index.html

@@ -0,0 +1,717 @@
+<script>
+    /* Vector Library */
+/*
+	Works with n-dimensional vectors: represented as arrays of numbers
+*/
+var V = {};
+V.Subtract = function(inV1, inV2)
+{
+	var out = [];
+	for(var i=0; i<inV1.length; i++)
+	{
+		out[i] = inV1[i] - inV2[i];
+	}
+	return out;
+};
+V.Add = function(inV1, inV2)
+{
+	var out = [];
+	for(var i=0; i<inV1.length; i++)
+	{
+		out[i] = inV1[i] + inV2[i];
+	}
+	return out;
+};
+V.Distance = function(inV1, inV2)
+{
+	return V.Length(V.Subtract(inV1, inV2))
+};
+V.Dot = function(inV1, inV2)
+{
+	var out = 0;
+	for(var i=0; i<inV1.length; i++)
+	{
+		out += inV1[i] * inV2[i];
+	}
+	return out;
+};
+V.Multiply = function(inV1, inV2)
+{
+	var out = [];
+	for(var i=0; i<inV1.length; i++)
+	{
+		out[i] = inV1[i] * inV2[i];
+	}
+	return out;
+};
+V.Length = function(inV1)
+{
+	return Math.sqrt(V.Dot(inV1, inV1));
+};
+V.Scale = function(inV1, inScalar)
+{
+	var out = [];
+	for(var i=0; i<inV1.length; i++)
+	{
+		out[i] = inV1[i] * inScalar;
+	}
+	return out;
+};
+V.Normalize = function(inV1)
+{
+    return V.Scale(inV1, 1/V.Length(inV1));
+};
+V.Clone = function(inV1)
+{
+	var out = [];
+	var i;
+	for(i=0; i<inV1.length; i++)
+	{
+		out[i] = inV1[i];
+	}
+	return out;
+};
+
+
+
+
+
+
+
+
+
+
+
+var M = {};
+
+/**************************
+M A T R I X
+*/
+// transform inC with inM
+// returns the transformed inC
+M.Transform = function(inM, inC)
+{
+	var outM = [];
+	var outV = [];
+	var i, j;
+	
+	for(i=0; i<inC.length; i++)
+	{
+		outV = [];
+		for(j=0; j<inM.length; j++)
+		{
+			outV[j] = V.Dot(inM[j], inC[i]);
+		}
+		outM.push(outV);
+	}
+	return outM;
+};
+
+
+// flip rows for columns in inM
+// returns the modified Matrix
+M.Transpose = function(inM)
+{
+	var dimensions = inM[0].length;
+	var i, j;
+	var outM = [];
+	var outV = [];
+	for(i=0; i<dimensions; i++)
+	{
+		outV = [];
+		for(j=0; j<inM.length; j++)
+		{
+			//the Ith componenth of the Jth member
+			outV[j] = inM[j][i];
+		}
+		outM.push(outV);
+	}
+	return outM;
+}
+
+// returns a matrix that is the result of the outer product of inV1 and inV2
+// where the Nth member of outM is a copy of V1, scaled by the Nth component of V2
+M.Outer = function(inV1, inV2)
+{
+	var outM = [];
+	
+	var i;
+	for(i=0; i<inV2.length; i++)
+	{
+		outM.push(V.Scale(inV1, inV2[i]));
+	}
+	
+	return outM;
+};
+
+
+
+
+
+/**************************
+B A T C H
+*/
+//smash the members of inM with a softmax
+M.Sigmoid = function(inM)
+{
+	var i, j;
+	var outM = [];
+	var outV = [];
+	for(i=0; i<inM.length; i++)
+	{
+		outV = [];
+		for(j=0; j<inM[i].length; j++)
+		{
+			outV[j] = 1/(1 + Math.pow(Math.E, -inM[i][j]));
+		}
+		outM.push(outV);
+	}
+	return outM;
+};
+// return the derivatives of the members of inM (that have been run through the softmax)
+M.Derivative = function(inM)
+{
+	var i, j;
+	var component;
+	var outM = [];
+	var outV = [];
+	for(i=0; i<inM.length; i++)
+	{
+		outV = [];
+		for(j=0; j<inM[i].length; j++)
+		{
+			component = inM[i][j];
+			outV[j] = component*(1 - component);
+		}
+		outM.push(outV);
+	}
+	return outM;
+};
+// batch multiply these pairs of vectors
+M.Multiply = function(inCloud1, inCloud2)
+{
+	var i;
+	var outM = [];
+	for(i=0; i<inCloud1.length; i++)
+	{
+		outM.push(V.Multiply(inCloud1[i], inCloud2[i]));
+	};
+	return outM;
+};
+// batch add
+M.Add = function(inCloud1, inCloud2)
+{
+    var outM = [];
+    
+    var i;
+    for(i=0; i<inCloud1.length; i++)
+    {
+        outM.push(V.Add(inCloud1[i], inCloud2[i]));
+    }
+    return outM;
+};
+M.Subtract = function(inCloud1, inCloud2)
+{
+    var outM = [];
+    
+    var i;
+    for(i=0; i<inCloud1.length; i++)
+    {
+        outM.push(V.Subtract(inCloud1[i], inCloud2[i]));
+    }
+    return outM;
+};
+M.Scale = function(inCloud1, inScalar)
+{
+    var outM = [];
+    
+    var i;
+    for(i=0; i<inCloud1.length; i++)
+    {
+        outM.push(V.Scale(inCloud1[i], inScalar));
+    }
+    return outM;
+};
+M.Clone = function(inM)
+{
+    var i;
+    var outM;
+    var outV;
+    
+    outM =[];
+    for(i=0; i<inM.length; i++)
+    {
