SGBTRF(3)

💖 NAME 💖

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/sgbtrf.f

okay bestie, this is the SGBTRF(3) page from the Library Functions Manual — and yes, the entire NAME section is literally that source path. no cap. 💅

✨ SYNOPSIS ✨

🧚 Functions/Subroutines 🧚

• subroutine SGBTRF (m, n, kl, ku, ab, ldab, ipiv, info) — SGBTRF

🎀 Function/Subroutine Documentation 🎀

💅 subroutine SGBTRF (...) 💅

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

SGBTRF — that’s the whole function, bestie. 🫶

🔥 Purpose 🔥

okay so SGBTRF computes an LU factorization of a real m-by-n band matrix A using partial pivoting with row interchanges.

This is the blocked version of the algorithm, calling Level 3 BLAS. it’s giving optimized-band-matrix energy. ✨

🌸 Parameters 🌸

• M — INTEGER. The number of rows of the matrix A. M >= 0.
• N — INTEGER. The number of columns of the matrix A. N >= 0.
• KL — INTEGER. The number of subdiagonals within the band of A. KL >= 0.
• KU — INTEGER. The number of superdiagonals within the band of A. KU >= 0.
• AB — REAL 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 — INTEGER. The leading dimension of the array AB. LDAB >= 2*KL+KU+1.
• IPIV — 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 — 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 143 of file sgbtrf.f.

🎀 Author 🎀

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mwah 💋 — that’s LAPACK, Version 3.12.0, and the footer’s /home/abui...RC/sgbtrf.f(3). stay slay, bestie. 🫶💖