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

.in +1c
.ti -1c
.RI "subroutine \fBcla_lin_berr\fP (n, nz, nrhs, res, ayb, berr)"
.br
.RI "\fBCLA_LIN_BERR\fP computes a component-wise relative backward error\&. "
.ti -1c
.RI "subroutine \fBdla_lin_berr\fP (n, nz, nrhs, res, ayb, berr)"
.br
.RI "\fBDLA_LIN_BERR\fP computes a component-wise relative backward error\&. "
.ti -1c
.RI "subroutine \fBsla_lin_berr\fP (n, nz, nrhs, res, ayb, berr)"
.br
.RI "\fBSLA_LIN_BERR\fP computes a component-wise relative backward error\&. "
.ti -1c
.RI "subroutine \fBzla_lin_berr\fP (n, nz, nrhs, res, ayb, berr)"
.br
.RI "\fBZLA_LIN_BERR\fP computes a component-wise relative backward error\&. "
.in -1c
.SH "Detailed Description"
.PP 

.SH "Function Documentation"
.PP 
.SS "subroutine cla_lin_berr (integer n, integer nz, integer nrhs, complex, dimension( n, nrhs ) res, real, dimension( n, nrhs ) ayb, real, dimension( nrhs ) berr)"

.PP
\fBCLA_LIN_BERR\fP computes a component-wise relative backward error\&.  
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
    CLA_LIN_BERR computes componentwise relative backward error from
    the formula
        max(i) ( abs(R(i)) / ( abs(op(A_s))*abs(Y) + abs(B_s) )(i) )
    where abs(Z) is the componentwise absolute value of the matrix
    or vector Z\&.
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\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
\fINZ\fP 
.PP
.nf
          NZ is INTEGER
     We add (NZ+1)*SLAMCH( 'Safe minimum' ) to R(i) in the numerator to
     guard against spuriously zero residuals\&. Default value is N\&.
.fi
.PP
.br
\fINRHS\fP 
.PP
.nf
          NRHS is INTEGER
     The number of right hand sides, i\&.e\&., the number of columns
     of the matrices AYB, RES, and BERR\&.  NRHS >= 0\&.
.fi
.PP
.br
\fIRES\fP 
.PP
.nf
          RES is COMPLEX array, dimension (N,NRHS)
     The residual matrix, i\&.e\&., the matrix R in the relative backward
     error formula above\&.
.fi
.PP
.br
\fIAYB\fP 
.PP
.nf
          AYB is REAL array, dimension (N, NRHS)
     The denominator in the relative backward error formula above, i\&.e\&.,
     the matrix abs(op(A_s))*abs(Y) + abs(B_s)\&. The matrices A, Y, and B
     are from iterative refinement (see cla_gerfsx_extended\&.f)\&.
.fi
.PP
.br
\fIBERR\fP 
.PP
.nf
          BERR is REAL array, dimension (NRHS)
     The componentwise relative backward error from the formula above\&.
.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 "subroutine dla_lin_berr (integer n, integer nz, integer nrhs, double precision, dimension( n, nrhs ) res, double precision, dimension( n, nrhs ) ayb, double precision, dimension( nrhs ) berr)"

.PP
\fBDLA_LIN_BERR\fP computes a component-wise relative backward error\&.  
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
    DLA_LIN_BERR computes component-wise relative backward error from
    the formula
        max(i) ( abs(R(i)) / ( abs(op(A_s))*abs(Y) + abs(B_s) )(i) )
    where abs(Z) is the component-wise absolute value of the matrix
    or vector Z\&.
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\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
\fINZ\fP 
.PP
.nf
          NZ is INTEGER
     We add (NZ+1)*SLAMCH( 'Safe minimum' ) to R(i) in the numerator to
     guard against spuriously zero residuals\&. Default value is N\&.
.fi
.PP
.br
\fINRHS\fP 
.PP
.nf
          NRHS is INTEGER
     The number of right hand sides, i\&.e\&., the number of columns
     of the matrices AYB, RES, and BERR\&.  NRHS >= 0\&.
.fi
.PP
.br
\fIRES\fP 
.PP
.nf
          RES is DOUBLE PRECISION array, dimension (N,NRHS)
     The residual matrix, i\&.e\&., the matrix R in the relative backward
     error formula above\&.
.fi
.PP
.br
\fIAYB\fP 
.PP
.nf
          AYB is DOUBLE PRECISION array, dimension (N, NRHS)
     The denominator in the relative backward error formula above, i\&.e\&.,
     the matrix abs(op(A_s))*abs(Y) + abs(B_s)\&. The matrices A, Y, and B
     are from iterative refinement (see dla_gerfsx_extended\&.f)\&.
.fi
.PP
.br
\fIBERR\fP 
.PP
.nf
          BERR is DOUBLE PRECISION array, dimension (NRHS)
     The component-wise relative backward error from the formula above\&.
.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 "subroutine sla_lin_berr (integer n, integer nz, integer nrhs, real, dimension( n, nrhs ) res, real, dimension( n, nrhs ) ayb, real, dimension( nrhs ) berr)"

