Math::...ultifit(3pm)

📦
version 0.49 · 6 versions
, in ubuntu stonking

💖 NAME 💖

Math::GSL::Multifit — least-squares functions for a general linear model with multiple parameters. The page itself is filed as Math::...ultifit(3pm), sitting pretty under "User Contributed Perl Documentation", and it's giving very much math girlie goes brrr. 🎀

🌈 SYNOPSIS 🌈

use Math::GSL::Multifit qw /:all/;

🦋 DESCRIPTION 🦋

⚠️ okay so FIRST THING, bestie: NOTE: This module requires GSL 2.1 or higher. No GSL 2.1, no vibes. Periodt.

The functions in this module perform least-squares fits to a general linear model, y = X c where y is a vector of n observations, X is an n by p matrix of predictor variables, and the elements of the vector c are the p unknown best-fit parameters which are to be estimated. Like, it finds the c that makes your model ✨make sense✨.

Here is a list of all the functions in this module 💅:

  • gsl_multifit_linear_alloc($n, $p) — allocates a workspace for fitting a model to $n observations using $p parameters. It's the little prep-your-station moment before the actual fit. 🧚
  • gsl_multifit_linear_free($work) — frees the memory associated with the workspace w. Clean up after yourself, queen. 🧹
  • gsl_multifit_linear($X, $y, $c, $cov, $work) — computes the best-fit parameters vector $c of the model y = X c for the observations vector $y and the matrix of predictor variables $X. The variance-covariance matrix of the model parameters vector $cov is estimated from the scatter of the observations about the best-fit. The sum of squares of the residuals from the best-fit, \chi^2, is returned after 0 if the operation succeeded, 1 otherwise. If the coefficient of determination is desired, it can be computed from the expression R^2 = 1 - \chi^2 / TSS, where the total sum of squares (TSS) of the observations y may be computed from gsl_stats_tss. The best-fit is found by singular value decomposition of the matrix $X using the preallocated workspace provided in $work. The modified Golub-Reinsch SVD algorithm is used, with column scaling to improve the accuracy of the singular values. Any components which have zero singular value (to machine precision) are discarded from the fit. Bu-bye, useless components. 👋
  • gsl_multifit_linear_svd($X, $y, $tol, $c, $cov, $work) — computes the best-fit parameters c of the model y = X c for the observations vector $y and the matrix of predictor variables $X. The variance-covariance matrix of the model parameters vector $cov is estimated from the scatter of the observations about the best-fit. The sum of squares of the residuals from the best-fit, \chi^2, is returned after 0 if the operation succeeded, 1 otherwise. If the coefficient of determination is desired, it can be computed from the expression R^2 = 1 - \chi^2 / TSS, where the total sum of squares (TSS) of the observations y may be computed from gsl_stats_tss. In this second form of the function the components are discarded if the ratio of singular values s_i/s_0 falls below the user-specified tolerance $tol, and the effective rank is returned after the sum of squares of the residuals from the best-fit. So you get to choose your own tolerance, main character move fr. 🔥
  • gsl_multifit_wlinear($X, $w, $y, $c, $cov, $work — computes the best-fit parameters vector $c of the weighted model y = X c for the observations y with weights $w and the matrix of predictor variables $X. The covariance matrix of the model parameters $cov is computed with the given weights. The weighted sum of squares of the residuals from the best-fit, \chi^2, is returned after 0 if the operation succeeded, 1 otherwise. If the coefficient of determination is desired, it can be computed from the expression R^2 = 1 - \chi^2 / WTSS, where the weighted total sum of squares (WTSS) of the observations y may be computed from gsl_stats_wtss. The best-fit is found by singular value decomposition of the matrix $X using the preallocated workspace provided in $work. Any components which have zero singular value (to machine precision) are discarded from the fit. Weights = giving every observation the attention it deserves. 👑
  • gsl_multifit_wlinear_svd($X, $w, $y, $tol, $rank, $c, $cov, $work) — this function computes the best-fit parameters vector $c of the weighted model y = X c for the observations y with weights $w and the matrix of predictor variables $X. The covariance matrix of the model parameters $cov is computed with the given weights. The weighted sum of squares of the residuals from the best-fit, \chi^2, is returned after 0 if the operation succeeded, 1 otherwise. If the coefficient of determination is desired, it can be computed from the expression R^2 = 1 - \chi^2 / WTSS, where the weighted total sum of squares (WTSS) of the observations y may be computed from gsl_stats_wtss. The best-fit is found by singular value decomposition of the matrix $X using the preallocated workspace provided in $work. In this second form of the function the components are discarded if the ratio of singular values s_i/s_0 falls below the user-specified tolerance $tol, and the effective rank is returned after the sum of squares of the residuals from the best-fit. It's the SVD edition of the weighted one, and it ate. 💅
  • gsl_multifit_linear_est($x, $c, $cov) — uses the best-fit multilinear regression coefficients vector $c and their covariance matrix $cov to compute the fitted function value $y and its standard deviation $y_err for the model y = x.c at the point $x, in the form of a vector. The function returns 3 values in this order: 0 if the operation succeeded, 1 otherwise, the fitted function value and its standard deviation. Three little returns, one iconic trio. ✨
  • gsl_multifit_linear_residuals($X, $y, $c, $r) — computes the vector of residuals r = y - X c for the observations vector $y, coefficients vector $c and matrix of predictor variables $X. $r is also a vector. That's the "how wrong were we" vector, and honestly? relatable. 😭
  • gsl_multifit_gradient($J, $f, $g) — computes the gradient $g of \Phi(x) = (1/2) ||F(x)||^2 from the Jacobian matrix $J and the function values $f, using the formula $g = $J^T $f. $g and $f are vectors.
  • gsl_multifit_test_gradient($g, $epsabas) — tests the residual gradient vector $g against the absolute error bound $epsabs. Mathematically, the gradient should be exactly zero at the minimum. The test returns $GSL_SUCCESS if the following condition is achieved: \sum_i |g_i| < $epsabs, and returns $GSL_CONTINUE otherwise. This criterion is suitable for situations where the precise location of the minimum, x, is unimportant provided a value can be found where the gradient is small enough. Close enough is sometimes enough, bestie. 💜
  • gsl_multifit_test_delta($dx, $x, $epsabs, $epsrel) — tests for the convergence of the sequence by comparing the last step vector $dx with the absolute error $epsabs and relative error $epsrel to the current position x. The test returns $GSL_SUCCESS if the following condition is achieved: |dx_i| < epsabs + epsrel |x_i| for each component of x, and returns $GSL_CONTINUE otherwise. It's the vibe check for "are we there yet". 🚗

