pocon(3)

NAME
pocon - pocon: condition number estimate

SYNOPSIS

  Functions

subroutine cpocon (uplo, n, a, lda, anorm, rcond, work, rwork, info)
CPOCON
subroutine dpocon (uplo, n, a, lda, anorm, rcond, work, iwork, info)
DPOCON
subroutine spocon (uplo, n, a, lda, anorm, rcond, work, iwork, info)
SPOCON
subroutine zpocon (uplo, n, a, lda, anorm, rcond, work, rwork, info)
ZPOCON

Detailed Description

Function Documentation

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

CPOCON

Purpose:

    !>
    !> CPOCON estimates the reciprocal of the condition number (in the
    !> 1-norm) of a complex Hermitian positive definite matrix using the
    !> Cholesky factorization A = U**H*U or A = L*L**H computed by CPOTRF.
    !>
    !> An estimate is obtained for norm(inv(A)), and the reciprocal of the
    !> condition number is computed as RCOND = 1 / (ANORM * norm(inv(A))).
    !>

Parameters
    UPLO

    !>          UPLO is CHARACTER*1
    !>          = 'U':  Upper triangle of A is stored;
    !>          = 'L':  Lower triangle of A is stored.
    !>

    N

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

    A

    !>          A is COMPLEX array, dimension (LDA,N)
    !>          The triangular factor U or L from the Cholesky factorization
    !>          A = U**H*U or A = L*L**H, as computed by CPOTRF.
    !>

    LDA

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

    ANORM

    !>          ANORM is REAL
    !>          The 1-norm (or infinity-norm) of the Hermitian matrix A.
    !>

    RCOND

    !>          RCOND is REAL
    !>          The reciprocal of the condition number of the matrix A,
    !>          computed as RCOND = 1/(ANORM * AINVNM), where AINVNM is an
    !>          estimate of the 1-norm of inv(A) computed in this routine.
    !>

    WORK

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

    RWORK

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

    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 dpocon (character uplo, integer n, double precision, dimension( lda, * ) a, integer lda, double precision anorm, double precision rcond, double precision, dimension( * ) work, integer, dimension( * ) iwork, integer info)

DPOCON

Purpose:

    !>
    !> DPOCON estimates the reciprocal of the condition number (in the
    !> 1-norm) of a real symmetric positive definite matrix using the
    !> Cholesky factorization A = U**T*U or A = L*L**T computed by DPOTRF.
    !>
    !> An estimate is obtained for norm(inv(A)), and the reciprocal of the
    !> condition number is computed as RCOND = 1 / (ANORM * norm(inv(A))).
    !>

Parameters
    UPLO

    !>          UPLO is CHARACTER*1
    !>          = 'U':  Upper triangle of A is stored;
    !>          = 'L':  Lower triangle of A is stored.
    !>

    N

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

    A

    !>          A is DOUBLE PRECISION array, dimension (LDA,N)
    !>          The triangular factor U or L from the Cholesky factorization
    !>          A = U**T*U or A = L*L**T, as computed by DPOTRF.
    !>

    LDA

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

    ANORM

    !>          ANORM is DOUBLE PRECISION
    !>          The 1-norm (or infinity-norm) of the symmetric matrix A.
    !>

    RCOND

    !>          RCOND is DOUBLE PRECISION
    !>          The reciprocal of the condition number of the matrix A,
    !>          computed as RCOND = 1/(ANORM * AINVNM), where AINVNM is an
    !>          estimate of the 1-norm of inv(A) computed in this routine.
    !>

    WORK

    !>          WORK is DOUBLE PRECISION array, dimension (3*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
    !>

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

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

SPOCON

Purpose:

    !>
    !> SPOCON estimates the reciprocal of the condition number (in the
    !> 1-norm) of a real symmetric positive definite matrix using the
    !> Cholesky factorization A = U**T*U or A = L*L**T computed by SPOTRF.
    !>
    !> An estimate is obtained for norm(inv(A)), and the reciprocal of the
    !> condition number is computed as RCOND = 1 / (ANORM * norm(inv(A))).
    !>

Parameters
    UPLO

    !>          UPLO is CHARACTER*1
    !>          = 'U':  Upper triangle of A is stored;
    !>          = 'L':  Lower triangle of A is stored.
    !>

    N

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

    A

    !>          A is REAL array, dimension (LDA,N)
    !>          The triangular factor U or L from the Cholesky factorization
    !>          A = U**T*U or A = L*L**T, as computed by SPOTRF.
    !>

    LDA

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

    ANORM

    !>          ANORM is REAL
    !>          The 1-norm (or infinity-norm) of the symmetric matrix A.
    !>

    RCOND

    !>          RCOND is REAL
    !>          The reciprocal of the condition number of the matrix A,
    !>          computed as RCOND = 1/(ANORM * AINVNM), where AINVNM is an
    !>          estimate of the 1-norm of inv(A) computed in this routine.
    !>

    WORK

    !>          WORK is REAL array, dimension (3*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
    !>

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

  subroutine zpocon (character uplo, 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)

ZPOCON

Purpose:

    !>
    !> ZPOCON estimates the reciprocal of the condition number (in the
    !> 1-norm) of a complex Hermitian positive definite matrix using the
    !> Cholesky factorization A = U**H*U or A = L*L**H computed by ZPOTRF.
    !>
    !> An estimate is obtained for norm(inv(A)), and the reciprocal of the
    !> condition number is computed as RCOND = 1 / (ANORM * norm(inv(A))).
    !>

Parameters
    UPLO

    !>          UPLO is CHARACTER*1
    !>          = 'U':  Upper triangle of A is stored;
    !>          = 'L':  Lower triangle of A is stored.
    !>

    N

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

    A

    !>          A is COMPLEX*16 array, dimension (LDA,N)
    !>          The triangular factor U or L from the Cholesky factorization
    !>          A = U**H*U or A = L*L**H, as computed by ZPOTRF.
    !>

    LDA

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

    ANORM

    !>          ANORM is DOUBLE PRECISION
    !>          The 1-norm (or infinity-norm) of the Hermitian matrix A.
    !>

    RCOND

    !>          RCOND is DOUBLE PRECISION
    !>          The reciprocal of the condition number of the matrix A,
    !>          computed as RCOND = 1/(ANORM * AINVNM), where AINVNM is an
    !>          estimate of the 1-norm of inv(A) computed in this routine.
    !>

    WORK

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

    RWORK

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

    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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