DTBRFS(3)
provides error bounds and backward error estimates for the solution to a system of linear equations with a triangular band coefficient matrix
SYNOPSIS
- SUBROUTINE DTBRFS(
-
UPLO, TRANS, DIAG, N, KD, NRHS, AB, LDAB, B,
LDB, X, LDX, FERR, BERR, WORK, IWORK, INFO )
-
CHARACTER
DIAG, TRANS, UPLO
-
INTEGER
INFO, KD, LDAB, LDB, LDX, N, NRHS
-
INTEGER
IWORK( * )
-
DOUBLE
PRECISION AB( LDAB, * ), B( LDB, * ), BERR( * ),
FERR( * ), WORK( * ), X( LDX, * )
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.
ARGUMENTS
- UPLO (input) CHARACTER*1
-
= 'U': A is upper triangular;
= 'L': A is lower triangular.
- TRANS (input) 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 (input) CHARACTER*1
-
= 'N': A is non-unit triangular;
= 'U': A is unit triangular.
- N (input) INTEGER
-
The order of the matrix A. N >= 0.
- KD (input) INTEGER
-
The number of superdiagonals or subdiagonals of the
triangular band matrix A. KD >= 0.
- NRHS (input) INTEGER
-
The number of right hand sides, i.e., the number of columns
of the matrices B and X. NRHS >= 0.
- AB (input) 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 (input) INTEGER
-
The leading dimension of the array AB. LDAB >= KD+1.
- B (input) DOUBLE PRECISION array, dimension (LDB,NRHS)
-
The right hand side matrix B.
- LDB (input) INTEGER
-
The leading dimension of the array B. LDB >= max(1,N).
- X (input) DOUBLE PRECISION array, dimension (LDX,NRHS)
-
The solution matrix X.
- LDX (input) INTEGER
-
The leading dimension of the array X. LDX >= max(1,N).
- FERR (output) 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 (output) 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 (workspace) DOUBLE PRECISION array, dimension (3*N)
-
- IWORK (workspace) INTEGER array, dimension (N)
-
- INFO (output) INTEGER
-
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value