static void Main(string[] args)
{
Console.WriteLine("You are runnning the Mathematics example.");
Console.WriteLine("==========================================");
Console.WriteLine();
#region Fraction
// Fractions need some work... commenting out for now
//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 Basic Operations
Console.WriteLine(" Basics----------------------------------------------");
Console.WriteLine();
// Variables
Fraction32 clamp_a = (Fraction32)(-123d / 9d);
Fraction32 clamp_b = (Fraction32)(7d / 12d);
Fraction32 clamp_c = (Fraction32)(14d / 15d);
double[] summation_values = new double[]
{
random.NextDouble(),
random.NextDouble(),
random.NextDouble(),
random.NextDouble(),
};
// Examples
Console.WriteLine(" Negate(7): " + Negate(7));
Console.WriteLine(" Add(7, 7): " + Add(7m, 7m));
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]));
}
// multiple parameter add overload example (most math functions have this overload)
Console.WriteLine(") = " + string.Format("{0:0.00}", Add(summation_values.ToStepper())));
Console.WriteLine(" Subtract(14, 7): " + Subtract(14f, 7f));
Console.WriteLine(" Multiply(7, 7): " + Multiply((long)7, (long)7));
Console.WriteLine(" Divide(14, 7): " + Divide((short)14, (short)7));
Console.WriteLine(" AbsoluteValue(-7): " + AbsoluteValue((double)-7));
Console.WriteLine(" Clamp(" + clamp_a + ", " + clamp_b + ", " + clamp_c + "): " + Clamp(clamp_a, clamp_b, clamp_c));
Console.WriteLine(" Maximum(1, 2, 3): " + Maximum(1, 2, 3));
Console.WriteLine(" Minimum(1, 2, 3): " + Minimum(1, 2, 3));
Console.WriteLine(" LessThan(1, 2): " + LessThan((Fraction128)1, (Fraction128)2));
Console.WriteLine(" GreaterThan(1, 2): " + GreaterThan((Fraction64)1, (Fraction64)2));
Console.WriteLine(" Compare(7, 7): " + Compare((Fraction32)7, (Fraction32)7));
Console.WriteLine(" Equate(7, 6): " + Equal(7, 6));
Console.WriteLine(" EqualsLeniency(2, 1, 1): " + EqualLeniency(2, 1, 1));
Console.WriteLine();
#endregion
#region More Numeric Mathematics
Console.WriteLine(" More Numeric Mathematics----------------------------");
Console.WriteLine();
// Variables
int prime_check = random.Next(1, 100000);
int[] gcf = new int[] { random.Next(1, 500) * 2, random.Next(1, 500) * 2, random.Next(1, 500) * 2 };
int[] lcm = new int[] { random.Next(1, 500) * 2, random.Next(1, 500) * 2, random.Next(1, 500) * 2 };
int prime_factors = random.Next(1, 100000);
int check = random.Next(1, 1000);
// Examples
Console.WriteLine(" IsPrime(" + prime_check + "): " + IsPrime(prime_check));
Console.WriteLine(" IsNegative(" + check + "): " + IsNegative(check));
Console.WriteLine(" IsNonNegative(" + check + "): " + IsNonNegative(check));
Console.WriteLine(" IsPositive(" + check + "): " + IsPositive(check));
Console.WriteLine(" IsOdd(" + check + "): " + IsOdd(check));
Console.WriteLine(" IsEven(" + check + "): " + IsEven(check));
Console.WriteLine(" GCF(" + gcf[0] + ", " + gcf[1] + ", " + gcf[2] + "): " + GreatestCommonFactor(gcf.ToStepper()));
Console.WriteLine(" LCM(" + lcm[0] + ", " + lcm[1] + ", " + lcm[2] + "): " + LeastCommonMultiple(lcm.ToStepper()));
Console.Write(" Prime Factors(" + prime_factors + "): ");
FactorPrimes(prime_factors)(i => Console.Write(i + " "));
Console.WriteLine();
Console.WriteLine(" 7!: " + Factorial(7));
Console.WriteLine(" 7! / (3! * 4!): " + Combinations(7, new int[] { 3, 4 }));
Console.WriteLine(" 7 choose 2: " + BinomialCoefficient(7, 2));
Console.WriteLine();
#endregion
#region Trigonometry
Console.WriteLine(" Trigonometry -----------------------------------------");
Console.WriteLine();
double randomDouble = random.NextDouble();
Angle <double> randomAngle = new Angle <double>(randomDouble, Angle.Units.Radians);
Console.WriteLine(" SinTaylorSeries(" + randomAngle + ") = " + SineTaylorSeries(randomAngle));
Console.WriteLine(" CosinTaylorSeries(" + randomAngle + ") = " + CosineTaylorSeries(randomAngle));
Console.WriteLine();
#endregion
#region Statistics
Console.WriteLine(" Statistics-----------------------------------------");
Console.WriteLine();
