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CGBRFS

Section: LAPACK routine (version 3.2) (1)
Updated: April 2011
Index

NAME

LAPACK-3 - 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

SYNOPSIS

SUBROUTINE CGBRFS(: TRANS, N, KL, KU, NRHS, AB, LDAB, AFB, LDAFB,IPIV, B, LDB, X, LDX, FERR, BERR, WORK, RWORK,INFO )
: CHARACTERTRANS
: INTEGERINFO, KL, KU, LDAB, LDAFB, LDB, LDX, N, NRHS
: INTEGERIPIV( * )
: REALBERR( * ), FERR( * ), RWORK( * )
: COMPLEXAB( LDAB, * ), AFB( LDAFB, * ), B( LDB, * ),WORK( * ), X( LDX, * )

PURPOSE

CGBRFS improves the computed solution to a system of linearequations when the coefficient matrix is banded, and provideserror bounds and backward error estimates for the solution.

ARGUMENTS

TRANS (input) CHARACTER*1: Specifies the form of the system of equations:

= aqNaq:  A * X = B     (No transpose)

= aqTaq:  A**T * X = B  (Transpose)

= aqCaq:  A**H * X = B  (Conjugate transpose)
N (input) INTEGER: The order of the matrix A. N >= 0.
KL (input) INTEGER: The number of subdiagonals within the band of A. KL >= 0.
KU (input) INTEGER: The number of superdiagonals within the band of A. KU >= 0.
NRHS (input) INTEGER: The number of right hand sides, i.e., the number of columns
of the matrices B and X. NRHS >= 0.
AB (input) COMPLEX 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 (input) INTEGER: The leading dimension of the array AB. LDAB >= KL+KU+1.
AFB (input) COMPLEX array, dimension (LDAFB,N): Details of the LU factorization of the band matrix A, as
computed by CGBTRF. 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 (input) INTEGER: The leading dimension of the array AFB. LDAFB >= 2*KL*KU+1.
IPIV (input) INTEGER array, dimension (N): The pivot indices from CGBTRF; for 1<=i<=N, row i of the
matrix was interchanged with row IPIV(i).
B (input) COMPLEX array, dimension (LDB,NRHS): The right hand side matrix B.
LDB (input) INTEGER: The leading dimension of the array B. LDB >= max(1,N).
X (input/output) COMPLEX array, dimension (LDX,NRHS): On entry, the solution matrix X, as computed by CGBTRS.
On exit, the improved solution matrix X.
LDX (input) INTEGER: The leading dimension of the array X. LDX >= max(1,N).
FERR (output) 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.
BERR (output) 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).
WORK (workspace) COMPLEX array, dimension (2*N)
RWORK (workspace) REAL array, dimension (N)
INFO (output) INTEGER: = 0: successful exit

< 0: if INFO = -i, the i-th argument had an illegal value

PARAMETERS

ITMAX is the maximum number of steps of iterative refinement.

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