DGTTRF(3)

Hey bestie 💖 welcome to the dgttrf.f(3) page from the Library Functions Manual. This is the LAPACK tea on DGTTRF, and it's lowkey iconic: LU factorization of a real tridiagonal matrix, no cap. 🦋✨

🌸 NAME 🌸

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/dgttrf.f

That's the source file path, periodt. 💅

✨ 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 🎀

Okay so DGTTRF computes an LU factorization of a real tridiagonal matrix A using elimination with partial pivoting and row interchanges. It's giving very structured main character energy. 👑

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. ✨

🎀 Parameters 🎀

• N — N is INTEGER. The order of the matrix A. 💅
• 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). 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. 👀
• 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. 💀

Bestie, that INFO > 0 case is not a cute little warning — it means U is exactly singular and division by zero is coming if you use it to solve a system. Periodt. 🚨

🎀 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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Final footer sign-off, bestie: this page is from LAPACK, Version 3.12.0, and the footer path is /home/abui...RC/dgttrf.f(3). The footer doesn't give a date, so we're not inventing one — no cap. 🫶💖