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https://github.com/xibyte/jsketcher
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638 lines
No EOL
16 KiB
JavaScript
638 lines
No EOL
16 KiB
JavaScript
import numeric from 'numeric';
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import {_vec, _matrix} from './math'
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const SUCCESS = 1, ITER_LIMIT = 2, SMALL_DELTA = 3, SMALL_STEP = 4, DIVERGENCE = 5, INVALID_STATE = 6;
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//Added strong wolfe condition to numeric's uncmin
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export function fmin_bfgs(f,x0,tol,gradient,maxit,callback,options) {
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var grad = numeric.gradient;
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if(typeof options === "undefined") { options = {}; }
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if(typeof tol === "undefined") { tol = 1e-8; }
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if(typeof gradient === "undefined") { gradient = function(x) { return grad(f,x); }; }
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if(typeof maxit === "undefined") maxit = 1000;
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x0 = numeric.clone(x0);
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var n = x0.length;
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var f0 = f(x0),f1,df0;
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if(isNaN(f0)) throw new Error('uncmin: f(x0) is a NaN!');
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var max = Math.max, norm2 = numeric.norm2;
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tol = max(tol,numeric.epsilon);
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var step,g0,g1,H1 = options.Hinv || numeric.identity(n);
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var dot = numeric.dot, inv = numeric.inv, sub = numeric.sub, add = numeric.add, ten = numeric.tensor, div = numeric.div, mul = numeric.mul;
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var all = numeric.all, isfinite = numeric.isFinite, neg = numeric.neg;
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var it=0,i,s,x1,y,Hy,Hs,ys,i0,t,nstep,t1,t2;
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var msg = "";
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g0 = gradient(x0);
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while(it<maxit) {
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if(typeof callback === "function") { if(callback(it,x0,f0,g0,H1)) { msg = "Callback returned true"; break; } }
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if(!all(isfinite(g0))) { msg = "Gradient has Infinity or NaN"; break; }
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step = neg(dot(H1,g0));
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if(!all(isfinite(step))) { msg = "Search direction has Infinity or NaN"; break; }
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nstep = norm2(step);
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if(nstep < tol) { msg="Newton step smaller than tol"; break; }
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t = 1;
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df0 = dot(g0,step);
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// line search
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x1 = x0;
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var tL = 0;
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var tR = 100;
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while(it < maxit) {
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if(t*nstep < tol) { break; }
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s = mul(step,t);
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x1 = add(x0,s);
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f1 = f(x1);
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//Nocadel, 3.7(a,b)
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if(f1-f0 >= 0.1*t*df0 || isNaN(f1)) {
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tR = t;
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t = (tL + tR) * 0.5;
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++it;
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} else {
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var slope = dot(gradient(x1), step);
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if (slope <= 0.9 * Math.abs(df0)){
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break;
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}else if ( slope >= 0.9 * df0) {
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tR = t;
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t = (tL+ tR) * 0.5;
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}else{
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tL = t;
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t = (tL+ tR)*0.5;
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}
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}
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}
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if(t*nstep < tol) { msg = "Line search step size smaller than tol"; break; }
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if(it === maxit) { msg = "maxit reached during line search"; break; }
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g1 = gradient(x1);
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y = sub(g1,g0);
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ys = dot(y,s);
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Hy = dot(H1,y);
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// BFGS update on H1
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H1 = sub(add(H1,
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mul(
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(ys+dot(y,Hy))/(ys*ys),
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ten(s,s) )),
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div(add(ten(Hy,s),ten(s,Hy)),ys));
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x0 = x1;
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f0 = f1;
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g0 = g1;
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++it;
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}
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return {solution: x0, f: f0, gradient: g0, invHessian: H1, iterations:it, message: msg};
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};
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var bfgs = function(f,x0,tol,gradient,maxit,callback,options) {
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var grad = numeric.gradient;
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if(typeof options === "undefined") { options = {}; }
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if(typeof tol === "undefined") { tol = 1e-8; }
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if(typeof gradient === "undefined") { gradient = function(x) { return grad(f,x); }; }