+        outM.push(V.Clone(inM[i]));
+    }
+    return outM;
+};
+
+
+/**************************
+B O U N D S
+*/
+// return the bounding box of inM as a two-member Matrix
+M.Bounds = function(inM)
+{
+	var dimensions = inM[0].length;
+	var i, j;
+	var min = [];
+	var max = [];
+	for(i=0; i<dimensions; i++)
+	{
+		min[i] = 9999999;
+		max[i] = -999999;
+	}
+	for(i=0; i<inM.length; i++)
+	{
+		for(j=0; j<dimensions; j++)
+		{
+			if(inM[i][j] < min[j])
+			{
+				min[j] = inM[i][j];
+			}
+			if(inM[i][j] > max[j])
+			{
+				max[j] = inM[i][j];
+			}			
+		}
+	}
+	return [min, max];
+};
+
+// find the local coordinates for all the members of inM, within the bounding box inB
+// returns a new Matrix of relative vectors
+M.GlobalToLocal = function(inM, inB)
+{
+	var dimensions = inB[0].length;
+	var i, j;
+	var outM = [];
+	var outV = [];
+	var size;
+	var min;
+	var denominator;
+	for(i=0; i<inM.length; i++)
+	{
+		outV = [];
+		for(j=0; j<dimensions; j++)
+		{
+			denominator = inB[1][j] - inB[0][j];
+			if(denominator == 0)
+			{
+				outV[j] = inB[1][j];// if min and max are the same, just output max
+			}
+			else
+			{
+				outV[j] = (inM[i][j] - inB[0][j])/denominator;	
+			}
+		}
+		outM.push(outV);
+	}
+	return outM;
+};
+// find the global coordinates for all the members of inM, within the bounding box inB
+// returns a new Matrix of global vectors
+M.LocalToGlobal = function(inM, inB)
+{
+	var dimensions = inB[0].length;
+	var i, j;
+	var outM = [];
+	var outV = [];
+	var size;
+	var min;
+	for(i=0; i<inM.length; i++)
+	{
+		outV = [];
+		for(j=0; j<dimensions; j++)
+		{
+			outV[j] = inB[0][j] + inM[i][j] * (inB[1][j] - inB[0][j]);
+		}
+		outM.push(outV);
+	}
+	return outM;
+};
+
+
+/**************************
+C L O U D
+*/
+// return some number of points from inM as a new Matrix
+M.Reduce = function(inM, inCount)
+{
+	var largeGroupSize;
+	var largeGroupCount;
+	var smallGroupSize;
+	var outM = [];
+	
+	largeGroupSize = Math.floor(inM.length/inM);
+	smallGroupSize = inM.length%inCount
+	for(i=0; i<inM-1; i++)
+	{
+		index = i*largeGroupSize + Math.floor(Math.random()*largeGroupSize);
+		outM.push( V.Clone(inM[index]) );
+	}
+	if(smallGroupSize != 0)
+	{
+		index = i*largeGroupSize + Math.floor(Math.random()*smallGroupSize)
+		outM.push( V.Clone(inM[index]) );
+	}
+	return outM;
+};
+
+// return a Matrix of length inCount, where all the members fall within the circle paramemters, including a bias
+M.Circle = function(inCenter, inRadius, inBias, inCount)
+{
+	var i, j;
+	var vector;
+	var length;
+	var outM = [];
+	
+	for(i=0; i<inCount; i++)
+	{
+		//generate a random vector
+		vector = [];
+		for(j=0; j<inCenter.length; j++)
+		{
+			vector[j] = (Math.random() - 0.5);
+		}
+		
+		//normalize the vector
+		vector = V.Scale(vector, 1/V.Length(vector));
+		
+		//set a random length (with a bias)
+		length = Math.pow(Math.random(), Math.log(inBias)/Math.log(0.5))*inRadius;
+		vector = V.Scale(vector, length);
+		
+		//move the vector to the center
+		vector = V.Add(vector, inCenter);
+		
+		outM.push(vector);
+	}
+	return outM;
+};
+
+// return a Matrix of length inCount, where all the members fall within inBounds
+M.Box = function(inBounds, inCount)
+{
+	var vector;
+	var dimensions = inBounds[0].length;
+	var i, j;
+	var min, max;
+	var outM = [];
+	
+	for(i=0; i<inCount; i++)
+	{
+		vector = [];
+		for(j=0; j<dimensions; j++)
+		{
+			min = inBounds[0][j];
+			max = inBounds[1][j];
+			
+			vector[j] = min + Math.random()*(max - min);
+		}
+		outM.push(vector);
+	}
+	return outM;
+};
+
+//combine all the matricies in inList into one long Matrix
+M.Combine = function(inList)
+{
+	var i, j;
+	var outM = [];
+	for(i=0; i<inList.length; i++)
+	{
+		for(j=0; j<inList[i].length; j++)
+		{
+			outM.push(V.Clone(inList[i][j]));
+		}
+	}
+	return outM;
+};
+
+/*
+PLEASE NOTE: These padding routines are unique to this library in that they
+actually modify the input object(s) rather than returning modified copies!
+*/
+// add a new component (set to '1') to each member of inM
+M.Pad = function(inM)
+{
+	var i;
+	for(i=0; i<inM.length; i++)
+	{
