for v2 of paper, datasets are smaller and add fluid flow examples

data/DiscreteSpectrumExample.m

@@ -1,5 +1,5 @@
 
-numICs = 200*200*21/20;
+numICs = 5000;
 filenamePrefix = 'DiscreteSpectrumExample';
 
 x1range = [-.5, .5];

data/DiscreteSpectrumExampleFn.m

@@ -1,6 +1,7 @@
 function X = DiscreteSpectrumExampleFn(x1range, x2range, numICs, tSpan, mu, lambda, seed)
 
 % Koopman example from 3.4.2 (pg 51) of the DMD book
+% (Dynamic Mode Decomposition by Kutz, Brunton, Brunton, and Proctor)
 % nonlinear dynamical system in two variables, but with 3D Koopman
 % observables, have linear dynamical system
 
@@ -18,6 +19,8 @@
 X = zeros(numICs*lenT, 2);
 
 count = 1;
+% in order to solve more accurately than ode45, map into 3D linear system
+% and use exact analytic solution 
 for j = 1:numICs
     Y0 = [x1(j); x2(j); x1(j)^2];
     c1 = Y0(1);

data/FluidFlowBox.m

@@ -0,0 +1,26 @@
+
+numTest_ICs = 5000;
+filenamePrefix = 'FluidFlowBox';
+
+x1range = [-1.1,1.1];
+x2range = [-1.1,1.1];
+x3range = [0,2.42];
+tSpan = 0:0.01:1;
+max_x3 = 2.5;
+
+seed = 1;
+X_test = FluidFlowBoxFn(x1range, x2range, x3range, numTest_ICs, tSpan, seed, max_x3);
+filename_test = strcat(filenamePrefix, '_test_x.csv');
+dlmwrite(filename_test, X_test, 'precision', '%.14f')
+
+seed = 2;
+X_val = FluidFlowBoxFn(x1range, x2range, x3range, numTest_ICs, tSpan, seed, max_x3);
+filename_val = strcat(filenamePrefix, '_val_x.csv');
+dlmwrite(filename_val, X_val, 'precision', '%.14f')
+
+for j = 1:20
+	seed = 2+j;
+	X_train = FluidFlowBoxFn(x1range, x2range, x3range, numTest_ICs, tSpan, seed, max_x3);
+	filename_train = strcat(filenamePrefix, sprintf('_train%d_x.csv', j));
+	dlmwrite(filename_train, X_train, 'precision', '%.14f')
+end

data/FluidFlowBoxFn.m

@@ -0,0 +1,48 @@
+function X = FluidFlowBoxFn(x1range, x2range, x3range, numICs, tSpan, seed, max_x3)
+
+
+% try some initial conditions for x1, x2
+rng(seed)
+
+b = 0;
+mu = 0.1;
+omega = 1;
+lambda = -10;
+A = -mu;
+dynsys = @(t,x) weaklyNL(x,b,mu,omega,lambda,A);
+
+lenT = length(tSpan);
+
+X = zeros(numICs*lenT, 3);
+count = 1;
+
+for j = 1:10*numICs
+    % randomly start from x1range(1) to x1range(2)
+    x1 = (x1range(2)-x1range(1))*rand+x1range(1);
+
+    % randomly start from x2range(1) to x2range(2)
+    x2 = (x2range(2)-x2range(1))*rand+x2range(1);
+
+    % randomly start from x3range(1) to x3range(2)
+    x3 = (x3range(2)-x3range(1))*rand+x3range(1);
+
+
+    ic = [x1; x2; x3];
+
+    [T, temp] = ode45(dynsys, tSpan, ic);
+
+    if max(temp(:,3)) > max_x3
+        sprintf('traj goes too big: %.15f', max(temp(:,3)))
+        continue
+    else
+        X(1+(count-1)*lenT : lenT + (count-1)*lenT,:) = temp;
+
+        if count == numICs
+            break
+        end
+        count = count + 1;
+    end
+end
+
+
+

data/FluidFlowOnAttractor.m

@@ -0,0 +1,25 @@
+
+numTest_ICs = 5000;
+filenamePrefix = 'FluidFlowOnAttractor';
+
+Rrange = [0,1.1];
+Trange = [0,2*pi];
+tSpan = 0:0.05:6;
+
+
+seed = 1;
+X_test = FluidFlowOnAttractorFn(Rrange, Trange, numTest_ICs, tSpan, seed);
+filename_test = strcat(filenamePrefix, '_test_x.csv');
+dlmwrite(filename_test, X_test, 'precision', '%.14f')
+
+seed = 2;
+X_val = FluidFlowOnAttractorFn(Rrange, Trange, numTest_ICs, tSpan, seed);
+filename_val = strcat(filenamePrefix, '_val_x.csv');
+dlmwrite(filename_val, X_val, 'precision', '%.14f')
+
+for j = 1:20
+	seed = 2+j;
+	X_train = FluidFlowOnAttractorFn(Rrange, Trange, numTest_ICs, tSpan, seed);
+	filename_train = strcat(filenamePrefix, sprintf('_train%d_x.csv', j));
+	dlmwrite(filename_train, X_train, 'precision', '%.14f')
+end

