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ultimatepp/bazaar/STEM4U_DemoTest/DemoTest.cpp
koldo 135674ca35 STEM4U_DemoTest: Added numerical integration 
git-svn-id: svn://ultimatepp.org/upp/trunk@14954 f0d560ea-af0d-0410-9eb7-867de7ffcac7
2020-09-01 07:52:44 +00:00

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#include <Core/Core.h>
#include <Functions4U/Functions4U.h>
#include <plugin/Eigen/Eigen.h>
#include <STEM4U/IntInf.h>
#include <STEM4U/Rational.h>
#include <STEM4U/Polynomial.h>
#include <STEM4U/Sundials.h>
#include <STEM4U/Integral.h>
#include <STEM4U/TSP.h>
using namespace Upp;
void TestIntInf() {
UppLog() << "\n\nintInf demo. A signed integer type with arbitrary-precision including the usual arithmetic.";
intInf a = "12345678901234567890";
intInf b = 2, c;
c = a%b; UppLog() << "\na%%b: " << c;
VERIFY(c == 0);
c = a;
c += b; UppLog() << "\nc += b: " << c;
c -= b; UppLog() << "\nc -= b: " << c;
c = c + 2; UppLog() << "\nc = 2 + b: " << c;
c = c - 2; UppLog() << "\nc = 2 - b: " << c;
c *= 2; UppLog() << "\nc *= b: " << c;
c /= 2; UppLog() << "\nc /= b: " << c;
c = c * 2; UppLog() << "\nc = c * 2: " << c;
c = c / 2; UppLog() << "\nc = c / 2: " << c;
VERIFY(c == a);
}
void TestPolynomial() {
UppLog() << "\n\nRational demo. A rational number based on an arbitrary precision integer";
int n = 6;
Rational NT = 111;
int r = int(pow(10, int(log10(int(NT))-1)));
int m = int(NT/2);
int M = int((NT-1) / 2);
int csi_n_num = 2*(2*n+1);
int csi_n_den = n+1;
Rational gamma_n_num = NT;
int gamma_n_den = 2 * n + 1;
for (int j = 1; j < n+1; ++j)
gamma_n_num *= NT*NT - j*j;
Rational gamma_n = gamma_n_num/gamma_n_den;
Upp::Vector<Polynomial<Rational>> q;
q << Polynomial<Rational>(1);
UppLog() << "\n" << q[0];
q << Polynomial<Rational>(0, 2);
UppLog() << "\n" << q[1];
for (int i = 2; i < n+2; ++i) {
Rational ii = i;
q << Polynomial<Rational>(0, (2*ii - 1)*2/ii) * q[i-1] - q[i-2] * (((ii-1)*(NT*NT - (ii-1)*(ii-1)))/i);
UppLog() << "\n" << q[i];
}
auto sg = q[n+1].Order(-1);
UppLog() << "\n" << "sg " << sg;
auto dsg = sg.Diff();
UppLog() << "\n" << "dsg " << dsg;
auto num = q[n].y(0).Simplify();
auto den = ((gamma_n * csi_n_num) / csi_n_den).Simplify();
UppLog() << "\n" << "num: " << num;
UppLog() << "\n" << "den: " << den;
Vector<Rational> b;
b.SetCount(int(NT), 0);
Rational sum_bN = 0;
for (int l = -m; l < 1; ++l) {
b[l+m] = (sg.y(l) *num) / den;
if (l == 0)
sum_bN += b[m + l];
else
sum_bN += 2*b[m + l];
if (l % r == 0)
UppLog() << Format("\nb[%5d] = ", l) << FormatRational(b[l+M], 20);
}
for (int l = 1; l < m+1; ++l)
b[m + l] = b[m - l];
UppLog() << "\nsumb = " << sum_bN.Simplify();
VERIFY(sum_bN.Simplify() == 1);
}
