/// <summary>Converts HSL color values to Towel.Graphics.Color values.</summary>
/// <param name="hue">The HSL hue component.</param>
/// <param name="saturation">The HSL hue saturation.</param>
/// <param name="lightness">The HSL hue lightness.</param>
/// <param name="alpha">The HSL hue alpha.</param>
/// <returns>The converted color value.</returns>
/// <citation>
/// This conversion algorithm was originally developed as part of the
/// OpenTK open source project. Hoever, it has been modified since its
/// addition to the Theta Framework.
/// </citation>
public static Color FromHsl(float hue, float saturation, float lightness, float alpha)
{
hue = hue * 360.0f;
var C = (1.0f - Compute.AbsoluteValue(2.0f * lightness - 1.0f)) * saturation;
var h = hue / 60.0f;
var X = C * (1.0f - Compute.AbsoluteValue(h % 2.0f - 1.0f));
float r, g, b;
if (0.0f <= h && h < 1.0f)
{
r = C;
g = X;
b = 0.0f;
}
else if (1.0f <= h && h < 2.0f)
{
r = X;
g = C;
b = 0.0f;
}
else if (2.0f <= h && h < 3.0f)
{
r = 0.0f;
g = C;
b = X;
}
else if (3.0f <= h && h < 4.0f)
{
r = 0.0f;
g = X;
b = C;
}
else if (4.0f <= h && h < 5.0f)
{
r = X;
g = 0.0f;
b = C;
}
else if (5.0f <= h && h < 6.0f)
{
r = C;
g = 0.0f;
b = X;
}
else
{
r = 0.0f;
g = 0.0f;
b = 0.0f;
}
var m = lightness - (C / 2.0f);
return(new Color(r + m, g + m, b + m, alpha));
}
public Integer Modulus(Integer that)
{
Integer abs = Compute <Integer> .AbsoluteValue(that);
Integer result = Compute <Integer> .AbsoluteValue(this);
while (result < that)
{
result = result - that;
}
if ((this > 0 && that < 0) || (this > 0 && that < 0))
{
return(-result);
}
else
{
return(result);
}
}
public static void TestMath()
{
#region math stuffs
Console.WriteLine("Negate: " + (Compute <int> .Negate(7) == -7));
Console.WriteLine("Add: " + (Compute <int> .Add(7, 7) == 14));
Console.WriteLine("Subtract: " + (Compute <int> .Subtract(14, 7) == 7));
Console.WriteLine("Multiply: " + (Compute <int> .Multiply(7, 7) == 49));
Console.WriteLine("Divide: " + (Compute <int> .Divide(14, 7) == 2));
Console.WriteLine("AbsoluteValue: " + (Compute <int> .AbsoluteValue(7) == 7 && Compute <int> .AbsoluteValue(-7) == 7));
Console.WriteLine("Clamp: " + (Compute <int> .Clamp(7, 6, 8) == 7));
Console.WriteLine("Maximum: " + (Compute <int> .Maximum((Step <int> step) => { step(1); step(2); step(3); }) == 3));
Console.WriteLine("Minimum: " + (Compute <int> .Minimum((Step <int> step) => { step(1); step(2); step(3); }) == 1));
Console.WriteLine("LessThan: " + (Compute <int> .LessThan(1, 2) == true && Compute <int> .LessThan(2, 1) == false));
Console.WriteLine("GreaterThan: " + (Compute <int> .GreaterThan(2, 1) == true && Compute <int> .GreaterThan(1, 2) == false));
Console.WriteLine("Compare: " + (Compute <int> .Compare(2, 1) == Comparison.Greater && Compute <int> .Compare(1, 2) == Comparison.Less && Compute <int> .Compare(1, 1) == Comparison.Equal));
Console.WriteLine("Equate: " + (Compute <int> .Equate(2, 1) == false && Compute <int> .Equate(1, 1) == true));
Console.WriteLine("EqualsLeniency: " + (Compute <int> .Equals(2, 1, 1) == true && Compute <int> .Equals(2, 1, 0) == false && Compute <int> .Equals(1, 1, 0) == true));
#endregion
}
static void Main(string[] args)
{
Random random = new Random();
int test = 10;
Console.WriteLine("You are runnning the Data Structures example.");
Console.WriteLine("======================================================");
Console.WriteLine();
#region Link (aka Tuple)
Console.WriteLine(" Link------------------------------------");
Console.WriteLine();
Console.WriteLine(" A \"Link\" is like a System.Tuple that implements");
Console.WriteLine(" Towel.DataStructures.DataStructure. A Link/Tuple is");
Console.WriteLine(" used when you have a small, known-sized set of objects");
Console.WriteLine(" that you want to bundle together without making a custom");
Console.WriteLine(" custom class.");
Console.WriteLine();
Link link = new Link <int, int, int, int, int, int>(0, 1, 2, 3, 4, 5);
Console.Write(" Traversal: ");
link.Stepper(i => Console.Write(i));
Console.WriteLine();
Console.WriteLine(" Size: " + link.Size);
Console.WriteLine();
#endregion
#region Indexed (aka Array)
Console.WriteLine(" Indexed---------------------------------");
Console.WriteLine();
Console.WriteLine(" An \"Indexed\" is just a wrapper for arrays that implements");
Console.WriteLine(" Towel.DataStructures.DataStructure. An array is used when");
Console.WriteLine(" dealing with static-sized, known-sized sets of data. Arrays");
Console.WriteLine(" can be sorted along 1 dimensions for binary searching algorithms.");
Console.WriteLine();
IIndexed <int> indexed = new IndexedArray <int>(test);
Console.Write(" Filling in (0-" + (test - 1) + ")...");
for (int i = 0; i < test; i++)
{
indexed[i] = i;
}
Console.WriteLine();
Console.Write(" Traversal: ");
indexed.Stepper(i => Console.Write(i));
Console.WriteLine();
Console.WriteLine(" Length: " + indexed.Length);
Console.WriteLine();
#endregion
#region Addable (aka List)
Console.WriteLine(" Addable---------------------------------");
Console.WriteLine();
Console.WriteLine(" An \"Addable\" is like an IList that implements");
Console.WriteLine(" Towel.DataStructures.DataStructure. \"AddableArray\" is");
Console.WriteLine(" the array implementation while \"AddableLinked\" is the");
Console.WriteLine(" the linked-list implementation. An Addable/List is used");
Console.WriteLine(" when dealing with an unknown quantity of data that you");
Console.WriteLine(" will likely have to enumerate/step through everything. The");
Console.WriteLine(" AddableArray shares the properties of an Indexed/Array in");
Console.WriteLine(" that it can be relateively quickly sorted along 1 dimensions");