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if(typeof maxit === "undefined") maxit = 1000;
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x0 = numeric.clone(x0);
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var n = x0.length;
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var f0 = f(x0),f1,df0;
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if(isNaN(f0)) throw new Error('uncmin: f(x0) is a NaN!');
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var max = Math.max, norm2 = numeric.norm2;
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tol = max(tol,numeric.epsilon);
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var step,g0,g1,H1 = options.Hinv || numeric.identity(n);
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var dot = numeric.dot, inv = numeric.inv, sub = numeric.sub, add = numeric.add, ten = numeric.tensor, div = numeric.div, mul = numeric.mul;
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var all = numeric.all, isfinite = numeric.isFinite, neg = numeric.neg;
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var it=0,i,s,x1,y,Hy,Hs,ys,i0,t,nstep,t1,t2;
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var msg = "";
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g0 = gradient(x0);
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while(it<maxit) {
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if(typeof callback === "function") { if(callback(it,x0,f0,g0,H1)) { msg = "Callback returned true"; break; } }
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if(!all(isfinite(g0))) { msg = "Gradient has Infinity or NaN"; break; }
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step = neg(dot(H1,g0));
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if(!all(isfinite(step))) { msg = "Search direction has Infinity or NaN"; break; }
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nstep = norm2(step);
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if(nstep < tol) { msg="Newton step smaller than tol"; break; }
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df0 = dot(g0,step);
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// line search
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t1 = 0.0;
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f1 = f0;
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t2 = 1.0;
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s = mul(step,t2);
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x1 = add(x0,s);
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var f2 = f(x1);
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var t3 = 2.0;
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s = mul(step,t3);
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x1 = add(x0,s);
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var f3 = f(x1);
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var tMax = 1e23;
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while( (f2 > f1 || f2 > f3) && it < maxit) {
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if(t*nstep < tol) { break; }
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if (f2 > f1) {
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//If f2 is greater than f1 then we shorten alpha2 and alpha3 closer to f1
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//Effectively both are shortened by a factor of two.
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t3 = t2;
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f3 = f2;
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t2 = t2 / 2;
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s = mul(step,t2);
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x1 = add(x0,s);
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f2 = f(x1);
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}
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else if (f2 > f3) {
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if (t3 >= tMax)
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break;
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//If f2 is greater than f3 then we increase alpha2 and alpha3 away from f1
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//Effectively both are lengthened by a factor of two.
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t2 = t3;
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f2 = f3;
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t3 = t3 * 2;
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s = mul(step,t3);
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x1 = add(x0,s);
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f3 = f(x1);
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}
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it ++;
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}
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//Get the alpha for the minimum f of the quadratic approximation
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var ts = t2 + ((t2-t1)*(f1-f3))/(3*(f1-2*f2+f3));
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//Guarantee that the new alphaStar is within the bracket
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if (ts >= t3 || ts <= t1)
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ts = t2;
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if (ts > tMax)
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ts = tMax;
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if (ts != ts)
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ts = 0.;
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//Take a final step to alphaStar
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s = mul(step,ts);
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x1 = add(x0,s);
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f1 = f(x1);
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if(t*nstep < tol) { msg = "Line search step size smaller than tol"; break; }
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if(it === maxit) { msg = "maxit reached during line search"; break; }
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g1 = gradient(x1);
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y = sub(g1,g0);
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ys = dot(y,s);
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Hy = dot(H1,y);
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// BFGS update on H1
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H1 = sub(add(H1,
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mul(
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(ys+dot(y,Hy))/(ys*ys),
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ten(s,s) )),
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div(add(ten(Hy,s),ten(s,Hy)),ys));
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x0 = x1;
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f0 = f1;
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g0 = g1;
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++it;
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}
