public void ExampleTest3()
{
// Suppose we would like to map the continuous values in the
// second column to the integer values in the first column.
var inputs = new[]
{
new[] { 1.0, 1.0, 1.0, 1.0 },
new[] { 2.0, 4.0, 8.0, 16.0 },
new[] { 3.0, 9.0, 27.0, 81.0 },
new[] { 4.0, 16.0, 64.0, 256.0 },
};
var ouputs = new[] { 0.73, 3.24, 8.31, 16.72 };
var regression = new MultipleLinearRegression(4);
var nnls = new NonNegativeLeastSquares(regression)
{
MaxIterations = 100
};
nnls.Run(inputs, ouputs);
Assert.AreEqual(0.1, nnls.Coefficients[0], 1e-3);
Assert.AreEqual(0.5, nnls.Coefficients[1], 1e-3);
Assert.AreEqual(0.13, nnls.Coefficients[2], 1e-3);
Assert.AreEqual(0, nnls.Coefficients[3], 1e-3);
}
public void ExampleTest3()
{
var inputs = new[]
{
new[] { 1.0, 1.0, 1.0, 1.0 },
new[] { 2.0, 4.0, 8.0, 16.0 },
new[] { 3.0, 9.0, 27.0, 81.0 },
new[] { 4.0, 16.0, 64.0, 256.0 },
};
var ouputs = new[] { 0.73, 3.24, 8.31, 16.72 };
var regression = new MultipleLinearRegression(4);
var nnls = new NonNegativeLeastSquares(regression)
{
MaxIterations = 100
};
nnls.Run(inputs, ouputs);
Assert.AreEqual(0.1, nnls.Coefficients[0], 1e-3);
Assert.AreEqual(0.5, nnls.Coefficients[1], 1e-3);
Assert.AreEqual(0.13, nnls.Coefficients[2], 1e-3);
Assert.AreEqual(0, nnls.Coefficients[3], 1e-3);
Assert.AreEqual(0.1, regression.Coefficients[0], 1e-3);
Assert.AreEqual(0.5, regression.Coefficients[1], 1e-3);
Assert.AreEqual(0.13, regression.Coefficients[2], 1e-3);
}
public void ExampleTest2()
{
// Suppose we would like to map the continuous values in the
// second column to the integer values in the first column.
var inputs = new[]
{
new[] { 1.0, 1.0, 1.0 },
new[] { 2.0, 4.0, 8.0 },
new[] { 3.0, 9.0, 27.0 },
new[] { 4.0, 16.0, 64.0 },
};
var ouputs = new[] { 0.73, 3.24, 8.31, 16.72 };
var regression = new MultipleLinearRegression(3);
var nnls = new NonNegativeLeastSquares(regression)
{
MaxIterations = 100
};
nnls.Run(inputs, ouputs);
Assert.AreEqual(0.1, nnls.Coefficients[0], 1e-3);
Assert.AreEqual(0.5, nnls.Coefficients[1], 1e-3);
Assert.AreEqual(0.13, nnls.Coefficients[2], 1e-3);
}
public void learn_test()
{
#region doc_learn
// Declare training samples
var inputs = new double[][]
{
new[] { 1.0, 1.0, 1.0 },
new[] { 2.0, 4.0, 8.0 },
new[] { 3.0, 9.0, 27.0 },
new[] { 4.0, 16.0, 64.0 },
};
var outputs = new double[] { 0.23, 1.24, 3.81, 8.72 };
// Create a NN LS learning algorithm
var nnls = new NonNegativeLeastSquares()
{
MaxIterations = 100
};
// Use the algorithm to learn a multiple linear regression
MultipleLinearRegression regression = nnls.Learn(inputs, outputs);
// None of the regression coefficients should be negative:
double[] coefficients = regression.Weights; // should be
// Check the quality of the regression:
double[] prediction = regression.Transform(inputs);
double error = new SquareLoss(expected: outputs)
.Loss(actual: prediction); // should be
#endregion
Assert.AreEqual(0, error, 1e-10);