Console.WriteLine(" for binary search algorithms.");
Console.WriteLine();
// AddableArray ---------------------------------------
IAddable <int> addableArray = new AddableArray <int>(test);
Console.Write(" [AddableArray] Adding (0-" + (test - 1) + ")...");
for (int i = 0; i < test; i++)
{
addableArray.Add(i);
}
Console.WriteLine();
Console.Write(" [AddableArray] Traversal: ");
addableArray.Stepper(i => Console.Write(i));
Console.WriteLine();
Console.WriteLine(" [AddableArray] Count: " + addableArray.Count);
addableArray.Clear(); // Clears the addable
Console.WriteLine();
// AddableLinked ---------------------------------------
IAddable <int> addableLinked = new AddableLinked <int>();
Console.Write(" [AddableLinked] Adding (0-" + (test - 1) + ")...");
for (int i = 0; i < test; i++)
{
addableLinked.Add(i);
}
Console.WriteLine();
Console.Write(" [AddableLinked] Traversal: ");
addableLinked.Stepper(i => Console.Write(i));
Console.WriteLine();
Console.WriteLine(" [AddableLinked] Count: " + addableLinked.Count);
addableLinked.Clear(); // Clears the addable
Console.WriteLine();
#endregion
#region FirstInLastOut (aka stack)
{
Console.WriteLine(" FirstInLastOut---------------------------------");
Console.WriteLine();
Console.WriteLine(" An \"FirstInLastOut\" is a Stack that implements");
Console.WriteLine(" Towel.DataStructures.DataStructure. \"FirstInLastOutArray\" is");
Console.WriteLine(" the array implementation while \"FirstInLastOutLinked\" is the");
Console.WriteLine(" the linked-list implementation. A FirstInLastOut/Stack is used");
Console.WriteLine(" specifically when you need the algorithm provided by the Push");
Console.WriteLine(" and Pop functions.");
Console.WriteLine();
IFirstInLastOut <int> firstInLastOutArray = new FirstInLastOutArray <int>();
Console.Write(" [FirstInLastOutArray] Pushing (0-" + (test - 1) + ")...");
for (int i = 0; i < test; i++)
{
firstInLastOutArray.Push(i);
}
Console.WriteLine();
Console.Write(" [FirstInLastOutArray] Traversal: ");
firstInLastOutArray.Stepper(i => Console.Write(i));
Console.WriteLine();
Console.WriteLine(" [FirstInLastOutArray] Pop: " + firstInLastOutArray.Pop());
Console.WriteLine(" [FirstInLastOutArray] Pop: " + firstInLastOutArray.Pop());
Console.WriteLine(" [FirstInLastOutArray] Peek: " + firstInLastOutArray.Peek());
Console.WriteLine(" [FirstInLastOutArray] Pop: " + firstInLastOutArray.Pop());
Console.WriteLine(" [FirstInLastOutArray] Count: " + firstInLastOutArray.Count);
firstInLastOutArray.Clear(); // Clears the firstInLastOut
Console.WriteLine();
IFirstInLastOut <int> firstInLastOutLinked = new FirstInLastOutLinked <int>();
Console.Write(" [FirstInLastOutLinked] Pushing (0-" + (test - 1) + ")...");
for (int i = 0; i < test; i++)
{
firstInLastOutLinked.Push(i);
}
Console.WriteLine();
Console.Write(" [FirstInLastOutLinked] Traversal: ");
firstInLastOutLinked.Stepper(i => Console.Write(i));
Console.WriteLine();
Console.WriteLine(" [FirstInLastOutLinked] Pop: " + firstInLastOutLinked.Pop());
Console.WriteLine(" [FirstInLastOutLinked] Pop: " + firstInLastOutLinked.Pop());
Console.WriteLine(" [FirstInLastOutLinked] Peek: " + firstInLastOutLinked.Peek());
Console.WriteLine(" [FirstInLastOutLinked] Pop: " + firstInLastOutLinked.Pop());
Console.WriteLine(" [FirstInLastOutLinked] Count: " + firstInLastOutLinked.Count);
firstInLastOutLinked.Clear(); // Clears the firstInLastOut
Console.WriteLine();
}
#endregion
#region FirstInFirstOut (aka Queue)
{
Console.WriteLine(" FirstInFirstOut---------------------------------");
Console.WriteLine();
Console.WriteLine(" An \"FirstInFirstOut\" is a Queue that implements");
Console.WriteLine(" Towel.DataStructures.DataStructure. \"FirstInFirstOutArray\" is");
Console.WriteLine(" the array implementation while \"FirstInFirstOutLinked\" is the");
Console.WriteLine(" the linked-list implementation. A FirstInFirstOut/Stack is used");
Console.WriteLine(" specifically when you need the algorithm provided by the Queue");
Console.WriteLine(" and Dequeue functions.");
Console.WriteLine();
IFirstInFirstOut <int> firstInFirstOutArray = new FirstInFirstOutArray <int>();
Console.Write(" [FirstInFirstOutArray] Enqueuing (0-" + (test - 1) + ")...");
for (int i = 0; i < test; i++)
{
firstInFirstOutArray.Enqueue(i);
}
Console.WriteLine();
Console.Write(" [FirstInFirstOutArray] Traversal: ");
firstInFirstOutArray.Stepper(i => Console.Write(i));
Console.WriteLine();
Console.WriteLine(" [FirstInFirstOutArray] Dequeue: " + firstInFirstOutArray.Dequeue());
Console.WriteLine(" [FirstInFirstOutArray] Dequeue: " + firstInFirstOutArray.Dequeue());
Console.WriteLine(" [FirstInFirstOutArray] Peek: " + firstInFirstOutArray.Peek());
Console.WriteLine(" [FirstInFirstOutArray] Dequeue: " + firstInFirstOutArray.Dequeue());
Console.WriteLine(" [FirstInFirstOutArray] Count: " + firstInFirstOutArray.Count);
firstInFirstOutArray.Clear(); // Clears the firstInLastOut
Console.WriteLine();
IFirstInFirstOut <int> firstInFirstOutLinked = new FirstInFirstOutLinked <int>();
Console.Write(" [FirstInFirstOutLinked] Enqueuing (0-" + (test - 1) + ")...");
for (int i = 0; i < test; i++)
{
firstInFirstOutLinked.Enqueue(i);
}
Console.WriteLine();
Console.Write(" [FirstInFirstOutLinked] Traversal: ");
firstInFirstOutLinked.Stepper(i => Console.Write(i));
Console.WriteLine();
Console.WriteLine(" [FirstInFirstOutLinked] Pop: " + firstInFirstOutLinked.Dequeue());
Console.WriteLine(" [FirstInFirstOutLinked] Pop: " + firstInFirstOutLinked.Dequeue());
Console.WriteLine(" [FirstInFirstOutLinked] Peek: " + firstInFirstOutLinked.Peek());
Console.WriteLine(" [FirstInFirstOutLinked] Pop: " + firstInFirstOutLinked.Dequeue());