// val = 2/1 * 3/2 * 4/3 * ... If done n times, result has to be n
template<typename T>
T Loop() {
T val = 1;
for (T d = 1; d < 100; ++d)
val *= (d+1)/d;
return val;
}
void TestTSP() {
UppLog() << "\nTravelling salesman";
const Vector<Point_<int>> points = {{0, 0},{4, 4},{4, 0},{2, 4},{0, 4},{4, 2},{0, 2},{2, 0}};
Vector<int> orderp;
int distp = TSP(points, orderp, TSP_NEAREST_NEIGHBOR);
UppLog() << "\nTotal distance between points is: " << distp;
VERIFY(distp == 16);
String sorderp;
for (int i = 0; i < orderp.size(); ++i) {
if (i > 0)
sorderp << " -> ";
sorderp << orderp[i];
}
UppLog() << "\nOrder is: " << sorderp;
UppLog() << "\n";
VERIFY(sorderp == "0 -> 7 -> 2 -> 5 -> 1 -> 3 -> 4 -> 6 -> 0");
// Example from https://developers.google.com/optimization/routing/tsp#printer
const Vector<Vector<int>> cities = {
{0, 2451, 713, 1018, 1631, 1374, 2408, 213, 2571, 875, 1420, 2145, 1972},
{2451, 0, 1745, 1524, 831, 1240, 959, 2596, 403, 1589, 1374, 357, 579},
{7133, 1745, 0, 355, 920, 803, 1737, 851, 1858, 262, 940, 1453, 1260},
{1018, 1524, 355, 0, 700, 862, 1395, 1123, 1584, 466, 1056, 1280, 987},
{1631, 831, 920, 700, 0, 663, 1021, 1769, 949, 796, 879, 586, 371},
{1374, 1240, 803, 862, 663, 0, 1681, 1551, 1765, 547, 225, 887, 999},
{2408, 959, 1737, 1395, 1021, 1681, 0, 2493, 678, 1724, 1891, 1114, 701},
{213, 2596, 851, 1123, 1769, 1551, 2493, 0, 2699, 1038, 1605, 2300, 2099},
{2571, 403, 1858, 1584, 949, 1765, 678, 2699, 0, 1744, 1645, 653, 600},
{875, 1589, 262, 466, 796, 547, 1724, 1038, 1744, 0, 679, 1272, 1162},
{1420, 1374, 940, 1056, 879, 225, 1891, 1605, 1645, 679, 0, 1017, 1200},
{2145, 357, 1453, 1280, 586, 887, 1114, 2300, 653, 1272, 1017, 0, 504},
{1972, 579, 1260, 987, 371, 999, 701, 2099, 600, 1162, 1200, 504, 0},
};
Vector<int> order;
int dist = TSP(cities, order, TSP_CONSECUTIVE);
UppLog() << "\nTotal distance between cities is: " << dist;
VERIFY(dist == 7293);
String sorder;
for (int i = 0; i < order.size(); ++i) {
if (i > 0)
sorder << " -> ";
sorder << order[i];
}
UppLog() << "\nOrder is: " << sorder;
VERIFY(sorder == "0 -> 7 -> 2 -> 3 -> 4 -> 12 -> 6 -> 8 -> 1 -> 11 -> 10 -> 5 -> 9 -> 0");
}
void TestRational() {
UppLog() << "\n\nRounding errors test";
double dval = Loop<double>();
Rational rval = Loop<Rational>();
UppLog() << "\ndouble == 100: " << ((dval == 100) ? "true" : "false"); // Fails
UppLog() << "\nRational == 100: " << ((rval == 100) ? "true" : "false");
UppLog() << "\n";
UppLog() << "\nsin() calculation";
Polynomial<Rational> sinSeries;
intInf fact = 1;
int sign = 1;
for (int i = 1; i < 25; i++) {
fact *= i;
if (!((i-1)%2)) {
sinSeries[i] = Rational(intInf(sign), fact);
sign = -sign;
}
}
UppLog() << "\nsin() Taylor series is: " << sinSeries;
