public ParameterizedCovarianceFunction GetParameterizedCovarianceFunction(double[] p, int[] columnIndices)
{
if (terms.Count == 0)
{
throw new ArgumentException("at least one term is necessary for the product covariance function.");
}
var functions = new List <ParameterizedCovarianceFunction>();
foreach (var t in terms)
{
var numberOfParameters = t.GetNumberOfParameters(numberOfVariables);
functions.Add(t.GetParameterizedCovarianceFunction(p.Take(numberOfParameters).ToArray(), columnIndices));
p = p.Skip(numberOfParameters).ToArray();
}
var sum = new ParameterizedCovarianceFunction();
sum.Covariance = (x, i, j) => functions.Select(e => e.Covariance(x, i, j)).Sum();
sum.CrossCovariance = (x, xt, i, j) => functions.Select(e => e.CrossCovariance(x, xt, i, j)).Sum();
sum.CovarianceGradient = (x, i, j) => {
var g = new List <double>();
foreach (var e in functions)
{
g.AddRange(e.CovarianceGradient(x, i, j));
}
return(g);
};
return(sum);
}
public ParameterizedCovarianceFunction GetParameterizedCovarianceFunction(double[] p, int[] columnIndices)
{
double inverseLength, period, scale;
GetParameterValues(p, out scale, out period, out inverseLength);
var fixedInverseLength = HasFixedInverseLengthParameter;
var fixedPeriod = HasFixedPeriodParameter;
var fixedScale = HasFixedScaleParameter;
// create functions
var cov = new ParameterizedCovarianceFunction();
cov.Covariance = (x, i, j) => {
double k = i == j ? 0.0 : GetDistance(x, x, i, j, columnIndices);
k = Math.PI * k / period;
k = Math.Sin(k) * inverseLength;
k = k * k;
return(scale * Math.Exp(-2.0 * k));
};
cov.CrossCovariance = (x, xt, i, j) => {
double k = GetDistance(x, xt, i, j, columnIndices);
k = Math.PI * k / period;
k = Math.Sin(k) * inverseLength;
k = k * k;
return(scale * Math.Exp(-2.0 * k));
};
cov.CovarianceGradient = (x, i, j) => GetGradient(x, i, j, columnIndices, scale, period, inverseLength, fixedInverseLength, fixedPeriod, fixedScale);
return(cov);
}
public ParameterizedCovarianceFunction GetParameterizedCovarianceFunction(double[] p, int[] columnIndices)
{
double scale, shape;
double[] inverseLength;
GetParameterValues(p, out scale, out shape, out inverseLength);
var fixedInverseLength = HasFixedInverseLengthParameter;
var fixedScale = HasFixedScaleParameter;
var fixedShape = HasFixedShapeParameter;
// create functions
var cov = new ParameterizedCovarianceFunction();
cov.Covariance = (x, i, j) => {
double d = i == j
? 0.0
: Util.SqrDist(x, i, j, inverseLength, columnIndices);
return(scale * Math.Pow(1 + 0.5 * d / shape, -shape));
};
cov.CrossCovariance = (x, xt, i, j) => {
double d = Util.SqrDist(x, i, xt, j, inverseLength, columnIndices);
return(scale * Math.Pow(1 + 0.5 * d / shape, -shape));
};
cov.CovarianceGradient = (x, i, j) => GetGradient(x, i, j, columnIndices, scale, shape, inverseLength, fixedInverseLength, fixedScale, fixedShape);
return(cov);
}
private static double[,] CalculateL(double[,] x, ParameterizedCovarianceFunction cov, double sqrSigmaNoise)
{
int n = x.GetLength(0);
var l = new double[n, n];
// calculate covariances
for (int i = 0; i < n; i++)
{
for (int j = i; j < n; j++)
{
l[j, i] = cov.Covariance(x, i, j) / sqrSigmaNoise;
if (j == i)
{
l[j, i] += 1.0;
}
}
}
// cholesky decomposition
var res = alglib.trfac.spdmatrixcholesky(ref l, n, false);
if (!res)
{
throw new ArgumentException("Matrix is not positive semidefinite");
}
return(l);
}
public ParameterizedCovarianceFunction GetParameterizedCovarianceFunction(double[] p, IEnumerable<int> columnIndices) {
if (p.Length > 0) throw new ArgumentException("No parameters are allowed for the linear covariance function.");
// create functions
var cov = new ParameterizedCovarianceFunction();
cov.Covariance = (x, i, j) => Util.ScalarProd(x, i, j, 1, columnIndices);
cov.CrossCovariance = (x, xt, i, j) => Util.ScalarProd(x, i, xt, j, 1.0 , columnIndices);
cov.CovarianceGradient = (x, i, j) => Enumerable.Empty<double>();
