.TH "TESTING/LIN/zgbt05.f" 3 "Version 3.12.0" "LAPACK" \" -*- nroff -*-
.ad l
.nh
.SH NAME
TESTING/LIN/zgbt05.f
.SH SYNOPSIS
.br
.PP
.SS "Functions/Subroutines"

.in +1c
.ti -1c
.RI "subroutine \fBzgbt05\fP (trans, n, kl, ku, nrhs, ab, ldab, b, ldb, x, ldx, xact, ldxact, ferr, berr, reslts)"
.br
.RI "\fBZGBT05\fP "
.in -1c
.SH "Function/Subroutine Documentation"
.PP 
.SS "subroutine zgbt05 (character trans, integer n, integer kl, integer ku, integer nrhs, complex*16, dimension( ldab, * ) ab, integer ldab, complex*16, dimension( ldb, * ) b, integer ldb, complex*16, dimension( ldx, * ) x, integer ldx, complex*16, dimension( ldxact, * ) xact, integer ldxact, double precision, dimension( * ) ferr, double precision, dimension( * ) berr, double precision, dimension( * ) reslts)"

.PP
\fBZGBT05\fP 
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
!>
!> ZGBT05 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, A**T, or A**H, 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 COMPLEX*16 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 COMPLEX*16 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 COMPLEX*16 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 COMPLEX*16 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
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Definition at line \fB174\fP of file \fBzgbt05\&.f\fP\&.
.SH "Author"
.PP 
Generated automatically by Doxygen for LAPACK from the source code\&.