.TH "SRC/stbrfs.f" 3 "Version 3.12.0" "LAPACK" \" -*- nroff -*-
.ad l
.nh
.SH NAME
SRC/stbrfs.f
.SH SYNOPSIS
.br
.PP
.SS "Functions/Subroutines"

.in +1c
.ti -1c
.RI "subroutine \fBstbrfs\fP (uplo, trans, diag, n, kd, nrhs, ab, ldab, b, ldb, x, ldx, ferr, berr, work, iwork, info)"
.br
.RI "\fBSTBRFS\fP "
.in -1c
.SH "Function/Subroutine Documentation"
.PP 
.SS "subroutine stbrfs (character uplo, character trans, character diag, integer n, integer kd, integer nrhs, real, dimension( ldab, * ) ab, integer ldab, real, dimension( ldb, * ) b, integer ldb, real, dimension( ldx, * ) x, integer ldx, real, dimension( * ) ferr, real, dimension( * ) berr, real, dimension( * ) work, integer, dimension( * ) iwork, integer info)"

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

.PP
.nf
!>
!> STBRFS provides error bounds and backward error estimates for the
!> solution to a system of linear equations with a triangular band
!> coefficient matrix\&.
!>
!> The solution matrix X must be computed by STBTRS or some other
!> means before entering this routine\&.  STBRFS does not do iterative
!> refinement because doing so cannot improve the backward error\&.
!> 
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fIUPLO\fP 
.PP
.nf
!>          UPLO is CHARACTER*1
!>          = 'U':  A is upper triangular;
!>          = 'L':  A is lower triangular\&.
!> 
.fi
.PP
.br
\fITRANS\fP 
.PP
.nf
!>          TRANS is CHARACTER*1
!>          Specifies the form of the system of equations:
!>          = 'N':  A * X = B  (No transpose)
!>          = 'T':  A**T * X = B  (Transpose)
!>          = 'C':  A**H * X = B  (Conjugate transpose = Transpose)
!> 
.fi
.PP
.br
\fIDIAG\fP 
.PP
.nf
!>          DIAG is CHARACTER*1
!>          = 'N':  A is non-unit triangular;
!>          = 'U':  A is unit triangular\&.
!> 
.fi
.PP
.br
\fIN\fP 
.PP
.nf
!>          N is INTEGER
!>          The order of the matrix A\&.  N >= 0\&.
!> 
.fi
.PP
.br
\fIKD\fP 
.PP
.nf
!>          KD is INTEGER
!>          The number of superdiagonals or subdiagonals of the
!>          triangular band matrix A\&.  KD >= 0\&.
!> 
.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 B and X\&.  NRHS >= 0\&.
!> 
.fi
.PP
.br
\fIAB\fP 
.PP
.nf
!>          AB is REAL array, dimension (LDAB,N)
!>          The upper or lower triangular band matrix A, stored in the
!>          first kd+1 rows of the array\&. The j-th column of A is stored
!>          in the j-th column of the array AB as follows:
!>          if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;
!>          if UPLO = 'L', AB(1+i-j,j)    = A(i,j) for j<=i<=min(n,j+kd)\&.
!>          If DIAG = 'U', the diagonal elements of A are not referenced
!>          and are assumed to be 1\&.
!> 
.fi
.PP
.br
\fILDAB\fP 
.PP
.nf
!>          LDAB is INTEGER
!>          The leading dimension of the array AB\&.  LDAB >= KD+1\&.
!> 
.fi
.PP
.br
\fIB\fP 
.PP
.nf
!>          B is REAL array, dimension (LDB,NRHS)
!>          The right hand side matrix B\&.
!> 
.fi
.PP
.br
\fILDB\fP 
.PP
.nf
!>          LDB is INTEGER
!>          The leading dimension of the array B\&.  LDB >= max(1,N)\&.
!> 
.fi
.PP
.br
\fIX\fP 
.PP
.nf
!>          X is REAL array, dimension (LDX,NRHS)
!>          The solution matrix X\&.
!> 
.fi
.PP
.br
\fILDX\fP 
.PP
.nf
!>          LDX is INTEGER
!>          The leading dimension of the array X\&.  LDX >= max(1,N)\&.
!> 
.fi
.PP
.br
\fIFERR\fP 
.PP
.nf
!>          FERR is REAL array, dimension (NRHS)
!>          The estimated forward error bound for each solution vector
!>          X(j) (the j-th column of the solution matrix X)\&.
!>          If XTRUE is the true solution corresponding to X(j), FERR(j)
!>          is an estimated upper bound for the magnitude of the largest
!>          element in (X(j) - XTRUE) divided by the magnitude of the
!>          largest element in X(j)\&.  The estimate is as reliable as
!>          the estimate for RCOND, and is almost always a slight
!>          overestimate of the true error\&.
!> 
.fi
.PP
.br
\fIBERR\fP 
.PP
.nf
!>          BERR is REAL array, dimension (NRHS)
!>          The componentwise relative backward error of each solution
!>          vector X(j) (i\&.e\&., the smallest relative change in
!>          any element of A or B that makes X(j) an exact solution)\&.
!> 
.fi
.PP
.br
\fIWORK\fP 
.PP
.nf
!>          WORK is REAL array, dimension (3*N)
!> 
.fi
.PP
.br
\fIIWORK\fP 
.PP
.nf
!>          IWORK is INTEGER array, dimension (N)
!> 
.fi
.PP
.br
\fIINFO\fP 
.PP
.nf
!>          INFO is INTEGER
!>          = 0:  successful exit
!>          < 0:  if INFO = -i, the i-th argument had an illegal value
!> 
.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

.PP
Definition at line \fB186\fP of file \fBstbrfs\&.f\fP\&.
.SH "Author"
.PP 
Generated automatically by Doxygen for LAPACK from the source code\&.