public override FNode CloneOfMe()
{
FNodeResult Dolly = new FNodeResult(this.ParentNode, this._Func);
foreach (FNode n in this._Cache)
Dolly.AddChildNode(n.CloneOfMe());
return Dolly;
}
public static FNode operator %(FNode Left, FNode Right)
{
FNodeResult t = new FNodeResult(null, new CellBinMod());
t.AddChildren(Left, Right);
return t;
}
// A * 1 or 1 * A or A / 1 or A /? 1 or A % 1 -> A
// A * -1 or -1 * A or A / -1 or A /? -1 or A % -1 -> -A
// A * 0, 0 * A, 0 / A, 0 /? A, A /? 0, 0 % A -> 0
// A / 0, A % 0 -> null
private FNode CompactMultDivMod(FNode Node)
{
if (Node.Affinity != FNodeAffinity.ResultNode)
return Node;
FNodeResult x = (Node as FNodeResult);
string name = x.InnerFunction.NameSig;
if (name != FunctionNames.OP_MUL
&& name != FunctionNames.OP_DIV
&& name != FunctionNames.OP_DIV2
&& name != FunctionNames.OP_MOD)
return Node;
// A * 1 or A / 1 or A /? 1 or A % 1 //
if (IsStaticOne(Node.Children[1]))
{
this._Tocks++;
return Node.Children[0];
}
// 1 * A //
if (IsStaticOne(Node.Children[0]) && name == FunctionNames.OP_MUL)
{
this._Tocks++;
return Node.Children[1];
}
// A * -1 or A / -1 or A /? -1 or A % -1 //
if (IsStaticMinusOne(Node.Children[1]))
{
this._Tocks++;
FNode t = new FNodeResult(Node.ParentNode, new CellUniMinus());
t.AddChildNode(Node.Children[0]);
return t;
}
// -1 * A //
if (IsStaticMinusOne(Node.Children[0]) && name == FunctionNames.OP_MUL)
{
this._Tocks++;
FNode t = new FNodeResult(Node.ParentNode, new CellUniMinus());
t.AddChildNode(Node.Children[1]);
return t;
}
// Look 0 * A, 0 / A, 0 /? A, 0 % A //
if (IsStaticZero(Node.Children[0]))
{
this._Tocks++;
return new FNodeValue(Node.ParentNode, new Cell(0.00));
}
// A * 0, A /? 0 //
if (IsStaticZero(Node.Children[1]) && (name == FunctionNames.OP_MUL || name == FunctionNames.OP_DIV2))
{
this._Tocks++;
return new FNodeValue(Node.ParentNode, new Cell(0.00));
}
// A / 0, A % 0 //
if (IsStaticZero(Node.Children[1]) && (name == FunctionNames.OP_DIV || name == FunctionNames.OP_MOD))
{
this._Tocks++;
return new FNodeValue(Node.ParentNode, Cell.NULL_DOUBLE);
}
return Node;
}
public static Predicate NotEquals(FNode Left, FNode Right)
{
FNodeResult node = new FNodeResult(null, CellFunctionFactory.LookUp("!="));
node.AddChildNode(Left);
node.AddChildNode(Right);
return new Predicate(node);
}
public static Predicate And(params FNode[] Nodes)
{
FNodeResult and = new FNodeResult(null, new AndMany());
and.AddChildren(Nodes);
return new Predicate(and);
}
public override RecordSet Initialize(DataSet Data, Predicate Where, FNodeSet Fields, int Clusters)
{
AggregateSet set = new AggregateSet();
set.Add(new AggregateSum(FNodeFactory.Value(1D)), "CLUSTER_ELEMENT_COUNT");
for (int i = 0; i < Fields.Count; i++)
{
set.Add(new AggregateAverage(Fields[i].CloneOfMe()), Fields.Alias(i));
}
FNode rnd = new FNodeResult(null, new CellRandomInt());
rnd.AddChildNode(new FNodeValue(rnd, new Cell(this.Seed)));
rnd.AddChildNode(new FNodeValue(rnd, new Cell(0)));
rnd.AddChildNode(new FNodeValue(rnd, new Cell(Clusters)));
FNodeSet keys = new FNodeSet();
keys.Add(rnd);
RecordSet rs = AggregatePlan.Render(Data, Where, keys, set);
