.TH "TESTING/LIN/dgbt05.f" 3 "Version 3.12.0" "LAPACK" \" -*- nroff -*-
.ad l
.nh
.SH NAME
TESTING/LIN/dgbt05.f
.SH SYNOPSIS
.br
.PP
.SS "Functions/Subroutines"

.in +1c
.ti -1c
.RI "subroutine \fBdgbt05\fP (trans, n, kl, ku, nrhs, ab, ldab, b, ldb, x, ldx, xact, ldxact, ferr, berr, reslts)"
.br
.RI "\fBDGBT05\fP "
.in -1c
.SH "Function/Subroutine Documentation"
.PP 
.SS "subroutine dgbt05 (character trans, integer n, integer kl, integer ku, integer nrhs, double precision, dimension( ldab, * ) ab, integer ldab, double precision, dimension( ldb, * ) b, integer ldb, double precision, dimension( ldx, * ) x, integer ldx, double precision, dimension( ldxact, * ) xact, integer ldxact, double precision, dimension( * ) ferr, double precision, dimension( * ) berr, double precision, dimension( * ) reslts)"

.PP
\fBDGBT05\fP 
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
 DGBT05 tests the error bounds from iterative refinement for the
 computed solution to a system of equations op(A)*X = B, where A is a
 general band matrix of order n with kl subdiagonals and ku
 superdiagonals and op(A) = A or A**T, depending on TRANS\&.

 RESLTS(1) = test of the error bound
           = norm(X - XACT) / ( norm(X) * FERR )

 A large value is returned if this ratio is not less than one\&.

 RESLTS(2) = residual from the iterative refinement routine
           = the maximum of BERR / ( NZ*EPS + (*) ), where
             (*) = NZ*UNFL / (min_i (abs(op(A))*abs(X) +abs(b))_i )
             and NZ = max\&. number of nonzeros in any row of A, plus 1
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\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
\fIN\fP 
.PP
.nf
          N is INTEGER
          The number of rows of the matrices X, B, and XACT, and the
          order of the matrix A\&.  N >= 0\&.
.fi
.PP
.br
\fIKL\fP 
.PP
.nf
          KL is INTEGER
          The number of subdiagonals within the band of A\&.  KL >= 0\&.
.fi
.PP
.br
\fIKU\fP 
.PP
.nf
          KU is INTEGER
          The number of superdiagonals within the band of A\&.  KU >= 0\&.
.fi
.PP
.br
\fINRHS\fP 
.PP
.nf
          NRHS is INTEGER
          The number of columns of the matrices X, B, and XACT\&.
          NRHS >= 0\&.
.fi
.PP
.br
\fIAB\fP 
.PP
.nf
          AB is DOUBLE PRECISION array, dimension (LDAB,N)
          The original band matrix A, stored in rows 1 to KL+KU+1\&.
          The j-th column of A is stored in the j-th column of the
          array AB as follows:
          AB(ku+1+i-j,j) = A(i,j) for max(1,j-ku)<=i<=min(n,j+kl)\&.
.fi
.PP
.br
\fILDAB\fP 
.PP
.nf
          LDAB is INTEGER
          The leading dimension of the array AB\&.  LDAB >= KL+KU+1\&.
.fi
.PP
.br
\fIB\fP 
.PP
.nf
          B is DOUBLE PRECISION array, dimension (LDB,NRHS)
          The right hand side vectors for the system of linear
          equations\&.
.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 DOUBLE PRECISION array, dimension (LDX,NRHS)
          The computed solution vectors\&.  Each vector is stored as a
          column of the 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
\fIXACT\fP 
.PP
.nf
          XACT is DOUBLE PRECISION array, dimension (LDX,NRHS)
          The exact solution vectors\&.  Each vector is stored as a
          column of the matrix XACT\&.
.fi
.PP
.br
\fILDXACT\fP 
.PP
.nf
          LDXACT is INTEGER
          The leading dimension of the array XACT\&.  LDXACT >= max(1,N)\&.
.fi
.PP
.br
\fIFERR\fP 
.PP
.nf
          FERR is DOUBLE PRECISION array, dimension (NRHS)
          The estimated forward error bounds for each solution vector
          X\&.  If XTRUE is the true solution, FERR bounds the magnitude
          of the largest entry in (X - XTRUE) divided by the magnitude
          of the largest entry in X\&.
.fi
.PP
.br
\fIBERR\fP 
.PP
.nf
          BERR is DOUBLE PRECISION array, dimension (NRHS)
          The componentwise relative backward error of each solution
          vector (i\&.e\&., the smallest relative change in any entry of A
          or B that makes X an exact solution)\&.
.fi
.PP
.br
\fIRESLTS\fP 
.PP
.nf
          RESLTS is DOUBLE PRECISION array, dimension (2)
          The maximum over the NRHS solution vectors of the ratios:
          RESLTS(1) = norm(X - XACT) / ( norm(X) * FERR )
          RESLTS(2) = BERR / ( NZ*EPS + (*) )
.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 \fB174\fP of file \fBdgbt05\&.f\fP\&.
.SH "Author"
.PP 
Generated automatically by Doxygen for LAPACK from the source code\&.