+		inM[i].push(1);
+	}
+    	return inM;
+};
+// remove the last component of each memeber of inM
+M.Unpad = function(inM)
+{
+	var i;
+    	for(i=0; i<inM.length; i++)
+	{
+        	inM[i].pop();
+	}
+	return inM;
+};
+// set the last component of each member of inM to 1
+M.Repad = function(inM)
+{
+	var i;
+	var last = inM[0].length-1;
+    	for(i=0; i<inM.length; i++)
+	{
+        	inM[i][last] = 1;
+	}
+	return inM;
+};
+</script>
+
+<script>
+var NN = {};
+
+NN.TrainingSet = {};
+NN.TrainingSet.Instances = [];
+NN.TrainingSet.Create = function()
+{
+    var obj = {};
+
+    obj.Input = [];
+    obj.Output = [];
+    obj.Order = [];
+    
+    NN.TrainingSet.Instances.push(obj);
+    return obj;
+};
+NN.TrainingSet.AddPoint = function(inTrainingSet, inType, inData)
+{
+    inTrainingSet.Input.push(inData);
+    inTrainingSet.Output.push(inType);
+    inTrainingSet.Order.push(inTrainingSet.Order.length);
+};
+NN.TrainingSet.AddCloud = function(inTrainingSet, inLabel, inCloud)
+{
+    var i;
+    for(i=0; i<inCloud.length; i++)
+    {
+        NN.TrainingSet.AddPoint(inTrainingSet, inLabel, inCloud[i]);
+    }
+};
+NN.TrainingSet.Randomize = function(inTrainingSet)
+{
+      var newOrder = [];
+      var selection;
+      while(inTrainingSet.Order.length != 0)
+      {
+          selection = Math.floor(inTrainingSet.Order.length * Math.random());
+          inTrainingSet.Order.splice(selection, 1);
+          newOrder.push(selection);
+      }
+      inTrainingSet.Order = newOrder;
+};
+
+
+NN.Layer = {};
+NN.Layer.Create = function(sizeIn, sizeOut)
+{
+    var i;
+    var min = [];
+    var max = [];
+    var obj = {};
+    
+    sizeIn++;
+    
+    obj.Forward = {};
+    for(i=0; i<sizeIn; i++)
+    {
+        min.push(-1);
+        max.push(1);
+    }
+    obj.Forward.Matrix = M.Box([min, max], sizeOut);
+    obj.Forward.StageInput = [];
+    obj.Forward.StageAffine = [];
+    obj.Forward.StageSigmoid = [];
+    obj.Forward.StageDerivative = [];
+    
+    obj.Backward = {};
+    obj.Backward.Matrix = M.Transpose(obj.Forward.Matrix);
+    obj.Backward.StageInput = [];
+    obj.Backward.StageDerivative = [];
+    obj.Backward.StageAffine = [];
+    
+    return obj;
+};
+NN.Layer.Forward = function(inLayer, inInput)
+{
+    inLayer.Forward.StageInput = M.Pad(inInput); // Pad the input
+    inLayer.Forward.StageAffine = M.Transform(inLayer.Forward.Matrix, inLayer.Forward.StageInput);
+    inLayer.Forward.StageSigmoid = M.Sigmoid(inLayer.Forward.StageAffine);
+    
+    return inLayer.Forward.StageSigmoid;
+};
+NN.Layer.Error = function(inLayer, inTarget)
+{
+    return M.Subtract(inLayer.Forward.StageSigmoid, inTarget);
+};
+NN.Layer.Backward = function(inLayer, inInput)
+{
+    /* We need the derivative of the forward pass, but only during the backward pass.
+    That's why-- even though it "belongs" to the forward pass-- it is being calculated here. */
+    inLayer.Forward.StageDerivative = M.Derivative(inLayer.Forward.StageSigmoid);
+    
+    /* This transpose matrix is for sending the error back to a previous layer.
+    And again, even though it is derived directly from the forward matrix, it is only needed during the backward pass so we calculate it here.*/
+    inLayer.Backward.Matrix = M.Transpose(inLayer.Forward.Matrix);
+    
+    /* When the error vector arrives at a layer, it always needs to be multiplied (read 'supressed') by the derivative of
+    what the layer output earlier during the forward pass.
+    So despite its name, Backward.StageDerivative contains the result of this *multiplication* and not some new derivative calculation.*/
+    inLayer.Backward.StageInput = inInput;
+    inLayer.Backward.StageDerivative = M.Multiply(inLayer.Backward.StageInput, inLayer.Forward.StageDerivative);
+    inLayer.Backward.StageAffine = M.Transform(inLayer.Backward.Matrix, inLayer.Backward.StageDerivative);
+    
+    return M.Unpad(inLayer.Backward.StageAffine);// Unpad the output
+};
+NN.Layer.Adjust = function(inLayer, inLearningRate)
+{
+    var deltas;
+    var vector;
+    var scalar;
+    var i, j;
+    