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return {solution: x0, f: f0, gradient: g0, invHessian: H1, iterations:it, message: msg};
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};
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var bfgs_updater = function(gradient, x0) {
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var n = x0.length;
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var max = Math.max, norm2 = numeric.norm2;
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var g0,g1,H1 = numeric.identity(n);
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var dot = numeric.dot, inv = numeric.inv, sub = numeric.sub, add = numeric.add, ten = numeric.tensor, div = numeric.div, mul = numeric.mul;
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var all = numeric.all, isfinite = numeric.isFinite, neg = numeric.neg;
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var y,Hy,Hs,ys;
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var msg = "";
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g0 = gradient(x0);
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function step() {
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return neg(dot(H1,g0));
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}
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function update(x, real_step) {
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var s = real_step;
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g1 = gradient(x);
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y = sub(g1,g0);
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ys = dot(y,s);
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Hy = dot(H1,y);
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// BFGS update on H1
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H1 = sub(add(H1,
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mul(
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(ys+dot(y,Hy))/(ys*ys),
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ten(s,s) )),
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div(add(ten(Hy,s),ten(s,Hy)),ys));
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g0 = g1;
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}
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return {step:step, update:update};
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};
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var inv = function inv(A) {
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A = numeric.clone(A);
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var s = numeric.dim(A), abs = Math.abs, m = s[0], n = s[1];
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var Ai, Aj;
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var I = numeric.identity(m), Ii, Ij;
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var i,j,k,x;
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for(j=0;j<n;++j) {
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var i0 = -1;
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var v0 = -1;
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for(i=j;i!==m;++i) { k = abs(A[i][j]); if(k>v0) { i0 = i; v0 = k; } }
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Aj = A[i0]; A[i0] = A[j]; A[j] = Aj;
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Ij = I[i0]; I[i0] = I[j]; I[j] = Ij;
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x = Aj[j];
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if (x === 0) {
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console.log("CAN' INVERSE MATRIX");
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x = 1e-32
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}
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for(k=j;k!==n;++k) Aj[k] /= x;
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for(k=n-1;k!==-1;--k) Ij[k] /= x;
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for(i=m-1;i!==-1;--i) {
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if(i!==j) {
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Ai = A[i];
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Ii = I[i];
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x = Ai[j];
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for(k=j+1;k!==n;++k) Ai[k] -= Aj[k]*x;
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for(k=n-1;k>0;--k) { Ii[k] -= Ij[k]*x; --k; Ii[k] -= Ij[k]*x; }
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if(k===0) Ii[0] -= Ij[0]*x;
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}
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}
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}
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return I;
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};
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var _result = function(evalCount, error, returnCode) {
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return {
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evalCount, error, returnCode,
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success: returnCode === SUCCESS
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};
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};
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var dog_leg = function (subsys, rough) {
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//rough = true
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//var tolg = rough ? 1e-3 : 1e-4;
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var tolg, tolf;
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if (rough) {
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tolg = 1e-3;
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tolf = 1e-3;
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} else {
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tolg = 1e-6;
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tolf = 1e-6;
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}
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var tolx = 1e-80;
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var xsize = subsys.params.length;
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var csize = subsys.constraints.length;
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if (xsize == 0) {
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return _result(0, 0, 1);
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}
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var vec = _vec;
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var mx = _matrix;
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var n = numeric;
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var x = vec(xsize);
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var x_new = vec(xsize);
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var fx = vec(csize);
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var fx_new = vec(csize);
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var J = mx(csize, xsize);
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var J_new = mx(csize, xsize);
