SRC/sgtsv.f(3)

💖 NAME 💖

okay so bestie, this page is literally SRC/sgtsv.f(3) — that's the manual name — and it's all about the Fortran subroutine sgtsv. no cap, she's iconic.

✨ SYNOPSIS ✨

🧚 Functions/Subroutines 🧚

subroutine sgtsv (n, nrhs, dl, d, du, b, ldb, info)

the one-liner vibe is: SGTSV computes the solution to system of linear equations A * X = B for GT matrices.

🌸 Function/Subroutine Documentation 🌸

   subroutine sgtsv (integer n, integer nrhs, real, dimension( * ) dl, real,
       dimension( * ) d, real, dimension( * ) du, real, dimension( ldb, * ) b,
       integer ldb, integer info)

same energy, but now with the full type info: SGTSV computes the solution to system of linear equations A * X = B for GT matrices.

🎀 Purpose: 🎀

okay so SGTSV solves the equation

A*X = B,

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

also important, bestie: the equation

A**T*X = B

may be solved by interchanging the order of the arguments DU and DL. iykyk.

🍓 Parameters 🍓

• N — INTEGER. it's the order of the matrix A, and N >= 0. periodt.
• NRHS — INTEGER. the number of right hand sides, i.e., the number of columns of the matrix B. also NRHS >= 0.
• DL — REAL 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). she's getting rewritten, bestie.
• D — REAL 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 — REAL 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 — REAL 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 — INTEGER. the leading dimension of the array B. LDB >= max(1,N). don't play with her.
• INFO — INTEGER. the exit-code bestie:
  • = 0: successful exit, slay.
  • < 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.

🚨 bestie warning: if INFO > 0 and INFO = i, U(i,i) is exactly zero, so the solution has not been computed, and the factorization has not been completed unless i = N. that is not a drill. 💀

👑 Author 👑

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

Definition at line 126 of file sgtsv.f. — yes, she's literally defined there. 📌

💅 Author 💅

Generated automatically by Doxygen for LAPACK from the source code. no cap, the docs wrote themselves (well, Doxygen did). 🫶

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mwah 💋 — LAPACK Version 3.12.0, source SRC/sgtsv.f(3); no date in the footer, so no invented date bestie 🎀