dtbrfs.f (3) Linux Manual Page

dtbrfs.f –

Synopsis

Functions/Subroutines

subroutine dtbrfs (UPLO, TRANS, DIAG, N, KD, NRHS, AB, LDAB, B, LDB, X, LDX, FERR, BERR, WORK, IWORK, INFO)
DTBRFS

Function/Subroutine Documentation

subroutine dtbrfs (characterUPLO, characterTRANS, characterDIAG, integerN, integerKD, integerNRHS, double precision, dimension( ldab, * )AB, integerLDAB, 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)

DTBRFS

Purpose:

 DTBRFS provides error bounds and backward error estimates for the

 solution to a system of linear equations with a triangular band

 coefficient matrix.

 The solution matrix X must be computed by DTBTRS or some other

 means before entering this routine. DTBRFS does not do iterative

 refinement because doing so cannot improve the backward error.

 

Parameters:

UPLO

 UPLO is CHARACTER*1

 = ‘U’: A is upper triangular;

 = ‘L’: A is lower triangular.

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)

DIAG

 DIAG is CHARACTER*1

 = ‘N’: A is non-unit triangular;

 = ‘U’: A is unit triangular.

N

 N is INTEGER

 The order of the matrix A. N >= 0.

KD

 KD is INTEGER

 The number of superdiagonals or subdiagonals of the

 triangular band matrix A. KD >= 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 upper or lower triangular band matrix A, stored in the

 first kd+1 rows of the array. The j-th column of A is stored

 in the j-th column of the array AB as follows:

 if UPLO = ‘U’, AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;

 if UPLO = ‘L’, AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+kd).

 If DIAG = ‘U’, the diagonal elements of A are not referenced

 and are assumed to be 1.

LDAB

 LDAB is INTEGER

 The leading dimension of the array AB. LDAB >= KD+1.

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)

 The 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

 

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

November 2011

Definition at line 188 of file dtbrfs.f.

Author

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