dtbrfs (l)  Linux Manuals
dtbrfs: 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 dtbrfs
manual in Linux: $ man l dtbrfs
NAME
DTBRFS  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

= 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 = Transpose)
 DIAG (input) CHARACTER*1

= aqNaq: A is nonunit 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) 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 jth column of A is stored
in the jth column of the array AB as follows:
if UPLO = aqUaq, AB(kd+1+ij,j) = A(i,j) for max(1,jkd)<=i<=j;
if UPLO = aqLaq, AB(1+ij,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) 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 jth 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 ith argument had an illegal value
Pages related to dtbrfs
 dtbrfs (3)
 dtbcon (l)  estimates the reciprocal of the condition number of a triangular band matrix A, in either the 1norm or the infinitynorm
 dtbmv (l)  performs one of the matrixvector operations x := A*x, or x := Aaq*x,
 dtbsv (l)  solves one of the systems of equations A*x = b, or Aaq*x = b,
 dtbtrs (l)  solves a triangular system of the form A * X = B or A**T * X = B,
 dtfsm (l)  3 BLAS like routine for A in RFP Format
 dtftri (l)  computes the inverse of a triangular matrix A stored in RFP format