return rs;
}
public override void Extend(RecordWriter Output, DataSet Data, FNodeSet ClusterVariables, FNodeSet OtherKeepers, Predicate Where)
{
// Check that the ClusterVariable count matches the internal node set count //
if (ClusterVariables.Count != this._fields.Count)
throw new ArgumentException("The cluster variable count passed does not match the internal cluster variable count");
// Create the selectors //
FNodeSet values = OtherKeepers.CloneOfMe();
FNode n = new FNodeResult(null, new RowClusterCellFunction(this._rule, this._means));
foreach (FNode t in ClusterVariables.Nodes)
{
n.AddChildNode(t.CloneOfMe());
}
values.Add("CLUSTER_ID", n);
// Run a fast select //
FastReadPlan plan = new FastReadPlan(Data, Where, values, Output);
}
public static FNode Multiply(FNode Left, FNode Right)
{
FNode t = new FNodeResult(Left.ParentNode, CellFunctionFactory.LookUp(FunctionNames.OP_MUL));
t.AddChildren(Left, Right);
return t;
}
// F(X) = G(X) / H(X), F'(X) = (G'(X) * H(X) - G(X) * H'(X)) / (H(X) * H(X))
private static FNode GradientOfDivide(FNode Node, FNodePointer X)
{
if (Debug) Comm.WriteLine("GRADIENT : DIVIDE");
// Need to handle the case where H is not a function of X //
if (!FNodeAnalysis.ContainsPointerRef(Node[1], X.PointerName))
{
FNode a = Gradient(Node[0], X);
return FNodeFactory.Divide(a, Node[1]);
}
// G'(X) * H(X) //
FNodeResult t = new FNodeResult(Node.ParentNode, new CellBinMult());
t.AddChildNode(Gradient(Node.Children[0], X));
t.AddChildNode(Node.Children[1]);
// G(X) * H'(X) //
FNodeResult u = new FNodeResult(Node.ParentNode, new CellBinMult());
u.AddChildNode(Node.Children[0]);
u.AddChildNode(Gradient(Node.Children[1], X));
// G'(X) * H(X) - G(X) * H'(X) //
FNodeResult v = new FNodeResult(Node.ParentNode, new CellBinMinus());
v.AddChildNode(t);
v.AddChildNode(u);
// H(X) * H(X) //
FNodeResult w = new FNodeResult(Node.ParentNode, new CellFuncFVPower());
w.AddChildNode(Node.Children[1]);
w.AddChildNode(new FNodeValue(null, new Cell(2.00)));
// Final Node //
FNodeResult x = new FNodeResult(Node.ParentNode, new CellBinDiv());
x.AddChildNode(v);
x.AddChildNode(w);
return x;
}
// F(X) = G(X) * H(X), F'(X) = G'(X) * H(X) + G(X) * H'(X)
private static FNode GradientOfMultiply(FNode Node, FNodePointer X)
{
if (Debug) Comm.WriteLine("GRADIENT : MULT");
// G'(X) * H(X) //
FNodeResult t = new FNodeResult(Node.ParentNode, new CellBinMult());
t.AddChildNode(Gradient(Node.Children[0], X));
t.AddChildNode(Node.Children[1]);
// G(X) * H'(X) //
FNodeResult u = new FNodeResult(Node.ParentNode, new CellBinMult());
u.AddChildNode(Node.Children[0]);
u.AddChildNode(Gradient(Node.Children[1], X));
// Final Node //
FNodeResult v = new FNodeResult(Node.ParentNode, new CellBinPlus());
v.AddChildNode(t);
v.AddChildNode(u);
return v;
}
// F(X) = G(X) - H(X), F'(X) = G'(X) - H'(X)
private static FNode GradientOfSubtract(FNode Node, FNodePointer X)
{
if (Debug) Comm.WriteLine("GRADIENT : SUB");
FNodeResult t = new FNodeResult(Node.ParentNode, new CellBinMinus());
t.AddChildNode(Gradient(Node.Children[0], X));
t.AddChildNode(Gradient(Node.Children[1], X));
return t;
}
// F(X) = -G(X), F'(X) = -G'(X)
