Provided by: liblapack-doc_3.12.1-6build1_all 
NAME
la_herpvgrw - la_herpvgrw: reciprocal pivot growth
SYNOPSIS
Functions
real function cla_herpvgrw (uplo, n, info, a, lda, af, ldaf, ipiv, work)
CLA_HERPVGRW
real function cla_syrpvgrw (uplo, n, info, a, lda, af, ldaf, ipiv, work)
CLA_SYRPVGRW computes the reciprocal pivot growth factor norm(A)/norm(U) for a symmetric indefinite
matrix.
double precision function dla_syrpvgrw (uplo, n, info, a, lda, af, ldaf, ipiv, work)
DLA_SYRPVGRW computes the reciprocal pivot growth factor norm(A)/norm(U) for a symmetric indefinite
matrix.
real function sla_syrpvgrw (uplo, n, info, a, lda, af, ldaf, ipiv, work)
SLA_SYRPVGRW computes the reciprocal pivot growth factor norm(A)/norm(U) for a symmetric indefinite
matrix.
double precision function zla_herpvgrw (uplo, n, info, a, lda, af, ldaf, ipiv, work)
ZLA_HERPVGRW
double precision function zla_syrpvgrw (uplo, n, info, a, lda, af, ldaf, ipiv, work)
ZLA_SYRPVGRW computes the reciprocal pivot growth factor norm(A)/norm(U) for a symmetric indefinite
matrix.
Detailed Description
Function Documentation
real function cla_herpvgrw (character*1 uplo, integer n, integer info, complex, dimension( lda, * ) a,
integer lda, complex, dimension( ldaf, * ) af, integer ldaf, integer, dimension( * ) ipiv, real,
dimension( * ) work)
CLA_HERPVGRW
Purpose:
CLA_HERPVGRW 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.
N
N is INTEGER
The number of linear equations, i.e., the order of the
matrix A. N >= 0.
INFO
INFO is INTEGER
The value of INFO returned from SSYTRF, .i.e., the pivot in
column INFO is exactly 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 block diagonal matrix D and the multipliers used to
obtain the factor U or L as computed by CHETRF.
LDAF
LDAF is INTEGER
The leading dimension of the array AF. LDAF >= max(1,N).
IPIV
IPIV is INTEGER array, dimension (N)
Details of the interchanges and the block structure of D
as determined by CHETRF.
WORK
WORK is REAL array, dimension (2*N)
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
real function cla_syrpvgrw (character*1 uplo, integer n, integer info, complex, dimension( lda, * ) a,
integer lda, complex, dimension( ldaf, * ) af, integer ldaf, integer, dimension( * ) ipiv, real,
dimension( * ) work)
CLA_SYRPVGRW computes the reciprocal pivot growth factor norm(A)/norm(U) for a symmetric indefinite
matrix.
Purpose:
CLA_SYRPVGRW 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.
N
N is INTEGER
The number of linear equations, i.e., the order of the
matrix A. N >= 0.
INFO
INFO is INTEGER
The value of INFO returned from CSYTRF, .i.e., the pivot in
column INFO is exactly 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 block diagonal matrix D and the multipliers used to
obtain the factor U or L as computed by CSYTRF.
LDAF
LDAF is INTEGER
The leading dimension of the array AF. LDAF >= max(1,N).
IPIV
IPIV is INTEGER array, dimension (N)
Details of the interchanges and the block structure of D
as determined by CSYTRF.
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_syrpvgrw (character*1 uplo, integer n, integer info, double precision,
dimension( lda, * ) a, integer lda, double precision, dimension( ldaf, * ) af, integer ldaf, integer,
dimension( * ) ipiv, double precision, dimension( * ) work)
DLA_SYRPVGRW computes the reciprocal pivot growth factor norm(A)/norm(U) for a symmetric indefinite
matrix.
Purpose:
DLA_SYRPVGRW 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.
N
N is INTEGER
The number of linear equations, i.e., the order of the
matrix A. N >= 0.
INFO
INFO is INTEGER
The value of INFO returned from DSYTRF, .i.e., the pivot in
column INFO is exactly 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 block diagonal matrix D and the multipliers used to
obtain the factor U or L as computed by DSYTRF.
LDAF
LDAF is INTEGER
The leading dimension of the array AF. LDAF >= max(1,N).
IPIV
IPIV is INTEGER array, dimension (N)
Details of the interchanges and the block structure of D
as determined by DSYTRF.
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_syrpvgrw (character*1 uplo, integer n, integer info, real, dimension( lda, * ) a, integer
lda, real, dimension( ldaf, * ) af, integer ldaf, integer, dimension( * ) ipiv, real, dimension( * )
work)
SLA_SYRPVGRW computes the reciprocal pivot growth factor norm(A)/norm(U) for a symmetric indefinite
matrix.
Purpose:
SLA_SYRPVGRW 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.
N
N is INTEGER
The number of linear equations, i.e., the order of the
matrix A. N >= 0.
INFO
INFO is INTEGER
The value of INFO returned from SSYTRF, .i.e., the pivot in
column INFO is exactly 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 block diagonal matrix D and the multipliers used to
obtain the factor U or L as computed by SSYTRF.
LDAF
LDAF is INTEGER
The leading dimension of the array AF. LDAF >= max(1,N).
IPIV
IPIV is INTEGER array, dimension (N)
Details of the interchanges and the block structure of D
as determined by SSYTRF.
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_herpvgrw (character*1 uplo, integer n, integer info, complex*16, dimension(
lda, * ) a, integer lda, complex*16, dimension( ldaf, * ) af, integer ldaf, integer, dimension( * ) ipiv,
double precision, dimension( * ) work)
ZLA_HERPVGRW
Purpose:
ZLA_HERPVGRW 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.
N
N is INTEGER
The number of linear equations, i.e., the order of the
matrix A. N >= 0.
INFO
INFO is INTEGER
The value of INFO returned from ZHETRF, .i.e., the pivot in
column INFO is exactly 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 block diagonal matrix D and the multipliers used to
obtain the factor U or L as computed by ZHETRF.
LDAF
LDAF is INTEGER
The leading dimension of the array AF. LDAF >= max(1,N).
IPIV
IPIV is INTEGER array, dimension (N)
Details of the interchanges and the block structure of D
as determined by ZHETRF.
WORK
WORK is DOUBLE PRECISION array, dimension (2*N)
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
double precision function zla_syrpvgrw (character*1 uplo, integer n, integer info, complex*16, dimension(
lda, * ) a, integer lda, complex*16, dimension( ldaf, * ) af, integer ldaf, integer, dimension( * ) ipiv,
double precision, dimension( * ) work)
ZLA_SYRPVGRW computes the reciprocal pivot growth factor norm(A)/norm(U) for a symmetric indefinite
matrix.
Purpose:
ZLA_SYRPVGRW 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.
N
N is INTEGER
The number of linear equations, i.e., the order of the
matrix A. N >= 0.
INFO
INFO is INTEGER
The value of INFO returned from ZSYTRF, .i.e., the pivot in
column INFO is exactly 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 block diagonal matrix D and the multipliers used to
obtain the factor U or L as computed by ZSYTRF.
LDAF
LDAF is INTEGER
The leading dimension of the array AF. LDAF >= max(1,N).
IPIV
IPIV is INTEGER array, dimension (N)
Details of the interchanges and the block structure of D
as determined by ZSYTRF.
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 Thu Aug 28 2025 19:20:45 la_herpvgrw(3)