Console.WriteLine(" [FirstInFirstOutLinked] Count: " + firstInFirstOutLinked.Count);
firstInFirstOutLinked.Clear(); // Clears the firstInLastOut
Console.WriteLine();
}
#endregion
#region Heap
{
Console.WriteLine(" Heap---------------------------------");
Console.WriteLine();
Console.WriteLine(" An \"Heap\" is a binary tree that stores items based on priorities.");
Console.WriteLine(" It implements Towel.DataStructures.DataStructure like the others.");
Console.WriteLine(" It uses sifting algorithms to move nodes vertically through itself.");
Console.WriteLine(" It is often the best data structure for standard priority queues.");
Console.WriteLine(" \"HeapArray\" is an implementation where the tree has been flattened");
Console.WriteLine(" into an array.");
Console.WriteLine();
Console.WriteLine(" Let's say the priority is how close a number is to \"5\".");
Console.WriteLine(" So \"Dequeue\" will give us the next closest value to \"5\".");
Comparison Priority(int a, int b)
{
int _a = Compute.AbsoluteValue(a - 5);
int _b = Compute.AbsoluteValue(b - 5);
Comparison comparison = Compare.Wrap(_b.CompareTo(_a));
return(comparison);
}
Console.WriteLine();
IHeap <int> heapArray = new HeapArray <int>(Priority);
Console.Write(" [HeapArray] Enqueuing (0-" + (test - 1) + ")...");
for (int i = 0; i < test; i++)
{
heapArray.Enqueue(i);
}
Console.WriteLine();
Console.WriteLine(" [HeapArray] Dequeue: " + heapArray.Dequeue());
Console.WriteLine(" [HeapArray] Dequeue: " + heapArray.Dequeue());
Console.WriteLine(" [HeapArray] Peek: " + heapArray.Peek());
Console.WriteLine(" [HeapArray] Dequeue: " + heapArray.Dequeue());
Console.WriteLine(" [HeapArray] Count: " + heapArray.Count);
heapArray.Clear(); // Clears the heapArray
Console.WriteLine();
}
#endregion
#region Tree
//Console.WriteLine(" Tree-----------------------------");
//Tree<int> tree_Map = new TreeMap<int>(0, Compute.Equal, Hash.Default);
//for (int i = 1; i < test; i++)
//{
// tree_Map.Add(i, i / Compute.SquareRoot(i));
//}
//Console.Write(" Children of 0 (root): ");
//tree_Map.Children(0, (int i) => { Console.Write(i + " "); });
//Console.WriteLine();
//Console.Write(" Children of " + ((int)System.Math.Sqrt(test) - 1) + " (root): ");
//tree_Map.Children(((int)System.Math.Sqrt(test) - 1), (int i) => { Console.Write(i + " "); });
//Console.WriteLine();
//Console.Write(" Traversal: ");
//tree_Map.Stepper((int i) => { Console.Write(i + " "); });
//Console.WriteLine();
//Console.WriteLine();
#endregion
#region AVL Tree
{
Console.WriteLine(" AvlTree------------------------------------------------");
Console.WriteLine();
Console.WriteLine(" An AVL Tree is a sorted binary tree.");
Console.WriteLine(" It implements Towel.DataStructures.DataStructure like the others.");
Console.WriteLine(" It allows for very fast 1D ranged queries/traversals.");
Console.WriteLine(" It is very similar to an Red Black tree, but uses a different sorting algorithm.");
Console.WriteLine();
IAvlTree <int> avlTree = new AvlTreeLinked <int>();
Console.Write(" Adding (0-" + (test - 1) + ")...");
for (int i = 0; i < test; i++)
{
avlTree.Add(i);
}
Console.WriteLine();
Console.Write(" Traversal: ");
avlTree.Stepper(i => Console.Write(i));
Console.WriteLine();
//// Note: Because the nodes in AVL Tree linked do not have
//// a parent pointer, the IEnumerable "foreach" iteration
//// is extremely slow and should be avoided. It requires
//// a stack for it's iteration.
//
//Console.Write(" Traversal Foreach: ");
//foreach (int i in avlTree)
//{
// Console.Write(i);
//}
//Console.WriteLine();
int minimum = random.Next(1, test / 2);
int maximum = random.Next(1, test / 2) + test / 2;
Console.Write(" Ranged Traversal [" + minimum + "-" + maximum + "]: ");
avlTree.Stepper(i => Console.Write(i), minimum, maximum);
Console.WriteLine();
int removal = random.Next(0, test);
Console.Write(" Remove(" + removal + "): ");
avlTree.Remove(removal);
avlTree.Stepper(i => Console.Write(i));
Console.WriteLine();
int contains = random.Next(0, test);
Console.WriteLine(" Contains(" + contains + "): " + avlTree.Contains(contains));
Console.WriteLine(" Current Least: " + avlTree.CurrentLeast);
Console.WriteLine(" Current Greatest: " + avlTree.CurrentGreatest);
Console.WriteLine(" Count: " + avlTree.Count);
avlTree.Clear(); // Clears the AVL tree
Console.WriteLine();
}
#endregion
#region Red-Black Tree
{
Console.WriteLine(" Red-Black Tree------------------------------------------------");
Console.WriteLine();
Console.WriteLine(" An Red-Black Tree is a sorted binary tree.");
Console.WriteLine(" It implements Towel.DataStructures.DataStructure like the others.");
Console.WriteLine(" It allows for very fast 1D ranged queries/traversals.");
Console.WriteLine(" It is very similar to an AVL tree, but uses a different sorting algorithm.");
Console.WriteLine();
IRedBlackTree <int> redBlackTree = new RedBlackTreeLinked <int>();
Console.Write(" Adding (0-" + (test - 1) + ")...");
for (int i = 0; i < test; i++)
{
redBlackTree.Add(i);
}
Console.WriteLine();
Console.Write(" Traversal: ");
redBlackTree.Stepper(i => Console.Write(i));
Console.WriteLine();
int minimum = random.Next(1, test / 2);
int maximum = random.Next(1, test / 2) + test / 2;
Console.Write(" Ranged Traversal [" + minimum + "-" + maximum + "]: ");
redBlackTree.Stepper(i => Console.Write(i), minimum, maximum);
Console.WriteLine();
int removal = random.Next(0, test);
Console.Write(" Remove(" + removal + "): ");
redBlackTree.Remove(removal);
redBlackTree.Stepper(i => Console.Write(i));
Console.WriteLine();
int contains = random.Next(0, test);
Console.WriteLine(" Contains(" + contains + "): " + redBlackTree.Contains(contains));
Console.WriteLine(" Current Least: " + redBlackTree.CurrentLeast);
