September Morn Update
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Ingy döt Net
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6856 changed files with 141342 additions and 21127 deletions
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blsq ) {{1 1} {1 0}} 10 .*{mm}r[
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{{89 55} {55 34}}
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using System;
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using System.Collections;
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using System.Collections.Generic;
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using static System.Linq.Enumerable;
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public static class MatrixExponentation
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{
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public static double[,] Identity(int size) {
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double[,] matrix = new double[size, size];
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for (int i = 0; i < size; i++) matrix[i, i] = 1;
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return matrix;
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}
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public static double[,] Multiply(this double[,] left, double[,] right) {
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if (left.ColumnCount() != right.RowCount()) throw new ArgumentException();
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double[,] m = new double[left.RowCount(), right.ColumnCount()];
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foreach (var (row, column) in from r in Range(0, m.RowCount()) from c in Range(0, m.ColumnCount()) select (r, c)) {
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m[row, column] = Range(0, m.RowCount()).Sum(i => left[row, i] * right[i, column]);
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}
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return m;
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}
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public static double[,] Pow(this double[,] matrix, int exp) {
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if (matrix.RowCount() != matrix.ColumnCount()) throw new ArgumentException("Matrix must be square.");
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double[,] accumulator = Identity(matrix.RowCount());
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for (int i = 0; i < exp; i++) {
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accumulator = accumulator.Multiply(matrix);
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}
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return accumulator;
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}
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private static int RowCount(this double[,] matrix) => matrix.GetLength(0);
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private static int ColumnCount(this double[,] matrix) => matrix.GetLength(1);
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private static void Print(this double[,] m) {
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foreach (var row in Rows()) {
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Console.WriteLine("[ " + string.Join(" ", row) + " ]");
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}
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Console.WriteLine();
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IEnumerable<IEnumerable<double>> Rows() =>
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Range(0, m.RowCount()).Select(row => Range(0, m.ColumnCount()).Select(column => m[row, column]));
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}
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public static void Main() {
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var matrix = new double[,] {
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{ 3, 2 },
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{ 2, 1 }
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};
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matrix.Pow(0).Print();
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matrix.Pow(1).Print();
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matrix.Pow(2).Print();
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matrix.Pow(3).Print();
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matrix.Pow(4).Print();
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matrix.Pow(50).Print();
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}
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}
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package main
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import "fmt"
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type vector = []float64
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type matrix []vector
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func (m1 matrix) mul(m2 matrix) matrix {
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rows1, cols1 := len(m1), len(m1[0])
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rows2, cols2 := len(m2), len(m2[0])
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if cols1 != rows2 {
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panic("Matrices cannot be multiplied.")
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}
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result := make(matrix, rows1)
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for i := 0; i < rows1; i++ {
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result[i] = make(vector, cols2)
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for j := 0; j < cols2; j++ {
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for k := 0; k < rows2; k++ {
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result[i][j] += m1[i][k] * m2[k][j]
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}
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}
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}
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return result
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}
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func identityMatrix(n int) matrix {
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if n < 1 {
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panic("Size of identity matrix can't be less than 1")
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}
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ident := make(matrix, n)
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for i := 0; i < n; i++ {
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ident[i] = make(vector, n)
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ident[i][i] = 1
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}
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return ident
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}
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func (m matrix) pow(n int) matrix {
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le := len(m)
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if le != len(m[0]) {
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panic("Not a square matrix")
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}
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switch {
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case n < 0:
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panic("Negative exponents not supported")
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case n == 0:
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return identityMatrix(le)
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case n == 1:
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return m
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}
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pow := identityMatrix(le)
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base := m
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e := n
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for e > 0 {
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if (e & 1) == 1 {
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pow = pow.mul(base)
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}
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e >>= 1
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base = base.mul(base)
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}
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return pow
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}
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func main() {
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m := matrix{{3, 2}, {2, 1}}
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for i := 0; i <= 10; i++ {
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fmt.Println("** Power of", i, "**")
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fmt.Println(m.pow(i))
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fmt.Println()
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}
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}
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@ -0,0 +1,3 @@
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/Matrix Exponentiation
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/mpow.k
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pow: {:[0=y; :({a=/:a:!x}(#x))];a: x; do[y-1; a: x _mul a]; :a}
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class Mat(list) :
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def __matmul__(self, B) :
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A = self
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return Mat([[sum(A[i][k]*B[k][j] for k in range(len(B)))
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for j in range(len(B[0])) ] for i in range(len(A))])
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def identity(size):
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size = range(size)
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return [[(i==j)*1 for i in size] for j in size]
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def power(F, n):
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result = Mat(identity(len(F)))
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b = Mat(F)
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while n > 0:
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if (n%2) == 0:
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b = b @ b
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n //= 2
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else:
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result = b @ result
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b = b @ b
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n //= 2
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return result
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def printtable(data):
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for row in data:
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print (' '.join('%-5s' % ('%s' % cell) for cell in row))
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m = [[3,2], [2,1]]
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for i in range(5):
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print('\n%i:' % i)
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printtable(power(m, i))
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Option Base 1
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Private Function Identity(n As Integer) As Variant
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Dim I() As Variant
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ReDim I(n, n)
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For j = 1 To n
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For k = 1 To n
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I(j, k) = 0
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Next k
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Next j
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For j = 1 To n
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I(j, j) = 1
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Next j
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Identity = I
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End Function
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Function MatrixExponentiation(ByVal x As Variant, ByVal n As Integer) As Variant
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If n < 0 Then
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x = WorksheetFunction.MInverse(x)
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n = -n
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End If
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If n = 0 Then
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MatrixExponentiation = Identity(UBound(x))
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Exit Function
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End If
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Dim y() As Variant
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y = Identity(UBound(x))
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Do While n > 1
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If n Mod 2 = 0 Then
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x = WorksheetFunction.MMult(x, x)
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n = n / 2
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Else
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y = WorksheetFunction.MMult(x, y)
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x = WorksheetFunction.MMult(x, x)
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n = (n - 1) / 2
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End If
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Loop
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MatrixExponentiation = WorksheetFunction.MMult(x, y)
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End Function
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Public Sub pp(x As Variant)
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For i_ = 1 To UBound(x)
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For j_ = 1 To UBound(x)
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Debug.Print x(i_, j_),
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Next j_
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Debug.Print
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Next i_
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End Sub
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Public Sub main()
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M2 = [{3,2;2,1}]
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M3 = [{1,2,0;0,3,1;1,0,0}]
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pp MatrixExponentiation(M2, -1)
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Debug.Print
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pp MatrixExponentiation(M2, 0)
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Debug.Print
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pp MatrixExponentiation(M2, 10)
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Debug.Print
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pp MatrixExponentiation(M3, 10)
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End Sub
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