public static MP Expected <M, R, MP, RF>(this IDensity <IModuleWithExtension <M, R, MP, RF>, M, RF> d)
{
var g = d.BaseStructure;
var embeddedDensity = d.EmbedTo <M, R, MP, RF>();
return(embeddedDensity.Expected());
}
public static IList <M> SortedKeys <G, M, RF>(this IDensity <G, M, RF> d)
where G :
IBaseStructure <M>,
IComparer <M>
{
return(d.GetKeys().OrderBy(k => k, d.BaseStructure).ToList());
}
public static IDensity <S, N, RF> Op <G, M, S, N, RF>(this IDensity <G, M, RF> d,
S newBaseStructure,
Func <M, N> op,
Func <string, string> opStrFunc = null)
{
return(Op(d, newBaseStructure, op, opStrFunc));
}
public static PlotModel OxyPlot <G, M, RF>(this IDensity <G, M, RF> d, string title = null)
where G :
IBaseStructure <M>,
IRealEmbedding <M, RF>
where M :
struct
where RF :
struct
{
var oxyplotter = new OxyPlotter <G, M, RealFieldType <RF>, RF>(d.BaseStructure, new RealFieldType <RF>());
var rf = d.RealField;
title = title ?? d.GetTrimmedName();
// TODO: For Expected() and Stdev() much more assumptions are necessary!
// var subtitle = string.Format(
// CultureInfo.InvariantCulture,
// "Expected = {0:0.0000}, Stdev = {1:0.00}",
// d.Expected(),
// d.Stdev()
// );
var subtitle = "";
var plotModel = oxyplotter.GetPlot(
k => d[k],
d.SortedKeys(),
title: title,
subtitle: subtitle,
yMin: rf.EmbedFromReal(0.0),
valueLabelFormatter: p => rf.EmbedToReal(p).ToString("P", CultureInfo.InvariantCulture));
return(plotModel);
}
public static RF Prob(IDensity <G, M, RF> d, Func <M, bool> cond)
{
var rf = d.RealField;
var resSum = rf.Sum(d.GetKeys().Where(cond).Select(k => d[k]));
return(resSum);
}
public static IList <RF> SortedValues <G, M, RF>(this IDensity <G, M, RF> d)
where G :
IBaseStructure <M>,
IComparer <M>
{
return(d.SortedKeys().Select(k => d[k]).ToList());
}
public bool Equals(IDensity <G, M, RF> other)
{
var isNull = object.ReferenceEquals(other, null);
if (isNull)
{
return(false);
}
var countsDiffer = Dictionary.Count != other.Dictionary.Count;
if (countsDiffer)
{
return(false);
}
var keysDiffer = Dictionary.Keys.Except(other.Dictionary.Keys).Any();
if (keysDiffer)
{
return(false);
}
var valuesDiffer = Dictionary.Values.Except(other.Dictionary.Values).Any();
if (valuesDiffer)
{
return(false);
}
return(true);
}
public static IDensity <G, M, RF> Negate <G, M, RF>(this IDensity <G, M, RF> d)
where G :
IAdditiveGroup <M>
{
var g = d.BaseStructure;
return(d.Op(g, a => g.Negate(a), s => $"(-{s})"));
}
public static IDensity <G, M, RF> Subtract <G, M, RF>(this IDensity <G, M, RF> d, IDensity <G, M, RF> d2)
where G :
IAdditiveGroup <M>
{
var g = d.BaseStructure;
return(Density <G, M, RF> .BinaryOp <G, M>(g, d, d2, (a, b) => g.Subtract(a, b), (s, t) => $"({s}-{t})"));
}
public static IDensity <G, M, RF> Divide <G, M, RF>(this IDensity <G, M, RF> d, IDensity <G, M, RF> d2)
where G :
IMultiplicativeGroup <M>
{
var g = d.BaseStructure;
return(Density <G, M, RF> .BinaryOp <G, M>(g, d, d2, (a, b) => g.Divide(a, b), (s, t) => $"({s}/{t})"));
}
public static RF EqProb <G, M, RF>(this IDensity <G, M, RF> d, IDensity <G, M, RF> d2)
where G :
IBaseStructure <M>
{
var g = d.BaseStructure;
return(Density <G, M, RF> .BinaryProb(d, d2, (a, b) => g.Equals(a, b)));
