92 lines
2.7 KiB
C#
92 lines
2.7 KiB
C#
namespace Cryville.Common.Math {
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/// <summary>
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/// Represents a square matrix.
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/// </summary>
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public class SquareMatrix {
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readonly float[,] content;
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/// <summary>
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/// The size of the matrix.
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/// </summary>
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public int Size {
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get;
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private set;
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}
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/// <summary>
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/// Creates a square matrix with the specified size.
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/// </summary>
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/// <param name="size">The size of the matrix.</param>
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public SquareMatrix(int size) {
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content = new float[size, size];
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Size = size;
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}
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/// <summary>
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/// Gets or sets the element at the specified index.
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/// </summary>
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/// <param name="r">The zero-based row index.</param>
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/// <param name="c">The zero-based column index.</param>
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/// <returns>The element at the specified index.</returns>
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public float this[int r, int c] {
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get { return content[r, c]; }
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set { content[r, c] = value; }
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}
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/// <summary>
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/// Eliminates the square matrix against a column vector.
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/// </summary>
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/// <typeparam name="T">The vector type.</typeparam>
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/// <param name="v">The column vector.</param>
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/// <param name="o">The column operator.</param>
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/// <returns>The column vector eliminated.</returns>
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public ColumnVector<T> Eliminate<T>(ColumnVector<T> v, IVectorOperator<T> o) {
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int s = Size;
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float[,] d = (float[,])content.Clone();
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int[] refl = new int[s];
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for (int i = 0; i < s; i++)
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refl[i] = i;
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for (int r = 0; r < s; r++) {
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for (int r0 = r; r0 < s; r0++)
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if (d[refl[r0], r] != 0) {
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refl[r] = r0;
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refl[r0] = r;
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break;
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}
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int or = refl[r];
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float sf0 = d[or, r];
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for (int c0 = r; c0 < s; c0++)
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d[or, c0] /= sf0;
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v[or] = o.ScalarMultiply(1 / sf0, v[or]);
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for (int r1 = r + 1; r1 < s; r1++) {
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int or1 = refl[r1];
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float sf1 = d[or1, r];
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for (int c1 = r; c1 < s; c1++)
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d[or1, c1] -= d[or, c1] * sf1;
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v[or1] = o.Add(v[or1], o.ScalarMultiply(-sf1, v[or]));
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}
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}
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T[] res = new T[s];
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for (int r2 = s - 1; r2 >= 0; r2--) {
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var v2 = v[refl[r2]];
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for (int c2 = r2 + 1; c2 < s; c2++)
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v2 = o.Add(v2, o.ScalarMultiply(-d[refl[r2], c2], res[refl[c2]]));
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res[refl[r2]] = v2;
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}
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return new ColumnVector<T>(res);
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}
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/// <summary>
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/// Creates a square matrix and fills it with polynomial coefficients.
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/// </summary>
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/// <param name="size">The size of the square matrix.</param>
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/// <returns>A square matrix filled with polynomial coefficients.</returns>
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public static SquareMatrix WithPolynomialCoefficients(int size) {
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var m = new SquareMatrix(size);
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for (var r = 0; r < size; r++) {
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int d = 1;
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for (var c = 0; c < size; c++) {
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m[r, c] = d;
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d *= r;
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}
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}
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return m;
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}
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}
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}
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