Assert.AreEqual(0.1, nnls.Coefficients[0], 1e-3);
Assert.AreEqual(0, nnls.Coefficients[1], 1e-3);
Assert.AreEqual(0.13, nnls.Coefficients[2], 1e-3);
Assert.AreEqual(0.1, regression.Coefficients[0], 1e-3);
Assert.AreEqual(0, regression.Coefficients[1], 1e-3);
Assert.AreEqual(0.13, regression.Coefficients[2], 1e-3);
}
public void ExampleTest()
{
var inputs = new[]
{
new[] { 1.0, 1.0 },
new[] { 2.0, 4.0 },
new[] { 3.0, 9.0 },
new[] { 4.0, 16.0 },
};
var ouputs = new[] { 0.6, 2.2, 4.8, 8.4 };
var regression = new MultipleLinearRegression(2);
var nnls = new NonNegativeLeastSquares(regression)
{
MaxIterations = 100
};
nnls.Run(inputs, ouputs);
Assert.AreEqual(0.1, nnls.Coefficients[0], 1e-3);
Assert.AreEqual(0.5, nnls.Coefficients[1], 1e-3);
}
public void Execute()
{
int k = frameIndex;
var tmpPositions = new UnityEngine.Vector3[sharedJobData.numVertices];
var tmpNormals = new UnityEngine.Vector3[sharedJobData.numVertices];
var edgeLengths = null as float[];
var edgeCurvatures = null as float[];
// prepare b
var b = new double[sharedJobData.numEquations];
{
Array.Copy(sharedJobData.frames[k].deltaPositions, tmpPositions, tmpPositions.Length);
Array.Copy(sharedJobData.frames[k].deltaNormals, tmpNormals, tmpNormals.Length);
switch (sharedJobData.fittingParam)
{
case Param.DeltaPosition:
for (int i = 0; i != sharedJobData.numVertices; i++)
{
b[i * 3 + 0] = tmpPositions[i].x;
b[i * 3 + 1] = tmpPositions[i].y;
b[i * 3 + 2] = tmpPositions[i].z;
}
break;
case Param.OutputEdgeLength:
for (int i = 0; i != sharedJobData.numVertices; i++)
{
tmpPositions[i] += sharedJobData.meshBuffers.vertexPositions[i];
}
sharedJobData.meshEdges.ComputeLengths(ref edgeLengths, tmpPositions);
for (int i = 0; i != sharedJobData.numEquations; i++)
{
b[i] = edgeLengths[i];
}
break;
case Param.OutputEdgeCurvature:
for (int i = 0; i != sharedJobData.numVertices; i++)
{
tmpPositions[i] += sharedJobData.meshBuffers.vertexPositions[i];
tmpNormals[i] += sharedJobData.meshBuffers.vertexNormals[i];
tmpNormals[i].Normalize();
}
sharedJobData.meshEdges.ComputeCurvatures(ref edgeCurvatures, tmpPositions, tmpNormals);
for (int i = 0; i != sharedJobData.numEquations; i++)
{
b[i] = edgeCurvatures[i];
}
break;
}
}
// compute x*
var x = new double[sharedJobData.numVariables];
{
switch (sharedJobData.fittingMethod)
{
case Method.LinearLeastSquares:
sharedJobData.At_A_inv_At.Dot(b, x); // stores result in x
break;
case Method.NonNegativeLeastSquares:
{
var nnlsSolver = new NonNegativeLeastSquares()
{
MaxIterations = 200, Tolerance = 0.000000001
};
var nnlsOutput = nnlsSolver.Learn(sharedJobData.A_jagged, b);
Array.Copy(nnlsOutput.Weights, x, x.Length);
}
break;
}
//UnityEngine.Debug.Log("frame " + k + ": x* = " + x);
}
// remap weights to shape indices
for (int j = 0; j != sharedJobData.numVariables; j++)
{
sharedJobData.frames[k].fittedWeights[sharedJobData.blendShapeIndices[j]] = (float)x[j];
}
}