public static double PowerMethod(this Matrix <double> matrix)
{
var lambda = new DyamicList <double>(double.NaN);
Console.WriteLine(matrix);
var eigenVector = (Vector <double>)DenseVector.Create(matrix.ColumnCount, i => (i) + 3);
var index = -1;
do
{
index++;
eigenVector = matrix * eigenVector;
lambda[index] = eigenVector.HighestValue();
eigenVector /= lambda[index];
} while(lambda[index].Diff(lambda[index - 1]) > Error);
Console.WriteLine(lambda.ToString("lambda", true));
Console.WriteLine(eigenVector);
string.Format("Result: {0}", Math.Round(lambda[index], 5)).Print();
return(Math.Round(lambda[index], 5));
}
public static DyamicList <double> GaussElimination(this Matrix <double> m)
{
var equations = DenseMatrix.OfMatrix(m);
var x = new DyamicList <double>(double.NaN);
Console.WriteLine(equations);
var numZeros = 0;
for (var row = 0; row < equations.RowCount; row++)
{
for (var zeros = 0; zeros < numZeros; zeros++)
{
var topVector = equations.Row(row - (numZeros - zeros));
var currentVector = equations.Row(row);
var top = topVector.At(zeros);
var bot = currentVector.At(zeros);
var normal = bot / top;
currentVector -= topVector * normal;
equations.SetRow(row, currentVector);
}
numZeros++;
}
equations.Round();
Console.WriteLine(equations);
for (var row = equations.RowCount - 1; row >= 0; row--)
{
var rowVector = equations.Row(row);
var value = rowVector.At(rowVector.Count - 1);
for (var xNum = rowVector.Count - 2; xNum >= row; xNum--)
{
if (x[xNum].Equals(double.NaN))
{
value /= rowVector.At(xNum);
break;
}
value -= rowVector.At(xNum) * x[xNum];
}
x[row] = value;
}
Console.WriteLine("Result: ");
Console.WriteLine(x.ToString("x", true));
return(x);
}
public static DyamicList <T> Create(T[] array, T defaultReturn)
{
var list = new DyamicList <T>(defaultReturn);
for (var i = 0; i < array.Length; i++)
{
list[i] = array[i];
}
return(list);
}
public static double RombergTrapezoid(this Lookup expression, Expression low, Expression high, List <Expression> hList, bool convert = false)
{
var ts = new DyamicList <DyamicList <Expression> >();
for (var i = 0; i < hList.Count; i++)
{
ts[i] = new DyamicList <Expression>();
}
var round = 0;
Console.WriteLine("----------------------- " + round);
{
var index = 0;
foreach (var ex in hList)
{
var i = convert ? ((high - low) / ex).ToReal() : ex.ToReal();
var value = expression.RombergTrapezoidPart(low, high, (int)i).P();
("T" + index + "0: Trapezoid(n=" + i + ") = " + value.ToReal()).Print();
ts[round][index++] = value;
}
}
for (var i = 1; i < hList.Count; i++)
{
round++;
Console.WriteLine("----------------------- " + round);
for (var j = 0; j < hList.Count - round; j++)
{
var constant = Expression.Pow(4, i);
var t = ts[i - 1];
var value = (constant * t[j + 1] - t[j]) / (constant - 1);
string.Format("T{3}{4}: ({0}({1}) - {2}) / ({0} - 1) = {5}", constant.ToReal(), t[j + 1].ToReal(), t[j].ToReal(), i, j, value.ToReal()).Print();
ts[i][j] = value;
}
}
Console.WriteLine("----------------------- End");
ts[hList.Count - 1][0].ToReal().Print();
return(ts[hList.Count - 1][0].ToReal());
}
public static DyamicList <double> GaussJordanElimination(this Matrix <double> m)
{
var equations = DenseMatrix.OfMatrix(m);
Console.WriteLine(equations);
var numZeros = 0;
for (var row = 0; row < equations.RowCount; row++)
{
for (var zeros = 0; zeros < numZeros; zeros++)
{
var topVector = equations.Row(row - (numZeros - zeros));
var currentVector = equations.Row(row);
var top = topVector.At(zeros);
var bot = currentVector.At(zeros);
var normal = bot / top;
currentVector -= topVector * normal;
equations.SetRow(row, currentVector);
}
numZeros++;
}