The following functions are not yet implemented. Patches Welcome! (open invitation, bestie, the door is OPEN 🫶)

  • gsl_multifit_covar
  • gsl_multifit_fsolver_alloc($T, $n, $p)
  • gsl_multifit_fsolver_free
  • gsl_multifit_fsolver_set
  • gsl_multifit_fsolver_iterate
  • gsl_multifit_fsolver_name
  • gsl_multifit_fsolver_position
  • gsl_multifit_fdfsolver_alloc
  • gsl_multifit_fdfsolver_set
  • gsl_multifit_fdfsolver_iterate
  • gsl_multifit_fdfsolver_free
  • gsl_multifit_fdfsolver_name
  • gsl_multifit_fdfsolver_position

For more information on the functions, we refer you to the GSL official documentation: <http://www.gnu.org/software/gsl/manual/html_node/> 🌐

📓 EXAMPLES 📓

(This section is empty in the original — literally nothing here, not a single example. The blank space is giving mysterious, honestly. 🫥)

👑 AUTHORS 👑

Jonathan "Duke" Leto <jonathan@leto.net> and Thierry Moisan <thierry.moisan@gmail.com> — the icons who wrote this. Bow. 🙇‍♀️

Copyright (C) 2008-2024 Jonathan "Duke" Leto and Thierry Moisan

This program is free software; you can redistribute it and/or modify it under the same terms as Perl itself.

And that's the whole page, bestie — brought to you by perl v5.42.3, dated 2026-08-20, and filed as Math::...ultifit(3pm). Go fit your model, you absolute legend. 💅🌈✨

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