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 (character1 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 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 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.

Definition at line 104 of file cla_porpvgrw.f.

double precision function dla_porpvgrw (character1 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 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 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.

Definition at line 104 of file dla_porpvgrw.f.

real function sla_porpvgrw (character1 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 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 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.

Definition at line 103 of file sla_porpvgrw.f.

double precision function zla_porpvgrw (character1 uplo, integer ncols, complex16, dimension( lda, * ) a, integer lda, complex16, 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 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 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.

Definition at line 105 of file zla_porpvgrw.f.

Author

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