SRC/dgttrf.f(3)

🌸 NAME 🌸

SRC/dgttrf.f — okay bestie, this page is from the Library Functions Manual, and it’s all about the DGTTRF subroutine serving real tridiagonal LU factorization energy. 💅✨

✨ SYNOPSIS ✨

🧚 Functions/Subroutines 🧚

subroutine dgttrf (n, dl, d, du, du2, ipiv, info)
    DGTTRF

🎀 Function/Subroutine Documentation 🎀

subroutine dgttrf (integer n, double precision, dimension( * ) dl, double
precision, dimension( * ) d, double precision, dimension( * ) du, double
precision, dimension( * ) du2, integer, dimension( * ) ipiv, integer
info)

DGTTRF

💖 Purpose 💖

So like, DGTTRF computes an LU factorization of a real tridiagonal matrix A using elimination with partial pivoting and row interchanges. No cap. 🫶

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. Iconic behavior, honestly. 👑

🍓 Parameters 🍓

• N — N is INTEGER, and it’s the order of the matrix A. Main character dimension alert. 💫
• DL — DL is DOUBLE PRECISION 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.
• D — D is DOUBLE PRECISION 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.
• DU — DU is DOUBLE PRECISION 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.
• DU2 — DU2 is DOUBLE PRECISION array, dimension (N-2).
  • On exit, DU2 is overwritten by the (n-2) elements of the second super-diagonal of U.
• IPIV — IPIV is INTEGER array, dimension (N), and it’s giving pivot indices realness. 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. 🎯
• INFO — INFO is INTEGER.
  • = 0: successful exit. Slay.
  • < 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. ⚠️ This is the “bestie, be careful” part, fr fr.

👑 Author 👑

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

📍 Definition at line 123 of file dgttrf.f.

🫶 Author 🫶

Generated automatically by Doxygen for LAPACK from the source code.

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okay that’s the whole LAPACK Version 3.12.0 page for SRC/dgttrf.f(3) — bye bestie, go factor something cute! 💖✨🦋