data/FluidFlowOnAttractorFn.m

@@ -0,0 +1,42 @@
+function X = FluidFlowOnAttractorFn(Rrange, Trange, numICs, tSpan, seed)
+
+
+% try some initial conditions for R, T
+rng(seed)
+
+b = 0;
+mu = 0.1;
+omega = 1;
+lambda = -10;
+A = -mu;
+dynsys = @(t,x) weaklyNL(x,b,mu,omega,lambda,A);
+
+lenT = length(tSpan);
+
+X = zeros(numICs*lenT, 3);
+
+count = 1;
+for j = 1:2*numICs
+    % randomly start from Rrange(1) to Rrange(2)
+    R = (Rrange(2)-Rrange(1))*rand+Rrange(1);
+
+    % randomly start from Trange(1) to Trange(2)
+    T = (Trange(2)-Trange(1))*rand+Trange(1);
+
+    x1 = R*cos(T);
+    x2 = R*sin(T);
+    x3 = x1^2 + x2^2;
+
+    ic = [x1; x2; x3];
+
+    [T, temp] = ode45(dynsys, tSpan, ic);
+
+    X(1+(count-1)*lenT : lenT + (count-1)*lenT,:) = temp;
+    if count == numICs
+        break
+    end
+    count = count + 1;
+end
+
+
+

data/Pendulum.m

@@ -1,5 +1,5 @@
 
-numICs = 200*200*21/20;
+numICs = 5000;
 filenamePrefix = 'Pendulum';
 
 x1range = [-3.1,3.1];
@@ -9,18 +9,18 @@
 max_potential = .99;
 
 seed = 1;
-X_test = PendulumFnPotential(x1range, x2range, round(.1*numICs), tSpan, seed, max_potential);
+X_test = PendulumFn(x1range, x2range, round(.1*numICs), tSpan, seed, max_potential);
 filename_test = strcat(filenamePrefix, '_test_x.csv');
 dlmwrite(filename_test, X_test, 'precision', '%.14f')
 
 seed = 2;
-X_val = PendulumFnPotential(x1range, x2range, round(.2*numICs), tSpan, seed, max_potential);
+X_val = PendulumFn(x1range, x2range, round(.2*numICs), tSpan, seed, max_potential);
 filename_val = strcat(filenamePrefix, '_val_x.csv');
 dlmwrite(filename_val, X_val, 'precision', '%.14f')
 
 for j = 1:10
 	seed = 2+j;
-	X_train = PendulumFnPotential(x1range, x2range, round(.7*numICs), tSpan, seed, max_potential);
+	X_train = PendulumFn(x1range, x2range, round(.7*numICs), tSpan, seed, max_potential);
 	filename_train = strcat(filenamePrefix, sprintf('_train%d_x.csv', j));
 	dlmwrite(filename_train, X_train, 'precision', '%.14f')
 end

data/PendulumFnPotential.m → data/PendulumFn.m

@@ -1,4 +1,4 @@
-function X = PendulumFnPotential(x1range, x2range, numICs, tSpan, seed, max_potential)
+function X = PendulumFn(x1range, x2range, numICs, tSpan, seed, max_potential)
 
 
 % try some initial conditions for x1, x2
@@ -27,15 +27,15 @@
         [T, temp] = ode45(dynsys, tSpan, ic);
 
         X(1+(count-1)*lenT : lenT + (count-1)*lenT,:) = temp;
-	if count == numICs
-	    break
-	end
+        if count == numICs
+            break
+        end
         count = count + 1;
     end
 end
 
 if count < numICs
-	sprintf('oops, potential energy too small for IC box')
+    sprintf('oops, potential energy too small for IC box')
 end
 
 

data/weaklyNL.m

@@ -0,0 +1,7 @@
+function dy = weaklyNL(y,b,mu,omega,lambda,A)
+
+dy = [
+    mu*y(1) - omega*y(2) + A*y(1)*y(3);
+    omega*y(1) + mu*y(2) + A*y(2)*y(3) + b;
+    lambda*(y(3)-y(1).^2-y(2).^2);  
+];