Add DefiniteIntegral example for Tutorial. #1097

trick_source/trick_utils/SAIntegrator/examples/DefiniteIntegral/DefiniteIntegral.cpp

@@ -0,0 +1,44 @@
+#include <math.h>
+#include <stdio.h>
+#include "SAIntegrator.hh"
+
+struct DefiniteIntegral {
+    double lower_limit;
+    double upper_limit;
+    double result;
+    double Coeff[4];
+    SA::Integrator* integrator;
+    double evaluate ();
+};
+double DefiniteIntegral::evaluate () {
+    result = 0.0;
+    integrator->setIndyVar(lower_limit);
+    while(integrator->getIndyVar() < upper_limit){
+        integrator->integrate();
+    }
+    return result;
+}
+void Order3Polynomial( double x, double state[], double derivs[], void* udata) {
+    DefiniteIntegral& DI = *(DefiniteIntegral*)udata;
+    double x2 = x*x;
+    double x3 = x*x2;
+    derivs[0] = DI.Coeff[3] * x3 +
+                DI.Coeff[2] * x2 +
+                DI.Coeff[1] * x +
+                DI.Coeff[0];
+}
+int main (int argc, char* argv[]) {
+    unsigned int NSteps = 20;
+    DefiniteIntegral DI;
+    DI.Coeff[0] =  7.0;
+    DI.Coeff[1] = -5.0;
+    DI.Coeff[2] =  1.0;
+    DI.Coeff[3] =  2.0;
+    DI.lower_limit =  0.0;
+    DI.upper_limit =  2.0;
+    double dx = (DI.upper_limit - DI.lower_limit) / NSteps;
+    double* state[1] = { &DI.result };
+    DI.integrator = new SA::RK4Integrator(dx, 1, state, Order3Polynomial, &DI);
+    double result = DI.evaluate();
+    printf("Integral = %g.\n", result);
+}

trick_source/trick_utils/SAIntegrator/examples/DefiniteIntegral/README.md

@@ -0,0 +1,21 @@
+# DefiniteIntegral
+
+This is a code example of using SAIntegrator to compute a definite integral.
+
+This program will use the SA::RK4Integrator compute an integral of the form :
+
+![Equation](images/Eq1.png)
+
+It's specifically parameterized to compute :
+
+![Equation](images/Eq2.png)
+
+The correct answer is 14+2/3.
+
+```
+$ make
+$ ./DefiniteIntegral
+Integral = 14.6667.
+```
+
+

trick_source/trick_utils/SAIntegrator/examples/DefiniteIntegral/makefile

@@ -0,0 +1,19 @@
+
+RM = rm -rf
+CC = cc
+CPP = c++
+
+CXXFLAGS = -g -Wall
+INCLUDE_DIRS = -I../../include
+LIBDIR = ../../lib
+
+all: DefiniteIntegral
+
+DefiniteIntegral:
+	$(CPP) $(CXXFLAGS) DefiniteIntegral.cpp ${INCLUDE_DIRS} -L${LIBDIR} -lSAInteg -o DefiniteIntegral
+
+clean:
+	${RM} DefiniteIntegral.dSYM
+
+spotless: clean
+	${RM} DefiniteIntegral

trick_source/trick_utils/SAIntegrator/examples/DefiniteIntegral/plot_trajectory.py

@@ -0,0 +1,18 @@
+#!/usr/bin/env python
+  
+import matplotlib.pyplot as plt
+import numpy as np
+data = np.genfromtxt('cannon.csv',
+                     delimiter=',',
+                     skip_header=1,
+                     skip_footer=1,
+                     names=['t', 'px', 'py', 'vx', 'vx'],
+                     dtype=(float, float, float, float, float)
+                    )
+
+curve1 = plt.plot(data['px'], data['py'], 'C1-')
+plt.title('Cannonball Trajectory')
+plt.xlabel('pos-x')
+plt.ylabel('pos-y')
+plt.grid(True)
+plt.show()