ZGTTRF(3)

💖 ZGTTRF(3) — the tridiagonal glow-up page 💖

okay so bestie, welcome to the zgttrf.f page from LAPACK — yes, the whole path is part of the vibe: /home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/zgttrf.f

This is a Library Functions Manual moment, and honestly? iconic. Let's get into it. 🦋

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✨ SYNOPSIS ✨

Functions/Subroutines

• subroutine ZGTTRF (n, dl, d, du, du2, ipiv, info) — that's the whole squad right there, and yes, the description is literally just ZGTTRF. no notes. 💅

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🎀 Function/Subroutine Documentation 🎀

subroutine ZGTTRF (integer n, complex*16, dimension( * ) dl, complex*16, dimension( * ) d, complex*16, dimension( * ) du, complex*16, dimension( * ) du2, integer, dimension( * ) ipiv, integer info)

ZGTTRF — say it with me. Main character energy, no cap.

💜 Purpose:

!> !> ZGTTRF computes an LU factorization of a complex tridiagonal matrix A !> using elimination with partial pivoting and row interchanges. !> !> The factorization has the form !> A = L * U !> where L is a product of permutation and unit lower bidiagonal !> matrices and U is upper triangular with nonzeros in only the main !> diagonal and first two superdiagonals. !>

okay so like — it takes your complex tridiagonal matrix A and factorizes it as A = L * U. L is a product of permutation matrices and unit lower bidiagonal ones, and U is upper triangular but lowkey sparse: nonzeros only on the main diagonal and the first two superdiagonals. she's giving efficiency. she ate. 🔥

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🌸 Parameters 🌸

• N — N is INTEGER, the order of the matrix A. the queen herself, the size of the whole situation.
• DL — DL is COMPLEX*16 array, dimension (N-1). On entry, DL must contain the (n-1) sub-diagonal elements of A. On exit, DL is overwritten by the (n-1) multipliers that define the matrix L from the LU factorization of A. so it goes in as your sub-diagonal and comes out as L's multipliers, glow-up complete. ✨
• D — D is COMPLEX*16 array, dimension (N). On entry, D must contain the diagonal elements of A. On exit, D is overwritten by the n diagonal elements of the upper triangular matrix U from the LU factorization of A. the main diagonal stays booked and busy.
• DU — DU is COMPLEX*16 array, dimension (N-1). On entry, DU must contain the (n-1) super-diagonal elements of A. On exit, DU is overwritten by the (n-1) elements of the first super-diagonal of U. first superdiagonal, first in line, obsessed.
• DU2 — DU2 is COMPLEX*16 array, dimension (N-2). On exit, DU2 is overwritten by the (n-2) elements of the second super-diagonal of U. note: output only, bestie — don't come at her with input, she didn't ask. 🙈
• 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). IPIV(i) will always be either i or i+1; IPIV(i) = i indicates a row interchange was not required. so basically it only ever swaps with the next row or stays put — very "i'm not doing too much" of her. 💅
• INFO — INFO is INTEGER:
  • = 0: successful exit 🎉
  • < 0: if INFO = -k, the k-th argument had an illegal value
  • > 0: if INFO = k, U(k,k) 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.

⚠️ warning bestie: that INFO > 0 case is the dramatic one. the factorization did finish, but U is exactly singular, so if you go solve a system with it you're dividing by zero. no cap, that's a bad time. 😭

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👑 Author 👑

• Univ. of Tennessee
• Univ. of California Berkeley
• Univ. of Colorado Denver
• NAG Ltd.

Definition at line 123 of file zgttrf.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, bestie — LAPACK, Version 3.12.0, dated at /home/abui...RC/zgttrf.f(3). go forth and factorize your tridiagonal complex matrices with partial pivoting and row interchanges. slay, periodt. 🫶💖🎀