# la_porpvgrw - Man Page

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.

Definition at line **104** of file **cla_porpvgrw.f**.

### 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.

Definition at line **104** of file **dla_porpvgrw.f**.

### 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.

Definition at line **103** of file **sla_porpvgrw.f**.

### 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.

Definition at line **105** of file **zla_porpvgrw.f**.

## Author

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