Kinematic Equation for Differential Drive Explained
Kinematic Equation for Differential Drive Explained Read More »
Tutorials
Example of Test Driven Development with C++ and Google Test
To develop a software based on “Test Driven Development” one should follow the following steps:
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1)Write enough failing Test Code (include compile time and run time failures) 2)Write Production code to pass the failing tests. 3)Refactor the production code and verify the same with existing test. 4)Go to step 1 |
so let say we want to develop a binary search tree, here I’m using Google Test. Step 1, Write enough failing Test Code so the first step would be something like this:
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class testingTree: public ::testing::Test { protected: testingTree(){} ~testingTree(){} void SetUp(){} void TearDown(){} }; TEST_F(testingTree,makeTree) { std::shared_ptr<Tree> tree=makeTree(); EXPECT_NE(tree.get(),nullptr); } int main(int argc, char ** argv) { testing::InitGoogleTest(&argc, argv); return RUN_ALL_TESTS(); } |
Step 2, Write Production code to
Example of Test Driven Development with C++ and Google Test Read More »
Standard Exception Handler in C++ and Custom Exception Handler with Examples
Exception handling
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try { some code } catch (Exception e) { throw e; } catch (...)//... will catch any exception { throw; } |
C++ Standard Exceptions
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1)std::bad_alloc 2)std::bad_cast 3)std::bad_exception 4)std::bad_typeid 5)std::logic_error 5-1)std::domain_error: exception thrown when a mathematically invalid domain is used. 5-2)std::invalid_argument 5-3)std::length_error 5-4)std::out_of_range 6)std::runtime_error: An exception that theoretically cannot be detected by reading the code. 6-1)std::overflow_error : The only standard library components that throw std::overflow_error are std::bitset::to_ulong and std::bitset::to_ullong. 6-2)std::underflow_error 6-3)std::range_error |
List of Example
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struct Foo { virtual ~Foo() {} }; struct Bar { virtual ~Bar() {} }; void bad_allocExample() { try { while (true) { new int[100000000ul]; } } catch (const std::bad_alloc& e) { std::cout << "Allocation failed: " << e.what() << '\n'; } } void bad_castExample() { Bar b; try { Foo& f = dynamic_cast<Foo&>(b); } catch(const std::bad_cast& e) { std::cout << e.what() << '\n'; } } void bad_typeidExample() { Foo* p = nullptr; try { std::cout << typeid(*p).name() << '\n'; } catch(const std::bad_typeid& e) { std::cout << e.what() << '\n'; } } void logical_ErrorExample() { int amount, available; amount=10; available=9; if(amount>available) { throw std::logic_error("Error"); } catch ( std::exception &e ) { std::cerr << "Caught: " << e.what( ) << std::endl; std::cerr << "Type: " << typeid( e ).name( ) << std::endl; }; } void domain_errorExample() { try { const double x = std::acos(2.0); std::cout << x << '\n'; } catch (std::domain_error& e) { std::cout << e.what() << '\n'; } catch (...) { std::cout << "Something unexpected happened" << '\n'; } } void invalid_argumentExample() { try { // binary wrongly represented by char X std::bitset<32> bitset(std::string("0101001X01010110000")); } catch (std::exception &err) { std::cerr<<"Caught "<<err.what()<<std::endl; std::cerr<<"Type "<<typeid(err).name()<<std::endl; } } void length_errorExample() { try { // vector throws a length_error if resized above max_size std::vector<int> myvector; myvector.resize(myvector.max_size()+1); } catch (const std::length_error& le) { std::cerr << "Length error: " << le.what() << '\n'; } } void out_of_rangeExample() { std::vector<int> myvector(10); try { myvector.at(20)=100; // vector::at throws an out-of-range } catch (const std::out_of_range& oor) { std::cerr << "Out of Range error: " << oor.what() << '\n'; } } void overflow_errorExample() { try { std::bitset<100> bitset; bitset[99] = 1; bitset[0] = 1; // to_ulong(), converts a bitset object to the integer that would generate the sequence of bits unsigned long Test = bitset.to_ulong(); } catch(std::exception &err) { std::cerr<<"Caught "<<err.what()<<std::endl; std::cerr<<"Type "<<typeid(err).name()<<std::endl; } } void range_errorExample() { try { throw std::range_error( "The range is in error!" ); } catch (std::range_error &e) { std::cerr << "Caught: " << e.what( ) << std::endl; std::cerr << "Type: " << typeid( e ).name( ) << std::endl; } } //Defining your exceptions struct CustomException : public std::exception { const char * what () const throw () { return "CustomException happened"; } }; void customExceptionExample() { try { throw CustomException(); } catch(CustomException& e) { std::cout << "CustomException caught" << std::endl; std::cout << e.what() << std::endl; } catch(std::exception& e) { //Other errors } } |
Standard Exception Handler in C++ and Custom Exception Handler with Examples Read More »
Finding Memory leaking, Stack and Heap overflow
When you access an array index, C and C++ don’t do bound checking. Segmentation faults only happen when you try to read or write to a page that was not allocated (or try to do something on a page which isn’t permitted, e.g. trying to write to a read-only page), but since pages are usually
Finding Memory leaking, Stack and Heap overflow Read More »
Extended Kalman Filter Explained with Python Code
In the following code, I have implemented an Extended Kalman Filter for modeling the movement of a car with constant turn rate and velocity. The code is mainly based on this work (I did some bug fixing and some adaptation such that the code runs similar to the Kalman filter that I have earlier implemented).