// Variables/Data
double mode_temp = random.NextDouble() * 100;
double[] statistics_data = new double[random.Next(5, 7)];
for (int i = 0; i < statistics_data.Length; i++)
{
if (i == 1 || i == statistics_data.Length - 1)
{
statistics_data[i] = mode_temp;
}
else
{
statistics_data[i] = random.NextDouble() * 100;
}
}
string stat_data_string = " data: [" + string.Format("{0:0.00}", statistics_data[0]);
for (int i = 1; i < statistics_data.Length; i++)
{
stat_data_string += ", " + string.Format("{0:0.00}", statistics_data[i]);
}
stat_data_string += "]";
Console.WriteLine(stat_data_string);
Console.WriteLine();
// Examples
Console.WriteLine(" Mean(data): " + string.Format("{0:0.00}", Mean(statistics_data.ToStepper())));
Console.WriteLine(" Median(data): " + string.Format("{0:0.00}", Median(statistics_data.ToStepper())));
// I need to fix the "Mode" function
//Console.WriteLine(" Mode(data): ");
//Heap<Link<double, int>> modes = 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();
Console.WriteLine(" Geometric Mean(data): " + string.Format("{0:0.00}", GeometricMean(statistics_data.ToStepper())));
Range(out double min, out double max, statistics_data.ToStepper());
Console.WriteLine(" Range(data): " + string.Format("{0:0.00}", min) + "-" + string.Format("{0:0.00}", max));
Console.WriteLine(" Variance(data): " + string.Format("{0:0.00}", Variance(statistics_data.ToStepper())));
Console.WriteLine(" Standard Deviation(data): " + string.Format("{0:0.00}", StandardDeviation(statistics_data.ToStepper())));
Console.WriteLine(" Mean Deviation(data): " + string.Format("{0:0.00}", MeanDeviation(statistics_data.ToStepper())));
double[] quatiles = Quantiles(4, statistics_data.ToStepper());
Console.Write(" Quartiles(data):");
foreach (double i in quatiles)
{
Console.Write(string.Format(" {0:0.00}", i));
}
Console.WriteLine();
Console.WriteLine();
#endregion
#region Linear Algebra
Console.WriteLine(" Linear Algebra------------------------------------");
Console.WriteLine();
// Vector Construction
Vector <double> V = new Vector <double>(4, i => 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 Vector <double>(3, i => 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 = new Matrix <double>(4, 4, (row, column) => 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);
// 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(" ref(M): ");
ConsoleWrite(Matrix <double> .Echelon(M));
// 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 = null, u = null;
//Matrix<double>.DecomposeLowerUpper(M, ref l, ref u); // this method is probably bugged... working on it
//Console.WriteLine(" Lower-Upper Decomposition:");
//Console.WriteLine();
//Console.WriteLine(" lower(M):");
//ConsoleWrite(l);
//Console.WriteLine(" upper(M):");
//ConsoleWrite(u);
// Matrix Inverse
Matrix <double> inverse = M.Inverse();
Console.WriteLine(" Inverse(M):");
ConsoleWrite(inverse);
// 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) => 2d * (x / 7d);
var symbolicExpression1 = Symbolics.Parse(expression1);
Console.WriteLine(" Expression 1: " + symbolicExpression1);
Console.WriteLine(" Simplified: " + symbolicExpression1.Simplify());
Console.WriteLine(" Plugin(5): " + symbolicExpression1.Substitute("x", 5d).Simplify());
Expression <Func <double, double> > expression2 = (x) => 2d * x / 7d;
var symbolicExpression2 = Symbolics.Parse(expression2);
Console.WriteLine(" Expression 2: " + symbolicExpression2);
Console.WriteLine(" Simplified: " + symbolicExpression2.Simplify());
Console.WriteLine(" Plugin(5): " + symbolicExpression2.Substitute("x", 5d).Simplify());
Expression <Func <double, double> > expression3 = (x) => 2d - x + 7d;
var symbolicExpression3 = Symbolics.Parse(expression3);
Console.WriteLine(" Expression 3: " + symbolicExpression3);
Console.WriteLine(" Simplified: " + symbolicExpression3.Simplify());
Console.WriteLine(" Plugin(5): " + symbolicExpression3.Substitute("x", 5d).Simplify());
Expression <Func <double, double> > expression4 = (x) => 2d + (x - 7d);
var symbolicExpression4 = Symbolics.Parse(expression4);
