---
name: "ztbrfs"
section: "3lapack"
platform: "linux"
package: "liblapack-doc"
version: "3.2.1-8"
release: "Debian 6.0 (Squeeze)"
platforms: ["linux"]
url: "https://new.carta.tech/ztbrfs/3lapack"
---

# ztbrfs(3lapack)

provides error bounds and backward error estimates for the solution to a system of linear equations with a triangular band coefficient matrix

## NAME

ZTBRFS - provides error bounds and backward error estimates for the solution to a system of linear equations with a triangular band coefficient matrix

## SYNOPSIS

- SUBROUTINE ZTBRFS(

  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

- DOUBLE

  PRECISION BERR( \* ), FERR( \* ), RWORK( \* )

- COMPLEX\*16

  AB( LDAB, \* ), B( LDB, \* ), WORK( \* ), X( LDX, \* )

## PURPOSE

ZTBRFS 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 ZTBTRS or some other means before entering this routine.  ZTBRFS 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)

- 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) COMPLEX\*16 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) COMPLEX\*16 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\*16 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) COMPLEX\*16 array, dimension (2\*N)

  - RWORK (workspace) DOUBLE PRECISION array, dimension (N)

  - INFO (output) INTEGER

  \= 0:  successful exit\
   \< 0:  if INFO = -i, the i-th argument had an illegal value