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 zgbrfs.f(3) LAPACK zgbrfs.f(3)

zgbrfs.f -

SYNOPSIS

Functions/Subroutines

subroutine zgbrfs (TRANS, N, KL, KU, NRHS, AB, LDAB, AFB, LDAFB, IPIV, B, LDB, X, LDX, FERR, BERR, WORK, RWORK, INFO)

ZGBRFS

Function/Subroutine Documentation

subroutine zgbrfs (characterTRANS, integerN, integerKL, integerKU, integerNRHS, complex*16, dimension( ldab, * )AB, integerLDAB, complex*16, dimension( ldafb, * )AFB, integerLDAFB, integer, dimension( * )IPIV, complex*16, dimension( ldb, * )B, integerLDB, complex*16, dimension( ldx, * )X, integerLDX, double precision, dimension( * )FERR, double precision, dimension( * )BERR, complex*16, dimension( * )WORK, double precision, dimension( * )RWORK, integerINFO)

ZGBRFS
Purpose:
``` 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.
```
Parameters:
TRANS
```          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)
```
N
```          N is INTEGER
The order of the matrix A.  N >= 0.
```
KL
```          KL is INTEGER
The number of subdiagonals within the band of A.  KL >= 0.
```
KU
```          KU is INTEGER
The number of superdiagonals within the band of A.  KU >= 0.
```
NRHS
```          NRHS is INTEGER
The number of right hand sides, i.e., the number of columns
of the matrices B and X.  NRHS >= 0.
```
AB
```          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).
```
LDAB
```          LDAB is INTEGER
The leading dimension of the array AB.  LDAB >= KL+KU+1.
```
AFB
```          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.
```
LDAFB
```          LDAFB is INTEGER
The leading dimension of the array AFB.  LDAFB >= 2*KL*KU+1.
```
IPIV
```          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).
```
B
```          B is COMPLEX*16 array, dimension (LDB,NRHS)
The right hand side matrix B.
```
LDB
```          LDB is INTEGER
The leading dimension of the array B.  LDB >= max(1,N).
```
X
```          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.
```
LDX
```          LDX is INTEGER
The leading dimension of the array X.  LDX >= max(1,N).
```
FERR
```          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.
```
BERR
```          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).
```
WORK
```          WORK is COMPLEX*16 array, dimension (2*N)
```
RWORK
```          RWORK is DOUBLE PRECISION array, dimension (N)
```
INFO
```          INFO is INTEGER
= 0:  successful exit
< 0:  if INFO = -i, the i-th argument had an illegal value
```
Internal Parameters:
```  ITMAX is the maximum number of steps of iterative refinement.
```
Author:
Univ. of Tennessee
Univ. of California Berkeley
NAG Ltd.
Date:
November 2011
Definition at line 205 of file zgbrfs.f.

Author

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 Sat Nov 16 2013 Version 3.4.2

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