}
public static IDensity <G, M, RF> Add <G, M, RF>(this IDensity <G, M, RF> d, IDensity <G, M, RF> d2)
where G :
IAdditiveMonoid <M>
{
var g = d.BaseStructure;
return(Density <G, M, RF> .BinaryOp <G, M>(g, d, d2, (a, b) => g.Add(a, b), (s, t) => $"({s}+{t})"));
}
public static MP Expected <MP, RF>(this IDensity <IRealVectorspace <MP, RF>, MP, RF> d)
{
var gp = d.BaseStructure;
var grp = gp.BaseRealField;
var expected = gp.Sum(d.Dictionary.Select(p => gp.ScalarMult(p.Value, p.Key)));
return(expected);
}
public static IDensity <G, M, RF> Multiply <G, M, RF>(this IDensity <G, M, RF> d, IDensity <G, M, RF> d2)
where G :
IMultiplicativeMonoid <M>
{
var g = d.BaseStructure;
return(Density <G, M, RF> .BinaryOp <G, M>(g, d, d2, (a, b) => g.Multiply(a, b), (s, t) => $"({s}*{t})"));
}
public static MultiDensity <G, M, RF> AsMultiDensity <G, M, RF>(this IDensity <G, M, RF> d, int n)
where G :
IAdditiveMonoid <M>
{
var dList = Enumerable.Repeat(d, n).ToList();
var multiDensity = new MultiDensity <G, M, RF>(dList);
return(multiDensity);
}
public static RF GeqProb <G, M, RF>(this IDensity <G, M, RF> d, IDensity <G, M, RF> d2)
where G :
IBaseStructure <M>,
IComparer <M>
{
var g = d.BaseStructure;
return(Density <G, M, RF> .BinaryProb(d, d2, (a, b) => g.Compare(a, b) >= 0));
}
public static string GetTrimmedName <G, M, RF>(this IDensity <G, M, RF> d)
{
var trimmedName = d.Name;
while (trimmedName.StartsWith("(") && trimmedName.EndsWith(")"))
{
trimmedName = trimmedName.Substring(1, Math.Max(1, trimmedName.Length - 2));
}
return(trimmedName);
}
public static RF Cdf <G, M, RF>(this IDensity <G, M, RF> d, RF x)
where G :
IBaseStructure <M>,
IComparer <M>,
IRealEmbedding <M, RF>
{
var g = d.BaseStructure;
var rf = d.RealField;
return(d.Prob(a => rf.Compare(g.EmbedToReal(a), x) <= 0));
}
public static IDensity <S, N, RF> Op <S, N>(
IDensity <G, M, RF> d,
S newBaseStructure,
Func <M, N> op,
Func <string, string> opStrFunc = null)
{
var resDensity = GetOpDictionary(d, op);
var name = opStrFunc == null
? DefaultName
: opStrFunc(d.Name);
return(new Density <S, N, RF>(resDensity, newBaseStructure, d.RealField, name));
}
public static RF Variance <MP, RF>(this IDensity <IRealVectorspace <MP, RF>, MP, RF> d)
{
var gp = d.BaseStructure;
var grp = gp.BaseRealField;
var expected = d.Expected <MP, RF>();
Func <MP, RF> normFunc = mp => grp.ScalarPow(gp.Norm(gp.Subtract(expected, mp)), 2);
var squaredDistances = d.Dictionary
.Select(p => grp.Multiply(p.Value, normFunc(p.Key)))
.ToList();
var variance = grp.Sum(squaredDistances);
return(variance);
}
public static IDensity <G, M, RF> ConditionalDensity(
IDensity <G, M, RF> d,
Func <M, bool> cond,
Func <string, string> condStrFunc = null)
{
var resDict = GetConditionalDensityDictionary(d, cond);
var name = condStrFunc != null
? condStrFunc(d.Name)
: DefaultName;
var newDensity = new Density <G, M, RF>(resDict, d.BaseStructure, d.RealField, name);
return(newDensity);
}
public static IDensity <S, N, RF> BinaryOp <S, N>(
S newBaseStructure,
IDensity <G, M, RF> d1,
IDensity <G, M, RF> d2,
Func <M, M, N> op,
Func <string, string, string> binOpStrFunc = null)
where S :
IBaseStructure <N>
{
