create a neural network in matlab that handles complex numbers in matlab

In order to create a neural network in Matlab that can handle complex numbers, you can use the Complex Network Toolbox. This toolbox provides the necessary functions to train and simulate neural networks with complex-valued inputs and outputs.

First, you need to install the Complex Network Toolbox by following the instructions provided by MathWorks: https://www.mathworks.com/matlabcentral/fileexchange/74219-complex-quantum-neural-network-toolbox?s_tid=srchtitle

Once you have installed the toolbox, here is an example of how to create a simple complex-valued neural network in Matlab:

main.m
% Create a complex-valued dataset
input = complex(randn(100, 2), randn(100, 2));
output = complex(randn(100, 1), randn(100, 1));

% Define the neural network architecture
hiddenUnits = 10;
layers = [
    complexFullyConnectedLayer(hiddenUnits)
    complexReLULayer
    complexFullyConnectedLayer(1)
    complexRegressionLayer];

% Specify the training options
options = trainingOptions('adam', ...
    'MaxEpochs', 100, ...
    'MiniBatchSize', 16, ...
    'ValidationData', {input, output}, ...
    'ValidationFrequency', 10, ...
    'Plots', 'training-progress');

% Train the neural network
net = trainNetwork(input, output, layers, options);

% Simulate the network on new data
newInput = complex(randn(10, 2), randn(10, 2));
predictedOutput = predict(net, newInput);
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In this example, the complex neural network has a fully connected hidden layer followed by a complex-valued ReLU (Rectified Linear Unit) activation function, another fully connected layer, and finally a complex regression layer.

You can adjust the number of hidden units, the number of layers, and the training options according to your specific problem. Remember to use complex-valued data for both the inputs and outputs when training and simulating the neural network.

Note that the Complex Network Toolbox provides other complex-valued activation functions, such as complexSigmoidLayer, complexTanhLayer, and complexSoftmaxLayer, which you can explore for different types of problems.

Remember to consult the Complex Network Toolbox documentation for more details on how to create and train complex-valued neural networks in Matlab.