private static FNode GradientOfUniMinus(FNode Node, FNodePointer X)
{
if(Debug) Comm.WriteLine("GRADIENT : UNI_MINUS");
FNodeResult t = new FNodeResult(Node.ParentNode, new CellUniMinus());
t.AddChildNode(Gradient(Node.Children[0], X));
return t;
}
// Main Join Functions //
/// <summary>
/// Allows the user to perform a join based on the equality predicate AND each predicate link via 'AND'
/// </summary>
/// <param name="Output"></param>
/// <param name="JM"></param>
/// <param name="JA"></param>
/// <param name="T1"></param>
/// <param name="J1"></param>
/// <param name="T2"></param>
/// <param name="J2"></param>
/// <param name="CM"></param>
public static void Join(MergeMethod JM, MergeAlgorithm JA, RecordWriter Output, FNodeSet Fields, Predicate Where, DataSet Data1, DataSet Data2,
Key Equality1, Key Equality2, StaticRegister Memory1, StaticRegister Memory2)
{
// Do some checks first //
if (Where == null)
Where = Predicate.TrueForAll;
if (Equality1.Count != Equality2.Count)
throw new Exception("Both join keys must have the same length");
if (Equality1.Count == 0)
JA = MergeAlgorithm.NestedLoop;
// Nested loop; if the algorithm is nested loop and we have keys, we need to build a new where clause that has the equality predicates //
FNodeResult nl_node = new FNodeResult(null, new AndMany());
nl_node.AddChildNode(Where.Node.CloneOfMe());
for (int i = 0; i < Equality1.Count; i++)
{
FNodeFieldRef left = new FNodeFieldRef(null, Equality1[i], Data1.Columns.ColumnAffinity(Equality1[i]), Data1.Columns.ColumnSize(Equality1[i]), Memory1);
FNodeFieldRef right = new FNodeFieldRef(null, Equality2[i], Data2.Columns.ColumnAffinity(Equality2[i]), Data2.Columns.ColumnSize(Equality2[i]), Memory2);
FNodeResult eq = new FNodeResult(null, new CellBoolEQ());
eq.AddChildren(left, right);
nl_node.AddChildNode(eq);
}
Predicate nl_where = (Equality1.Count == 0 ? Where : new Predicate(nl_node));
// Switch //
switch (JA)
{
case MergeAlgorithm.SortMerge:
SortMerge(JM, Output, Fields, Where, Data1, Data2, Equality1, Equality2, Memory1, Memory2);
break;
case MergeAlgorithm.NestedLoop:
NestedLoop(JM, Output, Fields, nl_where, Data1, Data2, Memory1, Memory2);
break;
default:
HashTable(JM, Output, Fields, Where, Data1, Data2, Equality1, Equality2, Memory1, Memory2);
break;
}
}
public static FNode operator ^(FNode Left, FNode Right)
{
FNodeResult t = new FNodeResult(null, new CellFuncFVPower());
t.AddChildren(Left, Right);
return t;
}
// F(X) = power(Y, G(X)), F'(X) = LOG(Y) * power(Y, G(X)) * G'(X)
private static FNode GradientOfPowerUpper(FNode Node, FNodePointer X)
{
// Throw an exception if X is decendant of Y, in otherwords F(X) = Power(G(X), H(X))
if (FNodeAnalysis.IsDecendent(X, Node.Children[1]))
throw new Exception(string.Format("Cannot differentiate the power function with the form: Power(G(X), H(X)); G(X) cannot have a relation to X"));
// LOG(Y) //
FNode log_y = new FNodeResult(null, new CellFuncFVLog());
log_y.AddChildNode(Node.Children[0]);
// Get Power(Y, G(X)) * LOG(Y) //
FNode pow_f_dx = new FNodeResult(Node.ParentNode, new CellBinMult());
pow_f_dx.AddChildNode(Node.CloneOfMe());
