zgetrf.f(3)

✨ zgetrf.f — LAPACK manual, bestie edition ✨

okay so this is the LAPACK manual page for zgetrf.f, and it's lowkey a whole moment: LU factorization, pivoting, the works. no cap, it's giving linear algebra main character energy 💅

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📛 NAME

zgetrf.f

🫶 SYNOPSIS

🧚 Functions/Subroutines

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

🧩 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.

✍️ 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/LL/zgetrf.f.

🧾 Author

Generated automatically by Doxygen for LAPACK from the source code.

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and that's the page, bestie 💖 it's LAPACK Version 3.8.0, dated Tue Nov 14 2017. go forth and factor responsibly 🫶✨