public BarPlotValue Function(MatrixValue Y, ScalarValue nbins)
{
var nn = nbins.GetIntegerOrThrowException("nbins", Name);
var bp = new BarPlotValue();
if (Y.IsVector)
{
bp.AddPoints(YMath.Histogram(Y, nn));
}
else
{
var M = new MatrixValue();
for (var i = 1; i <= Y.DimensionX; i++)
{
var N = YMath.Histogram(Y.GetColumnVector(i), nn);
for (var j = 1; j <= N.Length; j++)
{
M[j, i] = N[j];
}
}
bp.AddPoints(M);
}
return(bp);
}
public MatrixValue Function(MatrixValue Y, MatrixValue x)
{
var X = new Double[x.Length];
for (var i = 0; i < x.Length; i++)
{
X[i] = x[i + 1].Re;
}
if (!Y.IsVector)
{
var M = new MatrixValue();
for (var i = 1; i <= Y.DimensionX; i++)
{
var N = YMath.Histogram(Y.GetColumnVector(i), X);
for (var j = 1; j <= N.Length; j++)
{
M[j, i] = N[j];
}
}
return(M);
}
return(YMath.Histogram(Y, X));
}
public BarPlotValue Function(MatrixValue Y, MatrixValue x)
{
var bp = new BarPlotValue();
var X = new double[x.Length];
for (var i = 0; i < x.Length; i++)
{
X[i] = x[i + 1].Re;
}
if (Y.IsVector)
{
bp.AddPoints(YMath.Histogram(Y, X));
}
else
{
var M = new MatrixValue();
for (var i = 1; i <= Y.DimensionX; i++)
{
var N = YMath.Histogram(Y.GetColumnVector(i), X);
for (var j = 1; j <= N.Length; j++)
{
M[j, i] = N[j];
}
}
bp.AddPoints(M);
}
return(bp);
}
public static Value Variance(MatrixValue M)
{
if (M.Length == 0)
{
return(ScalarValue.Zero);
}
if (M.IsVector)
{
var variance = ScalarValue.Zero;
var mean = M.Sum() / M.Length;
for (int i = 1; i <= M.Length; i++)
{
variance += (M[i] - mean).Square();
}
return(variance / M.Length);
}
var avg = (MatrixValue)YMath.Average(M);
var scale = 1.0;
var s = new MatrixValue(1, M.DimensionX);
for (var i = 1; i <= M.DimensionY; i++)
{
for (int j = 1; j <= M.DimensionX; j++)
{
s[1, j] += (M[i, j] - avg[j]).Square();
}
}
scale /= M.DimensionY;
for (var i = 1; i <= s.DimensionY; i++)
{
for (int j = 1; j <= s.DimensionX; j++)
{
s[i, j] *= scale;
}
}
return(s);
}
public MatrixValue Function(MatrixValue M, ScalarValue nLag)
{
if (M.Length <= 1)
{
return(new MatrixValue());
}
var nOffset = nLag.GetIntegerOrThrowException("nLag", Name);
if (nOffset < 0)
{
nOffset = 0;
}
else if (nOffset >= M.Length)
{
nOffset = M.Length - 1;
}
return(YMath.CrossCorrelation(M, M, nOffset));
}
public MatrixValue Function(MatrixValue M)
{
if (M.Length <= 1)
{
return(new MatrixValue());
}
else
{
int nOffset = (int)(10 * Math.Log10(M.Length));
if (nOffset < 0)
{
nOffset = 0;
}
else if (nOffset >= M.Length)
{
nOffset = M.Length - 1;
}
return(YMath.CrossCorrelation(M, M, nOffset));
}
}
public MatrixValue Function(MatrixValue M, MatrixValue N, ScalarValue lag)
{
if (M.Length != N.Length || M.Length <= 1)
{
return(new MatrixValue());
}
int nOffset = lag.GetIntegerOrThrowException("lag", Name);
if (nOffset < 0)
{
nOffset = 0;
}
else if (nOffset >= M.Length)
{
nOffset = M.Length - 1;
}
return(YMath.CrossCorrelation(M, N, nOffset));
}
public MatrixValue Function(MatrixValue M, MatrixValue N)
{
if (M.Length == N.Length && M.Length > 1)
{
var nOffset = (Int32)(10 * Math.Log10(M.Length));
if (nOffset < 0)
{
nOffset = 0;
}
else if (nOffset >= M.Length)
{
nOffset = M.Length - 1;
}
return(YMath.CrossCorrelation(M, N, nOffset));
}
return(new MatrixValue());
}
public ScalarValue Function(MatrixValue M)
{
return(YMath.Median(M));
}
public MatrixValue Function(MatrixValue cfgs, ScalarValue n, FunctionValue f, ArgumentsValue P)
{
var numberOfBootstrapSamples = n.GetIntegerOrThrowException("n", Name);
