SRC/zgttrf.f(3)

💅 NAME 💅

SRC/zgttrf.f — bestie, this is the page for the zgttrf subroutine, and no cap it's kind of a big deal 👑

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✨ SYNOPSIS ✨

🫶 Functions/Subroutines

subroutine zgttrf (n, dl, d, du, du2, ipiv, info)

That's it, that's the whole vibe check: ZGTTRF 🌸

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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 💖

🎀 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. !>

So basically it takes your complex tridiagonal matrix A and factorizes it into A = L * U — 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. Elimination with partial pivoting plus row interchanges, the whole thing. Slay 💅

💜 Parameters 💜

• N

!> N is INTEGER !> The order of the matrix A. !>

It's an INTEGER, and it's the order of the matrix A. Iconic.

• 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. !>

COMPLEX*16 array, dimension (N-1). On entry it must hold the (n-1) sub-diagonal elements of A — like, mandatory bestie, don't skip. On exit it gets overwritten by the (n-1) multipliers that define the matrix L from the LU factorization of A. She gets a whole new identity 😭

• 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. !>

COMPLEX*16 array, dimension (N). On entry: the diagonal elements of A. On exit: overwritten by the n diagonal elements of the upper triangular matrix U from the LU factorization of A. Main character energy, fr fr ✨

• 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. !>

COMPLEX*16 array, dimension (N-1). On entry: the (n-1) super-diagonal elements of A. On exit: overwritten by the (n-1) elements of the first super-diagonal of U. 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. !>

COMPLEX*16 array, dimension (N-2). Output only, bestie — on exit DU2 is overwritten by the (n-2) elements of the second super-diagonal of U. Note there's no "on entry" here, she's strictly exit-only 💀

• 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. !>

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, and IPIV(i) = i means a row interchange wasn't required. Consistent queen 👑

• 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. !>

INTEGER, the little status report at the end. Here's the tea:

• = 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. So like, it finished, but she's not okay 😭💀

🌈 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. (Yes, a robot wrote this, and honestly? It ate 🤖✨)

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And that's the whole page, bestie! 🫶 This little icon was brought to you by LAPACK, Version 3.12.0, served fresh from SRC/zgttrf.f(3) — go forth and factorize those complex tridiagonal matrices, mwah 💋💖