Console.WriteLine(" Current Greatest: " + redBlackTree.CurrentGreatest);
Console.WriteLine(" Count: " + redBlackTree.Count);
redBlackTree.Clear(); // Clears the Red Black tree
Console.WriteLine();
}
#endregion
#region BTree
{
Console.WriteLine(" B Tree------------------------------------------------");
Console.WriteLine();
Console.WriteLine(" A B Tree is a sorted binary tree that allows multiple values to");
Console.WriteLine(" be stored per node. This makes it sort of a hybrid between a");
Console.WriteLine(" binary tree and an array. Because multiple values are stored ");
Console.WriteLine(" per node, it means less nodes must be traversed to completely");
Console.WriteLine(" traverse the values in the B tree.");
Console.WriteLine();
Console.WriteLine(" The generic B Tree in Towel is still in development.");
Console.WriteLine();
}
#endregion
#region Set
{
Console.WriteLine(" Set------------------------------------------------");
Console.WriteLine();
Console.WriteLine(" A Set is like an Addable/List, but it does not allow duplicates. Sets are");
Console.WriteLine(" usually implemented using hash codes. Implementations with hash codes");
Console.WriteLine(" usually have very fast \"Contains\" checks to see if a value has already");
Console.WriteLine(" been added to the set.");
Console.WriteLine();
ISet <int> setHashLinked = new SetHashLinked <int>();
Console.Write(" Adding (0-" + (test - 1) + ")...");
for (int i = 0; i < test; i++)
{
setHashLinked.Add(i);
}
Console.WriteLine();
Console.Write(" Traversal: ");
setHashLinked.Stepper(i => Console.Write(i));
Console.WriteLine();
int a = random.Next(0, test);
setHashLinked.Remove(a);
Console.Write(" Remove(" + a + "): ");
setHashLinked.Stepper(i => Console.Write(i));
Console.WriteLine();
int b = random.Next(0, test);
Console.WriteLine(" Contains(" + b + "): " + setHashLinked.Contains(b));
Console.WriteLine(" Count: " + setHashLinked.Count);
Console.WriteLine();
}
#endregion
#region Map (aka Dictionary)
{
Console.WriteLine(" Map------------------------------------------------");
Console.WriteLine();
Console.WriteLine(" A Map (aka Dictionary) is similar to a Set, but it stores two values (a ");
Console.WriteLine(" key and a value). Maps do not allow duplicate keys much like Sets don't");
Console.WriteLine(" allow duplicate values. When provided with the key, the Map uses that key");
Console.WriteLine(" to look up the value that it is associated with. Thus, it allows you to ");
Console.WriteLine(" \"map\" one object to another. As with Sets, Maps are usually implemented");
Console.WriteLine(" using hash codes.");
Console.WriteLine();
// Note: the first generic is the value, the second is the key
IMap <string, int> mapHashLinked = new MapHashLinked <string, int>();
Console.WriteLine(" Let's map each int to its word representation (ex 1 -> One).");
Console.Write(" Adding (0-" + (test - 1) + ")...");
for (int i = 0; i < test; i++)
{
mapHashLinked.Add(i, ((decimal)i).ToEnglishWords());
}
Console.WriteLine();
Console.WriteLine(" Traversal: ");
mapHashLinked.Keys(i => Console.WriteLine(" " + i + "->" + mapHashLinked[i]));
Console.WriteLine();
int a = random.Next(0, test);
mapHashLinked.Remove(a);
Console.Write(" Remove(" + a + "): ");
mapHashLinked.Keys(i => Console.Write(i));
Console.WriteLine();
int b = random.Next(0, test);
Console.WriteLine(" Contains(" + b + "): " + mapHashLinked.Contains(b));
Console.WriteLine(" Count: " + mapHashLinked.Count);
Console.WriteLine();
}
#endregion
#region OmnitreePoints
{
Console.WriteLine(" OmnitreePoints--------------------------------------");
Console.WriteLine();
Console.WriteLine(" An Omnitree is an ND SPT that allows for");
Console.WriteLine(" multidimensional sorting. Any time you need to look");
Console.WriteLine(" items up based on multiple fields/properties, then");
Console.WriteLine(" you might want to use an Omnitree. If you need to");
Console.WriteLine(" perform ranged queries on multiple dimensions, then");
Console.WriteLine(" the Omnitree is the data structure for you.");
Console.WriteLine();
Console.WriteLine(" The \"OmnitreePoints\" stores individual points (vectors),");
Console.WriteLine(" and the \"OmnitreeBounds\" stores bounded objects (spaces).");
Console.WriteLine();
IOmnitreePoints <int, double, string, decimal> omnitree =
new OmnitreePointsLinked <int, double, string, decimal>(
// This is a location delegate. (how to locate the item along each dimension)
(int index, out double a, out string b, out decimal c) =>
{
a = index;
b = index.ToString();
c = index;
});
Console.Write(" Adding (0-" + (test - 1) + ")...");
for (int i = 0; i < test; i++)
{
omnitree.Add(i);
}
Console.WriteLine();
Console.Write(" Traversal: ");
omnitree.Stepper(i => Console.Write(i));
Console.WriteLine();
int minimumXZ = random.Next(1, test / 2);
int maximumXZ = random.Next(1, test / 2) + test / 2;
string minimumY = minimumXZ.ToString();
string maximumY = maximumXZ.ToString();
Console.Write(" Spacial Traversal [" +
"(" + minimumXZ + ", \"" + minimumY + "\", " + minimumXZ + ")->" +
"(" + maximumXZ + ", \"" + maximumY + "\", " + maximumXZ + ")]: ");
omnitree.Stepper(i => Console.Write(i),
minimumXZ, maximumXZ,
minimumY, maximumY,
minimumXZ, maximumXZ);
Console.WriteLine();
// Note: this "look up" is just a very narrow spacial query that (since we know the data)
// wil only give us one result.
int lookUp = random.Next(0, test);
string lookUpToString = lookUp.ToString();
Console.Write(" Look Up (" + lookUp + ", \"" + lookUpToString + "\", " + lookUp + "): ");
omnitree.Stepper(i => Console.Write(i),
lookUp, lookUp,
lookUp.ToString(), lookUp.ToString(),
lookUp, lookUp);
Console.WriteLine();
// Ignoring dimensions on traversals example.
