SRC/sgbtf2.f(3)

okay so bestie, welcome to SRC/sgbtf2.f(3) — this page lives in the Library Functions Manual, and it is literally giving LAPACK band-matrix main-character energy 💅✨

🌸 NAME 🌸

SRC/sgbtf2.f

✨ SYNOPSIS ✨

🧚 Functions/Subroutines 🧚

subroutine sgbtf2 (m, n, kl, ku, ab, ldab, ipiv, info)

SGBTF2 computes the LU factorization of a general band matrix using the unblocked version of the algorithm. periodt 🔥

📚 Function/Subroutine Documentation 📚

subroutine sgbtf2 (integer m, integer n, integer kl, integer ku, real, dimension( ldab, * ) ab, integer ldab, integer, dimension( * ) ipiv, integer info)

SGBTF2 computes the LU factorization of a general band matrix using the unblocked version of the algorithm.

🎯 Purpose: 🎯

SGBTF2 computes an LU factorization of a real m-by-n band matrix A using partial pivoting with row interchanges. 🫶 This is the unblocked version of the algorithm, calling Level 2 BLAS. ⭐

🧮 Parameters 🧮

• M — M is INTEGER. It's the number of rows of the matrix A. M >= 0. 💖
• N — N is INTEGER. It's the number of columns of the matrix A. N >= 0. 💖
• KL — KL is INTEGER. It's the number of subdiagonals within the band of A. KL >= 0. 💖
• KU — KU is INTEGER. It's the number of superdiagonals within the band of A. KU >= 0. 💖
• AB — AB is REAL array, dimension (LDAB,N). On entry, it's 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 — LDAB is INTEGER. It's the leading dimension of the array AB. LDAB >= 2*KL+KU+1. 💅
• IPIV — IPIV is INTEGER array, dimension (min(M,N)). These are 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.

🌈 Further Details: 🌈

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

On entry:                       On exit:

    *    *    *    +    +    +       *    *    *   u14  u25  u36
    *    *    +    +    +    +       *    *   u13  u24  u35  u46
    *   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. 🌸

Definition at line 144 of file sgbtf2.f.

👑 Author 👑

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okay bestie, that's the whole vibe: LAPACK, Version 3.12.0, page SRC/sgbtf2.f(3). go off and factor that band matrix responsibly 💖✨