cgbrfs-f(3)

cgbrfs.f –

Synopsis

Functions/Subroutines

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

Function/Subroutine Documentation

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

CGBRFS

Purpose:

 CGBRFS 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 is INTEGER
 The order of the matrix A. N >= 0.

 KL is INTEGER
 The number of subdiagonals within the band of A. KL >= 0.

 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 is 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

 LDAB is INTEGER
 The leading dimension of the array AB. LDAB >= KL+KU+1.

AFB

 AFB is 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

 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 CGBTRF; for 1<=i<=N, row i of the
 matrix was interchanged with row IPIV(i).

 B is COMPLEX 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 is COMPLEX array, dimension (LDX,NRHS)
 On entry, the solution matrix X, as computed by CGBTRS.
 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 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

 BERR is 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

 WORK is COMPLEX array, dimension (2*N)

RWORK

 RWORK is REAL 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

Univ. of Colorado Denver

NAG Ltd.

Date:

November 2011

Definition at line 205 of file cgbrfs.f.

Author

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