// If you want to ignore a column on a traversal, you can do so like this:
omnitree.Stepper(i => { /*Do Nothing*/ },
lookUp, lookUp,
Omnitree.Bound <string> .None, Omnitree.Bound <string> .None,
Omnitree.Bound <decimal> .None, Omnitree.Bound <decimal> .None);
Console.Write(" Counting Items In a Space [" +
"(" + minimumXZ + ", \"" + minimumY + "\", " + minimumXZ + ")->" +
"(" + maximumXZ + ", \"" + maximumY + "\", " + maximumXZ + ")]: ");
omnitree.CountSubSpace(
minimumXZ, maximumXZ,
minimumY, maximumY,
minimumXZ, maximumXZ);
Console.WriteLine();
int removalMinimum = random.Next(1, test / 2);
int removalMaximum = random.Next(1, test / 2) + test / 2;
string removalMinimumY = removalMinimum.ToString();
string removalMaximumY = removalMaximum.ToString();
Console.Write(" Remove (" + removalMinimum + "-" + removalMaximum + "): ");
omnitree.Remove(
removalMinimum, removalMaximum,
removalMinimumY, removalMaximumY,
removalMinimum, removalMaximum);
omnitree.Stepper(i => Console.Write(i));
Console.WriteLine();
Console.WriteLine(" Dimensions: " + omnitree.Dimensions);
Console.WriteLine(" Count: " + omnitree.Count);
omnitree.Clear(); // Clears the Omnitree
Console.WriteLine();
}
#endregion
#region OmnitreeBounds
{
Console.WriteLine(" OmnitreeBounds--------------------------------------");
Console.WriteLine();
Console.WriteLine(" An Omnitree is an ND SPT that allows for");
Console.WriteLine(" multidimensional sorting. Any time you need to look");
Console.WriteLine(" items up based on multiple fields/properties, then");
Console.WriteLine(" you might want to use an Omnitree. If you need to");
Console.WriteLine(" perform ranged queries on multiple dimensions, then");
Console.WriteLine(" the Omnitree is the data structure for you.");
Console.WriteLine();
Console.WriteLine(" The \"OmnitreePoints\" stores individual points (vectors),");
Console.WriteLine(" and the \"OmnitreeBounds\" stores bounded objects (spaces).");
Console.WriteLine();
IOmnitreeBounds <int, double, string, decimal> omnitree =
new OmnitreeBoundsLinked <int, double, string, decimal>(
// This is a location delegate. (how to locate the item along each dimension)
(int index,
out double min1, out double max1,
out string min2, out string max2,
out decimal min3, out decimal max3) =>
{
string indexToString = index.ToString();
min1 = index; max1 = index;
min2 = indexToString; max2 = indexToString;
min3 = index; max3 = index;
});
Console.Write(" Adding (0-" + (test - 1) + ")...");
for (int i = 0; i < test; i++)
{
omnitree.Add(i);
}
Console.WriteLine();
Console.Write(" Traversal: ");
omnitree.Stepper(i => Console.Write(i));
Console.WriteLine();
int minimumXZ = random.Next(1, test / 2);
int maximumXZ = random.Next(1, test / 2) + test / 2;
string minimumY = minimumXZ.ToString();
string maximumY = maximumXZ.ToString();
Console.Write(" Spacial Traversal [" +
"(" + minimumXZ + ", \"" + minimumY + "\", " + minimumXZ + ")->" +
"(" + maximumXZ + ", \"" + maximumY + "\", " + maximumXZ + ")]: ");
omnitree.StepperOverlapped(i => Console.Write(i),
minimumXZ, maximumXZ,
minimumY, maximumY,
minimumXZ, maximumXZ);
Console.WriteLine();
// Note: this "look up" is just a very narrow spacial query that (since we know the data)
// wil only give us one result.
int lookUpXZ = random.Next(0, test);
string lookUpY = lookUpXZ.ToString();
Console.Write(" Look Up (" + lookUpXZ + ", \"" + lookUpY + "\", " + lookUpXZ + "): ");
omnitree.StepperOverlapped(i => Console.Write(i),
lookUpXZ, lookUpXZ,
lookUpY, lookUpY,
lookUpXZ, lookUpXZ);
Console.WriteLine();
// Ignoring dimensions on traversals example.
// If you want to ignore a dimension on a traversal, you can do so like this:
omnitree.StepperOverlapped(i => { /*Do Nothing*/ },
lookUpXZ, lookUpXZ,
// The "None" means there is no bound, so all values are valid
Omnitree.Bound <string> .None, Omnitree.Bound <string> .None,
Omnitree.Bound <decimal> .None, Omnitree.Bound <decimal> .None);
Console.Write(" Counting Items In a Space [" +
"(" + minimumXZ + ", \"" + minimumY + "\", " + minimumXZ + ")->" +
"(" + maximumXZ + ", \"" + maximumY + "\", " + maximumXZ + ")]: " +
omnitree.CountSubSpaceOverlapped(
minimumXZ, maximumXZ,
minimumY, maximumY,
minimumXZ, maximumXZ));
Console.WriteLine();
int removalMinimumXZ = random.Next(1, test / 2);
int removalMaximumXZ = random.Next(1, test / 2) + test / 2;
string removalMinimumY = removalMinimumXZ.ToString();
string removalMaximumY = removalMaximumXZ.ToString();
Console.Write(" Remove (" + removalMinimumXZ + "-" + removalMaximumXZ + "): ");
omnitree.RemoveOverlapped(
removalMinimumXZ, removalMaximumXZ,
removalMinimumY, removalMaximumY,
removalMinimumXZ, removalMaximumXZ);
omnitree.Stepper(i => Console.Write(i));
Console.WriteLine();
Console.WriteLine(" Dimensions: " + omnitree.Dimensions);
Console.WriteLine(" Count: " + omnitree.Count);
omnitree.Clear(); // Clears the Omnitree
Console.WriteLine();
}
#endregion
#region KD Tree
{
Console.WriteLine(" KD Tree------------------------------------------------");
Console.WriteLine();
Console.WriteLine(" A KD Tree binary tree that stores points sorted along along an");
Console.WriteLine(" arbitrary number of dimensions. So it performs multidimensional");
Console.WriteLine(" sorting similar to the Omnitree (Quadtree/Octree) in Towel, but");
Console.WriteLine(" it uses a completely different algorithm and format.");
Console.WriteLine();
Console.WriteLine(" The generic KD Tree in Towel is still in development.");
Console.WriteLine();
}
#endregion
#region Graph
{
Console.WriteLine(" Graph------------------------------------------------");
Console.WriteLine();
Console.WriteLine(" A Graph is a data structure of nodes and edges. Nodes are values");
Console.WriteLine(" and edges are connections between those values. Graphs are often");
Console.WriteLine(" used to model real world data such as maps, and are often used in");
Console.WriteLine(" path finding algoritms. See the \"Algorithms\" example for path");
Console.WriteLine(" finding examples. This is just an example of how to make a graph.");
Console.WriteLine(" A \"GraphSetOmnitree\" is an implementation where nodes are stored.");
Console.WriteLine(" in a Set and edges are stored in an Omnitree (aka Quadtree).");
Console.WriteLine();
IGraph <int> graphSetOmnitree = new GraphSetOmnitree <int>();
Console.WriteLine(" Adding Nodes (0-" + (test - 1) + ")...");
for (int i = 0; i < test; i++)
{
graphSetOmnitree.Add(i);
}
int edgesPerNode = 3;
Console.WriteLine(" Adding Random Edges (0-3 per node)...");
for (int i = 0; i < test; i++)
{
// lets use a heap to randomize the edges using random priorities
IHeap <(int, int)> heap = new HeapArray <(int, int)>((x, y) => Compare.Wrap(x.Item2.CompareTo(y.Item2)));
for (int j = 0; j < test; j++)
{
if (j != i)
{
heap.Enqueue((j, random.Next()));
}
}
// dequeue some random edges from the heap and add them to the graph
int randomEdgeCount = random.Next(edgesPerNode + 1);
for (int j = 0; j < randomEdgeCount; j++)
{
graphSetOmnitree.Add(i, heap.Dequeue().Item1);
}
}
Console.Write(" Nodes (Traversal): ");
graphSetOmnitree.Stepper(i => Console.Write(i));
Console.WriteLine();
Console.WriteLine(" Edges (Traversal): ");
graphSetOmnitree.Stepper((from, to) => Console.WriteLine(" " + from + "->" + to));
Console.WriteLine();