return cov;
}
public ParameterizedCovarianceFunction GetParameterizedCovarianceFunction(double[] p, int[] columnIndices)
{
double length, scale;
int v = VParameter.Value.Value;
GetParameterValues(p, out length, out scale);
var fixedLength = HasFixedLengthParameter;
var fixedScale = HasFixedScaleParameter;
int exp = (int)Math.Floor(columnIndices.Count() / 2.0) + v + 1;
Func <double, double> f;
Func <double, double> df;
switch (v)
{
case 0:
f = (r) => 1.0;
df = (r) => 0.0;
break;
case 1:
f = (r) => 1 + (exp + 1) * r;
df = (r) => exp + 1;
break;
case 2:
f = (r) => 1 + (exp + 2) * r + (exp * exp + 4.0 * exp + 3) / 3.0 * r * r;
df = (r) => (exp + 2) + 2 * (exp * exp + 4.0 * exp + 3) / 3.0 * r;
break;
case 3:
f = (r) => 1 + (exp + 3) * r + (6.0 * exp * exp + 36 * exp + 45) / 15.0 * r * r +
(exp * exp * exp + 9 * exp * exp + 23 * exp + 45) / 15.0 * r * r * r;
df = (r) => (exp + 3) + 2 * (6.0 * exp * exp + 36 * exp + 45) / 15.0 * r +
(exp * exp * exp + 9 * exp * exp + 23 * exp + 45) / 5.0 * r * r;
break;
default: throw new ArgumentException();
}
// create functions
var cov = new ParameterizedCovarianceFunction();
cov.Covariance = (x, i, j) => {
double k = Math.Sqrt(Util.SqrDist(x, i, x, j, columnIndices, 1.0 / length));
return(scale * Math.Pow(Math.Max(1 - k, 0), exp + v) * f(k));
};
cov.CrossCovariance = (x, xt, i, j) => {
double k = Math.Sqrt(Util.SqrDist(x, i, xt, j, columnIndices, 1.0 / length));
return(scale * Math.Pow(Math.Max(1 - k, 0), exp + v) * f(k));
};
cov.CovarianceGradient = (x, i, j) => GetGradient(x, i, j, length, scale, v, exp, f, df, columnIndices, fixedLength, fixedScale);
return(cov);
}
public ParameterizedCovarianceFunction GetParameterizedCovarianceFunction(double[] p, IEnumerable <int> columnIndices)
{
if (p.Length > 0)
{
throw new ArgumentException("No parameters are allowed for the linear covariance function.");
}
// create functions
var cov = new ParameterizedCovarianceFunction();
cov.Covariance = (x, i, j) => Util.ScalarProd(x, i, j, 1, columnIndices);
cov.CrossCovariance = (x, xt, i, j) => Util.ScalarProd(x, i, xt, j, 1.0, columnIndices);
cov.CovarianceGradient = (x, i, j) => Enumerable.Empty <double>();
return(cov);
}
public ParameterizedCovarianceFunction GetParameterizedCovarianceFunction(double[] p, int[] columnIndices)
{
double scale;
GetParameterValues(p, out scale);
var fixedScale = HasFixedScaleParameter;
var subCov = CovarianceFunctionParameter.Value.GetParameterizedCovarianceFunction(p.Skip(1).ToArray(), columnIndices);
// create functions
var cov = new ParameterizedCovarianceFunction();
cov.Covariance = (x, i, j) => scale *subCov.Covariance(x, i, j);
cov.CrossCovariance = (x, xt, i, j) => scale *subCov.CrossCovariance(x, xt, i, j);
cov.CovarianceGradient = (x, i, j) => GetGradient(x, i, j, columnIndices, scale, subCov, fixedScale);
return(cov);
}
public ParameterizedCovarianceFunction GetParameterizedCovarianceFunction(double[] p, int[] columnIndices)
{
if (p.Length != GetNumberOfParameters(columnIndices.Length))
{
throw new ArgumentException("Illegal parametrization");
}
var myClone = (KernelBase)Clone();
myClone.SetParameter(p);
var cov = new ParameterizedCovarianceFunction {
Covariance = (x, i, j) => myClone.Get(GetNorm(x, x, i, j, columnIndices)),
CrossCovariance = (x, xt, i, j) => myClone.Get(GetNorm(x, xt, i, j, columnIndices)),
CovarianceGradient = (x, i, j) => new List <double> {
myClone.GetGradient(GetNorm(x, x, i, j, columnIndices))
}
};
return(cov);
}
public ParameterizedCovarianceFunction GetParameterizedCovarianceFunction(double[] p, int[] columnIndices)
{
double scale;
GetParameterValues(p, out scale);
// create functions
var cov = new ParameterizedCovarianceFunction();
cov.Covariance = (x, i, j) => scale;
cov.CrossCovariance = (x, xt, i, j) => scale;
if (HasFixedScaleParameter)
{
cov.CovarianceGradient = (x, i, j) => new double[0];
}
else
{
cov.CovarianceGradient = (x, i, j) => new[] { 2.0 * scale };
