/// <summary>
/// Maps the non-negative abscissas/weights from the interval [-1, 1] to the interval [intervalBegin, intervalEnd].
/// </summary>
/// <param name="intervalBegin">Where the interval starts, inclusive and finite.</param>
/// <param name="intervalEnd">Where the interval stops, inclusive and finite.</param>
/// <param name="gaussPoint">Object containing the non-negative abscissas/weights, order, and intervalBegin/intervalEnd. The non-negative abscissas/weights are generated over the interval [-1,1] for the given order.</param>
/// <returns>Object containing the abscissas/weights, order, and intervalBegin/intervalEnd.</returns>
private static GaussPoint <T> Map <T>(
T intervalBegin,
T intervalEnd,
GaussPoint gaussPoint) where T : unmanaged
{
//TODO: not sure wat this work for Complex
var la = LinearAlgebraFactory.GetLinearAlgebra <T>();
var abscissas = new T[gaussPoint.Order];
var weights = new T[gaussPoint.Order];
var num1 = la.Mult(la.Cast(0.5), la.Sub(intervalEnd, intervalBegin));
var num2 = la.Mult(la.Cast(0.5), la.Sum(intervalEnd, intervalBegin));
var num3 = gaussPoint.Order + 1 >> 1;
for (var index1 = 1; index1 <= num3; ++index1)
{
var index2 = gaussPoint.Order - index1;
var index3 = index1 - 1;
var index4 = num3 - index1;
abscissas[index2] = la.Sum(la.Mult(la.Cast(gaussPoint.Abscissas[index4]), num1), num2);
abscissas[index3] = la.Sum(la.Mult(la.Cast(gaussPoint.Abscissas[index4]), la.Mult(num1, la.Cast(-1))), num2);
weights[index2] = weights[index3] = la.Mult(la.Cast(gaussPoint.Weights[index4]), num1);
}
return(new GaussPoint <T>(gaussPoint.Order, abscissas, weights, intervalBegin, intervalEnd));
}
public static IMatrix <T> Mult <T>(this IMatrix <T> a, IMatrix <T> b) where T : unmanaged
{
//TODO: fix this check, problem with Columns for SpraseMatrix
if (a.ColumnsCount.Max() != b.RowCount)
{
throw new Exception("Cant multiplicate two matrix because ColumnsCount not Equal RowsCount");
}
var la = LinearAlgebraFactory.GetLinearAlgebra <T>();
//TODO: fix this allocation, problem with Columns for SpraseMatrix
var matrixC = new Matrix <T>(a.RowCount, b.ColumnsCount.Max());
for (var i = 0; i < a.RowCount; i++)
{
for (var k = 0; k < a.ColumnsCount[i]; k++)
{
for (var j = 0; j < b.ColumnsCount[k]; j++)
{
matrixC[i, j] = la.Sum(matrixC[i, j], la.Mult(a[i, k], b[k, j]));
}
}
}
return(matrixC);
}
public void WriteSolutionIntoConsoleMachineReadable()
{
var la = LinearAlgebraFactory.GetLinearAlgebra <long>();
if (Messages.Any())
{
Messages.ForEach(Console.WriteLine);
}
else
{
Console.WriteLine($"{CountOfFreeVariables}");
for (var i = 0; i < CountOfUnknown; ++i)
{
var stringBuilder = new StringBuilder("");
// Particular solution of the equation for i row
stringBuilder.Append($"{Matrix[i + CountOfEquation][CountOfUnknown]} ");
if (CountOfFreeVariables <= 0)
{
Console.WriteLine(stringBuilder.ToString());
continue;
}
// Free variables for i row
for (var j = 0; j < CountOfFreeVariables - 1; ++j)
{
stringBuilder.Append($"{Matrix[i + CountOfEquation][CountOfUnknown - CountOfFreeVariables + j]} ");
}
stringBuilder.Append($"{Matrix[i + CountOfEquation][CountOfUnknown - 1]} ");
Console.WriteLine(stringBuilder.ToString());
}
}
}
public static T Determinant <T>(this IMatrix <T> matrix) where T : unmanaged
{
//TODO: fix this check
if (matrix.RowCount != matrix.ColumnsCount.Max())
{
throw new Exception("matrix need to be square.");
}
if (matrix.RowCount == 1 && matrix.ColumnsCount.Max() == 1)
{
return(matrix[0, 0]);
}
var la = LinearAlgebraFactory.GetLinearAlgebra <T>();
if (matrix.RowCount == 2)
{
return(la.Sub(la.Mult(matrix[0, 0], matrix[1, 1]), la.Mult(matrix[0, 1], matrix[1, 0])));
}
T sum = la.GetZeroValue();
public void WriteSolutionIntoConsoleHumanReadable()
{
var la = LinearAlgebraFactory.GetLinearAlgebra <long>();
if (Messages.Any())
{
Messages.ForEach(Console.WriteLine);
}
else
{
Console.WriteLine($"Count of free variables : {CountOfFreeVariables}");
for (var i = 0; i < CountOfUnknown; ++i)
{
var stringBuilder = new StringBuilder($"Unknown({i})=");
// Particular solution of the equation for i row
stringBuilder.Append($"{Matrix[i + CountOfEquation][CountOfUnknown]}");
if (CountOfFreeVariables <= 0)
{
Console.WriteLine(stringBuilder.ToString());
continue;
}
// Free variables for i row
for (var j = 0; j < CountOfFreeVariables - 1; ++j)
{
stringBuilder.Append(la.Sign(Matrix[i + CountOfEquation][CountOfUnknown - CountOfFreeVariables + j]) >= 0 ? " + " : " - ");
stringBuilder.Append($"{Math.Abs(Matrix[i + CountOfEquation][CountOfUnknown - CountOfFreeVariables + j])}*Variable({j})");
}
stringBuilder.Append(la.Sign(Matrix[i + CountOfEquation][CountOfUnknown - 1]) >= 0 ? " + " : " - ");
stringBuilder.Append($"{Math.Abs(Matrix[i + CountOfEquation][CountOfUnknown - 1])}*Variable({CountOfFreeVariables})");
Console.WriteLine(stringBuilder.ToString());
}
}
}
public static IVector <T> Mult <T>(this IMatrix <T> a, IVector <T> b) where T : unmanaged
{
//TODO: fix this check, problem with Columns for SpraseMatrix
if (a.ColumnsCount.Max() != b.Count)
{
throw new Exception("Cant multiplicate matrix and vector because ColumnsCount not Equal Count");
}
var la = LinearAlgebraFactory.GetLinearAlgebra <T>();
var vector = new Vector <T>(a.RowCount);
for (var i = 0; i < a.RowCount; i++)
{
for (var j = 0; j < a.ColumnsCount[i]; j++)
{
vector[i] = la.Sum(vector[i], la.Mult(a[i, j], b[j]));
}
}
return(vector);
}
