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

.in +1c
.ti -1c
.RI "subroutine \fBzgbrfs\fP (trans, n, kl, ku, nrhs, ab, ldab, afb, ldafb, ipiv, b, ldb, x, ldx, ferr, berr, work, rwork, info)"
.br
.RI "\fBZGBRFS\fP "
.in -1c
.SH "Function/Subroutine Documentation"
.PP 
.SS "subroutine zgbrfs (character trans, integer n, integer kl, integer ku, integer nrhs, complex*16, dimension( ldab, * ) ab, integer ldab, complex*16, dimension( ldafb, * ) afb, integer ldafb, integer, dimension( * ) ipiv, complex*16, dimension( ldb, * ) b, integer ldb, complex*16, dimension( ldx, * ) x, integer ldx, double precision, dimension( * ) ferr, double precision, dimension( * ) berr, complex*16, dimension( * ) work, double precision, dimension( * ) rwork, integer info)"

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

.PP
.nf
!>
!> ZGBRFS improves the computed solution to a system of linear
!> equations when the coefficient matrix is banded, and provides
!> error bounds and backward error estimates for the solution\&.
!> 
.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)
!> 
.fi
.PP
.br
\fIN\fP 
.PP
.nf
!>          N is INTEGER
!>          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 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 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
\fIAFB\fP 
.PP
.nf
!>          AFB is COMPLEX*16 array, dimension (LDAFB,N)
!>          Details of the LU factorization of the band matrix A, as
!>          computed by ZGBTRF\&.  U is stored as an upper triangular band
!>          matrix with KL+KU superdiagonals in rows 1 to KL+KU+1, and
!>          the multipliers used during the factorization are stored in
!>          rows KL+KU+2 to 2*KL+KU+1\&.
!> 
.fi
.PP
.br
\fILDAFB\fP 
.PP
.nf
!>          LDAFB is INTEGER
!>          The leading dimension of the array AFB\&.  LDAFB >= 2*KL*KU+1\&.
!> 
.fi
.PP
.br
\fIIPIV\fP 
.PP
.nf
!>          IPIV is INTEGER array, dimension (N)
!>          The pivot indices from ZGBTRF; for 1<=i<=N, row i of the
!>          matrix was interchanged with row IPIV(i)\&.
!> 
.fi
.PP
.br
\fIB\fP 
.PP
.nf
!>          B is COMPLEX*16 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 COMPLEX*16 array, dimension (LDX,NRHS)
!>          On entry, the solution matrix X, as computed by ZGBTRS\&.
!>          On exit, the improved 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 DOUBLE PRECISION 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 DOUBLE PRECISION 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 COMPLEX*16 array, dimension (2*N)
!> 
.fi
.PP
.br
\fIRWORK\fP 
.PP
.nf
!>          RWORK is DOUBLE PRECISION 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
\fBInternal Parameters:\fP
.RS 4

.PP
.nf
!>  ITMAX is the maximum number of steps of iterative refinement\&.
!> 
.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 \fB203\fP of file \fBzgbrfs\&.f\fP\&.
.SH "Author"
.PP 
Generated automatically by Doxygen for LAPACK from the source code\&.