}
return(cov);
}
public ParameterizedCovarianceFunction GetParameterizedCovarianceFunction(double[] p, IEnumerable <int> columnIndices)
{
double[] inverseLength;
GetParameterValues(p, out inverseLength);
var fixedInverseLength = HasFixedInverseLengthParameter;
// create functions
var cov = new ParameterizedCovarianceFunction();
cov.Covariance = (x, i, j) => Util.ScalarProd(x, i, j, inverseLength, columnIndices);
cov.CrossCovariance = (x, xt, i, j) => Util.ScalarProd(x, i, xt, j, inverseLength, columnIndices);
if (fixedInverseLength)
{
cov.CovarianceGradient = (x, i, j) => Enumerable.Empty <double>();
}
else
{
cov.CovarianceGradient = (x, i, j) => GetGradient(x, i, j, inverseLength, columnIndices);
}
return(cov);
}
public ParameterizedCovarianceFunction GetParameterizedCovarianceFunction(double[] p, int[] columnIndices) {
if (terms.Count == 0) throw new ArgumentException("at least one term is necessary for the product covariance function.");
var functions = new List<ParameterizedCovarianceFunction>();
foreach (var t in terms) {
var numberOfParameters = t.GetNumberOfParameters(numberOfVariables);
functions.Add(t.GetParameterizedCovarianceFunction(p.Take(numberOfParameters).ToArray(), columnIndices));
p = p.Skip(numberOfParameters).ToArray();
}
var sum = new ParameterizedCovarianceFunction();
sum.Covariance = (x, i, j) => functions.Select(e => e.Covariance(x, i, j)).Sum();
sum.CrossCovariance = (x, xt, i, j) => functions.Select(e => e.CrossCovariance(x, xt, i, j)).Sum();
sum.CovarianceGradient = (x, i, j) => {
var g = new List<double>();
foreach (var e in functions)
g.AddRange(e.CovarianceGradient(x, i, j));
return g;
};
return sum;
}
public ParameterizedCovarianceFunction GetParameterizedCovarianceFunction(double[] p, IEnumerable <int> columnIndices)
{
double scale;
GetParameterValues(p, out scale);
// create functions
var cov = new ParameterizedCovarianceFunction();
cov.Covariance = (x, i, j) => scale;
cov.CrossCovariance = (x, xt, i, j) => scale;
if (HasFixedScaleParameter)
{
cov.CovarianceGradient = (x, i, j) => Enumerable.Empty <double>();
}
else
{
cov.CovarianceGradient = (x, i, j) => GetGradient(x, i, j, scale, columnIndices);
}
return(cov);
}
public ParameterizedCovarianceFunction GetParameterizedCovarianceFunction(double[] p, int[] columnIndices)
{
double length, scale;
GetParameterValues(p, out scale, out length);
var fixedLength = HasFixedLengthParameter;
var fixedScale = HasFixedScaleParameter;
var cov = new ParameterizedCovarianceFunction();
cov.Covariance = (x, i, j) => {
double sx = 1.0;
double s1 = 1.0;
double s2 = 1.0;
for (int c = 0; c < columnIndices.Length; c++)
{
var col = columnIndices[c];
sx += x[i, col] * x[j, col];
s1 += x[i, col] * x[i, col];
s2 += x[j, col] * x[j, col];
}
return(scale * Math.Asin(sx / (Math.Sqrt((length + s1) * (length + s2)))));
};
cov.CrossCovariance = (x, xt, i, j) => {
double sx = 1.0;
double s1 = 1.0;
double s2 = 1.0;
for (int c = 0; c < columnIndices.Length; c++)
{
var col = columnIndices[c];
sx += x[i, col] * xt[j, col];
s1 += x[i, col] * x[i, col];
s2 += xt[j, col] * xt[j, col];
}
return(scale * Math.Asin(sx / (Math.Sqrt((length + s1) * (length + s2)))));
};
cov.CovarianceGradient = (x, i, j) => GetGradient(x, i, j, length, scale, columnIndices, fixedLength, fixedScale);
return(cov);
}
public ParameterizedCovarianceFunction GetParameterizedCovarianceFunction(double[] p, IEnumerable <int> columnIndices)
{
double scale;
GetParameterValues(p, out scale);
var fixedScale = HasFixedScaleParameter;
// create functions
var cov = new ParameterizedCovarianceFunction();
cov.Covariance = (x, i, j) => i == j ? scale : 0.0;
cov.CrossCovariance = (x, xt, i, j) => Util.SqrDist(x, i, xt, j, 1.0, columnIndices) < 1e-9 ? scale : 0.0;
if (fixedScale)
{
cov.CovarianceGradient = (x, i, j) => Enumerable.Empty <double>();
}
else
{
cov.CovarianceGradient = (x, i, j) => Enumerable.Repeat(i == j ? 2.0 * scale : 0.0, 1);