+    for(i=0; i<inLayer.Forward.StageInput.length; i++)
+    {
+        deltas = M.Outer(inLayer.Forward.StageInput[i], inLayer.Backward.StageDerivative[i]);
+        deltas = M.Scale(deltas, inLearningRate);
+        
+        inLayer.Forward.Matrix = M.Subtract(inLayer.Forward.Matrix, deltas);
+    }
+};
+NN.Layer.Stochastic = function(inLayer, inTrainingSet, inIterations)
+{
+    /* this method is ONLY for testing individual layers, and does not translate to network-level training */
+    var i, j;
+    var current;
+    var error;
+    for(i=0; i<inIterations; i++)
+    {
+        NN.TrainingSet.Randomize(inTrainingSet);
+        for(j=0; j<inTrainingSet.Order.length; j++)
+        {
+            current = inTrainingSet.Order[j];
+            NN.Layer.Forward(inLayer, [inTrainingSet.Input[current]]);
+            error = M.Subtract(inLayer.Forward.StageSigmoid, [inTrainingSet.Output[current]]);
+            NN.Layer.Backward(inLayer, error);
+            NN.Layer.Adjust(inLayer, 0.1);
+        }
+    }
+};
+
+NN.Network = {};
+NN.Network.Instances = [];
+NN.Network.Create = function()
+{
+    var obj = {};
+    var i;    
+    
+    obj.Layers = [];
+    obj.LearningRate = 0.1;
+    obj.Error = [];
+    
+    for(i=0; i<arguments.length-1; i++)
+    {
+        obj.Layers.push(NN.Layer.Create(arguments[i], arguments[i+1]));
+    }
+    
+    NN.Network.Instances.push(obj);
+    return obj;
+};
+NN.Network.Observe = function(inNetwork, inBatch)
+{
+      var input = M.Clone(inBatch);
+      var i;
+      for(i=0; i<inNetwork.Layers.length; i++)
+      {
+          input = NN.Layer.Forward(inNetwork.Layers[i], input);
+      }
+      return inNetwork.Layers[inNetwork.Layers.length-1].Forward.StageSigmoid;
+};
+NN.Network.Error = function(inNetwork, inTraining)
+{
+      return M.Subtract(inNetwork.Layers[inNetwork.Layers.length-1].Forward.StageSigmoid, inTraining);
+};
+NN.Network.Learn = function(inNetwork, inError)
+{
+      var input = inError;
+      var i;
+      for(i=inNetwork.Layers.length-1; i>=0; i--)
+      {
+          input = NN.Layer.Backward(inNetwork.Layers[i], input);
+          NN.Layer.Adjust(inNetwork.Layers[i], inNetwork.LearningRate);
+      }
+};
+
+
+NN.Network.Batch = function(inNetwork, inTrainingSet, inIterations)
+{
+    var i;
+    for(i=0; i<inIterations; i++)
+    {
+        NN.Network.Observe(inNetwork, inTrainingSet.Input);
+        inNetwork.Error = NN.Network.Error(inNetwork, inTrainingSet.Output)
+        NN.Network.Learn(inNetwork, inNetwork.Error);
+    }
+};
+NN.Network.Stochastic = function(inNetwork, inTrainingSet, inIterations)
+{
+    var i, j;
+    var current;
+    
+    for(i=0; i<inIterations; i++)
+    {
+        NN.TrainingSet.Randomize(inTrainingSet);
+        for(j=0; j<inTrainingSet.Order.length; j++)
+        {
+            current = inTrainingSet.Order[j];
+            NN.Network.Observe(inNetwork, [inTrainingSet.Input[current]]);
+            inNetwork.Error = NN.Network.Error(inNetwork, [inTrainingSet.Output[current]]);
+            NN.Network.Learn(inNetwork, inNetwork.Error);
+        }
+    }
+};
+</script>
+
+<script>
+    let matrix1 = [
+    [-0.43662948305036675, -0.368590640707799, -0.23227179558890843],
+    [-0.004292653969505622, 0.38670055222186317, -0.2478421495365568],
+    [0.738181366836224, 0.3389203747353555, 0.4920200816404332]
+    ];
+
+    let matrix2 = [
+    [0.7098703863463034, 0.35485944251238033, 0.7642849892333241, 0.03046174288491077],
+	[-0.30655426258144347, 0.45509633551425077, -0.5013795222004322, -0.3421292736637427]
+    ];
+
+    let input = [
+    [ 0.1,  0.05],
+    [ 0.0, -0.06],
+    [ 0.99, 0.85],
+    [ 1.2,  1.05]
+    ];
+    let output = [
+    [1, 0],
+    [1, 0],
+    [0, 1],
+    [0, 1]
+    ];
+
+	let nn1 = NN.Network.Create(2, 3, 2);
+	nn1.Layers[0].Forward.Matrix = matrix1;
+	nn1.Layers[1].Forward.Matrix = matrix2;
+	nn1.LearningRate = 0.1;
+	//let logLayers = inNN => inNN.Layers.forEach(L=>console.log(L.Forward.Matrix));
+
+	NN.Network.Batch(nn1, {Input:input, Output:output}, 1000);
+	console.log(NN.Network.Observe(nn1, input));
+
+</script>