equations.Round();
Console.WriteLine(equations);
var lastRow = equations.RowCount - 1;
var lastCol = equations.ColumnCount - 1;
for (var row = lastRow; row >= 0; row--)
{
var rowVector = equations.Row(row);
for (var xNum = lastCol - 1; xNum >= row; xNum--)
{
if (xNum == row)
{
rowVector /= rowVector.At(xNum);
continue;
}
var helperVector = equations.Row(xNum);
var normal = rowVector.At(xNum);
rowVector -= helperVector * normal;
}
equations.SetRow(row, rowVector);
}
equations.Round();
var values = equations.Column(lastCol).ToArray();
var x = DyamicList <double> .Create(values, double.NaN);
Console.WriteLine("Result: ");
Console.WriteLine(x.ToString("x", true));
return(x);
}
public static Matrix Doolittle(this Matrix a, Matrix b)
{
Console.WriteLine("a:");
Console.WriteLine(a);
Console.WriteLine("b:");
Console.WriteLine(b);
var rows = a.RowCount;
var cols = a.ColumnCount;
Matrix <double> l = DenseMatrix.Create(rows, cols, double.NaN);
l.SetUpperTriangle(0);
l.SetDiagonal(DenseVector.Create(rows, 1));
Matrix <double> u = DenseMatrix.Create(rows, cols, double.NaN);
u.SetLowerTriangle(0);
// first row is known
u.SetRow(0, a.Row(0));
for (var row = 1; row < rows; row++)
{
for (var col = 0; col < cols; col++)
{
if (double.IsNaN(l[row, col]))
{
l[row, col] = DoolittleMultiplcation(row, col, l, u, a);
}
else if (double.IsNaN(u[row, col]))
{
u[row, col] = DoolittleMultiplcation(row, col, l, u, a);
}
}
}
Console.WriteLine("l:");
Console.WriteLine(l);
Console.WriteLine("u:");
Console.WriteLine(u);
Matrix <double> y = DenseMatrix.Create(rows, 1, double.NaN);
var yValue = new DyamicList <double>(double.NaN);
for (var row = 0; row < rows; row++)
{
var value = DoolittleMultiplcation(row, 0, l, y, b);
yValue[row] = value;
y[row, 0] = value;
}
Console.WriteLine(yValue.ToString("y"));
Matrix <double> x = DenseMatrix.Create(rows, 1, double.NaN);
var xValue = new DyamicList <double>(double.NaN);
for (var row = rows - 1; row >= 0; row--)
{
var valueType = DoolittleMultiplcation(row, 0, u, x, y);
x[row, 0] = valueType;
xValue[row] = valueType;
}
Console.WriteLine(xValue.ToString("x"));
return(null);
}
public static double Muller(this Func equation, double a, double b)
{
var x = new DyamicList <double>(double.NaN);
x[0] = a;
x[1] = (a + b) / 2;
x[2] = b;
var f = new DyamicList <double>(double.NaN);
f[0] = equation.Invoke(x[0]);
f[1] = equation.Invoke(x[1]);
f[2] = equation.Invoke(x[2]);
var d = new DyamicList <double>(double.NaN);
d[0] = x[1] - x[0];
d[1] = x[2] - x[1];
var g = new DyamicList <double>(double.NaN);
g[0] = (f[1] - f[0]) / d[0];
g[1] = (f[2] - f[1]) / d[1];
var i = 0;
var h = new DyamicList <double>(double.NaN);
var c = new DyamicList <double>(double.NaN);
while (true)
{
h[i] = (g[i + 1] - g[i]) / (d[i + 1] + d[i]);
c[i] = g[i + 1] + (d[i + 1] * h[i]);
var sqr = Math.Pow(c[i], 2) - (4 * f[i + 2] * h[i]);
if (sqr < 0)
{
Console.WriteLine("Cannot converge with interval.");
return(Double.NaN);
}
d[i + 2] = (-2 * f[i + 2]) / (c[i] + (Math.Sign(c[i]) * Math.Sqrt(sqr)));
x[i + 3] = x[i + 2] + d[i + 2];
f[i + 3] = equation.Invoke(x[i + 3]);
if (Equals(f[i + 3], 0d))
{
f[i + 3] = 0.0000000000000001;
}
g[i + 2] = (f[i + 3] - f[i + 2]) / (d[i + 2]);
Console.WriteLine(x[i + 1]);
if (x[i + 1].Diff(x[i]) < Error)
{
break;
}
i++;
}
Console.WriteLine(x.ToString("x", true));
Console.WriteLine(d.ToString("d", true));
Console.WriteLine(c.ToString("c", true));
Console.WriteLine(g.ToString("g", true));
Console.WriteLine(h.ToString("h", true));
Console.WriteLine("Result: " + x[i + 1]);
return(x[i + 1]);
}
protected bool Equals(DyamicList <T> other)
{
return(Equals(Backend, other.Backend));
}