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import matplotlib.dates as mdates import numpy as np np.set_printoptions(threshold=3) np.set_printoptions(suppress=True) from numpy import genfromtxt import matplotlib.pyplot as plt from scipy.stats import norm from sympy import Symbol, symbols, Matrix, sin, cos from sympy import init_printing from sympy.utilities.codegen import codegen init_printing(use_latex=True) x0 = [] x1 = [] x2 = [] def prediction(X_hat_t_1,P_t_1,Q_t,drivingStraight): X_hat_t=X_hat_t_1 if drivingStraight: # Driving straight X_hat_t[0] = X_hat_t_1[0] + X_hat_t_1[3]*dt * np.cos(X_hat_t_1[2]) X_hat_t[1] = X_hat_t_1[1] + X_hat_t_1[3]*dt * np.sin(X_hat_t_1[2]) X_hat_t[2] = X_hat_t_1[2] X_hat_t[3] = X_hat_t_1[3] + X_hat_t_1[5]*dt X_hat_t[4] = 0.0000001 # avoid numerical issues in Jacobians X_hat_t[5] = X_hat_t_1[5] else: # otherwise X_hat_t[0] = X_hat_t_1[0] + (X_hat_t_1[3]/X_hat_t_1[4]) * (np.sin(X_hat_t_1[4]*dt+X_hat_t_1[2]) - np.sin(X_hat_t_1[2])) X_hat_t[1] = X_hat_t_1[1] + (X_hat_t_1[3]/X_hat_t_1[4]) * (-np.cos(X_hat_t_1[4]*dt+X_hat_t_1[2])+ np.cos(X_hat_t_1[2])) X_hat_t[2] = (X_hat_t_1[2] + X_hat_t_1[4]*dt + np.pi) % (2.0*np.pi) - np.pi X_hat_t[3] = X_hat_t_1[3] + X_hat_t_1[5]*dt X_hat_t[4] = X_hat_t_1[4] # Constant Turn Rate X_hat_t[5] = X_hat_t_1[5] # Constant Acceleration # Calculate the Jacobian of the Dynamic Matrix A # see "Calculate the Jacobian of the Dynamic Matrix with respect to the state vector" a13 = float((X_hat_t[3]/X_hat_t[4]) * (np.cos(X_hat_t[4]*dt+X_hat_t[2]) - np.cos(X_hat_t[2]))) a14 = float((1.0/X_hat_t[4]) * (np.sin(X_hat_t[4]*dt+X_hat_t[2]) - np.sin(X_hat_t[2]))) a15 = float((dt*X_hat_t[3]/X_hat_t[4])*np.cos(X_hat_t[4]*dt+X_hat_t[2]) - (X_hat_t[3]/X_hat_t[4]**2)*(np.sin(X_hat_t[4]*dt+X_hat_t[2]) - np.sin(X_hat_t[2]))) a23 = float((X_hat_t[3]/X_hat_t[4]) * (np.sin(X_hat_t[4]*dt+X_hat_t[2]) - np.sin(X_hat_t[2]))) a24 = float((1.0/X_hat_t[4]) * (-np.cos(X_hat_t[4]*dt+X_hat_t[2]) + np.cos(X_hat_t[2]))) a25 = float((dt*X_hat_t[3]/X_hat_t[4])*np.sin(X_hat_t[4]*dt+X_hat_t[2]) - (X_hat_t[3]/X_hat_t[4]**2)*(-np.cos(X_hat_t[4]*dt+X_hat_t[2]) + np.cos(X_hat_t[2]))) JA = np.matrix([[1.0, 0.0, a13, a14, a15, 0.0], [0.0, 1.0, a23, a24, a25, 0.0], [0.0, 0.0, 1.0, 0.0, dt, 0.0], [0.0, 0.0, 0.0, 1.0, 0.0, dt], [0.0, 0.0, 0.0, 0.0, 1.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 1.0]]) # Project the error covariance ahead P_t_1 = JA*P_t_1*JA.T + Q_t return X_hat_t,P_t_1 def update(X_hat_t,P_t,Z_t,R_t,GPSAvailable): hx = np.matrix([[float(X_hat_t[0])], [float(X_hat_t[1])], [float(X_hat_t[3])], [float(X_hat_t[4])], [float(X_hat_t[5])]]) if GPSAvailable: # with 10Hz, every 5th step JH = np.matrix([[1.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, 1.0, 0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 1.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 1.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 1.0]]) else: # every other step JH = np.matrix([[0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 1.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 1.