m.js

@@ -1,54 +0,0 @@
-const M =
-{
-    Iterate:
-    {
-        New(inDimensions, inCount, inFunction)
-        {
-            let row, i, outputCloud, outputVector;
-            outputCloud = [];
-            for(row=0; row<inCount; row++)
-            {
-                outputVector = [];
-                for(i=0; i<inDimensions; i++)
-                {
-                    outputVector.push(inFunction(i, row, outputVector));
-                }
-                outputCloud.push(outputVector);
-            }
-            return outputCloud;
-        },
-        Old(inCloud, inFunction)
-        {
-            return M.Iterate.New(inCloud[0].length, inCloud.length, inFunction);
-        }
-    },
-    Create:
-    {
-              Box: (inV1, inV2, inCount)=> M.Iterate.New(inV1.length,    inCount,           (i, row)=> inV1[i]+(inV2[i]-inV1[i])*Math.random()),
-        Transpose:             (inCloud)=> M.Iterate.New(inCloud.length, inCloud[0].length, (i, row)=> inCloud[i][row]),
-            Outer:          (inV1, inV2)=> M.Iterate.New(inV1.length,    inV2.length,       (i, row)=> inV1[i]*inV2[row]),
-            Clone:             (inCloud)=> M.Iterate.Old(inCloud,                           (i, row)=> inCloud[row][i])
-    },
-    Mutate:
-    {
-          Pad: inCloud=> inCloud.forEach(row=> row.push(1)),
-        Unpad: inCloud=> inCloud.forEach(row=> row.pop())
-    },
-    Single:
-    {
-        Subtract:    (inV1, inV2)=> inV1.map((component, i)=> component-inV2[i]),
-        Multiply:    (inV1, inV2)=> inV1.map((component, i)=> component*inV2[i]),
-          Affine: (inV, inMatrix)=> inMatrix.map(row=> row.reduce((sum, current, index)=> sum + current*inV[index]))
-    },
-    Batch:
-    {
-          Subtract: (inCloud1, inCloud2)=> inCloud1.map((row, rowIndex)=> M.Single.Subtract(row, inCloud2[rowIndex])),
-          Multiply: (inCloud1, inCloud2)=> inCloud1.map((row, rowIndex)=> M.Single.Multiply(row, inCloud2[rowIndex])),
-            Affine:  (inCloud, inMatrix)=> inCloud.map(row=> M.Single.Affine(row, inMatrix)),
-           Sigmoid:            (inCloud)=> M.Iterate.Old(inCloud, i=>1/(1+Math.Pow(Math.E, i))),
-        Derivative:            (inCloud)=> M.Iterate.Old(inCloud, i=>i*(1-i)),
-             Scale:  (inCloud, inScalar)=> M.Iterate.Old(inCloud, i=>i*inScalar)
-    }
-}
-
-export default M;

m.test.js

@@ -1,62 +1,67 @@
 import { assert, assertEquals } from "https://deno.land/std@0.102.0/testing/asserts.ts";
-import { default as M } from "./m.js";
+import M from "./m.ts";
 
-Deno.test("Iterate.New", ()=>
+Deno.test("Iterate.Loop", ()=>
 {
-    let dimensions = 3;
-    let count = 4;
-    let cloud = M.Iterate.New(dimensions, count, (i, j)=>i+j);
+    const dimensions = 3;
+    const count = 4;
+    const cloud = M.Iterate.Loop(dimensions, count, (i, j)=>i+j);
     assertEquals(cloud.length, count, "correct count");
     assertEquals(cloud[0].length, dimensions, "correct dimensions");
     assertEquals(cloud[0][0], 0);
     assertEquals(cloud[3][2], 5, "correct output");
 });
+Deno.test("Iterate.Edit", ()=>
+{
+    const c = [[1, 2], [3, 4]]
+    const t = M.Iterate.Edit(c, (i)=>i);
+    assertEquals(t.length, c.length, "correct count");
+    assertEquals(t[0][0], c[0][0], "correct dimensions");
+    assertEquals(t[1][1], c[1][1], "correct placement");
+});
 
 Deno.test("Create.Box", ()=>
 {
-    let min = [-1, -2, -3];
-    let max = [1, 2, 3];
-    let count = 10;
+    const min = [-1, -2, -3];
+    const max = [1, 2, 3];
+    const count = 10;
 
-    let box = M.Create.Box(min, max, count);
+    const box = M.Create.Box(min, max, count);
     assertEquals(box.length, count, "correct count");
     for(let i=0; i<box.length; i++)
     {
         assertEquals(box[i].length, min.length, "correct dimensions");
         for(let j=0; j<box[i].length; j++)
         {
-            assert(box[i][j] >= min[j], true);
-            assert(box[i][j] <= max[j], true, "correct range");
+            assert(box[i][j] >= min[j]);
+            assert(box[i][j] <= max[j], "correct range");
         }
     }
 });
-
 Deno.test("Create.Transpose", ()=>
 {
-    let v1 = [1, 2, 3];
-    let v2 = [4, 5, 6];
-    let tpose = M.Create.Transpose([v1, v2]);
+    const v1 = [1, 2, 3];
+    const v2 = [4, 5, 6];
+    const tpose = M.Create.Transpose([v1, v2]);
     assertEquals(tpose.length, 3, "correct count");
     assertEquals(tpose[0].length, 2, "correct dimensions");
     assertEquals(tpose[0][0], v1[0]);
     assertEquals(tpose[0][1], v2[0], "correct placement");
 });
-
 Deno.test("Create.Outer", ()=>
 {
-    let v1 = [1, 2, 3];
-    let v2 = [4, 5];
-    let outer = M.Create.Outer(v1, v2);
+    const v1 = [1, 2, 3];
+    const v2 = [4, 5];
+    const outer = M.Create.Outer(v1, v2);
     assertEquals(outer.length, v2.length, "correct count");
     assertEquals(outer[0].length, v1.length, "correct dimensions");
     assertEquals(outer[1][0], v1[0]*v2[1], "correct placement")
 });
-
 Deno.test("Create.Clone", ()=>
 {
-    let v1 = [1, 2, 3];
-    let v2 = [4, 5, 6];
-    let clone = M.Create.Clone([v1, v2]);
+    const v1 = [1, 2, 3];
+    const v2 = [4, 5, 6];
+    const clone = M.Create.Clone([v1, v2]);
     assertEquals(clone.length, 2, "correct count");
     assertEquals(clone[0].length, v1.length, "correct dimensions");
     assertEquals(clone[1][0], v2[0], "correct placement");
@@ -64,7 +69,7 @@ Deno.test("Create.Clone", ()=>
 