.PP
\fBSLA_LIN_BERR\fP computes a component-wise relative backward error\&.  
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
    SLA_LIN_BERR computes componentwise relative backward error from
    the formula
        max(i) ( abs(R(i)) / ( abs(op(A_s))*abs(Y) + abs(B_s) )(i) )
    where abs(Z) is the componentwise absolute value of the matrix
    or vector Z\&.
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\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
\fINZ\fP 
.PP
.nf
          NZ is INTEGER
     We add (NZ+1)*SLAMCH( 'Safe minimum' ) to R(i) in the numerator to
     guard against spuriously zero residuals\&. Default value is N\&.
.fi
.PP
.br
\fINRHS\fP 
.PP
.nf
          NRHS is INTEGER
     The number of right hand sides, i\&.e\&., the number of columns
     of the matrices AYB, RES, and BERR\&.  NRHS >= 0\&.
.fi
.PP
.br
\fIRES\fP 
.PP
.nf
          RES is REAL array, dimension (N,NRHS)
     The residual matrix, i\&.e\&., the matrix R in the relative backward
     error formula above\&.
.fi
.PP
.br
\fIAYB\fP 
.PP
.nf
          AYB is REAL array, dimension (N, NRHS)
     The denominator in the relative backward error formula above, i\&.e\&.,
     the matrix abs(op(A_s))*abs(Y) + abs(B_s)\&. The matrices A, Y, and B
     are from iterative refinement (see sla_gerfsx_extended\&.f)\&.
.fi
.PP
.br
\fIBERR\fP 
.PP
.nf
          BERR is REAL array, dimension (NRHS)
     The componentwise relative backward error from the formula above\&.
.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 "subroutine zla_lin_berr (integer n, integer nz, integer nrhs, complex*16, dimension( n, nrhs ) res, double precision, dimension( n, nrhs ) ayb, double precision, dimension( nrhs ) berr)"

.PP
\fBZLA_LIN_BERR\fP computes a component-wise relative backward error\&.  
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
    ZLA_LIN_BERR computes componentwise relative backward error from
    the formula
        max(i) ( abs(R(i)) / ( abs(op(A_s))*abs(Y) + abs(B_s) )(i) )
    where abs(Z) is the componentwise absolute value of the matrix
    or vector Z\&.
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\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
\fINZ\fP 
.PP
.nf
          NZ is INTEGER
     We add (NZ+1)*SLAMCH( 'Safe minimum' ) to R(i) in the numerator to
     guard against spuriously zero residuals\&. Default value is N\&.
.fi
.PP
.br
\fINRHS\fP 
.PP
.nf
          NRHS is INTEGER
     The number of right hand sides, i\&.e\&., the number of columns
     of the matrices AYB, RES, and BERR\&.  NRHS >= 0\&.
.fi
.PP
.br
\fIRES\fP 
.PP
.nf
          RES is COMPLEX*16 array, dimension (N,NRHS)
     The residual matrix, i\&.e\&., the matrix R in the relative backward
     error formula above\&.
.fi
.PP
.br
\fIAYB\fP 
.PP
.nf
          AYB is DOUBLE PRECISION array, dimension (N, NRHS)
     The denominator in the relative backward error formula above, i\&.e\&.,
     the matrix abs(op(A_s))*abs(Y) + abs(B_s)\&. The matrices A, Y, and B
     are from iterative refinement (see zla_gerfsx_extended\&.f)\&.
.fi
.PP
.br
\fIBERR\fP 
.PP
.nf
          BERR is DOUBLE PRECISION array, dimension (NRHS)
     The componentwise relative backward error from the formula above\&.
.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\&.