plot3 command error in dlode45

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Hi community,

I am runnig my code for Lorenz system but it gives error of plot3 command, kindly can someone error in this code

%%Code%%

% Initial conditions for Lorenz system

x0 = [-8; 27; 7];

sigma = 10;

rho = 28;

beta = 8/3;

trueModel = @(t, y) [sigma * (y(2) - y(1)); y(1) * (rho - y(3)) - y(2); y(1) * y(2) - beta * y(3)];

% Simulation parameters (same as before)

numTimeSteps = 2000;

T = 10;

odeOptions = odeset('RelTol', 1.e-7);

t = linspace(0, T, numTimeSteps);

[~, xTrain] = ode45(trueModel, t, x0, odeOptions);

xTrain = xTrain';

% True model visualization (updated for 3D Lorenz system)

figure

plot3(xTrain(1, :), xTrain(2, :), xTrain(3, :))

title("Ground Truth Dynamics")

xlabel("x(1)")

ylabel("x(2)")

zlabel("x(3)")

grid on

neuralOdeTimesteps = 100;

dt = t(2);

timesteps = (0:neuralOdeTimesteps)*dt;

neuralOdeParameters = struct;

stateSize = size(xTrain,1);

hiddenSize = 20;

neuralOdeParameters.fc1 = struct;

sz = [hiddenSize stateSize];

neuralOdeParameters.fc1.Weights = initializeGlorot(sz, hiddenSize, stateSize);

neuralOdeParameters.fc1.Bias = initializeZeros([hiddenSize 1]);

neuralOdeParameters.fc2 = struct;

sz = [stateSize hiddenSize];

neuralOdeParameters.fc2.Weights = initializeGlorot(sz, stateSize, hiddenSize);

neuralOdeParameters.fc2.Bias = initializeZeros([stateSize 1]);

neuralOdeParameters.fc1

ans = struct with fields:

Weights: [20×3 dlarray] Bias: [20×1 dlarray]

neuralOdeParameters.fc2

ans = struct with fields:

Weights: [3×20 dlarray] Bias: [3×1 dlarray]

gradDecay = 0.9;

sqGradDecay = 0.99;

learnRate = 0.9;

numIter = 100;

miniBatchSize = 200;

plotFrequency = 50;

f = figure;

f.Position(3) = 2*f.Position(3);

subplot(1,2,1)

C = colororder;

lineLossTrain = animatedline(Color=C(2,:));

ylim([0 inf])

xlabel("Iteration")

ylabel("Loss")

grid on

averageGrad = [];

averageSqGrad = [];

numTrainingTimesteps = numTimeSteps;

trainingTimesteps = 1:numTrainingTimesteps;

plottingTimesteps = 2:numTimeSteps;

start = tic;

for iter = 1:numIter

% Create batch

[X, targets] = createMiniBatch(numTrainingTimesteps, neuralOdeTimesteps, miniBatchSize, xTrain);

% Evaluate network and compute loss and gradients

[loss,gradients] = dlfeval(@modelLoss,timesteps,X,neuralOdeParameters,targets);

% Update network

[neuralOdeParameters,averageGrad,averageSqGrad] = adamupdate(neuralOdeParameters,gradients,averageGrad,averageSqGrad,iter,...

learnRate,gradDecay,sqGradDecay);

% Plot loss

subplot(1,2,1)

currentLoss = double(loss);

addpoints(lineLossTrain,iter,currentLoss);

D = duration(0,0,toc(start),Format="hh:mm:ss");

title("Elapsed: " + string(D))

drawnow

% Plot predicted vs. real dynamics

if mod(iter,plotFrequency) == 0 || iter == 1

subplot(1,2,2)

% Use ode45 to compute the solution

y = dlode45(@odeModel,t,dlarray(x0),neuralOdeParameters,DataFormat="CB");

size(y)

% y = squeeze(y)';

plot3(xTrain(1,plottingTimesteps),xTrain(2,plottingTimesteps),xTrain(3,plottingTimesteps),"r--")

hold on

plot3(y(1,:),y(2,:),y(3,:),'b-')

hold off

xlabel("x")

ylabel("y")

zlabel("z")

title("Predicted vs. Real Dynamics")

legend("Training Ground Truth", "Predicted")

drawnow

end

ans = 1×3

3 1 1999

Error using plot3
Data must be numeric, datetime, duration, categorical, or an array convertible to double.

