ZGBTF2(3)

💅 ZGBTF2(3) — Library Functions Manual 💅

Okay bestie, gather round, because this is the manual page for ZGBTF2 and it's giving “unblocked LU factorization of a complex band matrix” in the best way possible. No cap. ✨

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📛 NAME 📛

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/zgbtf2.f — literally the source file for this routine, periodt. 💖

🌈 SYNOPSIS 🌈

Functions/Subroutines

subroutine ZGBTF2 (m, n, kl, ku, ab, ldab, ipiv, info)

ZGBTF2 computes the LU factorization of a general band matrix using the unblocked version of the algorithm. Iconic. 💅

🛠️ Function/Subroutine Documentation 🛠️

subroutine ZGBTF2 (integer m, integer n, integer kl, integer ku, complex*16,
    dimension( ldab, * ) ab, integer ldab, integer, dimension( * ) ipiv,
    integer info)

ZGBTF2 computes the LU factorization of a general band matrix using the unblocked version of the algorithm. (Yes, same energy as the synopsis, because that's literally what it does, bestie.)

🎯 Purpose 🎯

Lowkey the whole point: ZGBTF2 computes an LU factorization of a complex m-by-n band matrix A using partial pivoting with row interchanges.

This is the unblocked version of the algorithm, calling Level 2 BLAS. Slay. ⭐

🧩 Parameters 🧩

• M — M is INTEGER; the number of rows of the matrix A. Constraint: M >= 0.
• N — N is INTEGER; the number of columns of the matrix A. Constraint: N >= 0.
• KL — KL is INTEGER; the number of subdiagonals within the band of A. Constraint: KL >= 0.
• KU — KU is INTEGER; the number of superdiagonals within the band of A. Constraint: KU >= 0.
• AB — AB is COMPLEX*16 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. Constraint: 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   *    *

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 zgbtf2.f.

🪄 Author 🪄

Generated automatically by Doxygen for LAPACK from the source code.

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That's the whole vibe, bestie. This page is from LAPACK Version 3.12.0, source path /home/abui...RC/zgbtf2.f(3) — mwah 💋✨