gecon(3)

NAME
gecon - gecon: condition number estimate

SYNOPSIS

  Functions

subroutine cgecon (norm, n, a, lda, anorm, rcond, work, rwork, info)
CGECON
subroutine dgecon (norm, n, a, lda, anorm, rcond, work, iwork, info)
DGECON
subroutine sgecon (norm, n, a, lda, anorm, rcond, work, iwork, info)
SGECON
subroutine zgecon (norm, n, a, lda, anorm, rcond, work, rwork, info)
ZGECON

Detailed Description

Function Documentation

  subroutine cgecon (character norm, integer n, complex, dimension( lda, * ) a, integer lda, real anorm, real rcond, complex, dimension( * ) work, real, dimension( * ) rwork, integer info)

CGECON

Purpose:

    !>
    !> CGECON estimates the reciprocal of the condition number of a general
    !> complex matrix A, in either the 1-norm or the infinity-norm, using
    !> the LU factorization computed by CGETRF.
    !>
    !> An estimate is obtained for norm(inv(A)), and the reciprocal of the
    !> condition number is computed as
    !>    RCOND = 1 / ( norm(A) * norm(inv(A)) ).
    !>

Parameters
    NORM

    !>          NORM is CHARACTER*1
    !>          Specifies whether the 1-norm condition number or the
    !>          infinity-norm condition number is required:
    !>          = '1' or 'O':  1-norm;
    !>          = 'I':         Infinity-norm.
    !>

    N

    !>          N is INTEGER
    !>          The order of the matrix A.  N >= 0.
    !>

    A

    !>          A is COMPLEX array, dimension (LDA,N)
    !>          The factors L and U from the factorization A = P*L*U
    !>          as computed by CGETRF.
    !>

    LDA

    !>          LDA is INTEGER
    !>          The leading dimension of the array A.  LDA >= max(1,N).
    !>

    ANORM

    !>          ANORM is REAL
    !>          If NORM = '1' or 'O', the 1-norm of the original matrix A.
    !>          If NORM = 'I', the infinity-norm of the original matrix A.
    !>

    RCOND

    !>          RCOND is REAL
    !>          The reciprocal of the condition number of the matrix A,
    !>          computed as RCOND = 1/(norm(A) * norm(inv(A))).
    !>

    WORK

    !>          WORK is COMPLEX array, dimension (2*N)
    !>

    RWORK

    !>          RWORK is REAL array, dimension (2*N)
    !>

    INFO

    !>          INFO is INTEGER
    !>          = 0:  successful exit
    !>          < 0:  if INFO = -i, the i-th argument had an illegal value.
    !>                NaNs are illegal values for ANORM, and they propagate to
    !>                the output parameter RCOND.
    !>                Infinity is illegal for ANORM, and it propagates to the output
    !>                parameter RCOND as 0.
    !>          = 1:  if RCOND = NaN, or
    !>                   RCOND = Inf, or
    !>                   the computed norm of the inverse of A is 0.
    !>                In the latter, RCOND = 0 is returned.
    !>

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

  subroutine dgecon (character norm, integer n, double precision, dimension( lda, * ) a, integer lda, double precision anorm, double precision rcond, double precision, dimension( * ) work, integer, dimension( * ) iwork, integer info)

DGECON

Purpose:

    !>
    !> DGECON estimates the reciprocal of the condition number of a general
    !> real matrix A, in either the 1-norm or the infinity-norm, using
    !> the LU factorization computed by DGETRF.
    !>
    !> An estimate is obtained for norm(inv(A)), and the reciprocal of the
    !> condition number is computed as
    !>    RCOND = 1 / ( norm(A) * norm(inv(A)) ).
    !>

Parameters
    NORM

    !>          NORM is CHARACTER*1
    !>          Specifies whether the 1-norm condition number or the
    !>          infinity-norm condition number is required:
    !>          = '1' or 'O':  1-norm;
    !>          = 'I':         Infinity-norm.
    !>

    N

    !>          N is INTEGER
    !>          The order of the matrix A.  N >= 0.
    !>

    A

    !>          A is DOUBLE PRECISION array, dimension (LDA,N)
    !>          The factors L and U from the factorization A = P*L*U
    !>          as computed by DGETRF.
    !>

    LDA

    !>          LDA is INTEGER
    !>          The leading dimension of the array A.  LDA >= max(1,N).
    !>

    ANORM

    !>          ANORM is DOUBLE PRECISION
    !>          If NORM = '1' or 'O', the 1-norm of the original matrix A.
    !>          If NORM = 'I', the infinity-norm of the original matrix A.
    !>

    RCOND

    !>          RCOND is DOUBLE PRECISION
    !>          The reciprocal of the condition number of the matrix A,
    !>          computed as RCOND = 1/(norm(A) * norm(inv(A))).
    !>

    WORK

    !>          WORK is DOUBLE PRECISION array, dimension (4*N)
    !>

    IWORK

    !>          IWORK is INTEGER array, dimension (N)
    !>

    INFO

    !>          INFO is INTEGER
    !>          = 0:  successful exit
    !>          < 0:  if INFO = -i, the i-th argument had an illegal value.
    !>                NaNs are illegal values for ANORM, and they propagate to
    !>                the output parameter RCOND.
    !>                Infinity is illegal for ANORM, and it propagates to the output
    !>                parameter RCOND as 0.
    !>          = 1:  if RCOND = NaN, or
    !>                   RCOND = Inf, or
    !>                   the computed norm of the inverse of A is 0.
    !>                In the latter, RCOND = 0 is returned.
    !>