}
return(cov);
}
public ParameterizedCovarianceFunction GetParameterizedCovarianceFunction(double[] p, int[] columnIndices)
{
double[] weight, frequency, lengthScale;
GetParameterValues(p, out weight, out frequency, out lengthScale);
var fixedWeight = HasFixedWeightParameter;
var fixedFrequency = HasFixedFrequencyParameter;
var fixedLengthScale = HasFixedLengthScaleParameter;
// create functions
var cov = new ParameterizedCovarianceFunction();
cov.Covariance = (x, i, j) => {
return(GetCovariance(x, x, i, j, QParameter.Value.Value, weight, frequency,
lengthScale, columnIndices));
};
cov.CrossCovariance = (x, xt, i, j) => {
return(GetCovariance(x, xt, i, j, QParameter.Value.Value, weight, frequency,
lengthScale, columnIndices));
};
cov.CovarianceGradient = (x, i, j) => GetGradient(x, i, j, QParameter.Value.Value, weight, frequency,
lengthScale, columnIndices, fixedWeight, fixedFrequency, fixedLengthScale);
return(cov);
}
public ParameterizedCovarianceFunction GetParameterizedCovarianceFunction(double[] p, int[] columnIndices)
{
double @const, scale;
int degree = DegreeParameter.Value.Value;
if (degree <= 0)
{
throw new ArgumentException("The degree parameter for CovariancePolynomial must be greater than zero.");
}
GetParameterValues(p, out @const, out scale);
var fixedConst = HasFixedConstParameter;
var fixedScale = HasFixedScaleParameter;
// create functions
var cov = new ParameterizedCovarianceFunction();
cov.Covariance = (x, i, j) => scale *Math.Pow(@const + Util.ScalarProd(x, i, j, columnIndices, 1.0), degree);
cov.CrossCovariance = (x, xt, i, j) => scale *Math.Pow(@const + Util.ScalarProd(x, i, xt, j, columnIndices, 1.0), degree);
cov.CovarianceGradient = (x, i, j) => GetGradient(x, i, j, @const, scale, degree, columnIndices, fixedConst, fixedScale);
return(cov);
}
public ParameterizedCovarianceFunction GetParameterizedCovarianceFunction(double[] p, int[] columnIndices)
{
if (factors.Count == 0)
{
throw new ArgumentException("at least one factor is necessary for the product covariance function.");
}
var functions = new List <ParameterizedCovarianceFunction>();
foreach (var f in factors)
{
int numberOfParameters = f.GetNumberOfParameters(numberOfVariables);
functions.Add(f.GetParameterizedCovarianceFunction(p.Take(numberOfParameters).ToArray(), columnIndices));
p = p.Skip(numberOfParameters).ToArray();
}
var product = new ParameterizedCovarianceFunction();
product.Covariance = (x, i, j) => functions.Select(e => e.Covariance(x, i, j)).Aggregate((a, b) => a * b);
product.CrossCovariance = (x, xt, i, j) => functions.Select(e => e.CrossCovariance(x, xt, i, j)).Aggregate((a, b) => a * b);
product.CovarianceGradient = (x, i, j) => GetGradient(x, i, j, functions);
return(product);
}
public ParameterizedCovarianceFunction GetParameterizedCovarianceFunction(double[] p, int[] columnIndices)
{
double scale;
GetParameterValues(p, out scale);
var fixedScale = HasFixedScaleParameter;
// create functions
var cov = new ParameterizedCovarianceFunction();
cov.Covariance = (x, i, j) => i == j ? scale : 0.0;
cov.CrossCovariance = (x, xt, i, j) => Util.SqrDist(x, i, xt, j, columnIndices, 1.0) < 1e-9 ? scale : 0.0;
if (fixedScale)
{
cov.CovarianceGradient = (x, i, j) => new double[0];
}
else
{
cov.CovarianceGradient = (x, i, j) => new double[1] {
i == j ? 2.0 * scale : 0.0
}
};
return(cov);
}
}
public ParameterizedCovarianceFunction GetParameterizedCovarianceFunction(double[] p, int[] columnIndices)
{
double inverseLength, scale;
int d = DParameter.Value.Value;
GetParameterValues(p, out scale, out inverseLength);
var fixedInverseLength = HasFixedInverseLengthParameter;
var fixedScale = HasFixedScaleParameter;
// create functions
var cov = new ParameterizedCovarianceFunction();
cov.Covariance = (x, i, j) => {
double dist = i == j
? 0.0
: Math.Sqrt(Util.SqrDist(x, i, j, columnIndices, Math.Sqrt(d) * inverseLength));
return(scale * m(d, dist));
