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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.