la_porpvgrw(3)

NAME
la_porpvgrw - la_porpvgrw: reciprocal pivot growth

SYNOPSIS

  Functions

real function cla_porpvgrw (uplo, ncols, a, lda, af, ldaf, work)
CLA_PORPVGRW computes the reciprocal pivot growth factor norm(A)/norm(U) for a symmetric or Hermitian positive-definite matrix.
double precision function dla_porpvgrw (uplo, ncols, a, lda, af, ldaf, work)
DLA_PORPVGRW computes the reciprocal pivot growth factor norm(A)/norm(U) for a symmetric or Hermitian positive-definite matrix.
real function sla_porpvgrw (uplo, ncols, a, lda, af, ldaf, work)
SLA_PORPVGRW computes the reciprocal pivot growth factor norm(A)/norm(U) for a symmetric or Hermitian positive-definite matrix.
double precision function zla_porpvgrw (uplo, ncols, a, lda, af, ldaf, work)
ZLA_PORPVGRW computes the reciprocal pivot growth factor norm(A)/norm(U) for a symmetric or Hermitian positive-definite matrix.

Detailed Description

Function Documentation

  real function cla_porpvgrw (character*1 uplo, integer ncols, complex, dimension( lda, * ) a, integer lda, complex, dimension( ldaf, * ) af, integer ldaf, real, dimension( * ) work)

CLA_PORPVGRW computes the reciprocal pivot growth factor norm(A)/norm(U) for a symmetric or Hermitian positive-definite matrix.

Purpose:

    !>
    !>
    !> CLA_PORPVGRW computes the reciprocal pivot growth factor
    !> norm(A)/norm(U). The  norm is used. If this is
    !> much less than 1, the stability of the LU factorization of the
    !> (equilibrated) matrix A could be poor. This also means that the
    !> solution X, estimated condition numbers, and error bounds could be
    !> unreliable.
    !>

Parameters
    UPLO

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

    NCOLS

    !>          NCOLS is INTEGER
    !>     The number of columns of the matrix A. NCOLS >= 0.
    !>

    A

    !>          A is COMPLEX array, dimension (LDA,N)
    !>     On entry, the N-by-N matrix A.
    !>

    LDA

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

    AF

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

    LDAF

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

    WORK

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

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

  double precision function dla_porpvgrw (character*1 uplo, integer ncols, double precision, dimension( lda, * ) a, integer lda, double precision, dimension( ldaf, * ) af, integer ldaf, double precision, dimension( * ) work)

DLA_PORPVGRW computes the reciprocal pivot growth factor norm(A)/norm(U) for a symmetric or Hermitian positive-definite matrix.

Purpose:

    !>
    !>
    !> DLA_PORPVGRW computes the reciprocal pivot growth factor
    !> norm(A)/norm(U). The  norm is used. If this is
    !> much less than 1, the stability of the LU factorization of the
    !> (equilibrated) matrix A could be poor. This also means that the
    !> solution X, estimated condition numbers, and error bounds could be
    !> unreliable.
    !>

Parameters
    UPLO

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

    NCOLS

    !>          NCOLS is INTEGER
    !>     The number of columns of the matrix A. NCOLS >= 0.
    !>

    A

    !>          A is DOUBLE PRECISION array, dimension (LDA,N)
    !>     On entry, the N-by-N matrix A.
    !>

    LDA

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

    AF

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

    LDAF

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

    WORK

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

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

  real function sla_porpvgrw (character*1 uplo, integer ncols, real, dimension( lda, * ) a, integer lda, real, dimension( ldaf, * ) af, integer ldaf, real, dimension( * ) work)

SLA_PORPVGRW computes the reciprocal pivot growth factor norm(A)/norm(U) for a symmetric or Hermitian positive-definite matrix.

Purpose:

    !>
    !>
    !> SLA_PORPVGRW computes the reciprocal pivot growth factor
    !> norm(A)/norm(U). The  norm is used. If this is
    !> much less than 1, the stability of the LU factorization of the
    !> (equilibrated) matrix A could be poor. This also means that the
    !> solution X, estimated condition numbers, and error bounds could be
    !> unreliable.
    !>

Parameters
    UPLO

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

    NCOLS

    !>          NCOLS is INTEGER
    !>     The number of columns of the matrix A. NCOLS >= 0.
    !>

    A

    !>          A is REAL array, dimension (LDA,N)
    !>     On entry, the N-by-N matrix A.
    !>

    LDA

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

    AF

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

    LDAF

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

    WORK

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

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

  double precision function zla_porpvgrw (character*1 uplo, integer ncols, complex*16, dimension( lda, * ) a, integer lda, complex*16, dimension( ldaf, * ) af, integer ldaf, double precision, dimension( * ) work)

ZLA_PORPVGRW computes the reciprocal pivot growth factor norm(A)/norm(U) for a symmetric or Hermitian positive-definite matrix.

Purpose:

    !>
    !>
    !> ZLA_PORPVGRW computes the reciprocal pivot growth factor
    !> norm(A)/norm(U). The  norm is used. If this is
    !> much less than 1, the stability of the LU factorization of the
    !> (equilibrated) matrix A could be poor. This also means that the
    !> solution X, estimated condition numbers, and error bounds could be
    !> unreliable.
    !>

Parameters
    UPLO

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

    NCOLS

    !>          NCOLS is INTEGER
    !>     The number of columns of the matrix A. NCOLS >= 0.
    !>

    A

    !>          A is COMPLEX*16 array, dimension (LDA,N)
    !>     On entry, the N-by-N matrix A.
    !>

    LDA

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

    AF

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

    LDAF

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

    WORK

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

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Author

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