Files
crtr/Assets/Cryville/Common/Math/SquareMatrix.cs
2022-10-14 23:32:43 +08:00

92 lines
2.7 KiB
C#

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