Provided by: liblapack-doc_3.12.1-4_all 
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 'max absolute element' 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 'max absolute element' 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 'max absolute element' 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 'max absolute element' 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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Version 3.12.0 Sun Jul 20 2025 01:40:05 la_porpvgrw(3)