int a = random.Next(0, test);
Console.Write(" Neighbors (" + a + "):");
graphSetOmnitree.Neighbors(a, i => Console.Write(" " + i));
Console.WriteLine();
int b = random.Next(0, test / 2);
int c = random.Next(test / 2, test);
Console.WriteLine(" Are Adjacent (" + b + ", " + c + "): " + graphSetOmnitree.Adjacent(b, c));
Console.WriteLine(" Node Count: " + graphSetOmnitree.NodeCount);
Console.WriteLine(" Edge Count: " + graphSetOmnitree.EdgeCount);
graphSetOmnitree.Clear(); // Clears the graph
Console.WriteLine();
}
#endregion
#region Trie
{
Console.WriteLine(" Trie------------------------------------------------");
Console.WriteLine();
Console.WriteLine(" A Trie is a tree where portions of the data are stored in each node");
Console.WriteLine(" such that when you traverse the tree to a leaf, you have read the contents");
Console.WriteLine(" of that leaf along the way. Because of this, a Trie allows for its values");
Console.WriteLine(" to share data, which is a form of compression. So a Trie may be used to save");
Console.WriteLine(" memory. A trie may also be a very useful tool in pattern matching, because it");
Console.WriteLine(" it allows for culling based are portions of the data.");
Console.WriteLine();
Console.WriteLine(" The generic Trie in Towel is still in development.");
Console.WriteLine();
}
#endregion
Console.WriteLine("============================================");
Console.WriteLine("Examples Complete...");
Console.ReadLine();
}
static void Main(string[] args)
{
Console.WriteLine("You are runnning the Mathematics example.");
Console.WriteLine("==========================================");
Console.WriteLine();
#region Basic Operations
Console.WriteLine(" Basics----------------------------------------------");
Console.WriteLine();
// Negation
Console.WriteLine(" Compute<int>.Negate(7): " + Compute <int> .Negate(7));
// Addition
Console.WriteLine(" Compute<double>.Add(7, 7): " + Compute <decimal> .Add(7, 7));
// Subtraction
Console.WriteLine(" Compute<float>.Subtract(14, 7): " + Compute <float> .Subtract(14, 7));
// Multiplication
Console.WriteLine(" Compute<long>.Multiply(7, 7): " + Compute <long> .Multiply(7, 7));
// Division
Console.WriteLine(" Compute<short>.Divide(14, 7): " + Compute <short> .Divide((short)14, (short)7));
// Absolute Value
Console.WriteLine(" Compute<decimal>.AbsoluteValue(-7): " + Compute <double> .AbsoluteValue(-7));
// Clamp
Console.WriteLine(" Compute<Fraction>.Clamp(-123, 7, 14): " + Compute <Fraction> .Clamp(-123, 7, 14));
// Maximum
Console.WriteLine(" Compute<byte>.Maximum(1, 2, 3): " + Compute <byte> .Maximum((Step <byte> step) => { step(1); step(2); step(3); }));
// Minimum
Console.WriteLine(" Compute<Integer>.Minimum(1, 2, 3): " + Compute <Integer> .Minimum((Step <Integer> step) => { step(1); step(2); step(3); }));
// Less Than
Console.WriteLine(" Compute<Fraction128>.LessThan(1, 2): " + Compute <Fraction128> .LessThan(1, 2));
// Greater Than
Console.WriteLine(" Compute<Fraction64>.GreaterThan(1, 2): " + Compute <Fraction64> .GreaterThan(1, 2));
// Compare
Console.WriteLine(" Compute<Fraction32>.Compare(7, 7): " + Compute <Fraction32> .Compare(7, 7));
// Equate
Console.WriteLine(" Compute<int>.Equate(7, 6): " + Compute <int> .Equate(7, 6));
// EqualsLeniency
Console.WriteLine(" Compute<int>.EqualsLeniency(2, 1, 1): " + Compute <int> .Equals(2, 1, 1));
Console.WriteLine();
#endregion
#region Number Theory
Console.WriteLine(" Number Theory--------------------------------------");
Console.WriteLine();
// Prime Checking
int prime_check = random.Next(0, 100000);
Console.WriteLine(" IsPrime(" + prime_check + "): " + Compute <int> .IsPrime(prime_check));
// GCF Checking
int[] gcf = new int[] { random.Next(0, 500) * 2, random.Next(0, 500) * 2, random.Next(0, 500) * 2 };
Console.WriteLine(" GCF(" + gcf[0] + ", " + gcf[1] + ", " + gcf[2] + "): " + Compute <int> .GreatestCommonFactor(gcf.Stepper()));
// LCM Checking
int[] lcm = new int[] { random.Next(0, 500) * 2, random.Next(0, 500) * 2, random.Next(0, 500) * 2 };
Console.WriteLine(" LCM(" + lcm[0] + ", " + lcm[1] + ", " + lcm[2] + "): " + Compute <int> .LeastCommonMultiple(lcm.Stepper()));
Console.WriteLine();
#endregion
#region Range
Console.WriteLine(" Range---------------------------------------------");
Console.WriteLine();
Console.WriteLine(" 1D int");
{
Range <int> range1 = new Range <int>(1, 7);
Console.WriteLine(" range1: " + range1);
Range <int> range2 = new Range <int>(4, 10);
Console.WriteLine(" range2: " + range2);
Range <int>[] range3 = range1 ^ range2;
Console.WriteLine(" range1 ^ range2 (Complement): " + range3[0]);
Range <int>[] range4 = range1 | range2;
Console.WriteLine(" range1 | range2 (Union): " + range4[0]);
Range <int> range5 = range1 & range2;
Console.WriteLine(" range1 & range2 (Intersection): " + range5);
}
Console.WriteLine();
#endregion
#region Angles
Console.WriteLine(" Angles--------------------------------------");
Console.WriteLine();
Angle <double> angle1 = Angle <double> .Factory_Degrees(90d);
Console.WriteLine(" angle1 = " + angle1);
Angle <double> angle2 = Angle <double> .Factory_Turns(0.5d);
Console.WriteLine(" angle2 = " + angle2);
Console.WriteLine(" angle1 + angle2 = " + (angle1 + angle2));
Console.WriteLine(" angle2 - angle1 = " + (angle1 + angle2));
Console.WriteLine(" angle1 * 2 = " + (angle1 * 2));
Console.WriteLine(" angle1 / 2 = " + (angle1 / 2));
Console.WriteLine(" angle1 > angle2 = " + (angle1 > angle2));
Console.WriteLine(" angle1 == angle2 = " + (angle1 == angle2));
Console.WriteLine(" angle1 * 2 == angle2 = " + (angle1 * 2 == angle2));
Console.WriteLine(" angle1 != angle2 = " + (angle1 != angle2));
Console.WriteLine();
// examples of non-doubles
Angle <float> angle10 = Angle <float> .Factory_Degrees(90f);
Angle <Fraction> angle11 = Angle <Fraction> .Factory_Degrees(new Fraction("90/1"));
Angle <decimal> angle12 = Angle <decimal> .Factory_Degrees(90m);
#endregion
#region Fraction
//Console.WriteLine(" Fractions-----------------------------------");
//Console.WriteLine();
//Fraction128 fraction1 = new Fraction128(2.5);
//Console.WriteLine(" fraction1 = " + fraction1);
//Fraction128 fraction2 = new Fraction128(3.75);
//Console.WriteLine(" fraction2 = " + fraction2);
//Console.WriteLine(" fraction1 + fraction2 = " + fraction1 + fraction2);
//Console.WriteLine(" fraction2 - fraction1 = " + fraction1 + fraction2);
//Console.WriteLine(" fraction1 * 2 = " + fraction1 * 2);
//Console.WriteLine(" fraction1 / 2 = " + fraction1 / 2);
//Console.WriteLine(" fraction1 > fraction2 = " + (fraction1 > fraction2));
//Console.WriteLine(" fraction1 == fraction2 = " + (fraction1 == fraction2));
//Console.WriteLine(" fraction1 * 2 == fraction2 = " + (fraction1 * 2 == fraction2));
//Console.WriteLine(" fraction1 != fraction2 = " + (fraction1 != fraction2));
//Console.WriteLine();
#endregion
#region Trigonometry
Console.WriteLine(" Trigonometry -----------------------------------------");
Console.WriteLine();
Angle <double> testingAngle = Angle <double> .Factory_Degrees(90d);
Console.WriteLine(" Sin(90degrees) = " + Compute <double> .Sine(testingAngle));
#endregion
#region Statistics
Console.WriteLine(" Statistics-----------------------------------------");
Console.WriteLine();
// Makin some random data...