};
cov.CrossCovariance = (x, xt, i, j) => {
double dist = Math.Sqrt(Util.SqrDist(x, i, xt, j, columnIndices, Math.Sqrt(d) * inverseLength));
return(scale * m(d, dist));
};
cov.CovarianceGradient = (x, i, j) => GetGradient(x, i, j, d, scale, inverseLength, columnIndices, fixedInverseLength, fixedScale);
return(cov);
}
public ParameterizedCovarianceFunction GetParameterizedCovarianceFunction(double[] p, IEnumerable <int> columnIndices)
{
double inverseLength, scale;
GetParameterValues(p, out scale, out inverseLength);
var fixedInverseLength = HasFixedInverseLengthParameter;
var fixedScale = HasFixedScaleParameter;
// create functions
var cov = new ParameterizedCovarianceFunction();
cov.Covariance = (x, i, j) => {
double d = i == j
? 0.0
: Util.SqrDist(x, i, j, inverseLength, columnIndices);
return(scale * Math.Exp(-d / 2.0));
};
cov.CrossCovariance = (x, xt, i, j) => {
double d = Util.SqrDist(x, i, xt, j, inverseLength, columnIndices);
return(scale * Math.Exp(-d / 2.0));
};
cov.CovarianceGradient = (x, i, j) => GetGradient(x, i, j, scale, inverseLength, columnIndices,
fixedInverseLength, fixedScale);
return(cov);
}
private static IList<double> GetGradient(double[,] x, int i, int j, int[] columnIndices, double scale, ParameterizedCovarianceFunction cov,
bool fixedScale) {
var gr = new List<double>((!fixedScale ? 1 : 0) + cov.CovarianceGradient(x, i, j).Count);
if (!fixedScale) {
gr.Add(2 * scale * cov.Covariance(x, i, j));
}
foreach (var g in cov.CovarianceGradient(x, i, j))
gr.Add(scale * g);
return gr;
}
public ParameterizedCovarianceFunction GetParameterizedCovarianceFunction(double[] p, int[] columnIndices) {
double[] weight, frequency, lengthScale;
GetParameterValues(p, out weight, out frequency, out lengthScale);
var fixedWeight = HasFixedWeightParameter;
var fixedFrequency = HasFixedFrequencyParameter;
var fixedLengthScale = HasFixedLengthScaleParameter;
// create functions
var cov = new ParameterizedCovarianceFunction();
cov.Covariance = (x, i, j) => {
return GetCovariance(x, x, i, j, QParameter.Value.Value, weight, frequency,
lengthScale, columnIndices);
};
cov.CrossCovariance = (x, xt, i, j) => {
return GetCovariance(x, xt, i, j, QParameter.Value.Value, weight, frequency,
lengthScale, columnIndices);
};
cov.CovarianceGradient = (x, i, j) => GetGradient(x, i, j, QParameter.Value.Value, weight, frequency,
lengthScale, columnIndices, fixedWeight, fixedFrequency, fixedLengthScale);
return cov;
}
private static IEnumerable <double> GetGradient(double[,] x, int i, int j, IEnumerable <int> columnIndices, double scale, ParameterizedCovarianceFunction cov,
bool fixedScale)
{
if (!fixedScale)
{
yield return(2 * scale * cov.Covariance(x, i, j));
}
foreach (var g in cov.CovarianceGradient(x, i, j))
{
yield return(scale * g);
}
}
public ParameterizedCovarianceFunction GetParameterizedCovarianceFunction(double[] p, IEnumerable<int> columnIndices) {
if (factors.Count == 0) throw new ArgumentException("at least one factor is necessary for the product covariance function.");
var functions = new List<ParameterizedCovarianceFunction>();
foreach (var f in factors) {
int numberOfParameters = f.GetNumberOfParameters(numberOfVariables);
functions.Add(f.GetParameterizedCovarianceFunction(p.Take(numberOfParameters).ToArray(), columnIndices));
p = p.Skip(numberOfParameters).ToArray();
}
var product = new ParameterizedCovarianceFunction();
product.Covariance = (x, i, j) => functions.Select(e => e.Covariance(x, i, j)).Aggregate((a, b) => a * b);
product.CrossCovariance = (x, xt, i, j) => functions.Select(e => e.CrossCovariance(x, xt, i, j)).Aggregate((a, b) => a * b);
product.CovarianceGradient = (x, i, j) => GetGradient(x, i, j, functions);
return product;
}
public ParameterizedCovarianceFunction GetParameterizedCovarianceFunction(double[] p, IEnumerable<int> columnIndices) {
double scale;
GetParameterValues(p, out scale);
var fixedScale = HasFixedScaleParameter;