var nConfigs = cfgs.DimensionY;
var nData = cfgs.DimensionX;
var distribution = new DiscreteUniformDistribution(Rng)
{
Beta = nConfigs,
Alpha = 1
};
if (numberOfBootstrapSamples <= 1)
{
throw new YAMPException("Bootstrap: The number of bootstrap samples n is smaller or equal to 1!");
}
var parameters = new ArgumentsValue(cfgs);
foreach (var m in P.Values)
{
parameters.Insert(m);
}
var temp = f.Perform(Context, parameters);
var nResult = 0;//dimension of the result
if (temp is ScalarValue)
{
nResult = 1;
}
else if (temp is MatrixValue)
{
nResult = ((MatrixValue)temp).Length;
}
else
{
throw new YAMPException("Bootstrap: The observable f has to return either a scalar or a matrix!");
}
var BootstrapObservable = new MatrixValue(numberOfBootstrapSamples, nResult);
for (var i = 1; i <= numberOfBootstrapSamples; i++)
{
var BootstrapConfigs = new MatrixValue(nConfigs, nData);
for (var j = 1; j <= nConfigs; j++)
{
var idx = distribution.Next();
for (var k = 1; k <= nData; k++)
{
BootstrapConfigs[j, k] = cfgs[idx, k];
}
}
parameters = new ArgumentsValue(BootstrapConfigs);
foreach (var m in P.Values)
{
parameters.Insert(m);
}
temp = f.Perform(Context, parameters);
if (temp is ScalarValue)
{
BootstrapObservable[i] = (ScalarValue)temp;
}
else
{
var m = (MatrixValue)temp;
for (var k = 1; k <= nResult; k++)
{
BootstrapObservable[i, k] = m[k];
}
}
}
temp = YMath.Average(BootstrapObservable);
for (var i = 1; i <= numberOfBootstrapSamples; i++)
{
if (temp is ScalarValue)
{
BootstrapObservable[i] -= temp as ScalarValue;
BootstrapObservable[i] *= BootstrapObservable[i];
}
else
{
var T = temp as MatrixValue;
for (var k = 1; k <= nResult; k++)
{
BootstrapObservable[i, k] -= T[k];
BootstrapObservable[i, k] *= BootstrapObservable[i, k];
}
}
}
var error = YMath.Average(BootstrapObservable);
var sqrt = new SqrtFunction();
error = sqrt.Perform(error);
var result = new MatrixValue(2, nResult);
if (temp is ScalarValue)
{
result[1] = (ScalarValue)temp;
result[2] = (ScalarValue)error;
}
else
{
var T = (MatrixValue)temp;
var E = (MatrixValue)error;
for (var k = 1; k <= nResult; k++)
{
result[1, k] = T[k];
result[2, k] = E[k];
}
}
return(result);
}
public Value Function(MatrixValue M)
{
return(YMath.Average(M));
}
public MatrixValue Function(MatrixValue cfgs, ScalarValue n, FunctionValue f, ArgumentsValue P)
{
var numberOfBlocks = n.GetIntegerOrThrowException("n", Name);
var nConfigs = cfgs.DimensionY;
var nData = cfgs.DimensionX;
if (numberOfBlocks > nConfigs)
{
throw new YAMPException("Jackknife: The number of measurements n is greater than the number of configurations cfgs!");
}
if (numberOfBlocks <= 1)
{
throw new YAMPException("Jackknife: The number of measurements n <= 1!");
}
var parameters = new ArgumentsValue(cfgs);
foreach (var m in P.Values)
{
parameters.Insert(m);
}
var temp = f.Perform(Context, parameters);
int nResult;//dimension of the result
if (temp is ScalarValue)
{
nResult = 1;
}
else if (temp is MatrixValue)
{
nResult = ((MatrixValue)temp).Length;
}
else
{
throw new YAMPException("Jackknife: Observable f has to return either a scalar or a matrix!");
}
var JackknifeObservable = new MatrixValue(numberOfBlocks, nResult);
var BlockSize = nConfigs / numberOfBlocks;
var nConfigsBlocked = BlockSize * numberOfBlocks;
var residualConfigs = nConfigs - nConfigsBlocked;
for (var i = 1; i <= numberOfBlocks; i++)
{
if (i <= numberOfBlocks - residualConfigs)
{
//the first (NumberOfBlocks - residualConfigs) blocks discard (BlockSize) elements ...
