SRC/dgtsv.f(3)

okay so bestie, this is the SRC/dgtsv.f page from the Library Functions Manual 💅 welcome to the tridiagonal solver group chat ✨

💖 NAME 💖

SRC/dgtsv.f

✨ SYNOPSIS ✨

🧚 Functions/Subroutines 🧚

• subroutine dgtsv (n, nrhs, dl, d, du, b, ldb, info) — DGTSV computes the solution to system of linear equations A * X = B for GT matrices 💖

👑 Function/Subroutine Documentation 👑

subroutine dgtsv (integer n, integer nrhs, double precision, dimension( * )
    dl, double precision, dimension( * ) d, double precision, dimension( * )
    du, double precision, dimension( ldb, * ) b, integer ldb, integer info)

DGTSV computes the solution to system of linear equations A * X = B for GT matrices — no cap, that is literally the whole main-character job 👑

🎀 Purpose 🎀

okay so here's the vibe, bestie:

DGTSV  solves the equation

   A*X = B,

where A is an n by n tridiagonal matrix, by Gaussian elimination with
partial pivoting.

Note that the equation  A**T*X = B  may be solved by interchanging the
order of the arguments DU and DL.

so yes: tridiagonal matrix, Gaussian elimination, partial pivoting, and that little swap trick with DU and DL for A**T*X = B 🔥

🌸 Parameters 🌸

• N — N is INTEGER. The order of the matrix A. N >= 0. ✨
• NRHS — NRHS is INTEGER. The number of right hand sides, i.e., the number of columns of the matrix B. NRHS >= 0. 💖
• 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-2) elements of the second super-diagonal of the upper triangular matrix U from the LU factorization of A, in DL(1), ..., DL(n-2). 🦋
• 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 U. 🌸
• 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. 🌈
• B — B is DOUBLE PRECISION array, dimension (LDB,NRHS). On entry, the N by NRHS matrix of right hand side matrix B. On exit, if INFO = 0, the N by NRHS solution matrix X. 🫶
• LDB — LDB is INTEGER. The leading dimension of the array B. LDB >= max(1,N). 💅
• INFO — INFO is INTEGER. = 0: successful exit. < 0: if INFO = -i, the i-th argument had an illegal value. > 0: if INFO = i, U(i,i) is exactly zero, and the solution has not been computed. The factorization has not been completed unless i = N. 💀

💫 Author 💫

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

📌 Definition

Definition at line 126 of file dgtsv.f.

🫶 Author 🫶

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and that's the page, bestie — footer vibes are LAPACK, Version 3.12.0, and SRC/dgtsv.f(3) 🌈💖✨