TBRFS - 5.2 English - 68552

TBRFS provides error bounds and backward error estimates for the

solution to a system of linear equations.

Purpose:

  TBRFS 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 STBTRS or some other
  means before entering this routine.  STBRFS does not do iterative
  refinement because doing so cannot improve the backward error.

Parameters:

• UPLO – [in]

  UPLO is CHARACTER*1

  = ‘U’: A is upper triangular;

  = ‘L’: A is lower triangular.

• TRANS – [in]

  TRANS is 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 – [in]

  DIAG is CHARACTER*1

  = ‘N’: A is non-unit triangular;

  = ‘U’: A is unit triangular.

• N – [in]

  N is INTEGER

  The order of the matrix A. N >= 0.

• KD – [in]

  KD is INTEGER

  The number of superdiagonals or subdiagonals of the triangular band matrix A. KD >= 0.

• NRHS – [in]

  NRHS is INTEGER

  The number of right hand sides, i.e., the number of columns of the matrices B and X. NRHS >= 0.

• AB – [in]

  AB is REAL 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 fla_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 – [in]

  LDAB is INTEGER

  The leading dimension of the array AB. LDAB >= KD+1.

• B – [in]

  B is REAL array, dimension (LDB,NRHS)

  The right hand side matrix B.

• LDB – [in]

  LDB is INTEGER

  The leading dimension of the array B. LDB >= fla_max(1,N).

• X – [in]

  X is REAL array, dimension (LDX,NRHS)

  The solution matrix X.

• LDX – [in]

  LDX is INTEGER

  The leading dimension of the array X. LDX >= fla_max(1,N).

• FERR – [out]

  FERR is 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 – [out]

  BERR is 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 – [out] WORK is REAL array, dimension (3*N)

• IWORK – [out] IWORK is INTEGER array, dimension (N)

• INFO – [out]

  INFO is INTEGER

  = 0: successful exit

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