Ceres.js is a javascript port of the Ceres solver. Ceres Solver is an open source C++ library ported to javascript with emscripten for modeling and solving large, complicated optimization problems. It can be used to solve Non-linear Least Squares problems with bounds constraints and general unconstrained optimization problems. It is a mature, feature rich, and performant library.

Visit our website at https://pterodactylus.github.io/Ceres.js/

You can install Ceres.js by including the Ceres.js file in your HTML or js code.

<script src="https://cdn.jsdelivr.net/gh/Pterodactylus/Ceres.js@master/Ceres-v1.4.13.js"></script>

Ceres.js takes a vector of residual equations that are all equal to zero when the problem is solved. The equations can be non-linear. Here is a basic example.

<script type="module">
	import {Ceres} from 'https://cdn.jsdelivr.net/gh/Pterodactylus/Ceres.js@master/Ceres-v1.4.13.js' //Always imported via ES6 import

	var fn1 = function f1(x){
		return (x[0]+10*x[1]-20); //this equation is of the form f1(x) = 0 
	}

	var fn2 = function f2(x){
		return (Math.sqrt(5)*x[0]-Math.pow(x[1], 2)); //this equation is of the form f2(x) = 0 
	}
	var c1 = function callback1(x, evaluate_jacobians, new_evaluation_point){
			console.log(x);
	}

	var solver = new Ceres();
	solver.promise.then(function(result) { 
		solver.add_function(fn1) //Add the first equation to the solver.
		solver.add_function(fn2) //Add the second equation to the solver.
		solver.add_callback(c1) //Add the callback to the solver.
		//solver.add_lowerbound(0,1.6) //Add a lower bound to the x[0] variable
		//solver.add_upperbound(1,1.7) //Add a upper bound to the x[1] variable
		var x_guess = [1,2] //Guess the initial values of the solution.
		var s = solver.solve(x_guess) //Solve the equation
		var x = s.x //assign the calculated solution array to the variable x
		console.log(s.report); //Print solver report
		
		solver.reset() //enables the solver to run agin without reloading
		solver.add_function(fn1) //Add the first equation to the solver.
		solver.add_function(fn2) //Add the second equation to the solver.
		solver.add_callback(c1) //Add the callback to the solver.
		var x_guess = [2,3] //Guess the initial values of the solution.
		var s = solver.solve(x_guess) //Solve the equation
		console.log(s.report); //Print solver report
		
		solver.remove() //required to free the memory in C++
	})
</script>

The Ceres class starts an instance of the Ceres solver. It has four methods.

1. The Ceres() constructor method takes no inputs and creates a new Solver instance.
2. The add_function(fxn_handle) method takes a function that has input of an array of number equal in length to the total number of functions. Each of the function should return a residule. The residuals returned should equal zero at the solution point i.e. F(x) = 0.
3. The add_callback(callback_handle) method takes a function that has input of an array of number equal in length to the total number of functions. This callback function is run every time before a function evaluation. You can use it to print intermediate results.
4. The solve(initial_guesses, max_num_iterations = 2000, parameter_tolerance = 1e-10, function_tolerance = 1e-16, gradient_tolerance = 1e-16, max_solver_time_in_seconds = 100, initial_trust_region_radius = 1e4, max_trust_region_radius = 1e16, max_num_consecutive_invalid_steps = 5) function requires an array initial_guesses = [x1_init, x2_init, etc.. ] that defines the solver starting point. This function returns an x solution array and a report variable with a full report of the solver output.