SRC/cgbtf2.f(3)

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💅 SRC/cgbtf2.f(3) — Library Functions Manual, but make it cute ✨

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✨ NAME ✨

SRC/cgbtf2.f

🌸 SYNOPSIS 🌸

🧚 Functions/Subroutines 🧚

  • subroutine cgbtf2 (m, n, kl, ku, ab, ldab, ipiv, info) — CGBTF2 computes the LU factorization of a general band matrix using the unblocked version of the algorithm. 💅

💖 Function/Subroutine Documentation 💖

subroutine cgbtf2 (integer m, integer n, integer kl, integer ku, complex, dimension( ldab, * ) ab, integer ldab, integer, dimension( * ) ipiv, integer info)

CGBTF2 computes the LU factorization of a general band matrix using the unblocked version of the algorithm. That's the whole assignment. ✨

🫶 Purpose 🫶

Real talk: CGBTF2 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. Periodt. 🔥

🎀 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 COMPLEX 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. 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. Here's the status tea:

  • = 0: successful exit. Slay. ✅
  • < 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 cgbtf2.f.

🌈 Author 🌈

This page was generated automatically by Doxygen for LAPACK from the source code. 🤖✨

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