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

  subroutine sgecon (character norm, integer n, real, dimension( lda, * ) a, integer lda, real anorm, real rcond, real, dimension( * ) work, integer, dimension( * ) iwork, integer info)

SGECON

Purpose:

    !>
    !> SGECON estimates the reciprocal of the condition number of a general
    !> real matrix A, in either the 1-norm or the infinity-norm, using
    !> the LU factorization computed by SGETRF.
    !>
    !> An estimate is obtained for norm(inv(A)), and the reciprocal of the
    !> condition number is computed as
    !>    RCOND = 1 / ( norm(A) * norm(inv(A)) ).
    !>

Parameters
    NORM

    !>          NORM is CHARACTER*1
    !>          Specifies whether the 1-norm condition number or the
    !>          infinity-norm condition number is required:
    !>          = '1' or 'O':  1-norm;
    !>          = 'I':         Infinity-norm.
    !>

    N

    !>          N is INTEGER
    !>          The order of the matrix A.  N >= 0.
    !>

    A

    !>          A is REAL array, dimension (LDA,N)
    !>          The factors L and U from the factorization A = P*L*U
    !>          as computed by SGETRF.
    !>

    LDA

    !>          LDA is INTEGER
    !>          The leading dimension of the array A.  LDA >= max(1,N).
    !>

    ANORM

    !>          ANORM is REAL
    !>          If NORM = '1' or 'O', the 1-norm of the original matrix A.
    !>          If NORM = 'I', the infinity-norm of the original matrix A.
    !>

    RCOND

    !>          RCOND is REAL
    !>          The reciprocal of the condition number of the matrix A,
    !>          computed as RCOND = 1/(norm(A) * norm(inv(A))).
    !>

    WORK

    !>          WORK is REAL array, dimension (4*N)
    !>

    IWORK

    !>          IWORK is INTEGER array, dimension (N)
    !>

    INFO

    !>          INFO is INTEGER
    !>          = 0:  successful exit
    !>          < 0:  if INFO = -i, the i-th argument had an illegal value.
    !>                NaNs are illegal values for ANORM, and they propagate to
    !>                the output parameter RCOND.
    !>                Infinity is illegal for ANORM, and it propagates to the output
    !>                parameter RCOND as 0.
    !>          = 1:  if RCOND = NaN, or
    !>                   RCOND = Inf, or
    !>                   the computed norm of the inverse of A is 0.
    !>                In the latter, RCOND = 0 is returned.
    !>

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

  subroutine zgecon (character norm, integer n, complex*16, dimension( lda, * ) a, integer lda, double precision anorm, double precision rcond, complex*16, dimension( * ) work, double precision, dimension( * ) rwork, integer info)

ZGECON

Purpose:

    !>
    !> ZGECON estimates the reciprocal of the condition number of a general
    !> complex matrix A, in either the 1-norm or the infinity-norm, using
    !> the LU factorization computed by ZGETRF.
    !>
    !> An estimate is obtained for norm(inv(A)), and the reciprocal of the
    !> condition number is computed as
    !>    RCOND = 1 / ( norm(A) * norm(inv(A)) ).
    !>

Parameters
    NORM

    !>          NORM is CHARACTER*1
    !>          Specifies whether the 1-norm condition number or the
    !>          infinity-norm condition number is required:
    !>          = '1' or 'O':  1-norm;
    !>          = 'I':         Infinity-norm.
    !>

    N

    !>          N is INTEGER
    !>          The order of the matrix A.  N >= 0.
    !>

    A

    !>          A is COMPLEX*16 array, dimension (LDA,N)
    !>          The factors L and U from the factorization A = P*L*U
    !>          as computed by ZGETRF.
    !>

    LDA

    !>          LDA is INTEGER
    !>          The leading dimension of the array A.  LDA >= max(1,N).
    !>

    ANORM

    !>          ANORM is DOUBLE PRECISION
    !>          If NORM = '1' or 'O', the 1-norm of the original matrix A.
    !>          If NORM = 'I', the infinity-norm of the original matrix A.
    !>

    RCOND

    !>          RCOND is DOUBLE PRECISION
    !>          The reciprocal of the condition number of the matrix A,
    !>          computed as RCOND = 1/(norm(A) * norm(inv(A))).
    !>

    WORK

    !>          WORK is COMPLEX*16 array, dimension (2*N)
    !>

    RWORK

    !>          RWORK is DOUBLE PRECISION array, dimension (2*N)
    !>

    INFO

    !>          INFO is INTEGER
    !>          = 0:  successful exit
    !>          < 0:  if INFO = -i, the i-th argument had an illegal value.
    !>                NaNs are illegal values for ANORM, and they propagate to
    !>                the output parameter RCOND.
    !>                Infinity is illegal for ANORM, and it propagates to the output
    !>                parameter RCOND as 0.
    !>          = 1:  if RCOND = NaN, or
    !>                   RCOND = Inf, or
    !>                   the computed norm of the inverse of A is 0.
    !>                In the latter, RCOND = 0 is returned.
    !>

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Author

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