Console.WriteLine(" Expression 4: " + symbolicExpression4);
Console.WriteLine(" Simplified: " + symbolicExpression4.Simplify());
Console.WriteLine(" Plugin(5): " + symbolicExpression4.Substitute("x", 5d).Simplify());
//Expression<Func<double, double, double, double>> expression5 = (x, y, z) => Power(x, 3d) + 2d * x * y * Power(z, 2d) - y * z + 1d;
//var symbolicExpression5 = Symbolics.Parse(expression5);
//Console.WriteLine(" Expression 5: " + symbolicExpression5);
//Console.WriteLine(" Simplified: " + symbolicExpression5.Simplify());
//Console.WriteLine(" Plugin(x = 5): " + symbolicExpression5.Substitute("x", 5d).Simplify());
var symbolicExpression6 = Symbolics.Parse <double>("2 * (7 / [x])", double.TryParse);
Console.WriteLine(" Expression 6: " + symbolicExpression6);
Console.WriteLine(" Simplified: " + symbolicExpression6.Simplify());
Symbolics.Expression symbolicExpression6Simplified = symbolicExpression6.Substitute("x", 9d).Simplify();
Console.WriteLine(" Plugin(x = 9): " + symbolicExpression6Simplified);
var symbolicExpression7 = Symbolics.Parse <double>("10 + 8 * (7 / [x]) + 7 ^ 2", double.TryParse);
Console.WriteLine(" Expression 7: " + symbolicExpression7);
Console.WriteLine(" Simplified: " + symbolicExpression7.Simplify());
Console.WriteLine(" Plugin(x = 11): " + symbolicExpression7.Substitute("x", 11d).Simplify());
Console.WriteLine();
#endregion
Console.WriteLine();
Console.WriteLine("=================================================");
Console.WriteLine("Example Complete...");
Console.ReadLine();
}
static void Main()
{
Console.WriteLine("You are runnning the Mathematics example.");
Console.WriteLine("==========================================");
Console.WriteLine();
#region Basic Operations
Console.WriteLine(" Basics----------------------------------------------");
Console.WriteLine();
// Variables
Fraction <short> clampA = new Fraction <short>(-123, 9); // -123 / 9
Fraction <short> clampB = new Fraction <short>(7, 12); // 7 / 12
Fraction <short> clampC = new Fraction <short>(14, 15); // 14 / 15
double[] values = new double[4];
Stepper <double> valueStepper = values.ToStepper();
values.Format(x => random.NextDouble());
// Examples
double negation = Negation(7);
Console.WriteLine(" Negate(7): " + negation);
decimal addition = Addition(7m, 7m);
Console.WriteLine(" Add(7, 7): " + addition);
double summation = Σ(valueStepper);
Console.WriteLine(" Σ (" + string.Join(", ", values.Select(x => Format(x))) + ") = " + summation);
float subtraction = Subtraction(14f, 7f);
Console.WriteLine(" Subtract(14, 7): " + subtraction);
long multiplication = Multiplication(7L, 7L);
Console.WriteLine(" Multiply(7, 7): " + multiplication);
double product = Π(valueStepper);
Console.WriteLine(" Π (" + string.Join(", ", values.Select(x => Format(x))) + ") = " + product);
short division = Division((short)14, (short)7);
Console.WriteLine(" Divide(14, 7): " + division);
double absoluteValue = AbsoluteValue(-7d);
Console.WriteLine(" AbsoluteValue(-7): " + absoluteValue);
Fraction <short> clamp = Clamp(clampA, clampB, clampC);
Console.WriteLine(" Clamp(" + clampA + ", " + clampB + ", " + clampC + "): " + clamp);
int maximum = Maximum(1, 2, 3);
Console.WriteLine(" Maximum(1, 2, 3): " + maximum);
int minimum = Minimum(1, 2, 3);
Console.WriteLine(" Minimum(1, 2, 3): " + minimum);
bool lessThan = LessThan((Fraction <int>) 1, (Fraction <int>) 2);
Console.WriteLine(" LessThan(1, 2): " + lessThan);
bool greaterThan = GreaterThan((Fraction <int>) 1, (Fraction <int>) 2);
Console.WriteLine(" GreaterThan(1, 2): " + greaterThan);
CompareResult compare = Comparison((Fraction <short>) 7, (Fraction <short>) 7);
Console.WriteLine(" Compare(7, 7): " + compare);
bool equality = Equality(7, 6);
Console.WriteLine(" Equate(7, 6): " + equality);
bool equalsLeniency = EqualityLeniency(2, 1, 1);
Console.WriteLine(" EqualsLeniency(2, 1, 1): " + equalsLeniency);
Console.WriteLine();
#endregion
#region More Numeric Mathematics
Console.WriteLine(" More Numeric Mathematics----------------------------");