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 1.0]]) S = JH*P_t*JH.T + R_t K = (P_t*JH.T) * np.linalg.inv(S) #print("K:\n",K) # Update the estimate via Z = Z_t.reshape(JH.shape[0],1) #print("Z:\n",Z) y = Z - (hx) # Innovation or Residual X_t = X_hat_t + (K*y) # Update the error covariance I = np.eye(X_hat_t.shape[0]) P_t = (I - (K*JH))*P_t x0.append(float(X_t[0])) x1.append(float(X_t[1])) x2.append(float(X_t[2])) return X_t,P_t numstates=6 # States dt = 1.0/50.0 # Sample Rate of the Measurements is 50Hz dtGPS=1.0/10.0 # Sample Rate of GPS is 10Hz vs, psis, dpsis, dts, xs, ys, lats, lons, axs = symbols('v \psi \dot\psi T x y lat lon a') gs = Matrix([[xs+(vs/dpsis)*(sin(psis+dpsis*dts)-sin(psis))], [ys+(vs/dpsis)*(-cos(psis+dpsis*dts)+cos(psis))], [psis+dpsis*dts], [axs*dts + vs], [dpsis], [axs]]) state = Matrix([xs,ys,psis,vs,dpsis,axs]) #Initial State cov P_t = np.diag([1000.0, 1000.0, 1000.0, 1000.0, 1000.0, 1000.0]) #Measurment cov varGPS = 5.0 # Standard Deviation of GPS Measurement varspeed = 3.0 # Variance of the speed measurement varyaw = 0.1 # Variance of the yawrate measurement varacc = 1.0 # Variance of the longitudinal Acceleration R_t = np.diag([varGPS**2, varGPS**2, varspeed**2, varyaw**2, varacc**2]) #Measurment Matrix hs = Matrix([[xs], [ys], [vs], [dpsis], [axs]]) #Process cov sGPS = 0.5*8.8*dt**2 # assume 8.8m/s2 as maximum acceleration, forcing the vehicle sCourse = 0.1*dt # assume 0.1rad/s as maximum turn rate for the vehicle sVelocity= 8.8*dt # assume 8.8m/s2 as maximum acceleration, forcing the vehicle sYaw = 1.0*dt # assume 1.0rad/s2 as the maximum turn rate acceleration for the vehicle sAccel = 0.5 Q_t = np.diag([sGPS**2, sGPS**2, sCourse**2, sVelocity**2, sYaw**2, sAccel**2]) path="data/" datafile = '2014-03-26-000-Data.csv' fullPath=path+datafile def bytespdate2num(fmt, encoding='utf-8'): strconverter = mdates.strpdate2num(fmt) def bytesconverter(b): s = b.decode(encoding) return strconverter(s) return bytesconverter date, time, millis, ax, ay, az, rollrate, pitchrate, yawrate, roll, pitch, yaw, speed, course, latitude, longitude, altitude, pdop, hdop, vdop, epe, fix, satellites_view, satellites_used, temp = np.loadtxt(fullPath, delimiter=',', unpack=True, converters={1:bytespdate2num('%H%M%S%f'), 0: bytespdate2num('%y%m%d')}, skiprows=1) # A course of 0 means the Car is traveling north bound # and 90 means it is traveling east bound. # In the Calculation following, East is Zero and North is 90 # We need an offset. course =(-course+90.0) # ## Approx. Lat/Lon to Meters to check Location # In[17]: RadiusEarth = 6378388.0 # m arc= 2.0*np.pi*(RadiusEarth+altitude)/360.0 # m/ dx = arc * np.cos(latitude*np.pi/180.0) * np.hstack((0.0, np.diff(longitude))) # in m dy = arc * np.hstack((0.0, np.diff(latitude))) # in m mx = np.cumsum(dx) my = np.cumsum(dy) ds = np.sqrt(dx**2+dy**2) GPS=(ds!=0.0).astype('bool') # GPS Trigger for Kalman Filter # ## Initial State X_hat_t = np.matrix([[mx[0], my[0], course[0]/180.0*np.pi, speed[0]/3.6+0.001, yawrate[0]/180.0*np.pi, ax[0]]]).T measurements = np.vstack((mx, my, speed/3.6, yawrate/180.0*np.pi, ax)) # Lenth of the measurement m = measurements.shape[1] for i in range(measurements.shape[1]): #for i in range(3): if np.abs(yawrate[i])<0.0001: drivingStraight=True else: drivingStraight=False X_hat_t,P_hat_t = prediction(X_hat_t,P_t,Q_t,drivingStraight) #print("Prediction:") #print("X_hat_t:\n",X_hat_t,"\nP_t:\n",P_hat_t) Z_t=measurements[:,i] if GPS[i]: GPSAvailable=True else: GPSAvailable=False X_t,P_t=update(X_hat_t,P_hat_t,Z_t,R_t,GPSAvailable) #print("Update:") #print("X_t:\n",X_t,"\nP_t:\n",P_t) X_hat_t=X_t P_hat_t=P_t fig = plt.figure(figsize=(16,9)) # EKF State plt.quiver(x0,x1,np.cos(x2), np.sin(x2), color='#94C600', units='xy', width=0.05, scale=0.5) plt.plot(x0,x1, label='EKF Position', c='k', lw=5) # Measurements plt.scatter(mx[::5],my[::5], s=50, label='GPS Measurements', marker='+') # Start/Goal plt.scatter(x0[0],x1[0], s=60, label='Start', c='g') plt.scatter(x0[-1],x1[-1], s=60, label='Goal', c='r') plt.xlabel('X [m]') plt.ylabel('Y [m]') plt.title('Position') plt.legend(loc='best') plt.axis('equal') plt.show() |
