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+mode(1)
+//
+// Demo of lsqnonlin.sci
+//
+
+//A simple non-linear least square example taken from leastsq default present in scilab
+function y=yth(t, x)
+y  = x(1)*exp(-x(2)*t)
+endfunction
+// we have the m measures (ti, yi):
+m = 10;
+tm = [0.25, 0.5, 0.75, 1.0, 1.25, 1.5, 1.75, 2.0, 2.25, 2.5]';
+ym = [0.79, 0.59, 0.47, 0.36, 0.29, 0.23, 0.17, 0.15, 0.12, 0.08]';
+// measure weights (here all equal to 1...)
+wm = ones(m,1);
+// and we want to find the parameters x such that the model fits the given
+// data in the least square sense:
+//
+//  minimize  f(x) = sum_i  wm(i)^2 ( yth(tm(i),x) - ym(i) )^2
+// initial parameters guess
+x0 = [1.5 ; 0.8];
+// in the first examples, we define the function fun and dfun
+// in scilab language
+function y=myfun(x, tm, ym, wm)
+y = wm.*( yth(tm, x) - ym )
+endfunction
+// the simplest call
+[xopt,resnorm,residual,exitflag,output,lambda,gradient] = lsqnonlin(myfun,x0)
+// Press ENTER to continue
+halt()   // Press return to continue
+ 
+//A basic example taken from leastsq default present in scilab with gradient
+function y=yth(t, x)
+y  = x(1)*exp(-x(2)*t)
+endfunction
+// we have the m measures (ti, yi):
+m = 10;
+tm = [0.25, 0.5, 0.75, 1.0, 1.25, 1.5, 1.75, 2.0, 2.25, 2.5]';
+ym = [0.79, 0.59, 0.47, 0.36, 0.29, 0.23, 0.17, 0.15, 0.12, 0.08]';
+// measure weights (here all equal to 1...)
+wm = ones(m,1);
+// and we want to find the parameters x such that the model fits the given
+// data in the least square sense:
+//
+//  minimize  f(x) = sum_i  wm(i)^2 ( yth(tm(i),x) - ym(i) )^2
+// initial parameters guess
+x0 = [1.5 ; 0.8];
+// in the first examples, we define the function fun and dfun
+// in scilab language
+function [y,dy]=myfun(x, tm, ym, wm)
+y = wm.*( yth(tm, x) - ym )
+v = wm.*exp(-x(2)*tm)
+dy = [v , -x(1)*tm.*v]
+endfunction
+options = list("GradObj", "on")
+[xopt,resnorm,residual,exitflag,output,lambda,gradient] = lsqnonlin(myfun,x0,[],[],options)
+//========= E N D === O F === D E M O =========//