Added layer backpropagation

layer.h

@@ -15,12 +15,20 @@ class Layer {
     Matrix activated_output;
     Matrix biases;
 
+    // Planning for back propagation
+    // Each layer needs the derivative of Z with respect to W, derivative of A with respect to Z and derivative of loss with respect to A
+    // Let's call them dzw, daz and dca
+    Matrix daz;
+
     static inline float Sigmoid(float);
     static inline float SigmoidPrime(float);
 
     inline void Forward(); // Forward Pass with sigmoid
     inline void Forward(float (*activation)(float)); // Forward Pass with custom activation function
 
+    inline void BackPropagate(Matrix);
+    inline void BackPropagate(Matrix, Matrix, float (*activation)(float)); // To backpropagate, we need the derivative of loss with respect to A and the derivative of used activation function
+
     inline void Feed(Matrix);
 
     // Constructors
@@ -29,6 +37,31 @@ class Layer {
     Layer();
 };
 
+void Layer::BackPropagate(Matrix dzw, Matrix dca, float (*derivative)(float)){
+    // Calculate daz ; derivative of activation function
+    this->daz = this->activated_output.Function(derivative);
+    // this->daz.Print("daz");
+
+    // We need to transpose dzw and extend down
+    // dzw.Print("dzw");
+    dzw = dzw.Transpose().ExtendDown(dca.values.size());
+    // dzw.Print("dzw extended transposed");
+
+    Matrix dcw = this->daz.Hadamard(&dca).ExtendRight(this->input.values.size());
+    // dcw.Print("daz . dca");
+    dcw = dcw.Hadamard(&dzw);
+    // dcw.Print("daz . dca . dzw : DCW");
+
+    // this->weights.Print("weights");
+
+    // Apply dcw to weights
+    float learning_rate = 0.1F;
+    Matrix reduced_dcw = dcw.Multiply(learning_rate);
+    // We SUBSTRACT the derivative of loss with respect to the weights.
+    this->weights = this->weights.Substract(&reduced_dcw);
+    // this->weights.Print("New weights");
+}
+
 Layer::Layer(){
 
 }