add numerical recipes library

lib/nr/cpp/recipes/linbcg.cpp

@@ -0,0 +1,90 @@
+#include <iostream>
+#include <iomanip>
+#include <cmath>
+#include "nr.h"
+using namespace std;
+
+void NR::linbcg(Vec_I_DP &b, Vec_IO_DP &x, const int itol, const DP tol,
+	const int itmax, int &iter, DP &err)
+{
+	DP ak,akden,bk,bkden=1.0,bknum,bnrm,dxnrm,xnrm,zm1nrm,znrm;
+	const DP EPS=1.0e-14;
+	int j;
+
+	int n=b.size();
+	Vec_DP p(n),pp(n),r(n),rr(n),z(n),zz(n);
+	iter=0;
+	atimes(x,r,0);
+	for (j=0;j<n;j++) {
+		r[j]=b[j]-r[j];
+		rr[j]=r[j];
+	}
+	//atimes(r,rr,0);
+	if (itol == 1) {
+		bnrm=snrm(b,itol);
+		asolve(r,z,0);
+	}
+	else if (itol == 2) {
+		asolve(b,z,0);
+		bnrm=snrm(z,itol);
+		asolve(r,z,0);
+	}
+	else if (itol == 3 || itol == 4) {
+		asolve(b,z,0);
+		bnrm=snrm(z,itol);
+		asolve(r,z,0);
+		znrm=snrm(z,itol);
+	} else nrerror("illegal itol in linbcg");
+	cout << fixed << setprecision(6);
+	while (iter < itmax) {
+		++iter;
+		asolve(rr,zz,1);
+		for (bknum=0.0,j=0;j<n;j++) bknum += z[j]*rr[j];
+		if (iter == 1) {
+			for (j=0;j<n;j++) {
+				p[j]=z[j];
+				pp[j]=zz[j];
+			}
+		} else {
+			bk=bknum/bkden;
+			for (j=0;j<n;j++) {
+				p[j]=bk*p[j]+z[j];
+				pp[j]=bk*pp[j]+zz[j];
+			}
+		}
+		bkden=bknum;
+		atimes(p,z,0);
+		for (akden=0.0,j=0;j<n;j++) akden += z[j]*pp[j];
+		ak=bknum/akden;
+		atimes(pp,zz,1);
+		for (j=0;j<n;j++) {
+			x[j] += ak*p[j];
+			r[j] -= ak*z[j];
+			rr[j] -= ak*zz[j];
+		}
+		asolve(r,z,0);
+		if (itol == 1)
+			err=snrm(r,itol)/bnrm;
+		else if (itol == 2)
+			err=snrm(z,itol)/bnrm;
+		else if (itol == 3 || itol == 4) {
+			zm1nrm=znrm;
+			znrm=snrm(z,itol);
+			if (fabs(zm1nrm-znrm) > EPS*znrm) {
+				dxnrm=fabs(ak)*snrm(p,itol);
+				err=znrm/fabs(zm1nrm-znrm)*dxnrm;
+			} else {
+				err=znrm/bnrm;
+				continue;
+			}
+			xnrm=snrm(x,itol);
+			if (err <= 0.5*xnrm) err /= xnrm;
+			else {
+				err=znrm/bnrm;
+				continue;
+			}
+		}
+		cout << "iter=" << setw(4) << iter+1 << setw(12) << err << endl;
+		if (err <= tol) break;
+	}
+}