SRC/cgbtrs.f(3)

✨ NAME ✨

SRC/cgbtrs.f — bestie, this is the manpage for SRC/cgbtrs.f, and honestly? She's a whole legend. 💅

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🎀 SYNOPSIS 🎀

Functions/Subroutines

• subroutine cgbtrs (trans, n, kl, ku, nrhs, ab, ldab, ipiv, b, ldb, info) — the icon herself, CGBTRS

Function/Subroutine Documentation

okay so here's the full signature, no cap, exactly as written:

subroutine cgbtrs (character trans, integer n, integer kl, integer ku,
     integer nrhs, complex, dimension( ldab, * ) ab, integer ldab, integer,
     dimension( * ) ipiv, complex, dimension( ldb, * ) b, integer ldb,
     integer info)

CGBTRS 🫶

💜 Purpose

!> !> CGBTRS solves a system of linear equations !> A * X = B, AT * X = B, or AH * X = B !> with a general band matrix A using the LU factorization computed !> by CGBTRF. !>

So like, it solves your linear system — three different flavors of it, depending on TRANS — for a general band matrix A, and it does it using the LU factorization that CGBTRF already computed for you. she's not doing the hard work from scratch, she's building on what CGBTRF left her. teamwork, periodt. 🌈

🌸 Parameters

• TRANS — TRANS is CHARACTER*1, and it specifies the form of the system of equations, like which version of the equation we're solving:
  • = 'N': A * X = B (No transpose) — the straightforward one, main character energy ⭐
  • = 'T': A**T * X = B (Transpose)
  • = 'C': A**H * X = B (Conjugate transpose)
• N — N is INTEGER, the order 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.
• NRHS — NRHS is INTEGER, the number of right hand sides, i.e., the number of columns of the matrix B. Constraint: NRHS >= 0. (right hand sides are literally the moment, yk?)
• AB — AB is COMPLEX array, dimension (LDAB,N). This is where the details of the LU factorization of the band matrix A live, as computed by CGBTRF. 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. weird layout? yes. iconic? also yes. 💀
• LDAB — LDAB is INTEGER, the leading dimension of the array AB. Constraint: LDAB >= 2*KL+KU+1.
• IPIV — IPIV is INTEGER array, dimension (N), the pivot indices; for 1 <= i <= N, row i of the matrix was interchanged with row IPIV(i). she remembers every swap, fr fr 🦋
• B — B is COMPLEX array, dimension (LDB,NRHS). On entry, the right hand side matrix B. On exit, the solution matrix X. glow-up in real time ✨
• LDB — LDB is INTEGER, the leading dimension of the array B. Constraint: LDB >= max(1,N).
• INFO — INFO is INTEGER, the vibe check:
  • = 0: successful exit 👑
  • < 0: if INFO = -i, the i-th argument had an illegal value 🙈

🧚 Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

⭐ Definition at line 136 of file cgbtrs.f.

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🔥 Author 🔥

Generated automatically by Doxygen for LAPACK from the source code. (she was literally born in a build script, and she still ate. 💖)

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ok that's the whole page bestie, go solve some banded systems responsibly 🫶

LAPACK, Version 3.12.0 — that's the flex, and SRC/cgbtrs.f(3) is the whole entire address. mwah 💋💅