Extended Kalman Filter Explained with Python Code Read More »
Parcticle Filter Explained With Python Code From Scratch
In the following code I have implemented a localization algorithm based on particle filter. I have used conda to run my code, you can run the following for installation of dependencies:
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conda create -n Filters python=3 conda activate Filters conda install -c menpo opencv3 conda install numpy scipy matplotlib sympy |
and the code:
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import numpy as np import scipy as scipy from numpy.random import uniform import scipy.stats np.set_printoptions(threshold=3) np.set_printoptions(suppress=True) import cv2 def drawLines(img, points, r, g, b): cv2.polylines(img, [np.int32(points)], isClosed=False, color=(r, g, b)) def drawCross(img, center, r, g, b): d = 5 t = 2 LINE_AA = cv2.LINE_AA if cv2.__version__[0] == '3' else cv2.CV_AA color = (r, g, b) ctrx = center[0,0] ctry = center[0,1] cv2.line(img, (ctrx - d, ctry - d), (ctrx + d, ctry + d), color, t, LINE_AA) cv2.line(img, (ctrx + d, ctry - d), (ctrx - d, ctry + d), color, t, LINE_AA) def mouseCallback(event, x, y, flags,null): global center global trajectory global previous_x global previous_y global zs center=np.array([[x,y]]) trajectory=np.vstack((trajectory,np.array([x,y]))) #noise=sensorSigma * np.random.randn(1,2) + sensorMu if previous_x >0: heading=np.arctan2(np.array([y-previous_y]), np.array([previous_x-x ])) if heading>0: heading=-(heading-np.pi) else: heading=-(np.pi+heading) distance=np.linalg.norm(np.array([[previous_x,previous_y]])-np.array([[x,y]]) ,axis=1) std=np.array([2,4]) u=np.array([heading,distance]) predict(particles, u, std, dt=1.) zs = (np.linalg.norm(landmarks - center, axis=1) + (np.random.randn(NL) * sensor_std_err)) update(particles, weights, z=zs, R=50, landmarks=landmarks) indexes = systematic_resample(weights) resample_from_index(particles, weights, indexes) previous_x=x previous_y=y WIDTH=800 HEIGHT=600 WINDOW_NAME="Particle Filter" #sensorMu=0 #sensorSigma=3 sensor_std_err=5 def create_uniform_particles(x_range, y_range, N): particles = np.empty((N, 2)) particles[:, 0] = uniform(x_range[0], x_range[1], size=N) particles[:, 1] = uniform(y_range[0], y_range[1], size=N) return particles def predict(particles, u, std, dt=1.): N = len(particles) dist = (u[1] * dt) + (np.random.randn(N) * std[1]) particles[:, 0] += np.cos(u[0]) * dist particles[:, 1] += np.sin(u[0]) * dist def update(particles, weights, z, R, landmarks): weights.fill(1.) for i, landmark in enumerate(landmarks): distance=np.power((particles[:,0] - landmark[0])**2 +(particles[:,1] - landmark[1])**2,0.5) weights *= scipy.stats.norm(distance, R).pdf(z[i]) weights += 1.e-300 # avoid round-off to zero weights /= sum(weights) def neff(weights): return 1. / np.sum(np.square(weights)) def systematic_resample(weights): N = len(weights) positions = (np.arange(N) + np.random.random()) / N indexes = np.zeros(N, 'i') cumulative_sum = np.cumsum(weights) i, j = 0, 0 while i < N and j<N: if positions[i] < cumulative_sum[j]: