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();
}