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var gn_step = vec(xsize);
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var dl_step = vec(xsize);
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subsys.fillParams(x);
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var err = subsys.calcResidual(fx);
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subsys.fillJacobian(J);
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function lsolve_slow(A, b) {
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var At = n.transpose(A);
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var res = n.dot(n.dot(At, inv(n.dot(A, At))), b);
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return res;
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}
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function lsolve(A, b) {
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if (csize < xsize) {
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var At = n.transpose(A);
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var sol = lu_solve(n.dot(A, At), b, true);
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return n.dot(At, sol);
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} else {
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return lu_solve(A, b, false);
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}
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}
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var g = n.dot(n.transpose(J), fx);
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var g_inf = n.norminf(g);
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var fx_inf = n.norminf(fx);
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var iterLimit = rough ? 100 : 500;
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var divergenceLimit = 1e6 * (err + 1e6);
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var delta = 10;
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var alpha = 0.;
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var iter = 0, returnCode = 0;
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//var log = [];
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while (returnCode === 0) {
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optim.DEBUG_HANDLER(iter, err);
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if (fx_inf <= tolf) {
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returnCode = SUCCESS;
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} else if (g_inf <= tolg) {
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returnCode = SUCCESS;
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} else if (iter >= iterLimit) {
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returnCode = ITER_LIMIT;
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} else if (delta <= tolx * (tolx + n.norm2(x))) {
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returnCode = SMALL_DELTA;
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} else if (err > divergenceLimit) {
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returnCode = DIVERGENCE;
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} else if (isNaN(err)) {
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returnCode = INVALID_STATE;
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}
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if (returnCode !== 0) {
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break;
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}
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// get the gauss-newton step
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//gn_step = n.solve(J, n.mul(fx, -1));
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gn_step = lsolve(J, n.mul(fx, -1));
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//LU-Decomposition
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//gn_step = lusolve(J, n.mul(fx, -1));
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//Conjugate gradient method
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//gn_step = cg(J, gn_step, n.mul(fx, -1), 1e-8, iterLimit);
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//solve linear problem using svd formula to get the gauss-newton step
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//gn_step = lls(J, n.mul(fx, -1));
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var hitBoundary = false;
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var gnorm = n.norm2(g);
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var gnNorm = n.norm2(gn_step);
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if (gnNorm < delta) {
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dl_step = gn_step;
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} else {
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var Jt = n.transpose(J);
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var B = n.dot(Jt, J);
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var gBg = n.dot(g, n.dot(B, g));
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alpha = n.norm2Squared(g) / gBg;
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if (alpha * gnorm >= delta) {
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dl_step = n.mul(g, - delta / gnorm);
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hitBoundary = true;
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} else {
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var sd_step = n.mul(g, - alpha);
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if (isNaN(gnNorm)) {
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dl_step = sd_step;
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} else {
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var d = n.sub(gn_step, sd_step);
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var a = n.dot(d, d);
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var b = 2 * n.dot(sd_step, d);
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var c = n.dot(sd_step, sd_step) - delta * delta;
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var sqrt_discriminant = Math.sqrt(b * b - 4 * a * c);
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var beta = (-b + sqrt_discriminant) / (2 * a);
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dl_step = n.add(sd_step, n.mul(beta, d));
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hitBoundary = true;
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}
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}
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}
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var dl_norm = n.norm2(dl_step);
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// if (dl_norm <= tolx) {
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// returnCode = SMALL_STEP;
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// break;
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// }
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x_new = n.add(x, dl_step);
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subsys.setParams(x_new);
