SRC/zpbtrs.f(3)

💅 NAME

SRC/zpbtrs.f — bestie, this is the page for the zpbtrs routine, and honestly? she's that girl. ✨

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🦋 SYNOPSIS

Functions/Subroutines

subroutine zpbtrs (uplo, n, kd, nrhs, ab, ldab, b, ldb, info)

ZPBTRS — say it with me now 👑

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🌸 Function/Subroutine Documentation

✨ subroutine zpbtrs

subroutine zpbtrs (character uplo, integer n, integer kd, integer nrhs,
    complex*16, dimension( ldab, * ) ab, integer ldab, complex*16,
    dimension( ldb, * ) b, integer ldb, integer info)

ZPBTRS — the icon herself. 🎀

💖 Purpose:

!>
!> ZPBTRS solves a system of linear equations A*X = B with a Hermitian
!> positive definite band matrix A using the Cholesky factorization
!> A = U**H *U or A = L*L**H computed by ZPBTRF.
!>

So like, lowkey the whole point: you've got a system A*X = B, A is a Hermitian positive definite band matrix, and you already ran ZPBTRF to get the Cholesky factorization (A = U**H *U or A = L*L**H). Now zpbtrs swoops in and actually solves it for you. Main character energy, fr fr. 💅

🌈 Parameters

• UPLO — UPLO is CHARACTER*1 — which triangle of the factor is chillin' in AB:
  • = 'U': upper triangular factor stored in AB;
  • = 'L': lower triangular factor stored in AB. 💖 Gotta match what you gave ZPBTRF, bestie, or it's giving chaos.
• N — N is INTEGER — the order of the matrix A. Requirement: N >= 0. ✨
• KD — KD is INTEGER — the number of superdiagonals of the matrix A if UPLO = 'U', or the number of subdiagonals if UPLO = 'L'. Requirement: KD >= 0. 🦋 Band width energy.
• NRHS — NRHS is INTEGER — the number of right hand sides, i.e. the number of columns of the matrix B. Requirement: NRHS >= 0. 🌸
• AB — AB is COMPLEX*16 array, dimension (LDAB,N) — the triangular factor U or L from the Cholesky factorization A = U**H *U or A = L*L**H of the band matrix A, stored in the first KD+1 rows of the array. The j-th column of U or L is stored in the j-th column of the array AB as follows:
  • if UPLO ='U', AB(kd+1+i-j,j) = U(i,j) for max(1,j-kd)<=i<=j;
  • if UPLO ='L', AB(1+i-j,j) = L(i,j) for j<=i<=min(n,j+kd).

🫶 Yes the indexing is a whole vibe. Write it down, don't guess.

• LDAB — LDAB is INTEGER — the leading dimension of the array AB. Requirement: LDAB >= KD+1. ⭐
• B — B is COMPLEX*16 array, dimension (LDB,NRHS) — on entry, the right hand side matrix B. On exit, the solution matrix X. 🔥 She goes in as B and comes out as X, okay?? Glow up.
• LDB — LDB is INTEGER — the leading dimension of the array B. Requirement: LDB >= max(1,N). 💜
• INFO — INFO is INTEGER — the receipts:
  • = 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 120 of file zpbtrs.f.

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🍓 Author

Generated automatically by Doxygen for LAPACK from the source code. (Not me, I just gave her a personality. 🙈)

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💀 Warning-ish reminder, no cap: those AB index formulas and all the >= bounds are load-bearing. Don't freestyle them. The INFO < 0 case literally exists to call you out on the i-th bad argument, so like… respect it. 🫶

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okay that's the whole page, mwah 💋 — LAPACK, Version 3.12.0, dated to that SRC/zpbtrs.f(3) moment. Slay, go solve your banded system. 🌈✨