PTRFS - 5.2 English - 68552

AOCL API Guide (68552)

Document ID
68552
Release Date
2025-12-29
Version
5.2 English
template<typename T>
void ptrfs(integer *n, integer *nrhs, T *d, T *e, T *df, T *ef, T *b, integer *ldb, T *x, integer *ldx, T *ferr, T *berr, T *work, integer *info)#

PTRFS improves the computed solution to a system of linear equations.

Purpose:

 PTRFS improves the computed solution to a system of linear
 equations when the coefficient matrix is symmetric positive definite
 and tridiagonal, and provides error bounds and backward error
 estimates for the solution.
Parameters:
  • 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 matrix B. NRHS >= 0.

  • D[in]

    D is REAL array, dimension (N)

    The n diagonal elements of the tridiagonal matrix A.

  • E[in]

    E is REAL array, dimension (N-1)

    The (n-1) subdiagonal elements of the tridiagonal matrix A.

  • DF[in]

    DF is REAL array, dimension (N)

    The n diagonal elements of the diagonal matrix D from the factorization computed by SPTTRF.

  • EF[in]

    EF is REAL array, dimension (N-1)

    The (n-1) subdiagonal elements of the unit bidiagonal factor L from the factorization computed by SPTTRF.

  • 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 SPTTRS. 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 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).
  • 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 (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 ptrfs(char *uplo, integer *n, integer *nrhs, Ta *d, T *e, Ta *df, T *ef, T *b, integer *ldb, T *x, integer *ldx, Ta *ferr, Ta *berr, T *work, Ta *rwork, integer *info)#