pow_f_dx.AddChildNode(log_y);
// Get Power(G(X), N-1) * G'(X) //
FNode t = new FNodeResult(Node.ParentNode, new CellBinMult());
t.AddChildNode(pow_f_dx);
t.AddChildNode(Gradient(Node.Children[1], X));
return t;
}
public static FNode LinkAnd(FNode Left, FNode Right)
{
FNodeResult node = new FNodeResult(null, CellFunctionFactory.LookUp("and"));
node.AddChildNode(Left);
node.AddChildNode(Right);
return node;
}
// F(X) = exp(G(X)), F'(X) = exp(G(X)) * G'(X), or simplified F(X) * G'(X)
private static FNode GradientOfExp(FNode Node, FNodePointer X)
{
// F(X) * G'(X) //
FNodeResult t = new FNodeResult(Node.ParentNode, new CellBinMult());
t.AddChildNode(Node.CloneOfMe());
t.AddChildNode(Gradient(Node.Children[0], X));
return t;
}
private bool ItterateOnce()
{
// Create the cluster mapping FNode; this node does the nearest neighbor test //
FNodeSet keys = new FNodeSet();
FNode n = new FNodeResult(null, new RowClusterCellFunction(this._rule, this._means));
foreach (FNode t in this._fields.Nodes)
{
n.AddChildNode(t.CloneOfMe());
}
keys.Add("CLUSTER_ID", n);
// Create the aggregate//
AggregateSet set = new AggregateSet();
// Add a counter to the aggregate //
set.Add(new AggregateSum(FNodeFactory.Value(1D)), "CLUSTER_ELEMENT_COUNT");
// load the aggregate with the mean aggregates //
for (int i = 0; i < this._fields.Count; i++)
{
set.Add(new AggregateAverage(this._fields[i].CloneOfMe()), this._fields.Alias(i));
}
// Load the aggregate with the variance aggregates //
for (int i = 0; i < this._fields.Count; i++)
{
set.Add(new AggregateVarianceP(this._fields[i].CloneOfMe()), "VAR_" + this._fields.Alias(i));
}
// Run the aggregate; this is basically a horse aggregate step with the cluster node mapping as the key, and averaging as the value
RecordSet rs = AggregatePlan.Render(this._data, this._where, keys, set);
// Need to chop up the recordset we just created //
Key mean_keeper = Key.Build(this._means.Columns.Count);
RecordSet means = FastReadPlan.Render(rs, Predicate.TrueForAll, mean_keeper, long.MaxValue);
Key stat_keeper = new Key(0,1); // keep the id and the count
for (int i = mean_keeper.Count; i < rs.Columns.Count; i++)
{
stat_keeper.Add(i);
}
this._stats = FastReadPlan.Render(rs, Predicate.TrueForAll, stat_keeper, long.MaxValue);
// Check for cluster misses; cluster misses occur when no node maps to a cluster correctly //
if (means.Count != this._means.Count)
{
this.HandleNullCluster(means);
}
// Compare the changes between itterations
double change = this.CompareChanges(this._means, means);
// Set the means to the newly calculated means //
this._means = means;
// Return a boolean indicating if we failed or not
return change < this._exit_condition;
}
// F(X) = log(G(X)), F'(X) = 1 / G(X) * G'(X)
private static FNode GradientOfLog(FNode Node, FNodePointer X)
{
// 1 / G(X) //
FNodeResult t = new FNodeResult(Node.ParentNode, new CellFuncFVPower());
t.AddChildNode(Node.Children[0]);
t.AddChildNode(new FNodeValue(null, new Cell(-1.00)));
// 1 / G(X) //
FNodeResult u = new FNodeResult(Node.ParentNode, new CellBinMult());
u.AddChildNode(t);
u.AddChildNode(Gradient(t.Children[0], X));