Console.WriteLine();
// some random ints for the examples
int random1 = random.Next(1, 100000);
int random2 = random.Next(1, 1000);
int random3 = random.Next(1, 1000);
int random4 = random.Next(1, 1000);
int random5 = random.Next(1, 1000);
int random6 = random.Next(1, 1000);
int random7 = random.Next(6, 10);
int random8 = random.Next(1, 100000);
int[] randomInts1 = new int[3];
randomInts1.Format(x => random.Next(1, 500) * 2);
Stepper <int> randomInts1Stepper = randomInts1.ToStepper();
int[] randomInts2 = new int[3];
randomInts2.Format(x => random.Next(1, 500) * 2);
Stepper <int> randomInts2Stepper = randomInts2.ToStepper();
bool isPrime = IsPrime(random1);
Console.WriteLine(" IsPrime(" + random1 + "): " + isPrime);
bool isNegative = IsNegative(random2);
Console.WriteLine(" IsNegative(" + random2 + "): " + isNegative);
bool isNonNegative = IsNonNegative(random3);
Console.WriteLine(" IsNonNegative(" + random3 + "): " + isNonNegative);
bool isPositive = IsPositive(random4);
Console.WriteLine(" IsPositive(" + random4 + "): " + isPositive);
bool isOdd = IsOdd(random5);
Console.WriteLine(" IsOdd(" + random5 + "): " + isOdd);
bool isEven = IsEven(random6);
Console.WriteLine(" IsEven(" + random6 + "): " + isEven);
int greatestCommonFactor = GreatestCommonFactor(randomInts1Stepper);
Console.WriteLine(" GCF(" + string.Join(", ", randomInts1) + "): " + greatestCommonFactor);
int leastCommonMultiple = LeastCommonMultiple(randomInts2Stepper);
Console.WriteLine(" LCM(" + string.Join(", ", randomInts2) + "): " + leastCommonMultiple);
int factorial = Factorial(random7);
Console.WriteLine(" " + random7 + "!: " + factorial);
int combinations = Combinations(7, new int[] { 3, 4 });
Console.WriteLine(" 7! / (3! * 4!): " + combinations);
int binomialCoefficient = BinomialCoefficient(7, 2);
Console.WriteLine(" 7 choose 2: " + binomialCoefficient);
Console.Write(" Prime Factors(" + random8 + "): ");
FactorPrimes(random8, prime => Console.Write(prime + " "));
Console.WriteLine();
Console.WriteLine();
#endregion
#region Trigonometry
Console.WriteLine(" Trigonometry -----------------------------------------");
Console.WriteLine();
double randomDouble = random.NextDouble();
Angle <double> randomAngle = new Angle <double>(randomDouble, Angle.Units.Radians);
double sineTaylorSeries = SineTaylorSeries(randomAngle);
Console.WriteLine(" SinTaylorSeries(" + randomAngle + ") = " + Format(sineTaylorSeries));
double cosineTaylorSeries = CosineTaylorSeries(randomAngle);
Console.WriteLine(" CosinTaylorSeries(" + randomAngle + ") = " + Format(cosineTaylorSeries));
Console.WriteLine();
#endregion
#region Statistics
Console.WriteLine(" Statistics-----------------------------------------");
Console.WriteLine();
// Data Generation
double mode_temp = random.NextDouble() * 100;
double[] dataArray = new double[random.Next(5, 7)];
dataArray.Format(x => random.NextDouble() * 100);
// Lets copy a value in the array to ensure there is at least one
// duplicate (so the "Mode" example will has something to show)
dataArray[dataArray.Length - 1] = dataArray[0];
// Print Data
Console.WriteLine(" data: [" + string.Join(", ", dataArray.Select(x => Format(x))) + "]");
Console.WriteLine();
Stepper <double> data = dataArray.ToStepper();
// Examples
double mean = Mean(data);
Console.WriteLine(" Mean(data): " + Format(mean));
double median = Median(data);
Console.WriteLine(" Median(data): " + Format(median));
//// Here is an example if you just want the values in a list
//
//IList<double> modes = new ListArray<double>();
//Mode(data, x => modes.Add(x));
//Console.WriteLine(" Mode(data): " +
// (modes.Count > 0
// ? string.Join(",", modes.Select(x => Format(x)))
// : "None"));
bool noModes = true;
Console.Write(" Mode(data): ");
Mode(data,
Step.Gaps <double>(
x => { Console.Write(Format(x)); noModes = false; },
x => Console.Write(", ")));
if (noModes)
{
Console.Write("None");
}
Console.WriteLine();
double geometricMean = GeometricMean(data);
Console.WriteLine(" Geometric Mean(data): " + Format(geometricMean));