 Deno.test("Mutate.Pad", ()=>
 {
-    let matrix = [
+    const matrix = [
         [1, 2, 3],
         [4, 5, 6]
     ];
@@ -73,10 +78,9 @@ Deno.test("Mutate.Pad", ()=>
     assertEquals(matrix[0].length, 4, "correct dimensions");
     assertEquals(matrix[0][3], 1, "correct placement");
 });
-
 Deno.test("Mutate.Unpad", ()=>
 {
-    let matrix = [
+    const matrix = [
         [1, 2, 3, 1],
         [4, 5, 6, 1]
     ];
@@ -88,53 +92,74 @@ Deno.test("Mutate.Unpad", ()=>
 
 Deno.test("Single.Affine", ()=>
 {
-    let v = [1, 2];
-    let m = [[0.1, 0.2], [0.3, 0.4]];
-    let t = M.Single.Affine(v, m);
+    const v = [1, 2];
+    const m = [[0.1, 0.2], [0.3, 0.4]];
+    const t = M.Single.Affine(v, m);
     assertEquals(t.length, 2, "correct dimensions");
     assertEquals(t[0], 0.5)
     assertEquals(t[1], 1.1, "correct placement");
+    console.log(t);
 });
-
 Deno.test("Single.Subtract", ()=>
 {
-    let v1 = [1, 2];
-    let v2 = [3, 4];
-    let t = M.Single.Subtract(v1, v2);
+    const v1 = [1, 2];
+    const v2 = [3, 4];
+    const t = M.Single.Subtract(v1, v2);
     assertEquals(t.length, 2, "correct dimensions");
     assertEquals(t[0], -2)
     assertEquals(t[1], -2, "correct placement");
 });
-
 Deno.test("Single.Multiply", ()=>
 {
-    let v1 = [1, 2];
-    let v2 = [3, 4];
-    let t = M.Single.Multiply(v1, v2);
+    const v1 = [1, 2];
+    const v2 = [3, 4];
+    const t = M.Single.Multiply(v1, v2);
     assertEquals(t.length, 2, "correct dimensions");
     assertEquals(t[0], 3)
     assertEquals(t[1], 8, "correct placement");
 });
 
-
-
 Deno.test("Batch.Affine", ()=>
 {
-    let c = [[1, 2], [3, 4]];
-    let m = [[0.1, 0.2], [0.3, 0.4]];
-    let t = M.Batch.Affine(c, m);
+    const c = [[1, 2], [3, 4]];
+    const m = [[0.1, 0.2], [0.3, 0.4]];
+    const t = M.Batch.Affine(c, m);
     assertEquals(t.length, 2, "correct count");
     assertEquals(t[0].length, 2, "correct dimensions")
     assertEquals(t[0][1], 1.1, "correct placement");
 });
-
 Deno.test("Batch.Scale", ()=>
 {
-    let c = [[1, 2], [3, 4]];
-    let s = 0.5;
-    let t = M.Batch.Scale(c, s);
+    const c = [[1, 2], [3, 4]];
+    const s = 0.5;
+    const t = M.Batch.Scale(c, s);
     assertEquals(t.length, 2, "correct count");
     assertEquals(t[0].length, 2, "correct dimensions");
-    console.log(t);
     assertEquals(t[1][0], 1.5, "correct placement");
 });
+Deno.test("Batch.Subtract", ()=>
+{
+    const c = [[1, 2], [3, 4]];
+    const s = [[0.5, 0.5], [0.5, 0.5]];
+    const t = M.Batch.Subtract(c, s);
+    assertEquals(t.length,    2,   "correct count");
+    assertEquals(t[0].length, 2,   "correct dimensions");
+    assertEquals(t[1][0],     2.5, "correct placement");
+});
+Deno.test("Batch.Sigmoid", ()=>
+{
+    const m = [[-1000, 1000]];
+    const t = M.Batch.Sigmoid(m);
+    assertEquals(t.length, 1, "correct count");
+    assertEquals(t[0].length, 2, "correct dimensions");
+    assert(t[0][0]>=0 && t[0][0]<0.5);
+    assert(t[0][1]<=1 && t[0][1]>0.5, "correct placement");
+});
+Deno.test("Batch.Derivative", ()=>
+{
+    const m = [[-1000, 0, 1000]];
+    const t = M.Batch.Derivative(M.Batch.Sigmoid(m));
+    assertEquals(t.length, 1, "correct count");
+    assertEquals(t[0].length, 3, "correct dimensions");
+    assert(t[0][0]<t[0][1] && t[0][1]>t[0][2]);
+});

