SRC/dgetrf2.f(3)

💖 SRC/dgetrf2.f(3) — Library Functions Manual 💖

okay bestie, gather round: this is the manual page for SRC/dgetrf2.f, and it's giving recursive LU factorization realness. no cap, it's a whole vibe. 💅

🌸 NAME 🌸

SRC/dgetrf2.f

✨ SYNOPSIS ✨

💅 Functions/Subroutines 💅

• recursive subroutine dgetrf2 (m, n, a, lda, ipiv, info) — DGETRF2

🦋 Function/Subroutine Documentation 🦋

💜 recursive subroutine dgetrf2 💜

recursive subroutine dgetrf2 (integer m, integer n, double precision, dimension( lda, * ) a, integer lda, integer, dimension( * ) ipiv, integer info)

DGETRF2

🌈 Purpose 🌈

bestie, DGETRF2 computes an LU factorization of a general M-by-N matrix A using partial pivoting with row interchanges. that's the whole assignment, fr fr. ✨

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). iconic triangular behavior, honestly. 🫶

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

Then the subroutine calls itself to factor this block:

                                      [ A11 ]
The subroutine calls itself to factor [ --- ],
                                      [ A12 ]

It does the swaps on:

                [ A12 ]
do the swaps on [ --- ], solve A12, update A22,
                [ A22 ]

and then calls itself to factor A22 and do the swaps on A21. recursion ate, left no crumbs. 🔥

🍓 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 DOUBLE PRECISION 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.

Definition at line 112 of file dgetrf2.f.

💫 Author 💫

Generated automatically by Doxygen for LAPACK from the source code.

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that's the whole vibe, bestie — LAPACK Version 3.12.0, source SRC/dgetrf2.f(3) 💖✨