GTTRF - 5.2 English - 68552

AOCL API Guide (68552)

Document ID
68552
Release Date
2025-12-29
Version
5.2 English
template<typename T>
void gttrf(integer *n, T *dl, T *d, T *du, T *du2, integer *ipiv, integer *info)#

GTTRF computes an LU factorization of a real tridiagonal matrix A.

Purpose:

    GTTRF computes an LU factorization of a real tridiagonal matrix A
    using elimination with partial pivoting and row interchanges.
    The factorization has the form
       A = L * U
    where L is a product of permutation and unit lower bidiagonal
    matrices and U is upper triangular with nonzeros in only the main
    diagonal and first two superdiagonals.
Parameters:
  • N[in]

    N is INTEGER

    The order of the matrix A.

  • DL[inout]

    DL is REAL array, dimension (N-1)

    On entry, DL must contain the (n-1) sub-diagonal elements of A.

    On exit, DL is overwritten by the (n-1) multipliers that define the matrix L from the LU factorization of A.
  • D[inout]

    D is REAL array, dimension (N)

    On entry, D must contain the diagonal elements of A.

    On exit, D is overwritten by the n diagonal elements of the upper triangular matrix U from the LU factorization of A.
  • DU[inout]

    DU is REAL array, dimension (N-1)

    On entry, DU must contain the (n-1) super-diagonal elements of A.

    On exit, DU is overwritten by the (n-1) elements of the first super-diagonal of U.
  • DU2[out]

    DU2 is REAL array, dimension (N-2)

    On exit, DU2 is overwritten by the (n-2) elements of the second super-diagonal of U.

  • IPIV[out]

    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.

  • INFO[out]

    INFO is INTEGER

    = 0: successful exit

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

    > 0: if INFO = k, U(k,k) is exactly zero. The factorization has been completed, but the factor U is exactly singular, and division by zero will occur if it is used to solve a system of equations.