ctbrfs (l) - Linux Manuals
ctbrfs: provides error bounds and backward error estimates for the solution to a system of linear equations with a triangular band coefficient matrix
Command to display ctbrfs
manual in Linux: $ man l ctbrfs
NAME
CTBRFS - provides error bounds and backward error estimates for the solution to a system of linear equations with a triangular band coefficient matrix
SYNOPSIS
- SUBROUTINE CTBRFS(
-
UPLO, TRANS, DIAG, N, KD, NRHS, AB, LDAB, B,
LDB, X, LDX, FERR, BERR, WORK, RWORK, INFO )
-
CHARACTER
DIAG, TRANS, UPLO
-
INTEGER
INFO, KD, LDAB, LDB, LDX, N, NRHS
-
REAL
BERR( * ), FERR( * ), RWORK( * )
-
COMPLEX
AB( LDAB, * ), B( LDB, * ), WORK( * ),
X( LDX, * )
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.
ARGUMENTS
- UPLO (input) CHARACTER*1
-
= aqUaq: A is upper triangular;
= aqLaq: A is lower triangular.
- TRANS (input) CHARACTER*1
-
Specifies the form of the system of equations:
= aqNaq: A * X = B (No transpose)
= aqTaq: A**T * X = B (Transpose)
= aqCaq: A**H * X = B (Conjugate transpose)
- DIAG (input) CHARACTER*1
-
= aqNaq: A is non-unit triangular;
= aqUaq: 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) 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 = aqUaq, AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;
if UPLO = aqLaq, AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+kd).
If DIAG = aqUaq, 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) COMPLEX 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) COMPLEX array, dimension (LDX,NRHS)
-
The solution matrix X.
- LDX (input) INTEGER
-
The leading dimension of the array X. LDX >= max(1,N).
- FERR (output) 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 (output) 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 (workspace) COMPLEX array, dimension (2*N)
-
- RWORK (workspace) REAL array, dimension (N)
-
- INFO (output) INTEGER
-
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
Pages related to ctbrfs
- ctbrfs (3)
- ctbcon (l) - estimates the reciprocal of the condition number of a triangular band matrix A, in either the 1-norm or the infinity-norm
- ctbmv (l) - performs one of the matrix-vector operations x := A*x, or x := Aaq*x, or x := conjg( Aaq )*x,
- ctbsv (l) - solves one of the systems of equations A*x = b, or Aaq*x = b, or conjg( Aaq )*x = b,
- ctbtrs (l) - solves a triangular system of the form A * X = B, A**T * X = B, or A**H * X = B,
- ctfsm (l) - 3 BLAS like routine for A in RFP Format
- ctftri (l) - computes the inverse of a triangular matrix A stored in RFP format