CGETRF(3)

🎀 NAME 🎀

Bestie, this is cgetrf.f(3) from the Library Functions Manual 💖. The source file path is exactly this, no cap:

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/VARIANTS/lu/REC/cgetrf.f

✨ SYNOPSIS ✨

🧩 Functions/Subroutines 🧩

subroutine CGETRF (m, n, a, lda, ipiv, info)
    CGETRF VARIANT: iterative version of Sivan Toledo's recursive LU
    algorithm

💫 Function/Subroutine Documentation 💫

subroutine CGETRF (integer m, integer n, complex, dimension( lda, * ) a,
    integer lda, integer, dimension( * ) ipiv, integer info)

The variant note is CGETRF VARIANT: iterative version of Sivan Toledo's recursive LU algorithm. Iconic ✨.

🌸 Purpose 🌸

Okay so here's the tea ☕: CGETRF 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 code implements an iterative version of Sivan Toledo's recursive LU algorithm[1]. For square matrices, this iterative versions should be within a factor of two of the optimum number of memory transfers.

The pattern is as follows, with the large blocks of U being updated in one call to DTRSM, and the dotted lines denoting sections that have had all pending permutations applied:

!>  1 2 3 4 5 6 7 8
!> +-+-+---+-------+------
!> | |1|   |       |
!> |.+-+ 2 |       |
!> | | |   |       |
!> |.|.+-+-+   4   |
!> | | | |1|       |
!> | | |.+-+       |
!> | | | | |       |
!> |.|.|.|.+-+-+---+  8
!> | | | | | |1|   |
!> | | | | |.+-+ 2 |
!> | | | | | | |   |
!> | | | | |.|.+-+-+
!> | | | | | | | |1|
!> | | | | | | |.+-+
!> | | | | | | | | |
!> |.|.|.|.|.|.|.|.+-----
!> | | | | | | | | |
!>

The 1-2-1-4-1-2-1-8-... pattern is the position of the last 1 bit in the binary expansion of the current column. Each Schur update is applied as soon as the necessary portion of U is available.

[1] Toledo, S. 1997. Locality of Reference in LU Decomposition with Partial Pivoting. SIAM J. Matrix Anal. Appl. 18, 4 (Oct. 1997), 1065-1081. http://dx.doi.org/10.1137/S0895479896297744

🧸 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 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 135 of file cgetrf.f.

👑 Author 👑

Generated automatically by Doxygen for LAPACK from the source code.

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That's the whole page, bestie 🫶. Footer says LAPACK Version 3.12.0 and /home/abui...EC/cgetrf.f(3), and the date is December 2016. Slay, bye! 💅