x = [32,37,42,47,52,57,62,67,72,77,82,87,92]
y = [749,1525,1947,2201,2380,2537,2671,2758,2803,2943,3007,2979,2992]
model = function(x,p){return x.map(function(x_i){return (
p[0]*Math.exp(-0.5*(Math.pow((x_i-p[1])/p[2],2))) + p[3]
)})}
p_init = [-60000,-90,40,3100];
// Define bounds for the parameters
Opt = {
return {
maxIter: 500, // Optional
bounds: [
[-70000, -50000], // Bounds for p[0] => [-Infinity, Infinity], // No bounds
[-90, 100], // Bounds for p[1]
[1, 40], // Bounds for p[2]
[3000, 3100] // Bounds for p[3]
],
}
};
// Modified fminsearch function with bounds: Please note that this implementation is not optimized.
// Adapted from: https://github.com/jonasalmeida/fminsearch
// See associated notebook: https://observablehq.com/@christophe-yamahata/nonlinear-regression-with-bounds-in-javascript
fminsearch = function(fun, Parm0, x, y, Opt) {
if (!Opt) { Opt = {} };
if (!Opt.maxIter) { Opt.maxIter = 1000 };
if (!Opt.step) { // initial step is 1/100 of initial value (remember not to use zero in Parm0)
Opt.step = Parm0.map(function(p) { return p / 100 });
Opt.step = Opt.step.map(function(si) { if (si == 0) { return 1 } else { return si } }); // convert null steps into 1's
};
if (typeof (Opt.display) == 'undefined') { Opt.display = true };
if (!Opt.objFun) { Opt.objFun = function(y, yp) { return y.map(function(yi, i) { return Math.pow((yi - yp[i]), 2) }).reduce(function(a, b) { return a + b }) } } //SSD
if (!Opt.bounds) { Opt.bounds = Parm0.map(function() { return [-Infinity, Infinity] }) }; // Default no bounds
var cloneVector = function(V) { return V.map(function(v) { return v }) };
var ya, y0, yb, fP0, fP1;
var P0 = cloneVector(Parm0), P1 = cloneVector(Parm0);
var n = P0.length;
// var step = Opt.step;
let step = cloneVector(Opt.step); // Ensure step is reinitialized
var funParm = function(P) { return Opt.objFun(y, fun(x, P)) } //function (of Parameters) to minimize
// Apply bounds
var applyBounds = function(P, bounds) {
return P.map(function(p, i) {
return Math.max(bounds[i][0], Math.min(bounds[i][1], p));
});
}
// Silly multi-univariate screening
for (var i = 0; i < Opt.maxIter; i++) {
for (var j = 0; j < n; j++) { // take a step for each parameter
P1 = cloneVector(P0);
P1[j] += step[j];
P1 = applyBounds(P1, Opt.bounds); // Apply bounds after updating the parameter
if (funParm(P1) < funParm(P0)) { // if parm value going in the right direction
step[j] = 1.2 * step[j]; // then go a little faster
P0 = cloneVector(P1);
}
else {
step[j] = -(0.5 * step[j]); // otherwise reverse and go slower
}
}
if (Opt.display) { if (i > (Opt.maxIter - 10)) { console.log(i + 1, funParm(P0), P0) } }
}
return P0
}
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