lagts(3)

💅 NAME 💅

okay bestie, this is lagts(3) from the Library Functions Manual, and the name is literally:

lagts — lagts: LU solve of (T - λI) x = y

periodt. That's the whole name. 💖

✨ SYNOPSIS ✨

okay so there are two iconique functions here, and both are giving solve the tridiagonal system with the LU factorization from slagtf energy. Here's the exact tea:

• dlagts — the double-precision one.

subroutine dlagts (job, n, a, b, c, d, in, y, tol, info)

DLAGTS 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.

• slagts — the real-precision one.

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.

🌸 Detailed Description 🌸

ngl this heading is lowkey just vibes — the real content is the function documentation right below, and that section is the main character. Vibe check: no cap, that's where the parameters live. 🫶

🎀 Function Documentation 🎀

💖 dlagts — double precision, double the slay

subroutine dlagts (integer job, integer n, double precision, dimension( * ) a, double precision, dimension( * ) b, double precision, dimension( * ) c, double precision, dimension( * ) d, integer, dimension( * ) in, double precision, dimension( * ) y, double precision tol, integer info)

DLAGTS 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.

🦋 Purpose

okay so here's the vibe: DLAGTS may be used to solve one of these systems for x:

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

where T is an n by n tridiagonal matrix, after (T - lambda*I) has been factored as:

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

by routine DLAGTF. The argument JOB controls which equation gets solved, and in each case there's an option to perturb zero or very small diagonal elements of U. That option is intended for applications such as inverse iteration. 💅

🔥 Parameters

• JOB — INTEGER. Specifies the job DLAGTS does, and the values are literally:
  • = 1: solve (T - lambda*I)x = y, but do not perturb diagonal elements of U.
  • = -1: solve (T - lambda*I)x = y, and if overflow would otherwise occur, perturb the diagonal elements of U. See TOL below.
  • = 2: solve (T - lambda*I)**Tx = y, but do not perturb diagonal elements of U.
  • = -2: solve (T - lambda*I)**Tx = y, and if overflow would otherwise occur, perturb the diagonal elements of U. See TOL below.
• N — INTEGER. The order of the matrix T.
• A — DOUBLE PRECISION array, dimension (N). On entry, A must contain the diagonal elements of U as returned from DLAGTF.
• B — DOUBLE PRECISION array, dimension (N-1). On entry, B must contain the first super-diagonal elements of U as returned from DLAGTF.
• C — DOUBLE PRECISION array, dimension (N-1). On entry, C must contain the sub-diagonal elements of L as returned from DLAGTF.
• D — DOUBLE PRECISION array, dimension (N-2). On entry, D must contain the second super-diagonal elements of U as returned from DLAGTF.
• IN — INTEGER array, dimension (N). On entry, IN must contain details of the matrix P as returned from DLAGTF.
• Y — DOUBLE PRECISION array, dimension (N). On entry, the right hand side vector y. On exit, Y is overwritten by the solution vector x. (not me, the solution is literally in Y now 💀)
• TOL — DOUBLE PRECISION. 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.
• INFO — INTEGER. Exit status tea:
  • = 0: successful exit. slay.
  • < 0: if INFO = -i, the i-th argument had an illegal value.
  • > 0: overflow would occur when computing the INFO(th) 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. ⚠️ this is the danger zone, bestie.

👑 Author

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

Definition at line 162 of file dlagts.f.

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💜 slagts — real precision, real iconic

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.

🦋 Purpose

okay so same energy as above but in REAL precision: SLAGTS may be used to solve one of these systems for x:

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

where T is an n by n tridiagonal matrix, after (T - lambda*I) has been factored as:

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

by routine SLAGTF. The argument JOB controls which equation gets solved, and in each case there's an option to perturb zero or very small diagonal elements of U. That option is intended for applications such as inverse iteration. 💅

🔥 Parameters

• JOB — INTEGER. Specifies the job SLAGTS does, and the values are literally:
  • = 1: solve (T - lambda*I)x = y, but do not perturb diagonal elements of U.
  • = -1: solve (T - lambda*I)x = y, and if overflow would otherwise occur, perturb the diagonal elements of U. See TOL below.
  • = 2: solve (T - lambda*I)**Tx = y, but do not perturb diagonal elements of U.
  • = -2: solve (T - lambda*I)**Tx = y, and if overflow would otherwise occur, perturb the diagonal elements of U. See TOL below.
• N — INTEGER. The order of the matrix T.
• A — REAL array, dimension (N). On entry, A must contain the diagonal elements of U as returned from SLAGTF.
• B — REAL array, dimension (N-1). On entry, B must contain the first super-diagonal elements of U as returned from SLAGTF.
• C — REAL array, dimension (N-1). On entry, C must contain the sub-diagonal elements of L as returned from SLAGTF.
• D — REAL array, dimension (N-2). On entry, D must contain the second super-diagonal elements of U as returned from SLAGTF.
• IN — INTEGER array, dimension (N). On entry, IN must contain details of the matrix P as returned from SLAGTF.
• Y — REAL array, dimension (N). On entry, the right hand side vector y. On exit, Y is overwritten by the solution vector x. (again, x is literally living in Y now 💀)
• TOL — 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.
• INFO — INTEGER. Exit status tea:
  • = 0: successful exit. slay.
  • < 0: if INFO = -i, the i-th argument had an illegal value.
  • > 0: overflow would occur when computing the INFO(th) 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. ⚠️ overflow warning, bestie.

👑 Author

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

Definition at line 162 of file slagts.f.

💖 Author 💖

Generated automatically by Doxygen for LAPACK from the source code.

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bestie, that's the whole lagts(3) page — brought to you by LAPACK Version 3.12.0, and there's no date on this footer, just the version and the page name lagts(3). periodt 💅✨