var JackknifeConfigs = new MatrixValue(nConfigs - BlockSize, nData);
var j = 1;
for (; j <= (i - 1) * BlockSize; j++)
{
for (var k = 1; k <= nData; k++)
{
JackknifeConfigs[j, k] = cfgs[j, k];
}
}
j += BlockSize;
for (; j <= nConfigs; j++)
{
for (var k = 1; k <= nData; k++)
{
JackknifeConfigs[j - BlockSize, k] = cfgs[j, k];
}
}
parameters = new ArgumentsValue(JackknifeConfigs);
}
else
{
//... whereas the residual (residualConfigs) blocks discard (BlockSize + 1) elements
var JackknifeConfigs = new MatrixValue(nConfigs - BlockSize - 1, nData);
var j = 1;
for (; j <= nConfigs - (numberOfBlocks - (i - 1)) * (BlockSize + 1); j++)
{
for (var k = 1; k <= nData; k++)
{
JackknifeConfigs[j, k] = cfgs[j, k];
}
}
j += BlockSize + 1;
for (; j <= nConfigs; j++)
{
for (var k = 1; k <= nData; k++)
{
JackknifeConfigs[j - BlockSize - 1, k] = cfgs[j, k];
}
}
parameters = new ArgumentsValue(JackknifeConfigs);
}
foreach (var m in P.Values)
{
parameters.Insert(m);
}
temp = f.Perform(Context, parameters);
if (temp is ScalarValue)
{
JackknifeObservable[i] = (ScalarValue)temp;
}
else
{
var T = (MatrixValue)temp;
for (var k = 1; k <= nResult; k++)
{
JackknifeObservable[i, k] = T[k];
}
}
}
temp = YMath.Average(JackknifeObservable);
for (var i = 1; i <= numberOfBlocks; i++)
{
if (temp is ScalarValue)
{
JackknifeObservable[i] -= temp as ScalarValue;
JackknifeObservable[i] *= JackknifeObservable[i];
}
else
{
var m = (MatrixValue)temp;
for (var k = 1; k <= nResult; k++)
{
JackknifeObservable[i, k] -= m[k];
JackknifeObservable[i, k] *= JackknifeObservable[i, k];
}
}
}
var error = YMath.Average(JackknifeObservable);
var scale = numberOfBlocks - 1.0;
if (error is ScalarValue)
{
error = ((ScalarValue)error) * scale;
}
else
{
var e = (MatrixValue)error;
for (var i = 1; i <= e.DimensionY; i++)
{
for (var j = 1; j <= e.DimensionX; j++)
{
e[i, j] *= scale;
}
}
}
var sqrt = new SqrtFunction();
error = sqrt.Perform(error);
var result = new MatrixValue(2, nResult);
if (temp is ScalarValue)
{
result[1] = (ScalarValue)temp;
result[2] = (ScalarValue)error;
}
else
{
var T = (MatrixValue)temp;
var E = (MatrixValue)error;
for (var k = 1; k <= nResult; k++)
{
result[1, k] = T[k];
result[2, k] = E[k];
}
}
return(result);
}
public Value Function(MatrixValue M)
{
return(YMath.Mean(M));
}
public FunctionValue Function(MatrixValue Y, ScalarValue nbins, ScalarValue nParameters)
{
var nn = nbins.GetIntegerOrThrowException("nbins", Name);
var nP = nParameters.GetIntegerOrThrowException("nParameters", Name);
var N = Y.Length;
var min_idx = Y.Min();
var min = Y[min_idx.Row, min_idx.Column];
var max_idx = Y.Max();
var max = Y[max_idx.Row, max_idx.Column];
var median = YMath.Median(Y);
var variance = ScalarValue.Zero;
var mean = Y.Sum() / Y.Length;
for (int i = 1; i <= Y.Length; i++)
{
variance += (Y[i] - mean).Square();
}
variance /= Y.Length;
var delta = (max - min) / nn;
var x = new MatrixValue(nn, 1);
for (int i = 0; i < nn; i++)
{
x[i + 1] = min + delta * i;
}
var histogram = new HistogramFunction();
var fx = histogram.Function(Y, x);
var linearfit = new LinfitFunction();
var dist = linearfit.Function(x, fx, new FunctionValue((context, argument) =>
{
var _x = (argument as ScalarValue - median / 2) / (variance / 4);
var _exp_x_2 = (-_x * _x).Exp();
var result = new MatrixValue(1, nP - 1);
for (int i = 0; i < nP - 1; i++)
{
result[i + 1] = _exp_x_2 * _x.Pow(new ScalarValue(i));
}
return(result);
}, true));
var norm = Y.Length * (max - min) / nbins;
var normed_dist = new FunctionValue((context, argument) =>
{
var temp = dist.Perform(context, argument);
if (temp is ScalarValue)
{
return((temp as ScalarValue) / norm);
}
else if (temp is MatrixValue)
{
return((temp as MatrixValue) / norm);
}
else
{
throw new YAMPOperationInvalidException();
}
}, true);
return(normed_dist);
}
public MatrixValue Function(MatrixValue M)
{
return(YMath.Correlation(M));
}
public Value Function(MatrixValue M)
{
return(YMath.Variance(M));
}