zgetrf.f(3)

💅 zgetrf.f(3) — LAPACK, bestie 💅

okay so this is the manual page for zgetrf.f(3) from LAPACK, and we are about to get into some crunchy LU factorization lore. no cap, it's giving iconic numerical linear algebra. ✨

💖 NAME 💖

zgetrf.f — the Crout Level 3 BLAS variant of the LU factorization algorithm. That's the whole vibe: a LAPACK subroutine page for zgetrf, and it's lowkey famous in the solve systems of equations friend group. 🫶

🌸 SYNOPSIS 🌸

Functions/Subroutines

• subroutine zgetrf (M, N, A, LDA, IPIV, INFO) — ZGETRF VARIANT: Crout Level 3 BLAS version of the algorithm.

🦋 Function/Subroutine Documentation 🦋

subroutine zgetrf (integer M, integer N, complex*16, dimension( lda, * ) A,
    integer LDA, integer, dimension( * ) IPIV, integer INFO)

ZGETRF VARIANT: Crout Level 3 BLAS version of the algorithm. 💅

Purpose:

ZGETRF computes an LU factorization of a general M-by-N matrix A using partial pivoting with row interchanges.

The factorization has the form A = P * L * U, where P is a permutation matrix, L is lower triangular with unit diagonal elements (lower trapezoidal if m > n), and U is upper triangular (upper trapezoidal if m < n).

This is the Crout Level 3 BLAS version of the algorithm. periodt. 🔥

Parameters:

• M — M is INTEGER; the number of rows of the matrix A. M >= 0.
• N — N is INTEGER; the number of columns of the matrix A. N >= 0.
• A — A is COMPLEX*16 array, dimension (LDA,N); on entry, the M-by-N matrix to be factored. On exit, the factors L and U from the factorization A = P*L*U; the unit diagonal elements of L are not stored.
• LDA — LDA is INTEGER; the leading dimension of the array A. LDA >= max(1,M).
• IPIV — IPIV is INTEGER array, dimension (min(M,N)); the pivot indices; for 1 <= i <= min(M,N), row i of the matrix was interchanged with row IPIV(i).
• INFO — INFO is INTEGER; = 0: successful exit; < 0: if INFO = -i, the i-th argument had an illegal value; > 0: if INFO = i, U(i,i) 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. 💀

Bestie, that INFO > 0 case is not cute: U(i,i) being exactly zero means U is exactly singular, and division by zero will occur if it is used to solve a system of equations. So like, handle with care. 😭

Author:

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

Date:

December 2016

Definition at line 102 of file VARIANTS/lu/CR/zgetrf.f.

👑 Author 👑

Generated automatically by Doxygen for LAPACK from the source code.

Cute sign-off: this page is from LAPACK Version 3.8.0, dated Tue Nov 14 2017. Bye bestie, go factor something safely! 💖✨