-
Notifications
You must be signed in to change notification settings - Fork 101
Commit
This commit does not belong to any branch on this repository, and may belong to a fork outside of the repository.
Notebook with experimental newton implementation
- Loading branch information
Showing
1 changed file
with
181 additions
and
0 deletions.
There are no files selected for viewing
This file contains bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters.
Learn more about bidirectional Unicode characters
Original file line number | Diff line number | Diff line change |
---|---|---|
@@ -0,0 +1,181 @@ | ||
{ | ||
"cells": [ | ||
{ | ||
"cell_type": "code", | ||
"execution_count": 1, | ||
"id": "ff134dc2-ad8c-41b9-a8da-8cc7b5352b9d", | ||
"metadata": {}, | ||
"outputs": [], | ||
"source": [ | ||
"from typing import Callable\n", | ||
"import pytensor\n", | ||
"import pytensor.tensor as pt\n", | ||
"from scipy import linalg\n", | ||
"from pytensor.scan.utils import until\n", | ||
"from functools import partial" | ||
] | ||
}, | ||
{ | ||
"cell_type": "code", | ||
"execution_count": 2, | ||
"id": "759d75fe-6b86-42a5-a9d3-96af6de75053", | ||
"metadata": {}, | ||
"outputs": [], | ||
"source": [ | ||
"def _newton_step(func, x, args):\n", | ||
" f_x = func(x, *args)\n", | ||
" jac = pt.jacobian(f_x, x)\n", | ||
"\n", | ||
" # TODO It would be nice to return the factored matrix for the pullback\n", | ||
" # TODO Handle errors of the factorization\n", | ||
" grad = pt.linalg.solve(jac, f_x, assume_a=\"sym\")\n", | ||
"\n", | ||
" return f_x, x - grad, grad, jac\n", | ||
"\n", | ||
"def _check_convergence(f_x, x, new_x, grad, tol):\n", | ||
" # TODO What convergence criterion? Norm of grad etc...\n", | ||
" converged = pt.lt(pt.linalg.norm(f_x, ord=1), tol)\n", | ||
" return converged\n", | ||
"\n", | ||
"def _scan_step(x, n_steps, *args, func, tol):\n", | ||
" f_x, new_x, grad, jac = _newton_step(func, x, args)\n", | ||
" is_converged = _check_convergence(f_x, x, new_x, grad, tol)\n", | ||
" return (new_x, n_steps + 1, jac), until(is_converged)\n", | ||
"\n", | ||
"def root(\n", | ||
" func: Callable,\n", | ||
" x0: pt.TensorVariable, # rank 1\n", | ||
" args: tuple[pt.Variable, ...],\n", | ||
" max_iter: int = 113,\n", | ||
" tol: float = 1e-8,\n", | ||
") -> tuple[\n", | ||
" pt.TensorVariable, dict,\n", | ||
"]:\n", | ||
" root_func = partial(\n", | ||
" _scan_step,\n", | ||
" func=func,\n", | ||
" tol=tol,\n", | ||
" )\n", | ||
"\n", | ||
" outputs, updates = pytensor.scan(\n", | ||
" root_func,\n", | ||
" outputs_info=[x0, pt.constant(0, dtype=\"int64\"), None],\n", | ||
" non_sequences=args,\n", | ||
" n_steps=max_iter,\n", | ||
" strict=True,\n", | ||
" )\n", | ||
"\n", | ||
" x_trace, n_steps_trace, jac_trace = outputs\n", | ||
" assert not updates\n", | ||
"\n", | ||
" return x_trace[-1], {\"n_steps\": n_steps_trace[-1], \"jac\": jac_trace[-1]}\n", | ||
"\n", | ||
"\n", | ||
"def minimize(cost: Callable, x0: pt.TensorVariable, args):\n", | ||
" def func(x):\n", | ||
" return pt.grad(cost(x), x)\n", | ||
"\n", | ||
" return root(func, x0, args)" | ||
] | ||
}, | ||
{ | ||
"cell_type": "code", | ||
"execution_count": 3, | ||
"id": "21304789-4eab-49de-9db7-a5bb327712b2", | ||
"metadata": {}, | ||
"outputs": [], | ||
"source": [ | ||
"import numpy as np" | ||
] | ||
}, | ||
{ | ||
"cell_type": "code", | ||
"execution_count": 4, | ||
"id": "b031e81a-c615-4af5-b2d9-897ee46f15dc", | ||
"metadata": {}, | ||
"outputs": [], | ||
"source": [ | ||
"x0 = pt.tensor(\"x0\", shape=(3,))\n", | ||
"#x0 = pt.full((3,), [2., 2., 2.])\n", | ||
"#x0 = x0.copy()\n", | ||
"\n", | ||
"mu = pt.tensor(\"mu\", shape=())\n", | ||
"\n", | ||
"def func(x, mu):\n", | ||
" cost = pt.sum((x ** 2 - mu) ** 2)\n", | ||
" return pt.grad(cost, x)\n", | ||
"\n", | ||
"\n", | ||
"x_root, stats = root(func, x0, args=[mu], tol=1e-8)\n", | ||
"\n", | ||
"(x_root_dmu,) = pt.grad(x_root[0], [mu])\n", | ||
"\n", | ||
"f_x = func(x_root, mu)\n", | ||
"dfunc_dmu = pt.jacobian(f_x, mu, consider_constant=[x_root])" | ||
] | ||
}, | ||
{ | ||
"cell_type": "code", | ||
"execution_count": 5, | ||
"id": "0d54e9a4-89ed-4670-b069-ea58bb4e85e5", | ||
"metadata": {}, | ||
"outputs": [], | ||
"source": [ | ||
"func = pytensor.function([x0, mu], [x_root, stats[\"n_steps\"], stats[\"jac\"], dfunc_dmu])" | ||
] | ||
}, | ||
{ | ||
"cell_type": "code", | ||
"execution_count": 8, | ||
"id": "07747b6d-71ca-4bc3-9546-45e3122890d4", | ||
"metadata": {}, | ||
"outputs": [], | ||
"source": [ | ||
"x_root, n_steps, jac, dfunc_dmu_val = func(np.ones(3) * 3, np.full((), 5.))" | ||
] | ||
}, | ||
{ | ||
"cell_type": "code", | ||
"execution_count": 9, | ||
"id": "2bf94004-465e-4c04-a23a-971c43b637a7", | ||
"metadata": {}, | ||
"outputs": [ | ||
{ | ||
"data": { | ||
"text/plain": [ | ||
"array([0.2236068, 0.2236068, 0.2236068])" | ||
] | ||
}, | ||
"execution_count": 9, | ||
"metadata": {}, | ||
"output_type": "execute_result" | ||
} | ||
], | ||
"source": [ | ||
"# Dervivative of x_root with respect to mu\n", | ||
"-linalg.solve(jac, dfunc_dmu_val, assume_a=\"sym\")" | ||
] | ||
} | ||
], | ||
"metadata": { | ||
"kernelspec": { | ||
"display_name": "dev-cuda", | ||
"language": "python", | ||
"name": "dev-cuda" | ||
}, | ||
"language_info": { | ||
"codemirror_mode": { | ||
"name": "ipython", | ||
"version": 3 | ||
}, | ||
"file_extension": ".py", | ||
"mimetype": "text/x-python", | ||
"name": "python", | ||
"nbconvert_exporter": "python", | ||
"pygments_lexer": "ipython3", | ||
"version": "3.11.9" | ||
} | ||
}, | ||
"nbformat": 4, | ||
"nbformat_minor": 5 | ||
} |