SRC/cgbtrf.f(3)

💅 SRC/cgbtrf.f 💅

okay so this is a LAPACK manpage, bestie — SRC/cgbtrf.f, the whole thing, and I'm gonna walk you through it like we're texting at 2am 🫶

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✨ SYNOPSIS ✨

🧚 Functions/Subroutines

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

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🌸 Function/Subroutine Documentation 🌸

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

CGBTRF

💖 Purpose:

!>
!> 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.
!>

So like, it factors your band matrix A into LU, with partial pivoting and row swaps. And it's the blocked version — it calls Level 3 BLAS, which is the fast one, iykyk 🔥

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🎀 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.
!>

okay so on entry this is your matrix A in band storage — rows KL+1 through 2*KL+KU+1, and rows 1 to KL? not needed, leave 'em alone 🙈 On exit it's holding the tea: U lives in rows 1 to KL+KU+1 as an upper triangular band matrix with KL+KU superdiagonals, and the multipliers go in rows KL+KU+2 to 2*KL+KU+1. Scroll down for the glow-up diagram 💅

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).
!>

the receipts of which rows got swapped, fr fr 🫶

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.
!>

⚠️ bestie listen — if INFO > 0, the factorization finished but U is exactly singular, and you will get division by zero if you try to solve with it. that's not a vibe 😭

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🌈 Author 🌈

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

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🦋 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.
!>

Translation bestie: * means the routine straight up does not touch it, and + means you don't gotta set it on entry, but the routine needs those slots to stash U elements because of fill-in from the row interchanges. iconic behavior honestly ✨

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Definition at line 143 of file cgbtrf.f.

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💜 Author 💜

Generated automatically by Doxygen for LAPACK from the source code.

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and that's the whole page, no cap 🎀 this lil beauty is from LAPACK, Version 3.12.0, dated SRC/cgbtrf.f(3) — mwah, go factor something 💋🌸