m.ts

@@ -0,0 +1,67 @@
+export namespace Cloud
+{
+    export type V = Array<number>
+    export type M = Array<Array<number>>
+    export type HandleLoop = (indexComponent:number, indexRow:number, array:Array<number>) => number
+    export type HandleEdit = (component:number, index:number, array:Array<number>) => number
+};
+
+const Methods = {
+    Iterate:
+    {
+        Loop: (inDimensions:number, inCount:number, inFunction:Cloud.HandleLoop):Cloud.M =>
+        {
+            let i:number, j:number, outputVector:Cloud.V;
+            const outputCloud:Cloud.M = [];
+            for(i=0; i<inCount; i++)
+            {
+                outputVector = [];
+                for(j=0; j<inDimensions; j++)
+                {
+                    outputVector.push(inFunction(j, i, outputVector));
+                }
+                outputCloud.push(outputVector);
+            }
+            return outputCloud;
+        },
+        Edit: (inCloud:Cloud.M, inFunction:Cloud.HandleEdit):Cloud.M=> inCloud.map((row:Cloud.V):Cloud.V=>row.map(inFunction))
+    },
+    Create:
+    {
+              Box: (inV1:Cloud.V, inV2:Cloud.V, inCount:number):Cloud.M=> Methods.Iterate.Loop(inV1.length, inCount, i=> inV1[i]+(inV2[i]-inV1[i])*Math.random()),
+        Transpose:                            (inCloud:Cloud.M):Cloud.M=> Methods.Iterate.Loop(inCloud.length, inCloud[0].length, (i, row)=> inCloud[i][row]),
+            Outer:                 (inV1:Cloud.V, inV2:Cloud.V):Cloud.M=> Methods.Iterate.Loop(inV1.length, inV2.length, (i, row)=> inV1[i]*inV2[row]),
+            Clone:                            (inCloud:Cloud.M):Cloud.M=> Methods.Iterate.Edit(inCloud, i=> i)
+    },
+    Mutate:
+    {
+          Pad: (inCloud:Cloud.M):Cloud.M=> {inCloud.forEach((row:Cloud.V)=> row.push(1)); return inCloud; },
+        Unpad: (inCloud:Cloud.M):Cloud.M=> {inCloud.forEach((row:Cloud.V)=> row.pop());   return inCloud; }
+    },
+    Test:
+    {
+        Dot:(v1:Cloud.V, v2:Cloud.V):number=> 
+        {
+            return v1.reduce((sum, current, index)=> sum + current*v2[index]);
+        }
+    },
+    Single:
+    {
+        Subtract:    (inV1:Cloud.V, inV2:Cloud.V):Cloud.V=> inV1.map((component, i)=> component-inV2[i]),
+        Multiply:    (inV1:Cloud.V, inV2:Cloud.V):Cloud.V=> inV1.map((component, i)=> component*inV2[i]),
+          Affine: (inV:Cloud.V, inMatrix:Cloud.M):Cloud.V=> inMatrix.map((row:Cloud.V)=> row.reduce((sum, current, index)=> sum + current*inV[index], 0))
+    },
+    Batch:
+    {
+          Subtract: (inCloud1:Cloud.M, inCloud2:Cloud.M):Cloud.M=> inCloud1.map((row:Cloud.V, rowIndex:number)=> Methods.Single.Subtract(row, inCloud2[rowIndex])),
+          Multiply: (inCloud1:Cloud.M, inCloud2:Cloud.M):Cloud.M=> inCloud1.map((row:Cloud.V, rowIndex:number)=> Methods.Single.Multiply(row, inCloud2[rowIndex])),
+            Affine: (inCloud1:Cloud.M, inCloud2:Cloud.M):Cloud.M=> inCloud1.map((row:Cloud.V)=> Methods.Single.Affine(row, inCloud2)),
+           Sigmoid:                    (inCloud:Cloud.M):Cloud.M=> Methods.Iterate.Edit(inCloud, i=>1/(1+Math.pow(Math.E, -i))),
+        Derivative:                    (inCloud:Cloud.M):Cloud.M=> Methods.Iterate.Edit(inCloud, i=>i*(1-i)),
+             Scale:   (inCloud:Cloud.M, inScalar:number):Cloud.M=> Methods.Iterate.Edit(inCloud, i=>i*inScalar)
+    }
+};
+
+
+
+export default Methods;

methods.md

@@ -7,8 +7,8 @@ pad(inCloud) // done
 unpad(inCloud) // done
 
 transform(inCloud, inMatrix) // done
-sigmoid(inCloud) // 1/(1+e^x) //
-derivative(inCloud) // x*(1-x) //
-scale(inCloud1, inV) //
+sigmoid(inCloud) // 1/(1+e^x) // done
+derivative(inCloud) // x*(1-x) // done
+scale(inCloud1, inV) // done
 subtract(inCloud1, inCloud2) // done
 multiply(inCloud1, inCloud2) // done