var resDensity = GetBinaryOpDictionary(d1, d2, op);
var name = binOpStrFunc == null
? DefaultName
: binOpStrFunc(d1.Name, d2.Name);
return(new Density <S, N, RF>(resDensity, newBaseStructure, d1.RealField, name));
}
public static RF BinaryProb(IDensity <G, M, RF> d1, IDensity <G, M, RF> d2, Func <M, M, bool> cond)
{
var resSum = default(RF);
var rf = d1.RealField;
foreach (var key1 in d1.GetKeys())
{
foreach (var key2 in d2.GetKeys())
{
if (cond(key1, key2))
{
resSum = rf.Add(resSum, rf.Multiply(d1[key1], d2[key2]));
}
}
}
return(resSum);
}
public static string GetOxyPlotSvg <G, M, RF>(this IDensity <G, M, RF> d, string title)
where G :
IBaseStructure <M>,
IRealEmbedding <M, RF>
where M :
struct
where RF :
struct
{
var oxyplot = d.OxyPlot(title);
var svgExporter = new SvgExporter {
Width = 600, Height = 400
};
var res = svgExporter.ExportToString(oxyplot);
return(res);
}
protected static IDictionary <N, RF> GetOpDictionary <N>(
IDensity <G, M, RF> d,
Func <M, N> op)
{
var resDensity = new Dictionary <N, RF>();
var rf = d.RealField;
foreach (var key in d.GetKeys())
{
var resKey = op(key);
if (!resDensity.ContainsKey(resKey))
{
resDensity[resKey] = default(RF);
}
resDensity[resKey] = rf.Add(resDensity[resKey], d[key]);
}
return(resDensity);
}
protected static IDictionary <M, RF> GetConditionalDensityDictionary(
IDensity <G, M, RF> d,
Func <M, bool> cond)
{
var resDict = new Dictionary <M, RF>();
var rf = d.RealField;
foreach (var key in d.GetKeys().Where(cond))
{
resDict[key] = d[key];
}
var conditionalProbability = rf.Sum(resDict.Values);
foreach (var key in resDict.Keys)
{
resDict[key] = rf.Divide(resDict[key], conditionalProbability);
}
return(resDict);
}
public int CompareTo(IDensity other)
{
if (ReferenceEquals(other, null))
{
return(1);
}
else if (this < other)
{
return(-1);
}
else if (this > other)
{
return(1);
}
else
{
return(0);
}
}
public static string Plot <G, M, RF>(this IDensity <G, M, RF> d, int plotWidth = 70)
where G :
IBaseStructure <M>
where RF :
struct
{
var rf = d.RealField;
var maxPercentage = rf.Max(d.GetValues());
var asciiPlotter = new AsciiPlotter <M, RealFieldType <RF>, RF>(new RealFieldType <RF>());
var plotStr = asciiPlotter.GetPlot(
k => d[k],
d.SortedKeys(),
plotWidth: plotWidth,
minP: rf.Zero(),
maxP: maxPercentage,
asPercentage: true);
return(plotStr);
}
public static void SaveOxyPlotPdf <G, M, RF>(this IDensity <G, M, RF> d, string filename = null)
where G :
IBaseStructure <M>,
IRealEmbedding <M, RF>
where M :
struct
where RF :
struct
{
filename = filename ?? d.GetTrimmedName() + ".pdf";
var oxyplot = d.OxyPlot(Path.GetFileName(filename));
using (var stream = File.Create(filename))
{
var pdfExporter = new PdfExporter {
Width = 600, Height = 400
};
pdfExporter.Export(oxyplot, stream);
}
}
public static IDensity <G, M, RF> ArithMult <G, M, RF>(this IDensity <G, M, RF> d, int n)
where G :
IAdditiveMonoid <M>
{
if (n < 0)
{
throw new ArgumentException();
}
if (n == 0)
{
return(new Zero <G, M, RF>(d.BaseStructure, d.RealField));
}
var newDensity = d;
foreach (var step in Enumerable.Range(1, n - 1))
{
newDensity = newDensity.Add(d);
}
newDensity.Name = $"({d.GetTrimmedName()}).ArithMult({n})";
return(newDensity);
}