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

.in +1c
.ti -1c
.RI "real function \fBcla_herpvgrw\fP (uplo, n, info, a, lda, af, ldaf, ipiv, work)"
.br
.RI "\fBCLA_HERPVGRW\fP "
.ti -1c
.RI "real function \fBcla_syrpvgrw\fP (uplo, n, info, a, lda, af, ldaf, ipiv, work)"
.br
.RI "\fBCLA_SYRPVGRW\fP computes the reciprocal pivot growth factor norm(A)/norm(U) for a symmetric indefinite matrix\&. "
.ti -1c
.RI "double precision function \fBdla_syrpvgrw\fP (uplo, n, info, a, lda, af, ldaf, ipiv, work)"
.br
.RI "\fBDLA_SYRPVGRW\fP computes the reciprocal pivot growth factor norm(A)/norm(U) for a symmetric indefinite matrix\&. "
.ti -1c
.RI "real function \fBsla_syrpvgrw\fP (uplo, n, info, a, lda, af, ldaf, ipiv, work)"
.br
.RI "\fBSLA_SYRPVGRW\fP computes the reciprocal pivot growth factor norm(A)/norm(U) for a symmetric indefinite matrix\&. "
.ti -1c
.RI "double precision function \fBzla_herpvgrw\fP (uplo, n, info, a, lda, af, ldaf, ipiv, work)"
.br
.RI "\fBZLA_HERPVGRW\fP "
.ti -1c
.RI "double precision function \fBzla_syrpvgrw\fP (uplo, n, info, a, lda, af, ldaf, ipiv, work)"
.br
.RI "\fBZLA_SYRPVGRW\fP computes the reciprocal pivot growth factor norm(A)/norm(U) for a symmetric indefinite matrix\&. "
.in -1c
.SH "Detailed Description"
.PP 

.SH "Function Documentation"
.PP 
.SS "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)"

.PP
\fBCLA_HERPVGRW\fP  
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
 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\&.
.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
\fIN\fP 
.PP
.nf
          N is INTEGER
     The number of linear equations, i\&.e\&., the order of the
     matrix A\&.  N >= 0\&.
.fi
.PP
.br
\fIINFO\fP 
.PP
.nf
          INFO is INTEGER
     The value of INFO returned from SSYTRF, \&.i\&.e\&., the pivot in
     column INFO is exactly 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 block diagonal matrix D and the multipliers used to
     obtain the factor U or L as computed by CHETRF\&.
.fi
.PP
.br
\fILDAF\fP 
.PP
.nf
          LDAF is INTEGER
     The leading dimension of the array AF\&.  LDAF >= max(1,N)\&.
.fi
.PP
.br
\fIIPIV\fP 
.PP
.nf
          IPIV is INTEGER array, dimension (N)
     Details of the interchanges and the block structure of D
     as determined by CHETRF\&.
.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 "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)"

.PP
\fBCLA_SYRPVGRW\fP computes the reciprocal pivot growth factor norm(A)/norm(U) for a symmetric indefinite matrix\&.  
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
 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\&.
.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
\fIN\fP 
.PP
.nf
          N is INTEGER
     The number of linear equations, i\&.e\&., the order of the
     matrix A\&.  N >= 0\&.
.fi
.PP
.br
\fIINFO\fP 
.PP
.nf
          INFO is INTEGER
     The value of INFO returned from CSYTRF, \&.i\&.e\&., the pivot in
     column INFO is exactly 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 block diagonal matrix D and the multipliers used to
     obtain the factor U or L as computed by CSYTRF\&.
.fi
.PP
.br
\fILDAF\fP 
.PP
.nf
          LDAF is INTEGER
     The leading dimension of the array AF\&.  LDAF >= max(1,N)\&.
.fi
.PP
.br
\fIIPIV\fP 
.PP
.nf
          IPIV is INTEGER array, dimension (N)
     Details of the interchanges and the block structure of D
     as determined by CSYTRF\&.
.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_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)"

