CGBTRF(3)

🎀 CGBTRF(3) 🎀

Okay bestie, welcome to CGBTRF(3), straight out of the Library Functions Manual. This is the page for the Fortran routine, and the file it documents is right here: /home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/cgbtrf.f. Yes, the whole giant path. We keep it. 💅

🌸 NAME 🌸

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

That’s it — the name is the file path, and we’re keeping every slash. 🫶

✨ SYNOPSIS ✨

Functions/Subroutines

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

🦋 Function/Subroutine Documentation 🦋

Here’s the full signature, no crumbs:

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

💖 Purpose 💖

Bestie, here’s the whole vibe: CGBTRF computes an LU factorization of a complex m-by-n band matrix A using partial pivoting with row interchanges.

This is the blocked version of the algorithm, calling Level 3 BLAS. Main character energy, honestly. ✨

🎀 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 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. 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. Like, do not use it to solve a system, bestie. 😭

👑 Author 👑

Shoutout to the author squad:

• 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. Don’t touch the *s — they’re not invited. 🙈

Definition at line 143 of file cgbtrf.f.

🌟 Author 🌟

Generated automatically by Doxygen for LAPACK from the source code.

---

That’s the whole page, bestie. The footer/source tag is LAPACK Version 3.12.0 with /home/abui...RC/cgbtrf.f(3). Bye, love you, go factor something cute. 💖✨