Provided by: liblapack-doc_3.12.1-6build1_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
Generated automatically by Doxygen for LAPACK from the source code.
Version 3.12.0 Thu Aug 28 2025 19:20:45 la_porpvgrw(3)