// create functions
var cov = new ParameterizedCovarianceFunction();
cov.Covariance = (x, i, j) => i == j ? scale : 0.0;
cov.CrossCovariance = (x, xt, i, j) => Util.SqrDist(x, i, xt, j, 1.0, columnIndices) < 1e-9 ? scale : 0.0;
if (fixedScale)
cov.CovarianceGradient = (x, i, j) => Enumerable.Empty<double>();
else
cov.CovarianceGradient = (x, i, j) => Enumerable.Repeat(i == j ? 2.0 * scale : 0.0, 1);
return cov;
}
public ParameterizedCovarianceFunction GetParameterizedCovarianceFunction(double[] p, int[] columnIndices) {
double length, scale;
int v = VParameter.Value.Value;
GetParameterValues(p, out length, out scale);
var fixedLength = HasFixedLengthParameter;
var fixedScale = HasFixedScaleParameter;
int exp = (int)Math.Floor(columnIndices.Count() / 2.0) + v + 1;
Func<double, double> f;
Func<double, double> df;
switch (v) {
case 0:
f = (r) => 1.0;
df = (r) => 0.0;
break;
case 1:
f = (r) => 1 + (exp + 1) * r;
df = (r) => exp + 1;
break;
case 2:
f = (r) => 1 + (exp + 2) * r + (exp * exp + 4.0 * exp + 3) / 3.0 * r * r;
df = (r) => (exp + 2) + 2 * (exp * exp + 4.0 * exp + 3) / 3.0 * r;
break;
case 3:
f = (r) => 1 + (exp + 3) * r + (6.0 * exp * exp + 36 * exp + 45) / 15.0 * r * r +
(exp * exp * exp + 9 * exp * exp + 23 * exp + 45) / 15.0 * r * r * r;
df = (r) => (exp + 3) + 2 * (6.0 * exp * exp + 36 * exp + 45) / 15.0 * r +
(exp * exp * exp + 9 * exp * exp + 23 * exp + 45) / 5.0 * r * r;
break;
default: throw new ArgumentException();
}
// create functions
var cov = new ParameterizedCovarianceFunction();
cov.Covariance = (x, i, j) => {
double k = Math.Sqrt(Util.SqrDist(x, i, x, j, columnIndices, 1.0 / length));
return scale * Math.Pow(Math.Max(1 - k, 0), exp + v) * f(k);
};
cov.CrossCovariance = (x, xt, i, j) => {
double k = Math.Sqrt(Util.SqrDist(x, i, xt, j, columnIndices, 1.0 / length));
return scale * Math.Pow(Math.Max(1 - k, 0), exp + v) * f(k);
};
cov.CovarianceGradient = (x, i, j) => GetGradient(x, i, j, length, scale, v, exp, f, df, columnIndices, fixedLength, fixedScale);
return cov;
}
public ParameterizedCovarianceFunction GetParameterizedCovarianceFunction(double[] p, int[] columnIndices) {
double inverseLength, scale;
int d = DParameter.Value.Value;
GetParameterValues(p, out scale, out inverseLength);
var fixedInverseLength = HasFixedInverseLengthParameter;
var fixedScale = HasFixedScaleParameter;
// create functions
var cov = new ParameterizedCovarianceFunction();
cov.Covariance = (x, i, j) => {
double dist = i == j
? 0.0
: Math.Sqrt(Util.SqrDist(x, i, j, columnIndices, Math.Sqrt(d) * inverseLength));
return scale * m(d, dist);
};
cov.CrossCovariance = (x, xt, i, j) => {
double dist = Math.Sqrt(Util.SqrDist(x, i, xt, j, columnIndices, Math.Sqrt(d) * inverseLength));
return scale * m(d, dist);
};
cov.CovarianceGradient = (x, i, j) => GetGradient(x, i, j, d, scale, inverseLength, columnIndices, fixedInverseLength, fixedScale);
return cov;
}
public ParameterizedCovarianceFunction GetParameterizedCovarianceFunction(double[] p, int[] columnIndices) {
double scale, shape, inverseLength;
GetParameterValues(p, out scale, out shape, out inverseLength);
var fixedInverseLength = HasFixedInverseLengthParameter;
var fixedScale = HasFixedScaleParameter;
var fixedShape = HasFixedShapeParameter;
// create functions
var cov = new ParameterizedCovarianceFunction();
cov.Covariance = (x, i, j) => {
double d = i == j
? 0.0
: Util.SqrDist(x, i, j, columnIndices, inverseLength);
return scale * Math.Pow(1 + 0.5 * d / shape, -shape);
};
cov.CrossCovariance = (x, xt, i, j) => {
double d = Util.SqrDist(x, i, xt, j, columnIndices, inverseLength);
return scale * Math.Pow(1 + 0.5 * d / shape, -shape);
};
cov.CovarianceGradient = (x, i, j) => GetGradient(x, i, j, columnIndices, scale, shape, inverseLength, fixedInverseLength, fixedScale, fixedShape);
return cov;
}
public ParameterizedCovarianceFunction GetParameterizedCovarianceFunction(double[] p, int[] columnIndices) {
