static ComplexPlotValue Plot(FunctionValue f, Double minx, Double maxx, Double miny, Double maxy)
{
var cp = new ComplexPlotValue();
cp.SetFunction(f);
cp.MinY = miny;
cp.MaxY = maxy;
cp.MinX = minx;
cp.MaxX = maxx;
return cp;
}
public ScalarValue Function(FunctionValue f, ScalarValue x)
{
var lambda = new Func<Double, Double>(t =>
{
var sv = f.Perform(Context, new ScalarValue(t));
if (sv is ScalarValue == false)
{
throw new YAMPArgumentInvalidException(Name, sv.Header, 1);
}
return ((ScalarValue)sv).Re;
});
var newton = new NewtonMethod(lambda, x.Re, 0.00001);
return new ScalarValue(newton.Result[0, 0]);
}
public FunctionValue Function(MatrixValue x, MatrixValue y, FunctionValue f)
{
var context = Context;
if (x.Length != y.Length)
throw new YAMPDifferentLengthsException(x.Length, y.Length);
var _fx = f.Perform(context, x[1]);
if (_fx is MatrixValue == false)
throw new YAMPArgumentInvalidException("Linfit", "f", 3);
var fx = _fx as MatrixValue;
var m = fx.Length;
if (m < 2)
throw new YAMPArgumentInvalidException("Linfit", "f", 3);
var M = new MatrixValue(x.Length, m);
for (var j = 1; j <= M.Rows; j++)
{
if (j > 1)
{
fx = f.Perform(context, x[j]) as MatrixValue;
}
for (var i = 1; i <= M.Columns; i++)
{
M[j, i] = fx[i];
}
}
var p = Function(x, y, M);
return new FunctionValue((parseContext, variable) => ((f.Perform(parseContext, variable) as MatrixValue) * p)[1], true);
}
public Plot2DValue Function(FunctionValue f, ScalarValue min, ScalarValue max, ScalarValue precision)
{
return(Plot(f, min.Re, max.Re, precision.Re));
}
/// <summary>
/// Sets the function to use for the complex plot.
/// </summary>
/// <param name="function">The function to consider.</param>
public void SetFunction(FunctionValue function)
{
f = function;
}
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 (var 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 (var 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(Context);
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 (var 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 ((ScalarValue)temp) / norm;
}
else if (temp is MatrixValue)
{
return ((MatrixValue)temp) / norm;
}
throw new YAMPOperationInvalidException();
}, true);
return normed_dist;
}
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 MatrixValue Function(MatrixValue cfgs, ScalarValue n, FunctionValue f)
{
return Function(cfgs, n, f, new ArgumentsValue());
}
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 = (temp as MatrixValue).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 (int i = 1; i <= numberOfBlocks; i++)
{
if (i <= numberOfBlocks - residualConfigs)
{
//the first (NumberOfBlocks - residualConfigs) blocks discard (BlockSize) elements ...
var JackknifeConfigs = new MatrixValue(nConfigs - BlockSize, nData);
int j = 1;
for (; j <= (i - 1) * BlockSize; j++)
{
for (int k = 1; k <= nData; k++)
{
JackknifeConfigs[j, k] = cfgs[j, k];
}
}
j += BlockSize;
for (; j <= nConfigs; j++)
{
for (int 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);
int j = 1;
for (; j <= nConfigs - (numberOfBlocks - (i - 1)) * (BlockSize + 1); j++)
{
for (int k = 1; k <= nData; k++)
{
JackknifeConfigs[j, k] = cfgs[j, k];
}
}
j += BlockSize + 1;
for (; j <= nConfigs; j++)
{
for (int 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 (int k = 1; k <= nResult; k++)
{
JackknifeObservable[i, k] = T[k];
}
}
}
temp = YMath.Average(JackknifeObservable);
for (int i = 1; i <= numberOfBlocks; i++)
{
if (temp is ScalarValue)
{
JackknifeObservable[i] -= temp as ScalarValue;
JackknifeObservable[i] *= JackknifeObservable[i];
}
else
{
var m = (MatrixValue)temp;
for (int 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 (int 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 (int k = 1; k <= nResult; k++)
{
result[1, k] = T[k];
result[2, k] = E[k];
}
}
return(result);
}
public ComplexPlotValue Function(FunctionValue f, ScalarValue minX, ScalarValue maxX, ScalarValue minY, ScalarValue maxY)
{
return Plot(f, minX.Re, maxX.Re, minY.Re, maxY.Re);
}
public ComplexPlotValue Function(FunctionValue f)
{
return Plot(f, -1.0, 1.0, -1.0, 1.0);
}
public Plot2DValue Function(FunctionValue f)
{
return(Plot(f, -1.0, 1.0, 0.05));
}
public Plot2DValue Function(FunctionValue f, ScalarValue min, ScalarValue max)
{
return(Plot(f, min.Re, max.Re, 0.05));
}
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 (var 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 (var 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(Context);
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 (var 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(((ScalarValue)temp) / norm);
}
else if (temp is MatrixValue)
{
return(((MatrixValue)temp) / norm);
}
throw new YAMPOperationInvalidException();
}, true);
return(normed_dist);
}
public ComplexPlotValue Function(FunctionValue f, ScalarValue minX, ScalarValue maxX, ScalarValue minY, ScalarValue maxY)
{
return(Plot(f, minX.Re, maxX.Re, minY.Re, maxY.Re));
}
public ComplexPlotValue Function(FunctionValue f, ScalarValue min, ScalarValue max)
{
return(Plot(f, min.Re, max.Re, min.Im, max.Im));
}
public ComplexPlotValue Function(FunctionValue f)
{
return(Plot(f, -1.0, 1.0, -1.0, 1.0));
}
/// <summary>
/// Sets the function to use for the complex plot.
/// </summary>
/// <param name="function">The function to consider.</param>
public void SetFunction(FunctionValue function)
{
f = function;
}
public override Value Interpret(IDictionary<String, Value> symbols)
{
var f = new FunctionValue(Name, Arguments, Body.Container);
Query.Context.AddFunction(Name, f);
return f;
}
public Plot2DValue Function(FunctionValue f)
{
return Plot(f, -1.0, 1.0, 0.05);
}
public ComplexPlotValue Function(FunctionValue f, ScalarValue min, ScalarValue max)
{
return Plot(f, min.Re, max.Re, min.Im, max.Im);
}
public Plot2DValue Function(FunctionValue f, ScalarValue min, ScalarValue max)
{
return Plot(f, min.Re, max.Re, 0.05);
}
public Plot2DValue Function(FunctionValue f, ScalarValue min, ScalarValue max, ScalarValue precision)
{
return Plot(f, min.Re, max.Re, precision.Re);
}
public MatrixValue Function(MatrixValue cfgs, ScalarValue n, FunctionValue f)
{
return(Function(cfgs, n, f, new ArgumentsValue()));
}
