SRC/stbrfs.f(3) | Library Functions Manual | SRC/stbrfs.f(3) |
NAME
SRC/stbrfs.f
SYNOPSIS
Functions/Subroutines
subroutine stbrfs (uplo, trans, diag, n, kd, nrhs, ab,
ldab, b, ldb, x, ldx, ferr, berr, work, iwork, info)
STBRFS
Function/Subroutine Documentation
subroutine stbrfs (character uplo, character trans, character diag, integer n, integer kd, integer nrhs, real, dimension( ldab, * ) ab, integer ldab, real, dimension( ldb, * ) b, integer ldb, real, dimension( ldx, * ) x, integer ldx, real, dimension( * ) ferr, real, dimension( * ) berr, real, dimension( * ) work, integer, dimension( * ) iwork, integer info)
STBRFS
Purpose:
STBRFS 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 STBTRS or some other means before entering this routine. STBRFS 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 REAL 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 REAL 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 REAL 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 REAL 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.
Definition at line 186 of file stbrfs.f.
Author
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