GTCON - 5.2 English - 68552

AOCL API Guide (68552)

Document ID
68552
Release Date
2025-12-29
Version
5.2 English
template<typename T>
void gtcon(char *norm, integer *n, T *dl, T *d, T *du, T *du2, integer *ipiv, T *anorm, T *rcond, T *work, integer *iwork, integer *info)#

GTCON estimates the reciprocal of the condition number of a real tridiagonal matrix A.

Purpose:

  GTCON estimates the reciprocal of the condition number of a real
  tridiagonal matrix A using the LU factorization as computed by
  SGTTRF.

  An estimate is obtained for norm(inv(A)), and the reciprocal of the
  condition number is computed as RCOND = 1 / (ANORM * norm(inv(A))).
Parameters:
  • NORM[in]

    NORM is CHARACTER*1

    Specifies whether the 1-norm condition number or the infinity-norm condition number is required:

    = ‘1’ or ‘O’: 1-norm;

    = ‘I’: Infinity-norm.

  • N[in]

    N is INTEGER

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

  • DL[in]

    DL is REAL array, dimension (N-1)

    The (n-1) multipliers that define the matrix L from the LU factorization of A as computed by SGTTRF.

  • D[in]

    D is REAL array, dimension (N)

    The n diagonal elements of the upper triangular matrix U from the LU factorization of A.

  • DU[in]

    DU is REAL array, dimension (N-1)

    The (n-1) elements of the first superdiagonal of U.

  • DU2[in]

    DU2 is REAL array, dimension (N-2)

    The (n-2) elements of the second superdiagonal of U.

  • IPIV[in]

    IPIV is INTEGER array, dimension (N)

    The pivot indices; for 1 <= i <= n, row i of the matrix was interchanged with row IPIV(i). IPIV(i) will always be either i or i+1; IPIV(i) = i indicates a row interchange was not required.

  • ANORM[in]

    ANORM is REAL

    If NORM = ‘1’ or ‘O’, the 1-norm of the original matrix A.

    If NORM = ‘I’, the infinity-norm of the original matrix A.
  • RCOND[out]

    RCOND is REAL

    The reciprocal of the condition number of the matrix A, computed as RCOND = 1/(ANORM * AINVNM), where AINVNM is an estimate of the 1-norm of inv(A) computed in this routine.

  • WORK[out] WORK is REAL array, dimension (2*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
template<typename T, typename Ta>
void gtcon(char *norm, integer *n, T *dl, T *d, T *du, T *du2, integer *ipiv, Ta *anorm, Ta *rcond, T *work, integer *info)#