SGBTF2(3)

🌸 SGBTF2(3) — Library Functions Manual 🌸

okay so bestie, welcome to the SGBTF2(3) page from the Library Functions Manual — this is the LAPACK subroutine that does the unblocked LU factorization of a real band matrix, and it is lowkey iconic. ✨ No cap, every parameter and caveat is below, so vibe check the details before you send it. 💅

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✨ NAME ✨

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/sgbtf2.f

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🫶 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.

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

🦋 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   *    *

Quick note, bestie: array elements marked * are not used by the routine; elements marked + need not be set on entry, but they 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.

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💀 Author 💀

Generated automatically by Doxygen for LAPACK from the source code.

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and that’s the tea ☕ — this page is from LAPACK Version 3.12.0, with footer path /home/abui...RC/sgbtf2.f(3). mwah, bestie 💋