indexes[i] = j i += 1 else: j += 1 return indexes def estimate(particles, weights): pos = particles[:, 0:1] mean = np.average(pos, weights=weights, axis=0) var = np.average((pos - mean)**2, weights=weights, axis=0) return mean, var def resample_from_index(particles, weights, indexes): particles[:] = particles[indexes] weights[:] = weights[indexes] weights /= np.sum(weights) x_range=np.array([0,800]) y_range=np.array([0,600]) #Number of partciles N=400 landmarks=np.array([ [144,73], [410,13], [336,175], [718,159], [178,484], [665,464] ]) NL = len(landmarks) particles=create_uniform_particles(x_range, y_range, N) weights = np.array([1.0]*N) # Create a black image, a window and bind the function to window img = np.zeros((HEIGHT,WIDTH,3), np.uint8) cv2.namedWindow(WINDOW_NAME) cv2.setMouseCallback(WINDOW_NAME,mouseCallback) center=np.array([[-10,-10]]) trajectory=np.zeros(shape=(0,2)) robot_pos=np.zeros(shape=(0,2)) previous_x=-1 previous_y=-1 DELAY_MSEC=50 while(1): cv2.imshow(WINDOW_NAME,img) img = np.zeros((HEIGHT,WIDTH,3), np.uint8) drawLines(img, trajectory, 0, 255, 0) drawCross(img, center, r=255, g=0, b=0) #landmarks for landmark in landmarks: cv2.circle(img,tuple(landmark),10,(255,0,0),-1) #draw_particles: for particle in particles: cv2.circle(img,tuple((int(particle[0]),int(particle[1]))),1,(255,255,255),-1) if cv2.waitKey(DELAY_MSEC) & 0xFF == 27: break cv2.circle(img,(10,10),10,(255,0,0),-1) cv2.circle(img,(10,30),3,(255,255,255),-1) cv2.putText(img,"Landmarks",(30,20),1,1.0,(255,0,0)) cv2.putText(img,"Particles",(30,40),1,1.0,(255,255,255)) cv2.putText(img,"Robot Trajectory(Ground truth)",(30,60),1,1.0,(0,255,0)) drawLines(img, np.array([[10,55],[25,55]]), 0, 255, 0) cv2.destroyAllWindows() |
Parcticle Filter Explained With Python Code From Scratch Read More »
Kalman Filter Explained With Python Code From Scratch
This snippet shows tracking mouse cursor with Python code from scratch and comparing the result with OpenCV. The CSV file that has been used are being created with below c++ code. A sample could be downloaded from here 1, 2, 3. Python Kalman Filter
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import numpy as np np.set_printoptions(threshold=3) np.set_printoptions(suppress=True) from numpy import genfromtxt #Notation used coming from: https://www.bzarg.com/p/how-a-kalman-filter-works-in-pictures/ def prediction(X_hat_t_1,P_t_1,F_t,B_t,U_t,Q_t): X_hat_t=F_t.dot(X_hat_t_1)+(B_t.dot(U_t).reshape(B_t.shape[0],-1) ) P_t=np.diag(np.diag(F_t.dot(P_t_1).dot(F_t.transpose())))+Q_t return X_hat_t,P_t def update(X_hat_t,P_t,Z_t,R_t,H_t): K_prime=P_t.dot(H_t.transpose()).dot( np.linalg.inv ( H_t.dot(P_t).dot(H_t.transpose()) +R_t ) ) print("K:\n",K_prime) X_t=X_hat_t+K_prime.dot(Z_t-H_t.dot(X_hat_t)) P_t=P_t-K_prime.dot(H_t).dot(P_t) return X_t,P_t acceleration=0 delta_t=1/20#milisecond groundTruth = genfromtxt('data/groundTruth.csv', delimiter=',',skip_header=1) #Observations: position_X, position_Y measurmens = genfromtxt('data/measurmens.csv', delimiter=',',skip_header=1) #Checking our result with OpenCV opencvKalmanOutput = genfromtxt('data/kalmanv.csv', delimiter=',',skip_header=1) #Transition matrix F_t=np.array([ [1 ,0,delta_t,0] , [0,1,0,delta_t] , [0,0,1,0] , [0,0,0,1] ]) #Initial State cov P_t= np.identity(4)*0.2 #Process cov Q_t= np.identity(4) #Control matrix B_t=np.array( [ [0] , [0], [0] , [0] ]) #Control vector U_t=acceleration #Measurment Matrix H_t = np.array([ [1, 