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Optimisation

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Copy a Tessero-tuned prompt for Optimisation, grounded in 16 real API signatures , into your IDE's AI. No chatbot, just exact context.

These follow scipy.optimize. The objective functions are PHP callables, so they are driven from PHP; the linear algebra inside them runs natively. For linear and mixed-integer programs, see [Linear programming(https://github.com/DMJ-CV-91913/tessero/blob/main/docs/guide/linear-programming.md). Those solvers run entirely in C.

minimize

use Tessero\Optimize\Minimize;

$rosen = fn (array $x): float => 100 * ($x[1] - $x[0] ** 2) ** 2 + (1 - $x[0]) ** 2;

$r = Minimize::minimize($rosen, [-1.2, 1.0]);                        // BFGS
$r = Minimize::minimize($rosen, [-1.2, 1.0], method: 'Nelder-Mead');
$r = Minimize::minimize($rosen, [-1.2, 1.0], method: 'L-BFGS-B', bounds: [[-2, 2], [-2, 2]]);
$r = Minimize::minimize($rosen, [-1.2, 1.0], jac: $gradient);        // analytic gradient

$r->x;        // [1.0, 1.0] (approximately)
$r->fun; $r->success; $r->message; $r->nit; $r->nfev;
Method Notes
BFGS (default) SciPy's algorithm, including its Wolfe line search; same iterates as SciPy on the test problems
L-BFGS-B projected L-BFGS with bound constraints; same optimum as SciPy, different path
Nelder-Mead same iterates as SciPy (adaptive option supported)

Options go in options: ['maxiter' => …, 'gtol' => …, 'xatol' => …, 'fatol' => …] with SciPy's names. Without jac the gradient is approximated by forward differences, using SciPy's step size.

Roots

use Tessero\Optimize\Root;

Root::brentq(fn ($x) => $x ** 3 - 2 * $x - 5, 2, 3);     // 2.094551481542327
Root::newton(fn ($x) => cos($x) - $x, 1.0);              // secant method without fprime
Root::root($F, [1.0, 1.0]);                               // systems: damped Newton

brentq gives the same root and the same number of function calls as SciPy.

Least squares and curve fitting

use Tessero\Optimize\LeastSquares;

$model = fn (float $t, float $a, float $k): float => $a * exp(-$k * $t);
[$popt, $pcov] = LeastSquares::curveFit($model, $t, $y, p0: [1.0, 0.1]);
$stderr = array_map('sqrt', [$pcov[0][0], $pcov[1][1]]);

LeastSquares::solve($residuals, $p0);    // Levenberg-Marquardt on a residual function

curveFit scales the covariance as SciPy does, and supports sigma and absoluteSigma.

Limits

There are no trust-region methods and no general nonlinear constraints (only bounds, through L-BFGS-B). Use the [LP/MILP solvers(https://github.com/DMJ-CV-91913/tessero/blob/main/docs/guide/linear-programming.md) for linear constraints.

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