ctrrfs (l)  Linux Manuals
ctrrfs: provides error bounds and backward error estimates for the solution to a system of linear equations with a triangular coefficient matrix
Command to display ctrrfs
manual in Linux: $ man l ctrrfs
NAME
CTRRFS  provides error bounds and backward error estimates for the solution to a system of linear equations with a triangular coefficient matrix
SYNOPSIS
 SUBROUTINE CTRRFS(

UPLO, TRANS, DIAG, N, NRHS, A, LDA, B, LDB, X,
LDX, FERR, BERR, WORK, RWORK, INFO )

CHARACTER
DIAG, TRANS, UPLO

INTEGER
INFO, LDA, LDB, LDX, N, NRHS

REAL
BERR( * ), FERR( * ), RWORK( * )

COMPLEX
A( LDA, * ), B( LDB, * ), WORK( * ),
X( LDX, * )
PURPOSE
CTRRFS provides error bounds and backward error estimates for the
solution to a system of linear equations with a triangular
coefficient matrix.
The solution matrix X must be computed by CTRTRS or some other
means before entering this routine. CTRRFS 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 nonunit triangular;
= aqUaq: A is unit triangular.
 N (input) INTEGER

The order of the matrix A. N >= 0.
 NRHS (input) INTEGER

The number of right hand sides, i.e., the number of columns
of the matrices B and X. NRHS >= 0.
 A (input) COMPLEX array, dimension (LDA,N)

The triangular matrix A. If UPLO = aqUaq, the leading NbyN
upper triangular part of the array A contains the upper
triangular matrix, and the strictly lower triangular part of
A is not referenced. If UPLO = aqLaq, the leading NbyN lower
triangular part of the array A contains the lower triangular
matrix, and the strictly upper triangular part of A is not
referenced. If DIAG = aqUaq, the diagonal elements of A are
also not referenced and are assumed to be 1.
 LDA (input) INTEGER

The leading dimension of the array A. LDA >= max(1,N).
 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 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) 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 ith argument had an illegal value
Pages related to ctrrfs
 ctrrfs (3)
 ctrcon (l)  estimates the reciprocal of the condition number of a triangular matrix A, in either the 1norm or the infinitynorm
 ctrevc (l)  computes some or all of the right and/or left eigenvectors of a complex upper triangular matrix T
 ctrexc (l)  reorders the Schur factorization of a complex matrix A = Q*T*Q**H, so that the diagonal element of T with row index IFST is moved to row ILST
 ctrmm (l)  performs one of the matrixmatrix operations B := alpha*op( A )*B, or B := alpha*B*op( A ) where alpha is a scalar, B is an m by n matrix, A is a unit, or nonunit, upper or lower triangular matrix and op( A ) is one of op( A ) = A or op( A ) = Aaq or op( A ) = conjg( Aaq )
 ctrmv (l)  performs one of the matrixvector operations x := A*x, or x := Aaq*x, or x := conjg( Aaq )*x,
 ctrsen (l)  reorders the Schur factorization of a complex matrix A = Q*T*Q**H, so that a selected cluster of eigenvalues appears in the leading positions on the diagonal of the upper triangular matrix T, and the leading columns of Q form an orthonormal basis of the corresponding right invariant subspace
 ctrsm (l)  solves one of the matrix equations op( A )*X = alpha*B, or X*op( A ) = alpha*B,