0, 0, 0], [ 0, 1, 0, 0]]) #Measurment cov R_t= np.identity(2)*5 # Initial State X_hat_t = np.array( [[0],[0],[0],[0]] ) print("X_hat_t",X_hat_t.shape) print("P_t",P_t.shape) print("F_t",F_t.shape) print("B_t",B_t.shape) print("Q_t",Q_t.shape) print("R_t",R_t.shape) print("H_t",H_t.shape) for i in range(measurmens.shape[0]): X_hat_t,P_hat_t = prediction(X_hat_t,P_t,F_t,B_t,U_t,Q_t) print("Prediction:") print("X_hat_t:\n",X_hat_t,"\nP_t:\n",P_t) Z_t=measurmens[i].transpose() Z_t=Z_t.reshape(Z_t.shape[0],-1) print(Z_t.shape) X_t,P_t=update(X_hat_t,P_hat_t,Z_t,R_t,H_t) print("Update:") print("X_t:\n",X_t,"\nP_t:\n",P_t) X_hat_t=X_t P_hat_t=P_t print("=========================================") print("Opencv Kalman Output:") print("X_t:\n",opencvKalmanOutput[i]) |
C++ and OpenCV Kalman Filter Rapidcsv has been downloaded from
Kalman Filter Explained With Python Code From Scratch Read More »
Eigen unaryExpr (Function Pointer, Lambda Expression) Example
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double ramp(double x) { if (x > 0) return x; else return 0; } void unaryExprExample() { //unaryExpr is a const function so it will not give you the possibility to modify values in place Eigen::ArrayXd x = Eigen::ArrayXd::Random(5); std::cout<<x <<std::endl; x = x.unaryExpr([](double elem) // changed type of parameter { return elem < 0.0 ? 0.0 : 1.0; // return instead of assignment }); std::cout<<x <<std::endl; std::cout << x.unaryExpr(std::ptr_fun(ramp)) << std::endl; } |
Eigen unaryExpr (Function Pointer, Lambda Expression) Example Read More »
Matrix Decomposition with Eigen: QR, Cholesky Decomposition LU, UL
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void qRDecomposition(Eigen::MatrixXd &A,Eigen::MatrixXd &Q, Eigen::MatrixXd &R) { /* A=QR Q: is orthogonal matrix-> columns of Q are orthonormal R: is upper triangulate matrix this is possible when columns of A are linearly indipendent */ Eigen::MatrixXd thinQ(A.rows(),A.cols() ), q(A.rows(),A.rows()); Eigen::HouseholderQR<Eigen::MatrixXd> householderQR(A); q = householderQR.householderQ(); thinQ.setIdentity(); Q = householderQR.householderQ() * thinQ; R=Q.transpose()*A; } void qRExample() { Eigen::MatrixXd A; A.setRandom(3,4); std::cout<<"A" <<std::endl; std::cout<<A <<std::endl; Eigen::MatrixXd Q(A.rows(),A.rows()); Eigen::MatrixXd R(A.rows(),A.cols()); /////////////////////////////////HouseholderQR//////////////////////// Eigen::MatrixXd thinQ(A.rows(),A.cols() ), q(A.rows(),A.rows()); Eigen::HouseholderQR<Eigen::MatrixXd> householderQR(A); q = householderQR.householderQ(); thinQ.setIdentity(); Q = householderQR.householderQ() * thinQ; std::cout << "HouseholderQR" <<std::endl; std::cout << "Q" <<std::endl; std::cout << Q <<std::endl; R = householderQR.matrixQR().template triangularView<Eigen::Upper>(); std::cout << R<<std::endl; std::cout << R.rows()<<std::endl; std::cout << R.cols()<<std::endl; R=Q.transpose()*A; // std::cout << "R" <<std::endl; // std::cout << R<<std::endl; std::cout << "A-Q*R" <<std::endl; std::cout << A-Q*R <<std::endl; /////////////////////////////////ColPivHouseholderQR//////////////////////// Eigen::ColPivHouseholderQR<Eigen::MatrixXd> colPivHouseholderQR(A.rows(), A.cols()); colPivHouseholderQR.compute(A); //R = colPivHouseholderQR.matrixR().template triangularView<Upper>(); R = colPivHouseholderQR.matrixR(); Q = colPivHouseholderQR.matrixQ(); std::cout << "ColPivHouseholderQR" <<std::endl; std::cout << "Q" <<std::endl; std::cout << Q <<std::endl; std::cout << "R" <<std::endl; std::cout << R <<std::endl; std::cout << "A-Q*R" <<std::endl; std::cout << A-Q*R <<std::endl; /////////////////////////////////FullPivHouseholderQR//////////////////////// std::cout << "FullPivHouseholderQR" <<std::endl; Eigen::FullPivHouseholderQR<Eigen::MatrixXd> fullPivHouseholderQR(A.rows(), A.cols()); fullPivHouseholderQR.compute(A); Q=fullPivHouseholderQR.matrixQ(); R=fullPivHouseholderQR.matrixQR().template triangularView<Eigen::Upper>(); std::cout << "Q" <<std::endl; std::cout << Q <<std::endl; std::cout << "R" <<std::endl; std::cout << R <<std::endl; std::cout << "A-Q*R" <<std::endl; std::cout << A-Q*R <<std::endl; } void lDUDecomposition() { /* L: lower triangular matrix L U: upper triangular matrix U D: is a diagonal matrix A=LDU */ } void lUDecomposition() { /* L: lower triangular matrix L U: upper triangular matrix U A=LU */ } double exp(double x) // the functor we want to apply { std::setprecision(5); return std::trunc(x); } void gramSchmidtOrthogonalization(Eigen::MatrixXd &matrix,Eigen::MatrixXd &orthonormalMatrix) { /* In this method you make every column perpendicular to it's previous columns, here if a and b are representation vector of two columns, c=b-((b.a)/|a|).a ^ / b / / / ----------> a ^ /| b / | / | c / | ----------> a you just have to normilze every vector after make it perpendicular to previous columns so: q1=a.normalized(); q2=b-(b.q1).q1 q2=q2.normalized(); q3=c-(c.q1).q1 - (c.q2).q2 q3=q3.normalized(); Now we have Q, but we want A=QR so we just multiply both side by Q.transpose(), since Q is orthonormal, Q*Q.transpose() is I A=QR; Q.transpose()*A=R; */ Eigen::VectorXd col; for(int i=0;i<matrix.cols();i++) { col=matrix.col(i); col=col.normalized(); for(int j=0;j<i-1;j++) { //orthonormalMatrix.col(i) } orthonormalMatrix.col(i)=col; } Eigen::MatrixXd A(4,3); A<<1,2,3,-1,1,1,1,1,1,1,1,1; Eigen::Vector4d a=A.col(0); Eigen::Vector4d b=A.col(1); Eigen::Vector4d c=A.col(2); Eigen::Vector4d q1= a.normalized(); Eigen::Vector4d q2=b-(b.dot(q1))*q1; q2=q2.normalized(); Eigen::Vector4d q3=c-(c.dot(q1))*q1 - (c.dot(q2))*q2; q3=q3.normalized(); std::cout<< "q1:"<<std::endl; std::cout<< q1<<std::endl; std::cout<< "q2"<<std::endl; std::cout<< q2<<std::endl; std::cout<< "q3:"<<std::endl; std::cout<< q3<<std::endl; Eigen::MatrixXd Q(4,3); Q.col(0)=q1; Q.col(1)=q2; Q.col(2)=q3; Eigen::MatrixXd R(3,3); R=Q.transpose()*(A); std::cout<<"Q"<<std::endl; std::cout<< Q<<std::endl; std::cout<<"R"<<std::endl; std::cout<< R.unaryExpr(std::ptr_fun(exp))<<std::endl; //MatrixXd A(4,3), thinQ(4,3), Q(4,4); Eigen::MatrixXd thinQ(4,3), q(4,4); //A.setRandom(); Eigen::HouseholderQR<Eigen::MatrixXd> qr(A); q = qr.householderQ(); thinQ.setIdentity(); thinQ = qr.householderQ() * thinQ; std::cout << "Q computed by Eigen" << "\n\n" << thinQ << "\n\n"; std::cout << q << "\n\n" << thinQ << "\n\n"; } void gramSchmidtOrthogonalizationExample() { Eigen::MatrixXd matrix(3,4),orthonormalMatrix(3,4) ; matrix=Eigen::MatrixXd::Random(3,4);////A.setRandom(); gramSchmidtOrthogonalization(matrix,orthonormalMatrix); } void choleskyDecompositionExample() { /* Positive-definite matrix: Matrix Mnxn is said to be positive definite if the scalar zTMz is strictly positive for every non-zero column vector z n real numbers. zTMz>0 Hermitian matrix: Matrix Mnxn is said to be positive definite if the scalar z*Mz is strictly positive for every non-zero column