SRC/zgetrf2.f(3)

🌸 NAME 🌸

SRC/zgetrf2.f — okay bestie, this is the manual page for that exact file, and it lives in the Library Functions Manual. We're about to get into the zgetrf2 lore, and it's lowkey iconic. 💅

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✨ SYNOPSIS ✨

Functions/Subroutines

• recursive subroutine zgetrf2 (m, n, a, lda, ipiv, info) — the one and only ZGETRF2, showing up in the synopsis like main character energy. 👑

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💖 Function/Subroutine Documentation 💖

recursive subroutine zgetrf2 (integer m, integer n, complex*16, dimension( lda, * ) a, integer lda, integer, dimension( * ) ipiv, integer info)

ZGETRF2 — that's the routine name, no cap. 🫶

🎀 Purpose 🎀

Okay so, ZGETRF2 computes an LU factorization of a general M-by-N matrix A using partial pivoting with row interchanges. Slay. ✨

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 recursive version of the algorithm. It divides the matrix into four submatrices:

       [  A11 | A12  ]  where A11 is n1 by n1 and A22 is n2 by n2
   A = [ -----|----- ]  with n1 = min(m,n)/2
       [  A21 | A22  ]       n2 = n-n1

                                      [ A11 ]
The subroutine calls itself to factor [ --- ],
                                      [ A12 ]
                [ A12 ]
do the swaps on [ --- ], solve A12, update A22,
                [ A22 ]

then calls itself to factor A22 and do the swaps on A21.

🧚 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. Bestie, here's the status tea:
  • = 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.

Definition at line 112 of file zgetrf2.f. 📌

👑 Author 👑

Generated automatically by Doxygen for LAPACK from the source code.

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And that's the whole page, bestie. Footer vibes: this is from the LAPACK manual, Version 3.12.0, and the page is SRC/zgetrf2.f(3). No separate date in that footer, just the source/version/page combo. Stay recursive, stay slay. 💜✨