ctbrfs-f(3)

ctbrfs.f –

Synopsis

Functions/Subroutines

subroutine ctbrfs (UPLO, TRANS, DIAG, N, KD, NRHS, AB, LDAB, B, LDB, X, LDX, FERR, BERR, WORK, RWORK, INFO)
CTBRFS

Function/Subroutine Documentation

subroutine ctbrfs (characterUPLO, characterTRANS, characterDIAG, integerN, integerKD, integerNRHS, complex, dimension( ldab, * )AB, integerLDAB, complex, dimension( ldb, * )B, integerLDB, complex, dimension( ldx, * )X, integerLDX, real, dimension( * )FERR, real, dimension( * )BERR, complex, dimension( * )WORK, real, dimension( * )RWORK, integerINFO)

CTBRFS

Purpose:

 CTBRFS 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 CTBTRS or some other
 means before entering this routine. CTBRFS 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)

DIAG

 DIAG is CHARACTER*1
 = 'N': A is non-unit triangular;
 = 'U': A is unit triangular.

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

 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 is COMPLEX 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 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)
 The 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

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

November 2011

Definition at line 188 of file ctbrfs.f.

Author

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