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var err_new = subsys.calcResidual(fx_new);
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subsys.fillJacobian(J_new);
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var fxNormSq = n.norm2Squared(fx);
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var dF = fxNormSq - n.norm2Squared(fx_new);
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var dL = fxNormSq - n.norm2Squared( n.add(fx, n.dot(J, dl_step)) );
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var acceptCandidate;
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if (dF == 0 || dL == 0) {
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acceptCandidate = true;
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} else {
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var rho = dF / dL;
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if (rho < 0.25) {
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// if the model is a poor predictor reduce the size of the trust region
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delta = 0.25 * dl_norm;
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//delta *= 0.5;
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} else {
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// only increase the size of the trust region if it is taking a step of maximum size
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// otherwise just assume it's doing good enough job
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if (rho > 0.75 && hitBoundary) {
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//delta = Math.max(delta,3*dl_norm);
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delta *= 2;
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}
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}
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acceptCandidate = rho > 0; // could be 0 .. 0.25
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}
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//log.push([stepKind,err, delta,rho]);
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if (acceptCandidate) {
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x = n.clone(x_new);
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J = n.clone(J_new);
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fx = n.clone(fx_new);
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err = err_new;
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g = n.dot(n.transpose(J), fx);
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// get infinity norms
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g_inf = n.norminf(g);
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fx_inf = n.norminf(fx);
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}
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iter++;
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}
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//log.push(returnCode);
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//window.___log(log);
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return _result(iter, err, returnCode);
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};
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function gaussElimination(A) {
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let h = 0;
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let k = 0;
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const m = A.length;
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const n = A[0].length;
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while (h < m && k < n) {
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let i_max = h;
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for (let i = h + 1; i < m; i++) {
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if (Math.abs(A[i][k]) > Math.abs(A[i_max][k]) ) {
|
||
i_max = i;
|
||
}
|
||
}
|
||
|
||
if (A[i_max][k] === 0) {
|
||
/* No pivot in this column, pass to next column */
|
||
k ++;
|
||
} else {
|
||
let t = A[h];
|
||
A[h] = A[i_max];
|
||
A[i_max] = t;
|
||
|
||
|
||
for (let i = h + 1; i < m; i++) {
|
||
let f = A[i][k] / A[h][k]; //it cant be 0 here see condition up
|
||
A[i][k] = 0;
|
||
for (let j = k + 1; j < n; j++) {
|
||
A[i][j] = A[i][j] - A[h][j] * f;
|
||
}
|
||
}
|
||
h ++;
|
||
k ++;
|
||
}
|
||
}
|
||
|
||
}
|
||
|
||
function LU(A, fast) {
|
||
fast = fast || false;
|
||
|
||
var abs = Math.abs;
|
||
var i, j, k, absAjk, Akk, Ak, Pk, Ai;
|
||
var max;
|
||
var n = A.length, n1 = n-1;
|
||
var P = new Array(n);
|
||
if(!fast) A = numeric.clone(A);
|
||
|
||
for (k = 0; k < n; ++k) {
|
||
Pk = k;
|
||
Ak = A[k];
|
||
max = abs(Ak[k]);
|
||
for (j = k + 1; j < n; ++j) {
|
||
absAjk = abs(A[j][k]);
|
||
if (max < absAjk) {
|
||
max = absAjk;
|
||
Pk = j;
|
||
}
|
||
}
|
||
P[k] = Pk;
|
||
|
||
if (Pk != k) {
|
||
A[k] = A[Pk];
|
||
A[Pk] = Ak;
|
||
Ak = A[k];
|
||
}
|
||
|
||
Akk = Ak[k];
|
||
|
||
if (Akk === 0) {
|
||
Akk = 0.0000001;
|
||
}
|
||
|
||
for (i = k + 1; i < n; ++i) {
|
||
A[i][k] /= Akk;
|
||
}
|
||
|
||
for (i = k + 1; i < n; ++i) {
|
||
Ai = A[i];
|
||
for (j = k + 1; j < n1; ++j) {
|
||
Ai[j] -= Ai[k] * Ak[j];
|
||
++j;
|
||
Ai[j] -= Ai[k] * Ak[j];
|
||
}
|
||
if(j===n1) Ai[j] -= Ai[k] * Ak[j];
|
||
}
|
||
}
|
||
|
||
return {
|
||
LU: A,
|
||
P: P
|
||
};
|
||
}
|
||
|
||
function LUsolve(LUP, b) {
|
||
var i, j;
|
||
var LU = LUP.LU;
|
||
var n = LU.length;
|
||
var x = numeric.clone(b);
|
||
var P = LUP.P;
|
||
var Pi, LUi, LUii, tmp;
|
||
|
||
for (i=n-1;i!==-1;--i) x[i] = b[i];
|
||
for (i = 0; i < n; ++i) {
|
||
Pi = P[i];
|
||
if (P[i] !== i) {
|
||
tmp = x[i];
|
||
x[i] = x[Pi];
|
||
x[Pi] = tmp;
|
||
}
|
||
|
||
LUi = LU[i];
|
||
for (j = 0; j < i; ++j) {
|
||
x[i] -= x[j] * LUi[j];
|
||
}
|
||
}
|
||
|
||
for (i = n - 1; i >= 0; --i) {
|
||
LUi = LU[i];
|
||
for (j = i + 1; j < n; ++j) {
|
||
x[i] -= x[j] * LUi[j];
|
||
}
|
||
if (LUi[i] !== 0) { // We want it because it 99% of the time happens when penalty function returns ZERO gradient, so we just ignore zero-rows
|
||
x[i] /= LUi[i];
|
||
}
|
||
}
|
||
|
||
return x;
|
||
}
|
||
|
||
function lu_solve(A, b, fast) {
|
||
const lu = LU(A,fast);
|
||
return LUsolve(lu, b);
|
||
}
|
||
|
||
|
||
var cg = function(A, x, b, tol, maxIt) {
|
||
|
||
var _ = numeric;
|
||
|
||
var tr = _.transpose;
|
||
var At = tr(A);
|
||
if (A.length != A[0].length) {
|
||
A = _.dot(At, A);
|
||
b = _.dot(At, b);
|
||
}
|
||
|
||
var r = _.sub(_.dot(A, x), b);
|
||
var p = _.mul(r, -1);
|
||
var rr = _.dotVV(r, r);
|
||
|
||
var a;
|
||
var _rr;
|
||
var beta;
|
||
|
||
for (var i = 0; i < maxIt; ++i) {
|
||
if (_.norm2(r) <= tol) break;
|
||
var Axp =_.dot(A, p);
|
||
a = rr / _.dotVV(Axp, p);
|
||
x = _.add(x, _.mul(p, a));
|
||
r = _.add(r, _.mul(Axp, a));
|
||
_rr = rr;
|
||
rr = _.dotVV(r, r);
|
||
beta = rr / _rr;
|
||
p = _.add(_.mul(r, -1), _.mul(p, beta));
|
||
}
|
||
// console.log("liner problem solved in " + i);
|
||
return x;
|
||
};
|
||
|
||
var optim = {DEBUG_HANDLER : function() {}}; //backward compatibility
|
||
|
||
export {dog_leg, optim} |