DGBRFS (3) Linux Manual Page

dgbrfs.f –

Synopsis

Functions/Subroutines

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

Function/Subroutine Documentation

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

DGBRFS

Purpose:

 DGBRFS 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 = 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 DOUBLE PRECISION 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 DOUBLE PRECISION array, dimension (LDAFB,N)

 Details of the LU factorization of the band matrix A, as

 computed by DGBTRF. 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 DGBTRF; for 1<=i<=N, row i of the

 matrix was interchanged with row IPIV(i).

B

 B is DOUBLE PRECISION 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 DOUBLE PRECISION array, dimension (LDX,NRHS)

 On entry, the solution matrix X, as computed by DGBTRS.

 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 DOUBLE PRECISION array, dimension (3*N)

IWORK

 IWORK is INTEGER 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 204 of file dgbrfs.f.

Author

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