% Prediction and visualization (updated for 3D Lorenz system)

tPred = t;

x0Pred1 = [0; 2; 2];

x0Pred2 = [-1; -1.5; 0];

x0Pred3 = [2; 1; 0];

x0Pred4 = [-2; 0; 1];

[~, xTrue1] = ode45(trueModel, tPred, x0Pred1, odeOptions);

[~, xTrue2] = ode45(trueModel, tPred, x0Pred2, odeOptions);

[~, xTrue3] = ode45(trueModel, tPred, x0Pred3, odeOptions);

[~, xTrue4] = ode45(trueModel, tPred, x0Pred4, odeOptions);

xPred1 = dlode45(@odeModel, tPred, dlarray(x0Pred1), neuralOdeParameters, 'DataFormat', "CB");

size(xPred1)

xPred2 = dlode45(@odeModel, tPred, dlarray(x0Pred2), neuralOdeParameters, 'DataFormat', "CB");

xPred3 = dlode45(@odeModel, tPred, dlarray(x0Pred3), neuralOdeParameters, 'DataFormat', "CB");

xPred4 = dlode45(@odeModel, tPred, dlarray(x0Pred4), neuralOdeParameters, 'DataFormat', "CB");

figure

subplot(2, 2, 1)

plotTrueAndPredictedSolutions(xTrue1, xPred1);

subplot(2, 2, 2)

plotTrueAndPredictedSolutions(xTrue2, xPred2);

subplot(2, 2, 3)

plotTrueAndPredictedSolutions(xTrue3, xPred3);

subplot(2, 2, 4)

plotTrueAndPredictedSolutions(xTrue4, xPred4);

% Visualization function (updated for 3D Lorenz system)

function plotTrueAndPredictedSolutions(xTrue, xPred)

xPred = squeeze(xPred)';

err = mean(abs(xTrue(2:end, :) - xPred), "all");

plot3(xTrue(:, 1), xTrue(:, 2), xTrue(:, 3), "r--", xPred(:, 1), xPred(:, 2), xPred(:, 3), "b-", 'LineWidth', 1)

title("Absolute Error = " + num2str(err, "%.4f"))

xlabel("x(1)")

ylabel("x(2)")

zlabel("x(3)")

legend("Ground Truth", "Predicted")

grid on

end

function X = model(tspan,X0,neuralOdeParameters)

X = dlode45(@odeModel,tspan,X0,neuralOdeParameters,DataFormat="CB");

end

function y = odeModel(~,y,theta)

y = tanh(theta.fc1.Weights*y + theta.fc1.Bias);

y = theta.fc2.Weights*y + theta.fc2.Bias;

end

function [loss,gradients] = modelLoss(tspan,X0,neuralOdeParameters,targets)

% Compute predictions.

X = model(tspan,X0,neuralOdeParameters);

% Compute L1 loss.

loss = l1loss(X,targets,NormalizationFactor="all-elements",DataFormat="CBT");

% Compute gradients.

gradients = dlgradient(loss,neuralOdeParameters);

end

function [x0, targets] = createMiniBatch(numTimesteps,numTimesPerObs,miniBatchSize,X)

% Create batches of trajectories.

s = randperm(numTimesteps - numTimesPerObs, miniBatchSize);

x0 = dlarray(X(:, s));

targets = zeros([size(X,1) miniBatchSize numTimesPerObs]);

for i = 1:miniBatchSize

targets(:, i, 1:numTimesPerObs) = X(:, s(i) + 1:(s(i) + numTimesPerObs));

end

function weights = initializeGlorot(sz,numOut,numIn,className)

arguments

sz

numOut

numIn

className = 'single'

end

Z = 2*rand(sz,className) - 1;

bound = sqrt(6 / (numIn + numOut));

weights = bound * Z;

weights = dlarray(weights);

end

function parameter = initializeZeros(sz,className)

arguments

sz

className = 'single'

end

parameter = zeros(sz,className);

parameter = dlarray(parameter);

end

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Adam Danz 2023-7-20

I've formatted and run your code to produce the error message.

Muhammad 2023-7-20

thank you

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Answer 1

Star Strider 2023-7-20

1 个投票

The problem is that ‘y’ is a dlarray (the first time I’ve encountered one so I need to start working with the Deep Learning Toolbox).

Replace Line 89 with these two lines:

ys = extractdata(y)

plot3(ys(1,:),ys(2,:),ys(3,:),'b-')

to convert the dlarray to a single array, and the plot3 result magically appears! (I decided on the new variable ‘ys’ here to avoid converting ‘y’ and causing problems with the rest of your code, since the extractdata extraction only needs to be done for the plot3 call in this instance.)

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Muhammad 2023-7-20

thank you, problem solved

Star Strider 2023-7-20

As always, my pleasure!

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