nn.test.js

@@ -0,0 +1,52 @@
+import { assert, assertEquals } from "https://deno.land/std@0.102.0/testing/asserts.ts";
+import { Split, Build, Label, Learn, Check } from "./nn.ts";
+
+let data = [
+    [ 0.10,  0.05, 0, 1],
+    [ 0.00, -0.06, 0, 1],
+    [ 0.99,  0.85, 1, 0],
+    [ 1.20,  1.05, 1, 0]
+];
+let columns = [2, 3];
+let input, output;
+let layers = [];
+
+Deno.test("NN.Split", ()=>
+{
+    [input, output] = Split(data, columns);
+    assert(input);
+    assert(output);
+    assertEquals(input.length, output.length, "data split into equal input and output");
+
+    assertEquals(input[0].length, 3, "padded input");
+    assertEquals(output[0].length, 2, "unpadded output");
+});
+
+Deno.test("NN.Build", ()=>
+{
+    layers = Build(2, 5, 2);
+
+    assertEquals(layers.length, 2, "correct number of matrices");
+    assertEquals(layers[0][0].length, input[0].length, "input: padded input");
+    assertEquals(layers[0].length, 5, "input: unpadded output");
+
+    assertEquals(layers[1][0].length, 6, "hidden: padded input");
+    assertEquals(layers[1].length, output[0].length, "hidden: unpadded output");
+});
+
+Deno.test("NN.Label", ()=>
+{
+    let labels = Label(input, layers);
+    assertEquals(labels.length, output.length);
+    assertEquals(labels[0].length, output[0].length);
+});
+
+Deno.test("NN.Learn", ()=>
+{
+    let error = Learn(input, layers, output, 1000, 0.1);
+    assertEquals(error.length, output.length);
+    let total = 0;
+    let count = error.length*error[0].length;
+    error.forEach(row=> row.forEach(component=> total+=Math.abs(component)));
+    assert(total/count < 0.3);
+});

nn.ts

@@ -0,0 +1,78 @@
+import { default as M, Cloud } from "./m.ts";
+export type N = Array<Array<Array<number>>>
+
+const Forward = (inData:Cloud.M, inLayers:N):N =>
+{
+    let i:number;
+    let stages:N = [inData];
+    let process = (index:number):Cloud.M => M.Batch.Sigmoid(M.Batch.Affine(stages[index], inLayers[index]));
+
+    for(i=0; i<inLayers.length-1; i++){ stages[i+1] = M.Mutate.Pad(process(i)); }
+    stages[i+1] = process(i);
+    return stages;
+};
+const Backward = (inStages:N, inLayers:N, inGoals:Cloud.M, inRate:number):N =>
+{
+    let i:number;
+    let errorBack:Cloud.M = M.Batch.Subtract(inStages[inStages.length-1], inGoals);
+
+    for(i=inLayers.length-1; i>=0; i--)
+    {
+        let errorScaled:Cloud.M = M.Batch.Multiply(errorBack, M.Batch.Derivative(inStages[i+1]));
+        errorBack = M.Batch.Affine(errorScaled, M.Create.Transpose(inLayers[i]));
+        errorScaled.forEach((inScaledError:Cloud.V, inIndex:number)=>
+        {
+            inLayers[i] = M.Batch.Subtract(
+                inLayers[i],
+                M.Batch.Scale(M.Create.Outer(inStages[i][inIndex], inScaledError), inRate)
+            );
+        });
+    }
+    return inLayers;
+};
+const Split = (inTrainingSet:Cloud.M, inHeaderLabel:Cloud.V, inHeaderKeep:Cloud.V = []):N =>
+{
+    let data:Cloud.M = [];
+    let label:Cloud.M = [];
+    if(!inHeaderKeep.length)
+    {
+        inTrainingSet[0].forEach( (item:number, index:number)=> inHeaderLabel.includes(index) ? false : inHeaderKeep.push(index) );
+    }
+    inTrainingSet.forEach((row:Cloud.V):void =>
+    {
+        let vectorData = [ ...inHeaderKeep.map((i:number)=>row[i]), 1];
+        let vectorLabel = inHeaderLabel.map((i:number)=>row[i]) 
+         data.push( vectorData );
+        label.push( vectorLabel );
+    });
+    return [ data, label ];
+};
+const Build = (...inLayers:Array<number>):N =>
+{
+    let i:number;
+    let output:N = [];
+    let rand = (inDimensions:number, inCount:number):Cloud.M => M.Create.Box( new Array(inDimensions).fill(-1), new Array(inDimensions).fill(1), inCount);
+    for(i=0; i<inLayers.length-1; i++)
+    {
+        output.push(rand( inLayers[i]+1, inLayers[i+1]));
+    }
+    return output;
+};
+const Label = (inData:Cloud.M, inLayers:N):Cloud.M =>
+{
+    let stages:N = Forward(inData, inLayers);
+    return stages[stages.length-1];
+};
+const Learn = (inData:Cloud.M, inLayers:N, inLabels:Cloud.M, inIterations:number, inRate:number):Cloud.M =>
+{
+    let stages:N = [];
+    for(let i=0; i<inIterations; i++)
+    {
+        stages = Forward(inData, inLayers);
+        Backward(stages, inLayers, inLabels, inRate);
+    }
+    return M.Batch.Subtract(stages[stages.length-1], inLabels);
+};
+const Check = (inData:Cloud.M, inLayers:N, inLabels:Cloud.M):Cloud.M => Learn(inData, inLayers, inLabels, 1, 0);
+
+export { Split, Build, Label, Learn, Check, Forward, Backward };