GERFS - 5.2 English - 68552

AOCL API Guide (68552)

Document ID
68552
Release Date
2025-12-29
Version
5.2 English
template<typename T>
void gerfs(char *trans, integer *n, integer *nrhs, T *a, integer *lda, T *af, integer *ldaf, integer *ipiv, T *b, integer *ldb, T *x, integer *ldx, T *ferr, T *berr, T *work, integer *iwork, integer *info)#

GERFS improves the computed solution to a system of linear equations

and provides error bounds and backward error estimates for the solution.

Purpose:

  GERFS improves the computed solution to a system of linear
  equations and provides error bounds and backward error estimates for
  the solution.
Parameters:
  • 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)
  • N[in]

    N is INTEGER

    The order of the matrix A. N >= 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.

  • A[in]

    A is REAL array, dimension (LDA,N)

    The original N-by-N matrix A.

  • LDA[in]

    LDA is INTEGER

    The leading dimension of the array A. LDA >= fla_max(1,N).

  • AF[in]

    AF is REAL array, dimension (LDAF,N)

    The factors L and U from the factorization A = P*L*U as computed by GETRF.

  • LDAF[in]

    LDAF is INTEGER

    The leading dimension of the array AF. LDAF >= fla_max(1,N).

  • IPIV[in]

    IPIV is INTEGER array, dimension (N)

    The pivot indices from GETRF; for 1<=i<=N, row i of the matrix was interchanged with row IPIV(i).

  • 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[inout]

    X is REAL array, dimension (LDX,NRHS)

    On entry, the solution matrix X, as computed by GETRS. On exit, the improved 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 COMPLEX array, dimension (2*N)

  • RWORK[out] RWORK is REAL array, dimension (N)

  • INFO[out]

    INFO is INTEGER

    = 0: successful exit

    < 0: if INFO = -i, the i-th argument had an illegal value
template<typename T, typename Ta>
void gerfs(char *trans, integer *n, integer *nrhs, T *a, integer *lda, T *af, integer *ldaf, integer *ipiv, T *b, integer *ldb, T *x, integer *ldx, Ta *ferr, Ta *berr, T *work, Ta *rwork, integer *info)#