Range(out double min, out double max, data);
Console.WriteLine(" Range(data): " + Format(min) + "-" + Format(max));
double variance = Variance(dataArray.ToStepper());
Console.WriteLine(" Variance(data): " + Format(variance));
double standardDeviation = StandardDeviation(data);
Console.WriteLine(" Standard Deviation(data): " + Format(standardDeviation));
double meanDeviation = MeanDeviation(data);
Console.WriteLine(" Mean Deviation(data): " + Format(meanDeviation));
double[] quatiles = Quantiles(4, data);
Console.Write(" Quartiles(data):");
foreach (double i in quatiles)
{
Console.Write(Format(i));
}
Console.WriteLine();
Console.WriteLine();
#endregion
#region Linear Algebra
Console.WriteLine(" Linear Algebra------------------------------------");
Console.WriteLine();
// Vector Construction
Vector <double> V = new Vector <double>(4, i => 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: " + V.DotProduct(V));
Console.WriteLine();
// Vector Cross Product
Vector <double> V3 = new Vector <double>(3, i => 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 = new Matrix <double>(4, 4, (row, column) => 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);
// 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(" ref(M): ");
ConsoleWrite(Matrix <double> .Echelon(M));
// 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 = null, u = null;
//Matrix<double>.DecomposeLowerUpper(M, ref l, ref u); // this method is probably bugged... working on it
//Console.WriteLine(" Lower-Upper Decomposition:");
//Console.WriteLine();
//Console.WriteLine(" lower(M):");
//ConsoleWrite(l);
//Console.WriteLine(" upper(M):");
//ConsoleWrite(u);
// Matrix Inverse
Matrix <double> inverse = M.Inverse();
Console.WriteLine(" Inverse(M):");
ConsoleWrite(inverse);
// 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) => 2d * (x / 7d);
var symbolicExpression1 = Symbolics.Parse(expression1);
Console.WriteLine(" Expression 1: " + symbolicExpression1);
Console.WriteLine(" Simplified: " + symbolicExpression1.Simplify());
Console.WriteLine(" Plugin(5): " + symbolicExpression1.Substitute("x", 5d).Simplify());
Expression <Func <double, double> > expression2 = (x) => 2d * x / 7d;
var symbolicExpression2 = Symbolics.Parse(expression2);
Console.WriteLine(" Expression 2: " + symbolicExpression2);
Console.WriteLine(" Simplified: " + symbolicExpression2.Simplify());
Console.WriteLine(" Plugin(5): " + symbolicExpression2.Substitute("x", 5d).Simplify());
Expression <Func <double, double> > expression3 = (x) => 2d - x + 7d;
var symbolicExpression3 = Symbolics.Parse(expression3);
Console.WriteLine(" Expression 3: " + symbolicExpression3);
Console.WriteLine(" Simplified: " + symbolicExpression3.Simplify());
Console.WriteLine(" Plugin(5): " + symbolicExpression3.Substitute("x", 5d).Simplify());
Expression <Func <double, double> > expression4 = (x) => 2d + (x - 7d);
var symbolicExpression4 = Symbolics.Parse(expression4);
Console.WriteLine(" Expression 4: " + symbolicExpression4);
Console.WriteLine(" Simplified: " + symbolicExpression4.Simplify());
Console.WriteLine(" Plugin(5): " + symbolicExpression4.Substitute("x", 5d).Simplify());
var symbolicExpression6 = Symbolics.Parse <double>("2 * (7 / [x])");
Console.WriteLine(" Expression 6: " + symbolicExpression6);
Console.WriteLine(" Simplified: " + symbolicExpression6.Simplify());
Symbolics.Expression symbolicExpression6Simplified = symbolicExpression6.Substitute("x", 9d).Simplify();
Console.WriteLine(" Plugin(x = 9): " + symbolicExpression6Simplified);
var symbolicExpression7 = Symbolics.Parse <double>("10 + 8 * (7 / [x]) + 7 ^ 2");
Console.WriteLine(" Expression 7: " + symbolicExpression7);
Console.WriteLine(" Simplified: " + symbolicExpression7.Simplify());
Console.WriteLine(" Plugin(x = 11): " + symbolicExpression7.Substitute("x", 11d).Simplify());
Console.WriteLine();
#endregion
Console.WriteLine();
Console.WriteLine("=================================================");
Console.WriteLine("Example Complete...");
Console.ReadLine();
}