.PP
\fBDLA_SYRPVGRW\fP computes the reciprocal pivot growth factor norm(A)/norm(U) for a symmetric indefinite matrix\&.  
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
 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\&.
.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
\fIN\fP 
.PP
.nf
          N is INTEGER
     The number of linear equations, i\&.e\&., the order of the
     matrix A\&.  N >= 0\&.
.fi
.PP
.br
\fIINFO\fP 
.PP
.nf
          INFO is INTEGER
     The value of INFO returned from DSYTRF, \&.i\&.e\&., the pivot in
     column INFO is exactly 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 block diagonal matrix D and the multipliers used to
     obtain the factor U or L as computed by DSYTRF\&.
.fi
.PP
.br
\fILDAF\fP 
.PP
.nf
          LDAF is INTEGER
     The leading dimension of the array AF\&.  LDAF >= max(1,N)\&.
.fi
.PP
.br
\fIIPIV\fP 
.PP
.nf
          IPIV is INTEGER array, dimension (N)
     Details of the interchanges and the block structure of D
     as determined by DSYTRF\&.
.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_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)"

.PP
\fBSLA_SYRPVGRW\fP computes the reciprocal pivot growth factor norm(A)/norm(U) for a symmetric indefinite matrix\&.  
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
 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\&.
.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
\fIN\fP 
.PP
.nf
          N is INTEGER
     The number of linear equations, i\&.e\&., the order of the
     matrix A\&.  N >= 0\&.
.fi
.PP
.br
\fIINFO\fP 
.PP
.nf
          INFO is INTEGER
     The value of INFO returned from SSYTRF, \&.i\&.e\&., the pivot in
     column INFO is exactly 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 block diagonal matrix D and the multipliers used to
     obtain the factor U or L as computed by SSYTRF\&.
.fi
.PP
.br
\fILDAF\fP 
.PP
.nf
          LDAF is INTEGER
     The leading dimension of the array AF\&.  LDAF >= max(1,N)\&.
.fi
.PP
.br
\fIIPIV\fP 
.PP
.nf
          IPIV is INTEGER array, dimension (N)
     Details of the interchanges and the block structure of D
     as determined by SSYTRF\&.
.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_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)"

.PP
\fBZLA_HERPVGRW\fP  
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
 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\&.
.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
\fIN\fP 
.PP
.nf
          N is INTEGER
     The number of linear equations, i\&.e\&., the order of the
     matrix A\&.  N >= 0\&.
.fi
.PP
.br
\fIINFO\fP 
.PP
.nf
          INFO is INTEGER
     The value of INFO returned from ZHETRF, \&.i\&.e\&., the pivot in
     column INFO is exactly 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 block diagonal matrix D and the multipliers used to
     obtain the factor U or L as computed by ZHETRF\&.
.fi
.PP
.br
\fILDAF\fP 
.PP
.nf
          LDAF is INTEGER
     The leading dimension of the array AF\&.  LDAF >= max(1,N)\&.
.fi
.PP
.br
\fIIPIV\fP 
.PP
.nf
          IPIV is INTEGER array, dimension (N)
     Details of the interchanges and the block structure of D
     as determined by ZHETRF\&.
.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 "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)"

.PP
\fBZLA_SYRPVGRW\fP computes the reciprocal pivot growth factor norm(A)/norm(U) for a symmetric indefinite matrix\&.  
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
 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\&.
.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
\fIN\fP 
.PP
.nf
          N is INTEGER
     The number of linear equations, i\&.e\&., the order of the
     matrix A\&.  N >= 0\&.
.fi
.PP
.br
\fIINFO\fP 
.PP
.nf
          INFO is INTEGER
     The value of INFO returned from ZSYTRF, \&.i\&.e\&., the pivot in
     column INFO is exactly 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 block diagonal matrix D and the multipliers used to
     obtain the factor U or L as computed by ZSYTRF\&.
.fi
.PP
.br
\fILDAF\fP 
.PP
.nf
          LDAF is INTEGER
     The leading dimension of the array AF\&.  LDAF >= max(1,N)\&.
.fi
.PP
.br
\fIIPIV\fP 
.PP
.nf
          IPIV is INTEGER array, dimension (N)
     Details of the interchanges and the block structure of D
     as determined by ZSYTRF\&.
.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 
Generated automatically by Doxygen for LAPACK from the source code\&.