return u;
}
public override Table Extend(string Dir, string Name, DataSet Data, FNodeSet ClusterVariables, FNodeSet OtherKeepers, Predicate Where)
{
// Check that the ClusterVariable count matches the internal node set count //
if (ClusterVariables.Count != this._fields.Count)
throw new ArgumentException("The cluster variable count passed does not match the internal cluster variable count");
// Create the selectors //
FNodeSet values = OtherKeepers.CloneOfMe();
FNode n = new FNodeResult(null, new RowClusterCellFunction(this._rule, this._means));
foreach (FNode t in ClusterVariables.Nodes)
{
n.AddChildNode(t.CloneOfMe());
}
values.Add("CLUSTER_ID", n);
// Build a recordset //
Table tablix = new Table(Dir, Name, values.Columns, Data.MaxRecords);
RecordWriter w = tablix.OpenWriter();
// Run a fast select //
FastReadPlan plan = new FastReadPlan(Data, Where, values, w);
w.Close();
return tablix;
}
// F(X) = sin(G(X)), F'(X) = cos(G(X)) * G'(X)
private static FNode GradientOfSin(FNode Node, FNodePointer X)
{
// cos(G(X)) //
FNodeResult t = new FNodeResult(Node.ParentNode, new CellFuncFVCos());
t.AddChildNode(Node.Children[0]);
// 1 / G(X) //
FNodeResult u = new FNodeResult(Node.ParentNode, new CellBinMult());
u.AddChildNode(t);
u.AddChildNode(Gradient(t.Children[0], X));
return u;
}
public static Predicate IsNotNull(FNode N)
{
FNodeResult node = new FNodeResult(null, CellFunctionFactory.LookUp("isnotnull"));
node.AddChildNode(N);
return new Predicate(node);
}
// F(X) = cos(G(X)), F'(X) = -sin(G(X)) * G'(X)
private static FNode GradientOfCos(FNode Node, FNodePointer X)
{
// sin(G(X)) //
FNodeResult t = new FNodeResult(Node.ParentNode, new CellFuncFVSin());
t.AddChildNode(Node.Children[0]);
// -sin(G(X)) //
FNodeResult u = new FNodeResult(t, new CellUniMinus());
u.AddChildNode(t);
// -sin(G(X)) * G'(X) //
FNodeResult v = new FNodeResult(Node.ParentNode, new CellBinMult());
v.AddChildNode(u);
v.AddChildNode(Gradient(t.Children[0], X));
return v;
}
public static Predicate Or(params FNode[] Nodes)
{
FNodeResult or = new FNodeResult(null, new AndMany());
or.AddChildren(Nodes);
return new Predicate(or);
}
// F(X) = cosh(G(X)), F'(X) = sinh(G(X)) * G'(X)
private static FNode GradientOfCosh(FNode Node, FNodePointer X)
{
// sinh(G(X)) //
FNodeResult t = new FNodeResult(Node.ParentNode, new CellFuncFVSinh());
t.AddChildNode(Node.Children[0]);
// sinh(G(X)) * G'(X) //
FNodeResult u = new FNodeResult(Node.ParentNode, new CellBinMult());
u.AddChildNode(t);
u.AddChildNode(Gradient(Node.Children[0], X));
return u;
}
// A + 0 or 0 + A or A - 0 -> A
// 0 - A -> -A
// A + -B -> A - B
private FNode CompactAddSub(FNode Node)
{
if (Node.Affinity != FNodeAffinity.ResultNode)
return Node;
FNodeResult x = (Node as FNodeResult);
string name = x.InnerFunction.NameSig;
if (name != FunctionNames.OP_ADD && name != FunctionNames.OP_SUB)
return Node;
// Look for A + 0 or A - 0 -> A //
if (IsStaticZero(Node.Children[1]))
{
this._Tocks++;
return Node.Children[0];
}
// Look for 0 + A -> A //
if (IsStaticZero(Node.Children[0]) && name == FunctionNames.OP_ADD)
{
this._Tocks++;
return Node.Children[1];