double @const, scale;
int degree = DegreeParameter.Value.Value;
if (degree <= 0) throw new ArgumentException("The degree parameter for CovariancePolynomial must be greater than zero.");
GetParameterValues(p, out @const, out scale);
var fixedConst = HasFixedConstParameter;
var fixedScale = HasFixedScaleParameter;
// create functions
var cov = new ParameterizedCovarianceFunction();
cov.Covariance = (x, i, j) => scale * Math.Pow(@const + Util.ScalarProd(x, i, j, columnIndices, 1.0), degree);
cov.CrossCovariance = (x, xt, i, j) => scale * Math.Pow(@const + Util.ScalarProd(x, i, xt, j, columnIndices, 1.0), degree);
cov.CovarianceGradient = (x, i, j) => GetGradient(x, i, j, @const, scale, degree, columnIndices, fixedConst, fixedScale);
return cov;
}
public ParameterizedCovarianceFunction GetParameterizedCovarianceFunction(double[] p, IEnumerable<int> columnIndices) {
double length, scale;
GetParameterValues(p, out scale, out length);
var fixedLength = HasFixedLengthParameter;
var fixedScale = HasFixedScaleParameter;
var cov = new ParameterizedCovarianceFunction();
cov.Covariance = (x, i, j) => {
double sx = 1.0;
double s1 = 1.0;
double s2 = 1.0;
foreach (var col in columnIndices) {
sx += x[i, col] * x[j, col];
s1 += x[i, col] * x[i, col];
s2 += x[j, col] * x[j, col];
}
return (scale * Math.Asin(sx / (Math.Sqrt((length + s1) * (length + s2)))));
};
cov.CrossCovariance = (x, xt, i, j) => {
double sx = 1.0;
double s1 = 1.0;
double s2 = 1.0;
foreach (var col in columnIndices) {
sx += x[i, col] * xt[j, col];
s1 += x[i, col] * x[i, col];
s2 += xt[j, col] * xt[j, col];
}
return (scale * Math.Asin(sx / (Math.Sqrt((length + s1) * (length + s2)))));
};
cov.CovarianceGradient = (x, i, j) => GetGradient(x, i, j, length, scale, columnIndices, fixedLength, fixedScale);
return cov;
}
private static IEnumerable<double> GetGradient(double[,] x, int i, int j, IEnumerable<int> columnIndices, double scale, ParameterizedCovarianceFunction cov,
bool fixedScale) {
if (!fixedScale) {
yield return 2 * scale * cov.Covariance(x, i, j);
}
foreach (var g in cov.CovarianceGradient(x, i, j))
yield return scale * g;
}
private static double[,] CalculateL(double[,] x, ParameterizedCovarianceFunction cov, double sqrSigmaNoise) {
int n = x.GetLength(0);
var l = new double[n, n];
// calculate covariances
for (int i = 0; i < n; i++) {
for (int j = i; j < n; j++) {
l[j, i] = cov.Covariance(x, i, j) / sqrSigmaNoise;
if (j == i) l[j, i] += 1.0;
}
}
// cholesky decomposition
var res = alglib.trfac.spdmatrixcholesky(ref l, n, false);
if (!res) throw new ArgumentException("Matrix is not positive semidefinite");
return l;
}
public ParameterizedCovarianceFunction GetParameterizedCovarianceFunction(double[] p, int[] columnIndices) {
double inverseLength, period, scale;
GetParameterValues(p, out scale, out period, out inverseLength);
var fixedInverseLength = HasFixedInverseLengthParameter;
var fixedPeriod = HasFixedPeriodParameter;
var fixedScale = HasFixedScaleParameter;
// create functions
var cov = new ParameterizedCovarianceFunction();
cov.Covariance = (x, i, j) => {
double k = i == j ? 0.0 : GetDistance(x, x, i, j, columnIndices);
k = Math.PI * k / period;
k = Math.Sin(k) * inverseLength;
k = k * k;
return scale * Math.Exp(-2.0 * k);
};
cov.CrossCovariance = (x, xt, i, j) => {
double k = GetDistance(x, xt, i, j, columnIndices);
k = Math.PI * k / period;
k = Math.Sin(k) * inverseLength;
k = k * k;
return scale * Math.Exp(-2.0 * k);
};
cov.CovarianceGradient = (x, i, j) => GetGradient(x, i, j, columnIndices, scale, period, inverseLength, fixedInverseLength, fixedPeriod, fixedScale);
return cov;
}
public ParameterizedCovarianceFunction GetParameterizedCovarianceFunction(double[] p, IEnumerable<int> columnIndices) {
double scale;
GetParameterValues(p, out scale);
var fixedScale = HasFixedScaleParameter;