vector z n real numbers. z*Mz>0 z* is the conjugate transpose of z. Positive semi-definite same as above except zTMz>=0 or z*Mz>=0 Example: ┌2 -1 0┐ M= |-1 2 -1| |0 - 1 2| └ ┘ ┌ a ┐ z=| b | | c | └ ┘ zTMz=a^2 +c^2+ (a-b)^2+ (b-c)^2 Cholesky decomposition: Cholesky decomposition of a Hermitian positive-definite matrix A is: A=LL* L is a lower triangular matrix with real and positive diagonal entries L* is the conjugate transpose of L */ Eigen::MatrixXd A(3,3); A << 6, 0, 0, 0, 4, 0, 0, 0, 7; Eigen::MatrixXd L( A.llt().matrixL() ); Eigen::MatrixXd L_T=L.adjoint();//conjugate transpose std::cout << "L" << std::endl; std::cout << L << std::endl; std::cout << "L_T" << std::endl; std::cout << L_T << std::endl; std::cout << "A" << std::endl; std::cout << A << std::endl; std::cout << "L*L_T" << std::endl; std::cout << L*L_T << std::endl; } |
Matrix Decomposition with Eigen: QR, Cholesky Decomposition LU, UL Read More »
Eigen Memory Mapping
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struct point { double a; double b; }; void EigenMapExample() { ////////////////////////////////////////First Example///////////////////////////////////////// Eigen::VectorXd solutionVec(12,1); solutionVec<<1,2,3,4,5,6,7,8,9,10,11,12; Eigen::Map<Eigen::MatrixXd> solutionColMajor(solutionVec.data(),4,3); Eigen::Map<Eigen::Matrix<double, 3, 4, Eigen::RowMajor> >solutionRowMajor (solutionVec.data()); std::cout << "solutionColMajor: "<< std::endl; std::cout << solutionColMajor<< std::endl; std::cout << "solutionRowMajor"<< std::endl; std::cout << solutionRowMajor<< std::endl; ////////////////////////////////////////Second Example///////////////////////////////////////// // https://stackoverflow.com/questions/49813340/stdvectoreigenvector3d-to-eigenmatrixxd-eigen int array[9]; for (int i = 0; i < 9; ++i) { array[i] = i; } Eigen::MatrixXi a(9, 1); a = Eigen::Map<Eigen::Matrix3i>(array); std::cout << a << std::endl; std::vector<point> pointsVec; point point1, point2, point3; point1.a = 1.0; point1.b = 1.5; point2.a = 2.4; point2.b = 3.5; point3.a = -1.3; point3.b = 2.4; pointsVec.push_back(point1); pointsVec.push_back(point2); pointsVec.push_back(point3); Eigen::Matrix2Xd pointsMatrix2d = Eigen::Map<Eigen::Matrix2Xd>( reinterpret_cast<double*>(pointsVec.data()), 2, long(pointsVec.size())); Eigen::MatrixXd pointsMatrixXd = Eigen::Map<Eigen::MatrixXd>( reinterpret_cast<double*>(pointsVec.data()), 2, long(pointsVec.size())); std::cout << pointsMatrix2d << std::endl; std::cout << "==============================" << std::endl; std::cout << pointsMatrixXd << std::endl; std::cout << "==============================" << std::endl; std::vector<Eigen::Vector3d> eigenPointsVec; eigenPointsVec.push_back(Eigen::Vector3d(2, 4, 1)); eigenPointsVec.push_back(Eigen::Vector3d(7, 3, 9)); eigenPointsVec.push_back(Eigen::Vector3d(6, 1, -1)); eigenPointsVec.push_back(Eigen::Vector3d(-6, 9, 8)); Eigen::MatrixXd pointsMatrix = Eigen::Map<Eigen::MatrixXd>(eigenPointsVec[0].data(), 3, long(eigenPointsVec.size())); std::cout << pointsMatrix << std::endl; std::cout << "==============================" << std::endl; pointsMatrix = Eigen::Map<Eigen::MatrixXd>(reinterpret_cast<double*>(eigenPointsVec.data()), 3, long(eigenPointsVec.size())); std::cout << pointsMatrix << std::endl; std::vector<double> aa = { 1, 2, 3, 4 }; Eigen::VectorXd b = Eigen::Map<Eigen::VectorXd, Eigen::Unaligned>(aa.data(), long(aa.size())); } |
Eigen Memory Mapping Read More »