double mode_temp = random.NextDouble() * 100;
double[] statistics_data = new double[]
{
random.NextDouble() * 100,
mode_temp,
random.NextDouble() * 100,
random.NextDouble() * 100,
random.NextDouble() * 100,
random.NextDouble() * 100,
mode_temp
};
// Print the data to the console...
Console.WriteLine(" data: [" +
string.Format("{0:0.00}", statistics_data[0]) + ", " +
string.Format("{0:0.00}", statistics_data[1]) + ", " +
string.Format("{0:0.00}", statistics_data[2]) + ", " +
string.Format("{0:0.00}", statistics_data[3]) + ", " +
string.Format("{0:0.00}", statistics_data[4]) + ", " +
string.Format("{0:0.00}", statistics_data[5]) + ", " +
string.Format("{0:0.00}", statistics_data[6]) + "]");
Console.WriteLine();
// Mean
Console.WriteLine(" Mean(data): " + string.Format("{0:0.00}", Compute <double> .Mean(statistics_data.Stepper())));
// Median
Console.WriteLine(" Median(data): " + string.Format("{0:0.00}", Compute <double> .Median(statistics_data.Stepper())));
// Mode
Console.WriteLine(" Mode(data): ");
Heap <Link <double, int> > modes = Compute <double> .Mode(statistics_data.Stepper());
while (modes.Count > 0)
{
Link <double, int> link = modes.Dequeue();
Console.WriteLine(" Point: " + string.Format("{0:0.00}", link._1) + " Occurences: " + link._2);
}
Console.WriteLine();
// Geometric Mean
Console.WriteLine(" Geometric Mean(data): " + string.Format("{0:0.00}", Compute <double> .GeometricMean(statistics_data.Stepper())));
// Range
Range <double> range = Compute <double> .Range(statistics_data.Stepper());
Console.WriteLine(" Range(data): " + string.Format("{0:0.00}", range.Min) + "-" + string.Format("{0:0.00}", range.Max));
// Variance
Console.WriteLine(" Variance(data): " + string.Format("{0:0.00}", Compute <double> .Variance(statistics_data.Stepper())));
// Standard Deviation
Console.WriteLine(" Standard Deviation(data): " + string.Format("{0:0.00}", Compute <double> .StandardDeviation(statistics_data.Stepper())));
// Mean Deviation
Console.WriteLine(" Mean Deviation(data): " + string.Format("{0:0.00}", Compute <double> .MeanDeviation(statistics_data.Stepper())));
Console.WriteLine();
// Quantiles
//double[] quatiles = Statistics<double>.Quantiles(4, statistics_data.Stepper());
//Console.Write(" Quartiles(data):");
//foreach (double i in quatiles)
// Console.Write(string.Format(" {0:0.00}", i));
//Console.WriteLine();
//Console.WriteLine();
#endregion
#region Algebra
Console.WriteLine(" Algebra---------------------------------------------");
Console.WriteLine();
// Prime Factorization
int prime_factors = random.Next(0, 100000);
Console.Write(" Prime Factors(" + prime_factors + "): ");
Compute <int> .FactorPrimes(prime_factors, (int i) => { Console.Write(i + " "); });
Console.WriteLine();
Console.WriteLine();
// Logarithms
int log_1 = random.Next(0, 11), log_2 = random.Next(0, 100000);
Console.WriteLine(" log_" + log_1 + "(" + log_2 + "): " + string.Format("{0:0.00}", Compute <double> .Logarithm((double)log_1, (double)log_2)));
Console.WriteLine();
// Summation
double[] summation_values = new double[]
{
random.NextDouble(),
random.NextDouble(),
random.NextDouble(),
random.NextDouble(),
};
double summation = Compute <double> .Add(summation_values.Stepper());
Console.Write(" Σ (" + string.Format("{0:0.00}", summation_values[0]));
for (int i = 1; i < summation_values.Length; i++)
{
Console.Write(", " + string.Format("{0:0.00}", summation_values[i]));
}
Console.WriteLine(") = " + string.Format("{0:0.00}", summation));
Console.WriteLine();
#endregion
#region Combinatorics
Console.WriteLine(" Combinatorics--------------------------------------");
Console.WriteLine();
// Factorials
Console.WriteLine(" 7!: " + Compute <int> .Factorial(7));
Console.WriteLine();
// Combinations
Console.WriteLine(" 7! / (3! * 4!): " + Compute <int> .Combinations(7, new int[] { 3, 4 }));
Console.WriteLine();
// Choose
Console.WriteLine(" 7 choose 2: " + Compute <int> .Choose(7, 2));
Console.WriteLine();
#endregion
#region Linear Algebra
Console.WriteLine(" Linear Algebra------------------------------------");
Console.WriteLine();
// Vector Construction
Vector <double> V = new double[]
{
random.NextDouble(),
random.NextDouble(),
random.NextDouble(),
random.NextDouble(),
};
Console.WriteLine(" Vector<double> V: ");
ConsoleWrite(V);
Console.WriteLine(" Normalize(V): ");
ConsoleWrite(V.Normalize());
// Vctor Negation
Console.WriteLine(" -V: ");
ConsoleWrite(-V);
// Vector Addition
Console.WriteLine(" V + V (aka 2V): ");
ConsoleWrite(V + V);
// Vector Multiplication
Console.WriteLine(" V * 2: ");
ConsoleWrite(V * 2);
// Vector Division
Console.WriteLine(" V / 2: ");
ConsoleWrite(V / 2);
// Vector Dot Product
Console.WriteLine(" V dot V: " + Vector <double> .DotProduct(V, V));
Console.WriteLine();
// Vector Cross Product
Vector <double> V3 = new double[]
{
random.NextDouble(),
random.NextDouble(),
random.NextDouble(),
};
Console.WriteLine(" Vector<double> V3: ");
ConsoleWrite(V3);
Console.WriteLine(" V3 cross V3: ");
ConsoleWrite(Vector <double> .CrossProduct(V3, V3));
// Matrix Construction
Matrix <double> M = (Matrix <double>) new double[, ]
{
{ random.NextDouble(), random.NextDouble(), random.NextDouble(), random.NextDouble() },
{ random.NextDouble(), random.NextDouble(), random.NextDouble(), random.NextDouble() },
{ random.NextDouble(), random.NextDouble(), random.NextDouble(), random.NextDouble() },
{ random.NextDouble(), random.NextDouble(), random.NextDouble(), random.NextDouble() },
};
Console.WriteLine(" Matrix<double>.Identity(4, 4): ");
ConsoleWrite(Matrix <double> .FactoryIdentity(4, 4));
Console.WriteLine(" Matrix<double> M: ");
ConsoleWrite(M);
// Matrix Negation
Console.WriteLine(" -M: ");
ConsoleWrite(-M);
// Matrix Addition
Console.WriteLine(" M + M (aka 2M): ");
ConsoleWrite(M + M);
// Matrix Subtraction
Console.WriteLine(" M - M: ");
ConsoleWrite(M - M);
// Matrix Multiplication
Console.WriteLine(" M * M (aka M ^ 2): ");
ConsoleWrite(M * M);
// If you have a large matrix that you want to multi-thread the multiplication,
// use the function: "LinearAlgebra.Multiply_parallel". This function will
// automatically parrallel the multiplication to the number of cores on your
// personal computer.
