.TH "la_porpvgrw" 3 "Wed Feb 7 2024 11:30:40" "Version 3.12.0" "LAPACK" \" -*- nroff -*-
.ad l
.nh
.SH NAME
la_porpvgrw \- la_porpvgrw: reciprocal pivot growth
.SH SYNOPSIS
.br
.PP
.SS "Functions"

.in +1c
.ti -1c
.RI "real function \fBcla_porpvgrw\fP (uplo, ncols, a, lda, af, ldaf, work)"
.br
.RI "\fBCLA_PORPVGRW\fP computes the reciprocal pivot growth factor norm(A)/norm(U) for a symmetric or Hermitian positive-definite matrix\&. "
.ti -1c
.RI "double precision function \fBdla_porpvgrw\fP (uplo, ncols, a, lda, af, ldaf, work)"
.br
.RI "\fBDLA_PORPVGRW\fP computes the reciprocal pivot growth factor norm(A)/norm(U) for a symmetric or Hermitian positive-definite matrix\&. "
.ti -1c
.RI "real function \fBsla_porpvgrw\fP (uplo, ncols, a, lda, af, ldaf, work)"
.br
.RI "\fBSLA_PORPVGRW\fP computes the reciprocal pivot growth factor norm(A)/norm(U) for a symmetric or Hermitian positive-definite matrix\&. "
.ti -1c
.RI "double precision function \fBzla_porpvgrw\fP (uplo, ncols, a, lda, af, ldaf, work)"
.br
.RI "\fBZLA_PORPVGRW\fP computes the reciprocal pivot growth factor norm(A)/norm(U) for a symmetric or Hermitian positive-definite matrix\&. "
.in -1c
.SH "Detailed Description"
.PP 

.SH "Function Documentation"
.PP 
.SS "real function cla_porpvgrw (character*1 uplo, integer ncols, complex, dimension( lda, * ) a, integer lda, complex, dimension( ldaf, * ) af, integer ldaf, real, dimension( * ) work)"

.PP
\fBCLA_PORPVGRW\fP computes the reciprocal pivot growth factor norm(A)/norm(U) for a symmetric or Hermitian positive-definite matrix\&.  
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
 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\&.
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fIUPLO\fP 
.PP
.nf
          UPLO is CHARACTER*1
       = 'U':  Upper triangle of A is stored;
       = 'L':  Lower triangle of A is stored\&.
.fi
.PP
.br
\fINCOLS\fP 
.PP
.nf
          NCOLS is INTEGER
     The number of columns of the matrix A\&. NCOLS >= 0\&.
.fi
.PP
.br
\fIA\fP 
.PP
.nf
          A is COMPLEX array, dimension (LDA,N)
     On entry, the N-by-N matrix A\&.
.fi
.PP
.br
\fILDA\fP 
.PP
.nf
          LDA is INTEGER
     The leading dimension of the array A\&.  LDA >= max(1,N)\&.
.fi
.PP
.br
\fIAF\fP 
.PP
.nf
          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\&.
.fi
.PP
.br
\fILDAF\fP 
.PP
.nf
          LDAF is INTEGER
     The leading dimension of the array AF\&.  LDAF >= max(1,N)\&.
.fi
.PP
.br
\fIWORK\fP 
.PP
.nf
          WORK is REAL array, dimension (2*N)
.fi
.PP
 
.RE
.PP
\fBAuthor\fP
.RS 4
Univ\&. of Tennessee 
.PP
Univ\&. of California Berkeley 
.PP
Univ\&. of Colorado Denver 
.PP
NAG Ltd\&. 
.RE
.PP

.SS "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)"

.PP
\fBDLA_PORPVGRW\fP computes the reciprocal pivot growth factor norm(A)/norm(U) for a symmetric or Hermitian positive-definite matrix\&.  
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
 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\&.
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fIUPLO\fP 
.PP
.nf
          UPLO is CHARACTER*1
       = 'U':  Upper triangle of A is stored;
       = 'L':  Lower triangle of A is stored\&.
.fi
.PP
.br
\fINCOLS\fP 
.PP
.nf
          NCOLS is INTEGER
     The number of columns of the matrix A\&. NCOLS >= 0\&.
.fi
.PP
.br
\fIA\fP 
.PP
.nf
          A is DOUBLE PRECISION array, dimension (LDA,N)
     On entry, the N-by-N matrix A\&.
.fi
.PP
.br
\fILDA\fP 
.PP
.nf
          LDA is INTEGER
     The leading dimension of the array A\&.  LDA >= max(1,N)\&.
.fi
.PP
.br
\fIAF\fP 
.PP
.nf
          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\&.
.fi
.PP
.br
\fILDAF\fP 
.PP
.nf
          LDAF is INTEGER
     The leading dimension of the array AF\&.  LDAF >= max(1,N)\&.
.fi
.PP
.br
\fIWORK\fP 
.PP
.nf
          WORK is DOUBLE PRECISION array, dimension (2*N)
.fi
.PP
 
