Add double integral example to trick_utils/SAIntegrator #1058

This commit is contained in:
Penn, John M 047828115 2020-10-02 16:29:55 -05:00
parent 64caa968da
commit fc83dbe6f3
9 changed files with 134 additions and 7 deletions

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@ -25,6 +25,7 @@ Some examples of using these integrators can be found in the **examples/** direc
* [CannonBall](examples/CannonBall/README.md) uses the RK2Integrator. * [CannonBall](examples/CannonBall/README.md) uses the RK2Integrator.
* [MassSpringDamper](examples/MassSpringDamper/README.md) uses the EulerCromerIntegrator. * [MassSpringDamper](examples/MassSpringDamper/README.md) uses the EulerCromerIntegrator.
* [Orbit](examples/Orbit/README.md) uses the EulerCromerIntegrator. * [Orbit](examples/Orbit/README.md) uses the EulerCromerIntegrator.
* [DoubleIntegral](examples/DoubleIntegral/README.md) shows an example of a double integral.
<a id=class-Integrator></a> <a id=class-Integrator></a>
## class Integrator ## class Integrator

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@ -0,0 +1,53 @@
#include <math.h>
#include <stdio.h>
#include "SAIntegrator.hh"
struct IContext {
SA::RK2Integrator* integ;
double start;
double end;
};
void deriv_y( double y, double state_y[], double derivs_y[], void* udata) {
double& x = state_y[0];
derivs_y[0] = 0.0; // (dx/dy) = 0, Hold x constant.
derivs_y[1] = cos(x)*cos(y); // area = ∫ f(X,y) dy
}
void deriv_x( double x, double state_x[], double derivs_x[], void* udata) {
IContext* context = (IContext*)udata;
double area = 0.0;
double* state_y[2] = { &x, &area };
SA::RK2Integrator* integ_y = context->integ;
integ_y->set_in_vars(state_y);
integ_y->set_out_vars(state_y);
integ_y->setTime(context->start);
while (integ_y->getTime() <= context->end) {
integ_y->load();
integ_y->step();
integ_y->unload();
}
derivs_x[0] = area; // volume = ∫ area dx
}
double doubleIntegral( double x_start, double x_end, double y_start, double y_end ) {
double volume = 0.0;
double dx = 0.01;
double dy = 0.01;
double* state_x[1] = { &volume };
SA::RK2Integrator integ_y (dy, 2, NULL, NULL, deriv_y, NULL);
IContext y_integ_context = {&integ_y, y_start, y_end};
SA::RK2Integrator integ_x (dx, 1, state_x, state_x, deriv_x, &y_integ_context);
integ_x.setTime(x_start);
while (integ_x.getTime()<=x_end) { // x-end
integ_x.load();
integ_x.step();
integ_x.unload();
}
return volume;
}
int main ( int argc, char* argv[]) {
double vol = doubleIntegral( -M_PI/2.0, M_PI/2.0, -M_PI/2.0, M_PI/2.0 );
printf("Volume = %g.\n", vol);
}

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@ -0,0 +1,17 @@
# Double Integral
This is a code example of how one can do a double integral.
This example code computes the following definate integral :
![Equation](images/Equation.png)
using the SA::RK2Integrator, with dx = dy = 0.01
```
$ make
$ ./DoubleIntegral
Volume = 3.99989.
```

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

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@ -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()

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@ -3,13 +3,16 @@ examples:
@make -C CannonBall @make -C CannonBall
@make -C MassSpringDamper @make -C MassSpringDamper
@make -C Orbit @make -C Orbit
@make -C DoubleIntegral
clean: clean:
@make -C CannonBall clean @make -C CannonBall clean
@make -C MassSpringDamper clean @make -C MassSpringDamper clean
@make -C Orbit clean @make -C Orbit clean
@make -C DoubleIntegral clean
spotless: spotless:
@make -C CannonBall spotless @make -C CannonBall spotless
@make -C MassSpringDamper spotless @make -C MassSpringDamper spotless
@make -C Orbit spotless @make -C Orbit spotless
@make -C DoubleIntegral spotless

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@ -13,6 +13,7 @@ namespace SA {
virtual void load() = 0; virtual void load() = 0;
virtual void unload() = 0; virtual void unload() = 0;
double getTime() {return time;} double getTime() {return time;}
void setTime(double t) {time = t;}
}; };
typedef void (*derivsFunc)( double t, double state[], double derivs[], void* user_data); typedef void (*derivsFunc)( double t, double state[], double derivs[], void* user_data);
@ -32,10 +33,11 @@ namespace SA {
public: public:
FirstOrderODEIntegrator( double dt, int N, double* in_vars[], double* out_vars[], derivsFunc func, void* user_data); FirstOrderODEIntegrator( double dt, int N, double* in_vars[], double* out_vars[], derivsFunc func, void* user_data);
~FirstOrderODEIntegrator(); ~FirstOrderODEIntegrator();
// void init(double dt, int N, double* in_vars[], double* out_vars[], derivsFunc func);
virtual void undo_step(); virtual void undo_step();
void load(); void load();
void unload(); void unload();
void set_in_vars( double* in_vars[]);
void set_out_vars( double* out_vars[]);
}; };
class FirstOrderODEVariableStepIntegrator : public FirstOrderODEIntegrator { class FirstOrderODEVariableStepIntegrator : public FirstOrderODEIntegrator {

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@ -21,15 +21,29 @@ SA::FirstOrderODEIntegrator::~FirstOrderODEIntegrator() {
} }
void SA::FirstOrderODEIntegrator::load() { void SA::FirstOrderODEIntegrator::load() {
reset = false; reset = false;
for (int i=0 ; i<state_size; i++ ) { if (orig_vars != NULL) {
istate[i] = *(orig_vars[i]); for (int i=0 ; i<state_size; i++ ) {
istate[i] = *(orig_vars[i]);
}
} else {
std::cerr << "Error: SA::FirstOrderODEIntegrator::load(). orig_vars is not set." << std::endl;
} }
} }
void SA::FirstOrderODEIntegrator::unload() { void SA::FirstOrderODEIntegrator::unload() {
for (int i=0 ; i<state_size; i++ ) { if (dest_vars != NULL) {
*(dest_vars[i]) = ostate[i]; for (int i=0 ; i<state_size; i++ ) {
*(dest_vars[i]) = ostate[i];
}
} else {
std::cerr << "Error: SA::FirstOrderODEIntegrator::load(). dest_vars is not set." << std::endl;
} }
} }
void SA::FirstOrderODEIntegrator::set_in_vars( double* in_vars[]){
orig_vars = in_vars;
}
void SA::FirstOrderODEIntegrator::set_out_vars( double* out_vars[]){
dest_vars = out_vars;
}
void SA::FirstOrderODEIntegrator::undo_step() { void SA::FirstOrderODEIntegrator::undo_step() {
if (!reset) { // If we've not already reset the integrator, then reset it. if (!reset) { // If we've not already reset the integrator, then reset it.
for (int i=0 ; i<state_size; i++ ) { for (int i=0 ; i<state_size; i++ ) {