}
// Look for 0 - A -> -A //
if (IsStaticZero(Node.Children[0]) && name == FunctionNames.OP_SUB)
{
this._Tocks++;
FNode t = new FNodeResult(Node.ParentNode, CellFunctionFactory.LookUp(FunctionNames.UNI_MINUS));
t.AddChildNode(Node.Children[1]);
return t;
}
// Look for A + -B -> A - B //
if (IsUniNegative(Node.Children[1]) && name == FunctionNames.OP_ADD)
{
this._Tocks++;
FNode t = new FNodeResult(Node.ParentNode, CellFunctionFactory.LookUp(FunctionNames.OP_SUB));
t.AddChildNode(Node.Children[0]);
t.AddChildNode(Node.Children[1].Children[0]);
return t;
}
// Look for -A + B -> B - A //
if (IsUniNegative(Node.Children[0]) && name == FunctionNames.OP_ADD)
{
this._Tocks++;
FNode t = new FNodeResult(Node.ParentNode, CellFunctionFactory.LookUp(FunctionNames.OP_SUB));
t.AddChildNode(Node.Children[1]);
t.AddChildNode(Node.Children[0].Children[0]);
return t;
}
// Look for A - -B -> A + B //
if (IsUniNegative(Node.Children[1]) && name == FunctionNames.OP_SUB)
{
this._Tocks++;
FNode t = new FNodeResult(Node.ParentNode, CellFunctionFactory.LookUp(FunctionNames.OP_ADD));
t.AddChildNode(Node.Children[0]);
t.AddChildNode(Node.Children[1].Children[0]);
return t;
}
return Node;
}
// F(X) = tanh(X), F'(X) = Power(cosh(x) , -2.00)
private static FNode GradientOfTanh(FNode Node, FNodePointer X)
{
// cosh(G(X)) //
FNodeResult t = new FNodeResult(null, new CellFuncFVCosh());
t.AddChildNode(Node.Children[0]);
// power(cosh(G(x)),2) //
FNodeResult u = new FNodeResult(t, new CellFuncFVPower());
u.AddChildNode(t);
u.AddChildNode(new FNodeValue(null, new Cell(-2.00)));
// power(cosh(G(x)),2) * G'(X) //
FNodeResult v = new FNodeResult(Node.ParentNode, new CellBinMult());
v.AddChildNode(u);
v.AddChildNode(Gradient(Node.Children[0], X));
return u;
}
// F(X) = power(G(X), N), F'(X) = power(G(X), N - 1) * G'(X) * N, or G'(X) if N == 1, N must not be a decendant of X
private static FNode GradientOfPowerLower(FNode Node, FNodePointer X)
{
// Throw an exception if X is decendant of N, in otherwords F(X) = Power(G(X), H(X))
if (FNodeAnalysis.IsDecendent(X, Node.Children[1]))
throw new Exception(string.Format("Cannot differentiate the power function with the form: Power(G(X), H(X)); H(X) cannot have a relation to X"));
// Build 'N-1' //
FNode n_minus_one = new FNodeResult(Node.ParentNode, new CellBinMinus());
n_minus_one.AddChildNode(Node.Children[1]);
n_minus_one.AddChildNode(new FNodeValue(null, new Cell(1.00)));
// Get Power(G(X), N-1) //
FNode power_gx_n_minus_one = new FNodeResult(Node.ParentNode, new CellFuncFVPower());
power_gx_n_minus_one.AddChildNode(Node.Children[0]);
power_gx_n_minus_one.AddChildNode(n_minus_one);
// Get Power(G(X), N-1) * G'(X) //
FNode t = new FNodeResult(Node.ParentNode, new CellBinMult());
t.AddChildNode(power_gx_n_minus_one);
t.AddChildNode(Gradient(Node.Children[0], X));
// Get Power(G(X), N-1) * G'(X) * N //
FNode u = new FNodeResult(Node.ParentNode, new CellBinMult());
u.AddChildNode(t);
u.AddChildNode(Node.Children[1]);
return u;
}
// Statics //
public static FNode BuildParent(FNode L, CellFunction F)
{
FNode n = new FNodeResult(null, F);
n.AddChildNode(L);
return n;
}
