public override NDArray ReduceAMin(NDArray arr, int? axis_, bool keepdims = false, NPTypeCode? typeCode = null)
{
//in order to iterate an axis:
//consider arange shaped (1,2,3,4) when we want to summarize axis 1 (2nd dimension which its value is 2)
//the size of the array is [1, 2, n, m] all shapes after 2nd multiplied gives size
//the size of what we need to reduce is the size of the shape of the given axis (shape[axis])
var shape = arr.Shape;
if (shape.IsEmpty)
return arr;
if (shape.IsScalar || shape.size == 1 && shape.dimensions.Length == 1)
{
var r = typeCode.HasValue ? Cast(arr, typeCode.Value, true) : arr.Clone();
if (keepdims)
r.Storage.ExpandDimension(0);
else if (!r.Shape.IsScalar && r.Shape.size == 1 && r.ndim == 1)
r.Storage.Reshape(Shape.Scalar);
return r;
}
if (axis_ == null)
{
var r = NDArray.Scalar(amin_elementwise(arr, typeCode));
if (keepdims)
r.Storage.ExpandDimension(0);
else if (!r.Shape.IsScalar && r.Shape.size == 1 && r.ndim == 1)
r.Storage.Reshape(Shape.Scalar);
return r;
}
var axis = axis_.Value;
while (axis < 0)
axis = arr.ndim + axis; //handle negative axis
if (axis >= arr.ndim)
throw new ArgumentOutOfRangeException(nameof(axis));
if (shape[axis] == 1)
{
//if the given div axis is 1 and can be squeezed out.
if (keepdims)
return new NDArray(arr.Storage.Alias());
return np.squeeze_fast(arr, axis);
}
//handle keepdims
Shape axisedShape = Shape.GetAxis(shape, axis);
//prepare ret
var ret = new NDArray(typeCode ?? arr.GetTypeCode, axisedShape, false);
var iterAxis = new NDCoordinatesAxisIncrementor(ref shape, axis);
var iterRet = new NDCoordinatesIncrementor(ref axisedShape);
var iterIndex = iterRet.Index;
var slices = iterAxis.Slices;
#if _REGEN1
#region Compute
switch (arr.GetTypeCode)
{
%foreach supported_numericals,supported_numericals_lowercase%
case NPTypeCode.#1:
{
switch (ret.GetTypeCode)
{
%foreach supported_numericals,supported_numericals_lowercase,supported_numericals_defaultvals%
case NPTypeCode.#101:
{
do
{
var iter = arr[slices].AsIterator<#2>();
public override NDArray Cast(NDArray nd, NPTypeCode dtype, bool copy)
{
if (dtype == NPTypeCode.Empty)
{
throw new ArgumentNullException(nameof(dtype));
}
//incase its an empty array
if (nd.Shape.IsEmpty)
{
if (copy)
{
return(new NDArray(dtype));
}
nd.Storage = new UnmanagedStorage(dtype);
return(nd);
}
//incase its a scalar
if (nd.Shape.IsScalar)
{
var ret = NDArray.Scalar(nd.GetAtIndex(0), dtype);
if (copy)
{
return(ret);
}
nd.Storage = ret.Storage;
return(nd);
}
//incase its a (1,) shaped
if (nd.Shape.size == 1 && nd.Shape.NDim == 1)
{
var ret = new NDArray(ArraySlice.Scalar(nd.GetAtIndex(0), dtype), Shape.Vector(1));
if (copy)
{
return(ret);
}
nd.Storage = ret.Storage;
return(nd);
}
//regular clone
if (nd.GetTypeCode == dtype)
{
//casting not needed
return(copy ? clone() : nd);
}
else
{
//casting needed
if (copy)
{
if (nd.Shape.IsSliced)
{
nd = clone();
}
return(new NDArray(new UnmanagedStorage(ArraySlice.FromMemoryBlock(nd.Array.CastTo(dtype), false), nd.Shape)));
}
else
{
var storage = nd.Shape.IsSliced ? nd.Storage.Clone() : nd.Storage;
nd.Storage = new UnmanagedStorage(ArraySlice.FromMemoryBlock(storage.InternalArray.CastTo(dtype), false), storage.Shape);
return(nd);
}
}
NDArray clone() => nd.Clone();
}
//This function feeds an image into the neural network and applies the backpropagation
public void ProcessNeuralNetwork(TestCase testCase, bool storeIncrementalSteps)
{
//Start
//10 fps: https://www.youtube.com/watch?v=zpCFjNjuBaY&t=0
//60 fps: https://www.youtube.com/watch?v=IQdxHrfdMwk&t=0
NDArray image784x1 = testCase.AsNDArray();
//Hidden neuron calculations
//10 fps: https://www.youtube.com/watch?v=zpCFjNjuBaY&t=18
//60 fps: https://www.youtube.com/watch?v=IQdxHrfdMwk&t=18
var hiddenPreSigmoid20x1 = hiddenBiases20x1 + np.matmul(inputToHiddenWeights20x784, image784x1);
if (storeIncrementalSteps)
{
hiddenNeuronsBeforeSigmoid20x1 = hiddenPreSigmoid20x1.Clone();
}
//normalize with sigmoid
currentHiddenNeurons20X1 = np.divide(1, (np.add(1, np.exp(-hiddenPreSigmoid20x1))));
//Final output neuron calculation
//10 fps: https://www.youtube.com/watch?v=zpCFjNjuBaY&t=78
//60 fps: https://www.youtube.com/watch?v=IQdxHrfdMwk&t=78
//map from inputs to output and add bias
var outputPreSigmoid10x1 = outputBiases10x1 + np.matmul(hiddenToOutputWeights10x20, currentHiddenNeurons20X1);
