DDBTF2(3)

DDBTF2(3) — bestie, let's get this band matrix factored 💅

✨ NAME ✨

DDBTF2 — compute an LU factorization of a real m-by-n band matrix A without using partial pivoting with row interchanges.

🌸 SYNOPSIS 🌸

SUBROUTINE DDBTF2( M, N, KL, KU, AB, LDAB, INFO )
INTEGER INFO, KL, KU, LDAB, M, N
DOUBLE PRECISION AB( LDAB, * )

🦋 DESCRIPTION 🦋

Okay so Ddbtrf computes an LU factorization of a real m-by-n band matrix A without using partial pivoting with row interchanges. That's the whole assignment, bestie. 💖

This is the unblocked version of the algorithm, calling Level 2 BLAS. It's giving classic, no-blocking, straight-up energy. ✨

👑 ARGUMENTS 👑

• M (input) INTEGER — The number of rows of the matrix A. M >= 0. 💯
• N (input) INTEGER — The number of columns of the matrix A. N >= 0. 💯
• KL (input) INTEGER — The number of subdiagonals within the band of A. KL >= 0. 💅
• KU (input) INTEGER — The number of superdiagonals within the band of A. KU >= 0. 💅
• AB (input/output) DOUBLE PRECISION array, dimension (LDAB,N) — On entry, the matrix A in band storage, in rows KL+1 to 2*KL+KU+1; rows 1 to KL of the array need not be set. The j-th column of A is stored in the j-th column of the array AB as follows:

AB(kl+ku+1+i-j,j) = A(i,j) for max(1,j-ku)<=i<=min(m,j+kl)

On exit, details of the factorization: U is stored as an upper triangular band matrix with KL+KU superdiagonals in rows 1 to KL+KU+1, and the multipliers used during the factorization are stored in rows KL+KU+2 to 2*KL+KU+1. See below for further details. 👀

• LDAB (input) INTEGER — The leading dimension of the array AB. LDAB >= 2*KL+KU+1. 🫶
• INFO (output) 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. 💀

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The band storage scheme is illustrated by the following example, when M = N = 6, KL = 2, KU = 1:

On entry:                       On exit:

    *   a12  a23  a34  a45  a56      *   u12  u23  u34  u45  u56
   a11  a22  a33  a44  a55  a66     u11  u22  u33  u44  u55  u66
   a21  a32  a43  a54  a65   *      m21  m32  m43  m54  m65   *
   a31  a42  a53  a64   *    *      m31  m42  m53  m64   *    *

Array elements marked * are not used by the routine; elements marked + need not be set on entry, but are required by the routine to store elements of U, because of fill-in resulting from the row interchanges.

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And that's the whole page, bestie! This was brought to you by LAPACK version 3.0, dated 30 June 1999, and it's serving DDBTF2(3) realness. Periodt. 💖✨👑