var subCov = CovarianceFunctionParameter.Value.GetParameterizedCovarianceFunction(p.Skip(1).ToArray(), columnIndices);
// create functions
var cov = new ParameterizedCovarianceFunction();
cov.Covariance = (x, i, j) => scale * subCov.Covariance(x, i, j);
cov.CrossCovariance = (x, xt, i, j) => scale * subCov.CrossCovariance(x, xt, i, j);
cov.CovarianceGradient = (x, i, j) => GetGradient(x, i, j, columnIndices, scale, subCov, fixedScale);
return cov;
}
public ParameterizedCovarianceFunction GetParameterizedCovarianceFunction(double[] p, int[] columnIndices) {
double scale;
GetParameterValues(p, out scale);
var fixedScale = HasFixedScaleParameter;
// create functions
var cov = new ParameterizedCovarianceFunction();
cov.Covariance = (x, i, j) => i == j ? scale : 0.0;
cov.CrossCovariance = (x, xt, i, j) => Util.SqrDist(x, i, xt, j, columnIndices, 1.0) < 1e-9 ? scale : 0.0;
if (fixedScale)
cov.CovarianceGradient = (x, i, j) => new double[0];
else
cov.CovarianceGradient = (x, i, j) => new double[1] { i == j ? 2.0 * scale : 0.0 };
return cov;
}
private static IList <double> GetGradient(double[,] x, int i, int j, int[] columnIndices, double scale, ParameterizedCovarianceFunction cov,
bool fixedScale)
{
var gr = new List <double>((!fixedScale ? 1 : 0) + cov.CovarianceGradient(x, i, j).Count);
if (!fixedScale)
{
gr.Add(2 * scale * cov.Covariance(x, i, j));
}
foreach (var g in cov.CovarianceGradient(x, i, j))
{
gr.Add(scale * g);
}
return(gr);
}
public ParameterizedCovarianceFunction GetParameterizedCovarianceFunction(double[] p, IEnumerable<int> columnIndices) {
double[] inverseLength;
GetParameterValues(p, out inverseLength);
var fixedInverseLength = HasFixedInverseLengthParameter;
// create functions
var cov = new ParameterizedCovarianceFunction();
cov.Covariance = (x, i, j) => Util.ScalarProd(x, i, j, inverseLength, columnIndices);
cov.CrossCovariance = (x, xt, i, j) => Util.ScalarProd(x, i, xt, j, inverseLength, columnIndices);
if (fixedInverseLength)
cov.CovarianceGradient = (x, i, j) => Enumerable.Empty<double>();
else
cov.CovarianceGradient = (x, i, j) => GetGradient(x, i, j, inverseLength, columnIndices);
return cov;
}
public ParameterizedCovarianceFunction GetParameterizedCovarianceFunction(double[] p, int[] columnIndices) {
double scale;
GetParameterValues(p, out scale);
// create functions
var cov = new ParameterizedCovarianceFunction();
cov.Covariance = (x, i, j) => scale;
cov.CrossCovariance = (x, xt, i, j) => scale;
if (HasFixedScaleParameter) {
cov.CovarianceGradient = (x, i, j) => new double[0];
} else {
cov.CovarianceGradient = (x, i, j) => new[] { 2.0 * scale };
}
return cov;
}
public ParameterizedCovarianceFunction GetParameterizedCovarianceFunction(double[] p, IEnumerable<int> columnIndices) {
double inverseLength, scale;
GetParameterValues(p, out scale, out inverseLength);
var fixedInverseLength = HasFixedInverseLengthParameter;
var fixedScale = HasFixedScaleParameter;
// create functions
var cov = new ParameterizedCovarianceFunction();
cov.Covariance = (x, i, j) => {
double d = i == j
? 0.0
: Util.SqrDist(x, i, j, inverseLength, columnIndices);
return scale * Math.Exp(-d / 2.0);
};
cov.CrossCovariance = (x, xt, i, j) => {
double d = Util.SqrDist(x, i, xt, j, inverseLength, columnIndices);
return scale * Math.Exp(-d / 2.0);
};
cov.CovarianceGradient = (x, i, j) => GetGradient(x, i, j, scale, inverseLength, columnIndices,
fixedInverseLength, fixedScale);
return cov;
}
public ParameterizedCovarianceFunction GetParameterizedCovarianceFunction(double[] p, IEnumerable<int> columnIndices) {
double scale;
GetParameterValues(p, out scale);
// create functions
var cov = new ParameterizedCovarianceFunction();
cov.Covariance = (x, i, j) => scale;
cov.CrossCovariance = (x, xt, i, j) => scale;
if (HasFixedScaleParameter) {
cov.CovarianceGradient = (x, i, j) => Enumerable.Empty<double>();
} else {
cov.CovarianceGradient = (x, i, j) => GetGradient(x, i, j, scale, columnIndices);
}
return cov;
}
