SRC/slagts.f(3)

💅 SRC/slagts.f — from the Library Functions Manual, bestie

okay so this is a Fortran source file page from the LAPACK docs, and it's honestly kind of a big deal. it's all about a subroutine that solves tridiagonal systems after somebody else already did the factoring. very "i'm the cleanup crew" of it. anyway, let's get into it ✨

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✨ SYNOPSIS ✨

Functions/Subroutines 🎀

• subroutine slagts (job, n, a, b, c, d, in, y, tol, info) — SLAGTS solves the system of equations (T-λI)x = y or (T-λI)^Tx = y, where T is a general tridiagonal matrix and λ a scalar, using the LU factorization computed by slagtf.

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🦋 Function/Subroutine Documentation 🦋

subroutine slagts (integer job, integer n, real, dimension( * ) a, real,
    dimension( * ) b, real, dimension( * ) c, real, dimension( * ) d,
    integer, dimension( * ) in, real, dimension( * ) y, real tol, integer
    info)

SLAGTS solves the system of equations (T-λI)x = y or (T-λI)^Tx = y, where T is a general tridiagonal matrix and λ a scalar, using the LU factorization computed by slagtf. no cap, that's the whole gig 💖

Purpose 🌸

SLAGTS may be used to solve one of the systems of equations

(T - lambda*I)*x = y   or   (T - lambda*I)**T*x = y,

where T is an n by n tridiagonal matrix, for x, following the factorization of (T - lambda*I) as

(T - lambda*I) = P*L*U ,

by routine SLAGTF. The choice of equation to be solved is controlled by the argument JOB, and in each case there is an option to perturb zero or very small diagonal elements of U, this option being intended for use in applications such as inverse iteration.

so yeah, SLAGTF does the glow-up (the P*L*U factorization) and SLAGTS walks in afterwards and actually solves stuff. iconic teamwork honestly 🫶

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Parameters 👑

JOB

JOB is INTEGER Specifies the job to be performed by SLAGTS as follows:

• = 1: The equations (T - lambda*I)x = y are to be solved, but diagonal elements of U are not to be perturbed.
• = -1: The equations (T - lambda*I)x = y are to be solved and, if overflow would otherwise occur, the diagonal elements of U are to be perturbed. See argument TOL below.
• = 2: The equations (T - lambda*I)**Tx = y are to be solved, but diagonal elements of U are not to be perturbed.
• = -2: The equations (T - lambda*I)**Tx = y are to be solved and, if overflow would otherwise occur, the diagonal elements of U are to be perturbed. See argument TOL below.

so positive JOB = hands off the U diagonals, negative JOB = go ahead and nudge them if overflow is about to ruin the vibe 😭

N

N is INTEGER The order of the matrix T.

literally just how big the matrix is. that's it, that's the whole parameter 💀

A

A is REAL array, dimension (N) On entry, A must contain the diagonal elements of U as returned from SLAGTF.

B

B is REAL array, dimension (N-1) On entry, B must contain the first super-diagonal elements of U as returned from SLAGTF.

C

C is REAL array, dimension (N-1) On entry, C must contain the sub-diagonal elements of L as returned from SLAGTF.

D

D is REAL array, dimension (N-2) On entry, D must contain the second super-diagonal elements of U as returned from SLAGTF.

okay note that D is N-2 long, not N-1 — bestie do NOT mess that up 🙈 and all four of these bad boys come straight out of SLAGTF. don't go hand-crafting them, that's not the assignment.

IN

IN is INTEGER array, dimension (N) On entry, IN must contain details of the matrix P as returned from SLAGTF.

Y

Y is REAL array, dimension (N) On entry, the right hand side vector y. On exit, Y is overwritten by the solution vector x.

main character energy: y goes in, x comes out, same array. glow-up arc fr fr ✨

TOL

TOL is REAL On entry, with JOB < 0, TOL should be the minimum perturbation to be made to very small diagonal elements of U. TOL should normally be chosen as about eps*norm(U), where eps is the relative machine precision, but if TOL is supplied as non-positive, then it is reset to eps*max( abs( u(i,j) ) ). If JOB > 0 then TOL is not referenced. On exit, TOL is changed as described above, only if TOL is non-positive on entry. Otherwise TOL is unchanged.

so real talk: TOL only matters when JOB < 0. and it can get rewritten on the way out, but only if you fed it a non-positive value. otherwise it stays exactly as you left it 🎀

INFO

INFO is INTEGER

• = 0: successful exit
• < 0: if INFO = -i, the i-th argument had an illegal value
• > 0: overflow would occur when computing the INFOth element of the solution vector x. This can only occur when JOB is supplied as positive and either means that a diagonal element of U is very small, or that the elements of the right-hand side vector y are very large.

⚠️ heads up bestie: a positive INFO is not a slay. it means overflow happened at that element, and it can only happen when JOB is positive — i.e. when you told it not to perturb the U diagonals. tiny diagonal, huge y, boom. 💀

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🌈 Author 🌈

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 162 of file slagts.f.

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⭐ Author ⭐

Generated automatically by Doxygen for LAPACK from the source code.

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okay that's the whole page, bestie — every flag, every array bound, every INFO case, nothing skipped. this beauty is LAPACK Version 3.12.0, and it says goodbye from SRC/slagts.f(3) 🦋💜 stay factored, stay unbothered ✨