Matrix-exponentiation operator: Difference between revisions
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An alternative way would be to implement <tt>operator*=</tt> and conversion from number (giving multiples of the identity matrix) for the matrix and use the generic code from [[Exponentiation operator#C++]] with support for negative exponents removed (or alternatively, implement matrix inversion as well, implement /= in terms of it, and use the generic code unchanged). Note that the algorithm used there is much faster as well.
=={{header|C sharp}}==
<lang csharp>using System;
using System.Collections;
using System.Collections.Generic;
using static System.Linq.Enumerable;
public static class MatrixExponentation
{
public static double[,] Identity(int size) {
double[,] matrix = new double[size, size];
for (int i = 0; i < size; i++) matrix[i, i] = 1;
return matrix;
}
public static double[,] Multiply(this double[,] left, double[,] right) {
if (left.ColumnCount() != right.RowCount()) throw new ArgumentException();
double[,] m = new double[left.RowCount(), right.ColumnCount()];
foreach (var (row, column) in from r in Range(0, m.RowCount()) from c in Range(0, m.ColumnCount()) select (r, c)) {
m[row, column] = Range(0, m.RowCount()).Sum(i => left[row, i] * right[i, column]);
}
return m;
}
public static double[,] Pow(this double[,] matrix, int exp) {
if (matrix.RowCount() != matrix.ColumnCount()) throw new ArgumentException("Matrix must be square.");
double[,] accumulator = Identity(matrix.RowCount());
for (int i = 0; i < exp; i++) {
accumulator = accumulator.Multiply(matrix);
}
return accumulator;
}
private static int RowCount(this double[,] matrix) => matrix.GetLength(0);
private static int ColumnCount(this double[,] matrix) => matrix.GetLength(1);
private static void Print(this double[,] m) {
foreach (var row in Rows()) {
Console.WriteLine("[ " + string.Join(" ", row) + " ]");
}
Console.WriteLine();
IEnumerable<IEnumerable<double>> Rows() =>
Range(0, m.RowCount()).Select(row => Range(0, m.ColumnCount()).Select(column => m[row, column]));
}
public static void Main() {
var matrix = new double[,] {
{ 3, 2 },
{ 2, 1 }
};
matrix.Pow(0).Print();
matrix.Pow(1).Print();
matrix.Pow(2).Print();
matrix.Pow(3).Print();
matrix.Pow(4).Print();
matrix.Pow(50).Print();
}
}</lang>
{{out}}
<pre style="height:30ex;overflow:scroll">
[ 1 0 ]
[ 0 1 ]
[ 3 2 ]
[ 2 1 ]
[ 13 8 ]
[ 8 5 ]
[ 55 34 ]
[ 34 21 ]
[ 233 144 ]
[ 144 89 ]
[ 1.61305314249046E+31 9.9692166771893E+30 ]
[ 9.9692166771893E+30 6.16131474771528E+30 ]</pre>
=={{header|Common Lisp}}==
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