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---
:name: cgttrf
:md5sum: 113d7a17d7e56d36b76493ceda5cfa3e
:category: :subroutine
:arguments:
- n:
:type: integer
:intent: input
- dl:
:type: complex
:intent: input/output
:dims:
- n-1
- d:
:type: complex
:intent: input/output
:dims:
- n
- du:
:type: complex
:intent: input/output
:dims:
- n-1
- du2:
:type: complex
:intent: output
:dims:
- n-2
- ipiv:
:type: integer
:intent: output
:dims:
- n
- info:
:type: integer
:intent: output
:substitutions: {}
:fortran_help: " SUBROUTINE CGTTRF( N, DL, D, DU, DU2, IPIV, INFO )\n\n\
* Purpose\n\
* =======\n\
*\n\
* CGTTRF computes an LU factorization of a complex tridiagonal matrix A\n\
* using elimination with partial pivoting and row interchanges.\n\
*\n\
* The factorization has the form\n\
* A = L * U\n\
* where L is a product of permutation and unit lower bidiagonal\n\
* matrices and U is upper triangular with nonzeros in only the main\n\
* diagonal and first two superdiagonals.\n\
*\n\n\
* Arguments\n\
* =========\n\
*\n\
* N (input) INTEGER\n\
* The order of the matrix A.\n\
*\n\
* DL (input/output) COMPLEX array, dimension (N-1)\n\
* On entry, DL must contain the (n-1) sub-diagonal elements of\n\
* A.\n\
*\n\
* On exit, DL is overwritten by the (n-1) multipliers that\n\
* define the matrix L from the LU factorization of A.\n\
*\n\
* D (input/output) COMPLEX array, dimension (N)\n\
* On entry, D must contain the diagonal elements of A.\n\
*\n\
* On exit, D is overwritten by the n diagonal elements of the\n\
* upper triangular matrix U from the LU factorization of A.\n\
*\n\
* DU (input/output) COMPLEX array, dimension (N-1)\n\
* On entry, DU must contain the (n-1) super-diagonal elements\n\
* of A.\n\
*\n\
* On exit, DU is overwritten by the (n-1) elements of the first\n\
* super-diagonal of U.\n\
*\n\
* DU2 (output) COMPLEX array, dimension (N-2)\n\
* On exit, DU2 is overwritten by the (n-2) elements of the\n\
* second super-diagonal of U.\n\
*\n\
* IPIV (output) INTEGER array, dimension (N)\n\
* The pivot indices; for 1 <= i <= n, row i of the matrix was\n\
* interchanged with row IPIV(i). IPIV(i) will always be either\n\
* i or i+1; IPIV(i) = i indicates a row interchange was not\n\
* required.\n\
*\n\
* INFO (output) INTEGER\n\
* = 0: successful exit\n\
* < 0: if INFO = -k, the k-th argument had an illegal value\n\
* > 0: if INFO = k, U(k,k) is exactly zero. The factorization\n\
* has been completed, but the factor U is exactly\n\
* singular, and division by zero will occur if it is used\n\
* to solve a system of equations.\n\
*\n\n\
* =====================================================================\n\
*\n"
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