// Matrix Power
Console.WriteLine(" M ^ 3: ");
ConsoleWrite(M ^ 3);
// Matrix Multiplication
Console.WriteLine(" minor(M, 1, 1): ");
ConsoleWrite(M.Minor(1, 1));
// Matrix Reduced Row Echelon
Console.WriteLine(" rref(M): ");
ConsoleWrite(Matrix <double> .ReducedEchelon(M));
// Matrix Determinant
Console.WriteLine(" determinent(M): " + string.Format("{0:0.00}", Matrix <double> .Determinent(M)));
Console.WriteLine();
// Matrix-Vector Multiplication
Console.WriteLine(" M * V: ");
ConsoleWrite(M * V);
// Matrix Lower-Upper Decomposition
Matrix <double> l, u;
Matrix <double> .DecomposeLU(M, out l, out u);
Console.WriteLine(" Lower-Upper Decomposition:");
Console.WriteLine();
Console.WriteLine(" lower(M):");
ConsoleWrite(l);
Console.WriteLine(" upper(M):");
ConsoleWrite(u);
// Quaternion Construction
Quaternion <double> Q = new Quaternion <double>(
random.NextDouble(),
random.NextDouble(),
random.NextDouble(),
1.0d);
Console.WriteLine(" Quaternion<double> Q: ");
ConsoleWrite(Q);
// Quaternion Addition
Console.WriteLine(" Q + Q (aka 2Q):");
ConsoleWrite(Q + Q);
// Quaternion-Vector Rotation
Console.WriteLine(" Q * V3 * Q':");
// Note: the vector should be normalized on the 4th component
// for a proper rotation. (I did not do that)
ConsoleWrite(V3.RotateBy(Q));
#endregion
#region Convex Optimization
//Console.WriteLine(" Convex Optimization-----------------------------------");
//Console.WriteLine();
//double[,] tableau = new double[,]
//{
// { 0.0, -0.5, -3.0, -1.0, -4.0, },
// { 40.0, 1.0, 1.0, 1.0, 1.0, },
// { 10.0, -2.0, -1.0, 1.0, 1.0, },
// { 10.0, 0.0, 1.0, 0.0, -1.0, },
//};
//Console.WriteLine(" tableau (double): ");
//ConsoleWrite(tableau); Console.WriteLine();
//Vector<double> simplex_result = LinearAlgebra.Simplex(ref tableau);
//Console.WriteLine(" simplex(tableau): ");
//ConsoleWrite(tableau); Console.WriteLine();
//Console.WriteLine(" resulting maximization: ");
//ConsoleWrite(simplex_result);
#endregion
#region Symbolics
Console.WriteLine(" Symbolics---------------------------------------");
Console.WriteLine();
Expression <Func <double, double> > expression1 = (x) => 2 * (x / 7);
var syntax1 = Symbolics <double> .Parse(expression1);
Console.WriteLine(" Expression 1: " + syntax1);
Console.WriteLine(" Simplified: " + syntax1.Simplify());
Console.WriteLine(" Plugin(5): " + syntax1.Assign("x", 5).Simplify());
Expression <Func <double, double> > expression2 = (x) => 2 * x / 7;
var syntax2 = Symbolics <double> .Parse(expression2);
Console.WriteLine(" Expression 2: " + syntax2);
Console.WriteLine(" Simplified: " + syntax2.Simplify());
Console.WriteLine(" Plugin(5): " + syntax2.Assign("x", 5).Simplify());
Expression <Func <double, double> > expression3 = (x) => 2 - x + 7;
var syntax3 = Symbolics <double> .Parse(expression3);
Console.WriteLine(" Expression 3: " + syntax3);
Console.WriteLine(" Simplified: " + syntax3.Simplify());
Console.WriteLine(" Plugin(5): " + syntax3.Assign("x", 5).Simplify());
Expression <Func <double, double> > expression4 = (x) => 2 + (x - 7);
var syntax4 = Symbolics <double> .Parse(expression4);
Console.WriteLine(" Expression 4: " + syntax4);
Console.WriteLine(" Simplified: " + syntax4.Simplify());
Console.WriteLine(" Plugin(5): " + syntax4.Assign("x", 5).Simplify());
Expression <Func <double, double, double, double> > expression5 = (x, y, z) => Compute <double> .Power(x, 3) + 2 * x * y * Compute <double> .Power(z, 2) - y * z + 1;
var syntax5 = Symbolics <double> .Parse(expression5);
Console.WriteLine(" Expression 5: " + syntax5);
Console.WriteLine(" Simplified: " + syntax5.Simplify());
Console.WriteLine(" Plugin(x = 5): " + syntax5.Assign("x", 5).Simplify());
#endregion
var test = Symbolics <double> .Parse("less(5, 10)");
Console.WriteLine();
Console.WriteLine(" Parse (string) Test: " + test);
var test2 = Symbolics <double> .Parse("less(add(5, 10), 10)");
Console.WriteLine();
Console.WriteLine(" Parse (string) Test: " + test2);
Console.WriteLine(" Parse (string) Test Simplify: " + test2.Simplify());
Console.WriteLine();
Console.WriteLine("=================================================");
Console.WriteLine("Example Complete...");
Console.ReadLine();
}