if (storeIncrementalSteps)
{
outputNeuronsBeforeSigmoid10x1 = outputPreSigmoid10x1.Clone();
}
//normalize with sigmoid
currentOutputNeurons10x1 = 1 / (1 + np.exp(-outputPreSigmoid10x1));
expectedOutput10x1 = testCase.AsLabelNDArray();
//np.argmax(o) gives the index of the maximum number. This is simply checking to see which output was switched on
detected = np.argmax(currentOutputNeurons10x1);
//Start back propagation by figuring out by how much the output was "wrong"
//10 fps: https://www.youtube.com/watch?v=zpCFjNjuBaY&t=108
//60 fps: https://www.youtube.com/watch?v=IQdxHrfdMwk&t=108
expectedOutputDelta10X1 = currentOutputNeurons10x1 - expectedOutput10x1;
//Calculate the hidden to output weights "wrongness" using the output's "wrongness"
//10 fps: https://www.youtube.com/watch?v=zpCFjNjuBaY&t=138
//60 fps: https://www.youtube.com/watch?v=IQdxHrfdMwk&t=138
//Multiply difference from expected by the hidden neurons to make a matrix to adjust the hidden to output weights
hiddenToOutputWeightAdjustment10X20 = np.matmul(expectedOutputDelta10X1, np.transpose(currentHiddenNeurons20X1));
if (storeIncrementalSteps)
{
hiddenToOutputWeightsPreAdjust10x20 = hiddenToOutputWeights10x20.Clone();
}
//Adjust the hidden to output weights by the calculated "wrongness"
//10 fps: https://www.youtube.com/watch?v=zpCFjNjuBaY&t=198
//60 fps: https://www.youtube.com/watch?v=IQdxHrfdMwk&t=198"
//adjust the hidden to output weights
hiddenToOutputWeights10x20 += -learnRate * hiddenToOutputWeightAdjustment10X20;
if (storeIncrementalSteps)
{
outputBiasPreAdjust10x1 = outputBiases10x1.Clone();
}
//Adjust the output biases
outputBiases10x1 += -learnRate * expectedOutputDelta10X1;
//Now move on to building the matrix to adjust the input to hidden weights
//differential of sigmoid is sigmoid * (1 - sigmoid). Remember above where we used sigmoid function on currentHiddenNeurons?
//Result is 20x1 matrix
if (storeIncrementalSteps)
{
oneMinusHiddenNeurons20x1 = 1 - currentHiddenNeurons20X1;
}
//Calculate the sigmoid differential of the hidden neurons to use later
//10 fps: https://www.youtube.com/watch?v=zpCFjNjuBaY&t=204
//60 fps: https://www.youtube.com/watch?v=IQdxHrfdMwk&t=204
hiddenNeuronsSigmoidDifferential20X1 = (currentHiddenNeurons20X1 * (1 - currentHiddenNeurons20X1));
//Multiply the "wrongness" of the output by the adjusted hidden to output weights to get the weights "wrongness"
//10 fps: https://www.youtube.com/watch?v=zpCFjNjuBaY&t=264
//60 fps: https://www.youtube.com/watch?v=IQdxHrfdMwk&t=264
//Combine expectedOutputDelta (10X1) with the hiddenToOutputWeights (10x20), resulting in a 20x1 matrix
hiddenToOutputWeightsXExpectedOutputDelta20x1 = np.matmul(np.transpose(hiddenToOutputWeights10x20), expectedOutputDelta10X1);
//Multiply the "wrongness" of the adjusted hidden to output weights by the hidden neuron sigmoid differential to get the "wrongness" of each hidden neuron
//10 fps: https://www.youtube.com/watch?v=zpCFjNjuBaY&t=324
//60 fps: https://www.youtube.com/watch?v=IQdxHrfdMwk&t=324"
//Then combine in the differential of the sigmoid (20X1) X (20X1) = 20X1
expectedHiddenDelta20X1 = hiddenToOutputWeightsXExpectedOutputDelta20x1 * hiddenNeuronsSigmoidDifferential20X1;
//Multiply the "wrongness" of each hidden neuron by the original image to calculate the "wrongness" of the input to hidden matrix
//10 fps: https://www.youtube.com/watch?v=zpCFjNjuBaY&t=384
//60 fps: https://www.youtube.com/watch?v=IQdxHrfdMwk&t=384
//Then multiply by the image to make a 20x784 matrix
inputToHiddenWeightAdjustment20x784 = np.matmul(expectedHiddenDelta20X1, np.transpose(image784x1));
if (storeIncrementalSteps)
{
inputToHiddenWeightsPreAdjust20x784 = inputToHiddenWeights20x784.Clone();
}
//Apply the "wrongness" of the input to hidden matrix to the input to hidden matrix
//10 fps: https://www.youtube.com/watch?v=zpCFjNjuBaY&t=453
//60 fps: https://www.youtube.com/watch?v=IQdxHrfdMwk&t=453
//Finally we adjust the actual weights using our calculated adjustment matrix
inputToHiddenWeights20x784 += -learnRate * inputToHiddenWeightAdjustment20x784;
if (storeIncrementalSteps)
{
hiddenNeuronBiasPreAdjust20x1 = hiddenBiases20x1.Clone();
}
//And adjust the bias using a portion of how far off the hidden neurons were
hiddenBiases20x1 += -learnRate * expectedHiddenDelta20X1;
}