Rational sin_1_3 = sinSeries.y(Rational(1, 3));
UppLog() << "\nsin(1/3) = " << sin_1_3;
UppLog() << "\nsin(1/3) = " << FormatRational(sin_1_3, 32);
}
void TestDAESolver() {
UppLog() << "\n\nSolveDAE() solves an harmonic oscillator m·d2x + k·x = 0";
double y[] = {2, 0};
double dy[] = {0, 0};
double m = 1, k = 0.5;
SolveDAE(y, dy, 2, 0.1, 10,
[&](double t, Eigen::Index iiter, const double y[], const double dy[], double residual[])->int {
residual[0] = m*dy[1] + k*y[0];
residual[1] = y[1] - dy[0];
return true;
}, 2,
[&](double t, Eigen::Index iiter, const double y[], const double dy[], double residual[])->int {
residual[0] = y[0] - 0.0001;
residual[1] = y[1] - 0.0001;
return true;
},
[&](double t, Eigen::Index iiter, const double y[], const double dy[], bool isZero, int *whichZero)->bool {
UppLog() << Format("\n>T: %7.4f %8.4f %8.4f %s", t, y[0], y[1], isZero ? "Y" : "");
return true;
}
);
}
using namespace Eigen;
void TestIntegral() {
UppLog() << "\n\nIntegral demo";
double R = 1;
UppLog() << "\nSemicircle integral value is " << M_PI*sqr(R)/2;
UppLog() << "\nNumerically integrated with simple and composite versions:";
UppLog() << Format("\n%s\t%s\t\t%s\t\t%s\t\t%s\t%s", "#Points", "Trapezoidal", "Simpson 1/3", "Simpson 3/8", "Hermite 3 point", "Hermite 5 point");
for (int nump = 5; nump <= 30; ++nump) {
double dx = 2*R/(nump-1);
VectorXd y(nump), x(nump);
for (int i = 0; i < nump; ++i) {
x[i] = 2*R*i/(nump-1) - R;
y[i] = ::sqrt(sqr(R) - sqr(x[i]));
}
double yx_trap = Integral<VectorXd, double>(y, x, TRAPEZOIDAL);
double yx_simp13 = Integral<VectorXd, double>(y, x, SIMPSON_1_3);
double yx_simp38 = Integral<VectorXd, double>(y, x, SIMPSON_3_8);
double ydx_trap = Integral(y, dx, TRAPEZOIDAL);
double ydx_simp13 = Integral(y, dx, SIMPSON_1_3);
double ydx_simp38 = Integral(y, dx, SIMPSON_3_8);
double ydx_herm3 = Integral(y, dx, HERMITE_3);
double ydx_herm5 = Integral(y, dx, HERMITE_5);
UppLog() << Format("\n%d", nump);
UppLog() << Format("\t%7.5f = %7.5f", yx_trap, ydx_trap);
UppLog() << Format("\t%7.5f = %7.5f", yx_simp13, ydx_simp13);
UppLog() << Format("\t%7.5f = %7.5f", yx_simp38, ydx_simp38);
UppLog() << Format("\t%7.5f", ydx_herm3);
UppLog() << Format("\t\t%7.5f", ydx_herm5);
VERIFY(yx_trap - ydx_trap < 1E-10);
VERIFY(yx_simp13 - ydx_simp13 < 1E-10);
VERIFY(yx_simp38 - ydx_simp38 < 1E-10);
}
}
CONSOLE_APP_MAIN
{
StdLogSetup(LOG_COUT|LOG_FILE);
UppLog() << "STEM4U demo and test";
TestTSP();
TestRational();
TestDAESolver();
TestIntInf();
TestPolynomial();
TestIntegral();
#ifdef flagDEBUG
UppLog() << "\n";
Cout() << "\nPress enter key to end";
ReadStdIn();
#endif
}
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