mirror of
https://github.com/ultimatepp/ultimatepp.git
synced 2026-06-14 06:12:25 -06:00
336 lines
11 KiB
C++
336 lines
11 KiB
C++
#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>
|
|
#include <STEM4U/SeaWaves.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);
|
|
}
|
|
}
|
|
|
|
|
|
void TestSeaWaves() {
|
|
UppLog() << "\n\nSeaWaves demo";
|
|
|
|
double T = 12;
|
|
double depth = 50;
|
|
double H = 2;
|
|
|
|
SeaWaves::rho = 1028;
|
|
|
|
double waveNumber = SeaWaves::WaveNumber(T, depth, false);
|
|
UppLog() << "\n" << Format("Wave number: %f rad/m", waveNumber);
|
|
double waveNumberE = SeaWaves::WaveNumber(T, depth, true);
|
|
UppLog() << "\n" << Format("Wave number (exact): %f rad/m", waveNumberE);
|
|
double waveLength = SeaWaves::WaveLength(T, depth);
|
|
UppLog() << "\n" << Format("Wave length: %f m", waveLength);
|
|
double c = SeaWaves::Celerity(T, depth);
|
|
UppLog() << "\n" << Format("Celerity: %f m/s", c);
|
|
double gc = SeaWaves::GroupCelerity(T, depth);
|
|
UppLog() << "\n" << Format("Group celerity: %f m/s", gc);
|
|
SeaWaves::SEA_TYPE seaType = SeaWaves::GetSeaType(T, depth);
|
|
UppLog() << "\n" << Format("Sea: %s", seaType == SeaWaves::SHALLOW ? "shallow" : seaType == SeaWaves::INTERMEDIATE ? "intermediate" : "deep");
|
|
double power = SeaWaves::Power(T, H, depth);
|
|
UppLog() << "\n" << Format("Power: %f kW/m", power);
|
|
|
|
double Tz = 12;
|
|
double gamma = 2;
|
|
double Tp = Tp_fTz(Tz, gamma);
|
|
double gamma2 = gamma_fTp_Tz(Tp, Tz);
|
|
UppLog() << "\n" << Format("Tp: %.2f, Tz: %.2f, gamma: %.4f, %.4f", Tp, Tz, gamma, gamma2);
|
|
VERIFY(abs(gamma - gamma2) < 0.000001);
|
|
|
|
double freq = 2*M_PI/T;
|
|
double psd = SeaWaves::JONSWAP_Spectrum(H, T, 3.3, freq);
|
|
UppLog() << "\n" << Format("JONSWAP PSD (%f): %f", freq, psd);
|
|
|
|
{
|
|
SeaWaves waves;
|
|
|
|
double Tp = 12, Hs = 2;
|
|
waves.Init(Tp, Hs);
|
|
double x = 100, y = 100, z = -10, t = 10;
|
|
waves.Calc(x, y, z, t);
|
|
UppLog() << "\n" << Format("Sea data for Hs: %.2f m, Tp; %.2f s, at x: %.2f m, y: %.2f m, z: %.2f m, t: %.3f s", Hs, Tp, x, y, z, t);
|
|
UppLog() << "\n" << Format("Free surface z: %f m = %f m", waves.zSurf, waves.ZSurf(x, y, z, t));
|
|
VERIFY(abs(waves.zSurf - waves.ZSurf(x, y, z, t)) < 0.000001);
|
|
VERIFY(abs(waves.zSurf - 0.13560241) < 0.000001);
|
|
UppLog() << "\n" << Format("vx: %f m/s, vy: %f m/s, vz: %f m/s", waves.vx, waves.vy, waves.vz);
|
|
VERIFY(abs(waves.vz + 0.102412178) < 0.000001);
|
|
UppLog() << "\n" << Format("ax: %f m/s2, ay: %f m/s2, az: %f m/s2", waves.ax, waves.ay, waves.az);
|
|
VERIFY(abs(waves.az - 0.000565667) < 0.000001);
|
|
UppLog() << "\n" << Format("p: %.3f Pa = %.3f Pa", waves.p, waves.Pressure(x, y, z, t));
|
|
VERIFY(abs(waves.p - waves.Pressure(x, y, z, t)) < 0.000001);
|
|
}
|
|
}
|
|
|
|
|
|
CONSOLE_APP_MAIN
|
|
{
|
|
StdLogSetup(LOG_COUT|LOG_FILE);
|
|
|
|
UppLog() << "STEM4U demo and test";
|
|
|
|
TestTSP();
|
|
TestRational();
|
|
TestDAESolver();
|
|
TestIntInf();
|
|
TestPolynomial();
|
|
TestIntegral();
|
|
TestSeaWaves();
|
|
|
|
#ifdef flagDEBUG
|
|
UppLog() << "\n";
|
|
Cout() << "\nPress enter key to end";
|
|
ReadStdIn();
|
|
#endif
|
|
}
|
|
|