tasks a-s

Task/Resistor-mesh/Euler-Math-Toolbox/resistor-mesh-3.euler

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+function cgX (H:cpx, b:real column, x0:real column=none, f:index=10)
+## Conjugate gradient method to solve Hx=b for compressed H.
+##
+## This is the method of choice for large, sparse matrices. In most
+## cases, it will work well, fast, and accurate.
+##
+## H must be positive definite. Use cpxfit, if it is not.
+##
+## The accuarcy can be controlled with an additional parameter
+## eps. The algorithm stops, when the error gets smaller then eps, or
+## after f*n iterations, if the error gets larger. x0 is an optional
+## start vector.
+##
+## H : compressed matrix (nxm)
+## b : column vector (mx1)
+## x0 : optional start point (mx1)
+## f : number of steps, when the method should be restarted
+##
+## See: cpxfit, cg, cgXnormal
+	if isvar("eps") then localepsilon(eps); endif;
+	n=cols(H);
+	if x0==none then x=zeros(size(b));
+	else; x=x0;
+	endif;
+	loop 1 to 10
+		r=b-cpxmult(H,x); p=r; fehler=r'.r;
+		loop 1 to f*n
+			if sqrt(fehler)~=0 then return x; endif;
+			Hp=cpxmult(H,p);
+			a=fehler/(p'.Hp);
+			x=x+a*p;
+			rn=r-a*Hp;
+			fehlerneu=rn'.rn;
+			p=rn+fehlerneu/fehler*p;
+			r=rn; fehler=fehlerneu;
+		end;
+	end;
+	return x;
+endfunction