.RE
.PP
\fBAuthor\fP
.RS 4
Univ\&. of Tennessee 
.PP
Univ\&. of California Berkeley 
.PP
Univ\&. of Colorado Denver 
.PP
NAG Ltd\&. 
.RE
.PP

.SS "real function sla_porpvgrw (character*1 uplo, integer ncols, real, dimension( lda, * ) a, integer lda, real, dimension( ldaf, * ) af, integer ldaf, real, dimension( * ) work)"

.PP
\fBSLA_PORPVGRW\fP computes the reciprocal pivot growth factor norm(A)/norm(U) for a symmetric or Hermitian positive-definite matrix\&.  
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
 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\&.
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fIUPLO\fP 
.PP
.nf
          UPLO is CHARACTER*1
       = 'U':  Upper triangle of A is stored;
       = 'L':  Lower triangle of A is stored\&.
.fi
.PP
.br
\fINCOLS\fP 
.PP
.nf
          NCOLS is INTEGER
     The number of columns of the matrix A\&. NCOLS >= 0\&.
.fi
.PP
.br
\fIA\fP 
.PP
.nf
          A is REAL array, dimension (LDA,N)
     On entry, the N-by-N matrix A\&.
.fi
.PP
.br
\fILDA\fP 
.PP
.nf
          LDA is INTEGER
     The leading dimension of the array A\&.  LDA >= max(1,N)\&.
.fi
.PP
.br
\fIAF\fP 
.PP
.nf
          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\&.
.fi
.PP
.br
\fILDAF\fP 
.PP
.nf
          LDAF is INTEGER
     The leading dimension of the array AF\&.  LDAF >= max(1,N)\&.
.fi
.PP
.br
\fIWORK\fP 
.PP
.nf
          WORK is REAL array, dimension (2*N)
.fi
.PP
 
.RE
.PP
\fBAuthor\fP
.RS 4
Univ\&. of Tennessee 
.PP
Univ\&. of California Berkeley 
.PP
Univ\&. of Colorado Denver 
.PP
NAG Ltd\&. 
.RE
.PP

.SS "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)"

.PP
\fBZLA_PORPVGRW\fP computes the reciprocal pivot growth factor norm(A)/norm(U) for a symmetric or Hermitian positive-definite matrix\&.  
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
 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\&.
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fIUPLO\fP 
.PP
.nf
          UPLO is CHARACTER*1
       = 'U':  Upper triangle of A is stored;
       = 'L':  Lower triangle of A is stored\&.
.fi
.PP
.br
\fINCOLS\fP 
.PP
.nf
          NCOLS is INTEGER
     The number of columns of the matrix A\&. NCOLS >= 0\&.
.fi
.PP
.br
\fIA\fP 
.PP
.nf
          A is COMPLEX*16 array, dimension (LDA,N)
     On entry, the N-by-N matrix A\&.
.fi
.PP
.br
\fILDA\fP 
.PP
.nf
          LDA is INTEGER
     The leading dimension of the array A\&.  LDA >= max(1,N)\&.
.fi
.PP
.br
\fIAF\fP 
.PP
.nf
          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\&.
.fi
.PP
.br
\fILDAF\fP 
.PP
.nf
          LDAF is INTEGER
     The leading dimension of the array AF\&.  LDAF >= max(1,N)\&.
.fi
.PP
.br
\fIWORK\fP 
.PP
.nf
          WORK is DOUBLE PRECISION array, dimension (2*N)
.fi
.PP
 
.RE
.PP
\fBAuthor\fP
.RS 4
Univ\&. of Tennessee 
.PP
Univ\&. of California Berkeley 
.PP
Univ\&. of Colorado Denver 
.PP
NAG Ltd\&. 
.RE
.PP

.SH "Author"
.PP 
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