (M) if JOB = 'E'
    !>                               dimension (min(M,N)) if JOB = 'L' or 'R'
    !>          The reciprocal condition numbers of the vectors.
    !>

    INFO

    !>          INFO is INTEGER
    !>          = 0:  successful exit.
    !>          < 0:  if INFO = -i, the i-th argument had an illegal value.
    !>

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

  subroutine sdisna (character job, integer m, integer n, real, dimension( * ) d, real, dimension( * ) sep, integer info)

SDISNA

Purpose:

    !>
    !> SDISNA computes the reciprocal condition numbers for the eigenvectors
    !> of a real symmetric or complex Hermitian matrix or for the left or
    !> right singular vectors of a general m-by-n matrix. The reciprocal
    !> condition number is the 'gap' between the corresponding eigenvalue or
    !> singular value and the nearest other one.
    !>
    !> The bound on the error, measured by angle in radians, in the I-th
    !> computed vector is given by
    !>
    !>        SLAMCH( 'E' ) * ( ANORM / SEP( I ) )
    !>
    !> where ANORM = 2-norm(A) = max( abs( D(j) ) ).  SEP(I) is not allowed
    !> to be smaller than SLAMCH( 'E' )*ANORM in order to limit the size of
    !> the error bound.
    !>
    !> SDISNA may also be used to compute error bounds for eigenvectors of
    !> the generalized symmetric definite eigenproblem.
    !>

Parameters
    JOB

    !>          JOB is CHARACTER*1
    !>          Specifies for which problem the reciprocal condition numbers
    !>          should be computed:
    !>          = 'E':  the eigenvectors of a symmetric/Hermitian matrix;
    !>          = 'L':  the left singular vectors of a general matrix;
    !>          = 'R':  the right singular vectors of a general matrix.
    !>

    M

    !>          M is INTEGER
    !>          The number of rows of the matrix. M >= 0.
    !>

    N

    !>          N is INTEGER
    !>          If JOB = 'L' or 'R', the number of columns of the matrix,
    !>          in which case N >= 0. Ignored if JOB = 'E'.
    !>

    D

    !>          D is REAL array, dimension (M) if JOB = 'E'
    !>                              dimension (min(M,N)) if JOB = 'L' or 'R'
    !>          The eigenvalues (if JOB = 'E') or singular values (if JOB =
    !>          'L' or 'R') of the matrix, in either increasing or decreasing
    !>          order. If singular values, they must be non-negative.
    !>

    SEP

    !>          SEP is REAL array, dimension (M) if JOB = 'E'
    !>                               dimension (min(M,N)) if JOB = 'L' or 'R'
    !>          The reciprocal condition numbers of the vectors.
    !>

    INFO

    !>          INFO is INTEGER
    !>          = 0:  successful exit.
    !>          < 0:  if INFO = -i, the i-th argument had an illegal value.
    !>

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Author

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