SRC/cgttrf.f(3)

💖 NAME 💖

SRC/cgttrf.f is the file this whole page is about, and it lives in the Library Functions Manual — short, sweet, iconic 🎀

✨ SYNOPSIS ✨

Functions/Subroutines

subroutine cgttrf (n, dl, d, du, du2, ipiv, info)

CGTTRF — that's the subroutine label, bestie 💅

🌸 Function/Subroutine Documentation 🌸

Full signature, no cuts 🫶

subroutine cgttrf (integer n, complex, dimension( * ) dl, complex,
     dimension( * ) d, complex, dimension( * ) du, complex, dimension( * )
     du2, integer, dimension( * ) ipiv, integer info)

CGTTRF — yes, same energy, full type-and-dimension reveal ✨

Purpose

CGTTRF computes an LU factorization of a complex 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. That's the whole purpose, and it literally ate 💅🔥

Parameters

• N — N is INTEGER; the order of the matrix A. 🫶
• DL — DL is COMPLEX 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 — D is COMPLEX 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 — DU is COMPLEX 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 — DU2 is COMPLEX array, dimension (N-2).
  • On exit, DU2 is overwritten by the (n-2) elements of the second super-diagonal of U.
• IPIV — 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 — 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. 🚨 This is the serious one, bestie — division by zero is not a vibe.

👑 Author 👑

• Univ. of Tennessee
• Univ. of California Berkeley
• Univ. of Colorado Denver
• NAG Ltd.

Definition at line 123 of file cgttrf.f.

🧚 Author 🧚

Generated automatically by Doxygen for LAPACK from the source code.

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💖 okay that's the whole page, bestie! It's SRC/cgttrf.f(3) from LAPACK Version 3.12.0 — go forth and factorize responsibly 💅✨