線形代数ベクトル; Vector
概要
ベクトルとは向きと量を持った値で、スカラーとは異なり複数の実数成分を内包する。
行列と並び数学には無くてはならない存在のため、ベクトルを表現するクラスはアルゴリズムを扱うこのサイトで最も使用頻度の高いクラスである。
ソースコード
namespace Algebra {
///<summary>ベクトルクラス</summary>
public class Vector : ICloneable {
protected readonly double[] v;
/// <summary>コンストラクタ</summary>
public Vector(params double[] v) {
this.v = (double[])v.Clone();
}
/// <summary>インデクサ</summary>
public double this[int index] {
get {
return v[index];
}
set {
v[index] = value;
}
}
/// <summary>X成分</summary>
public double X {
get {
return v[0];
}
set {
v[0] = value;
}
}
/// <summary>Y成分</summary>
public double Y {
get {
return v[1];
}
set {
v[1] = value;
}
}
/// <summary>Z成分</summary>
public double Z {
get {
return v[2];
}
set {
v[2] = value;
}
}
/// <summary>W成分</summary>
public double W {
get {
return v[3];
}
set {
v[3] = value;
}
}
/// <summary>次元数</summary>
public int Dim => v.Length;
/// <summary>ノルム</summary>
public double Norm => Math.Sqrt(SquareNorm);
/// <summary>ノルム2乗</summary>
public double SquareNorm {
get {
double norm = 0;
foreach(var vi in v) {
norm += vi * vi;
}
return norm;
}
}
/// <summary>行ベクトル</summary>
public Matrix Horizontal {
get {
Matrix ret = new Matrix(1, Dim);
for(int i = 0; i < Dim; i++) {
ret[0, i] = v[i];
}
return ret;
}
}
/// <summary>列ベクトル</summary>
public Matrix Vertical {
get {
Matrix ret = new Matrix(Dim, 1);
for(int i = 0; i < Dim; i++) {
ret[i, 0] = v[i];
}
return ret;
}
}
/// <summary>正規化</summary>
public Vector Normal => this / Norm;
/// <summary>単項プラス</summary>
public static Vector operator +(Vector vector) {
return (Vector)vector.Clone();
}
/// <summary>単項マイナス</summary>
public static Vector operator -(Vector vector) {
double[] v = new double[vector.Dim];
for(int i = 0; i < vector.Dim; i++) {
v[i] = -vector[i];
}
return new Vector(v);
}
/// <summary>ベクトル加算</summary>
public static Vector operator +(Vector vector1, Vector vector2) {
if(vector1.Dim != vector2.Dim) {
throw new ArgumentException();
}
int size = vector1.Dim;
double[] v = new double[size];
for(int i = 0; i < size; i++) {
v[i] = vector1[i] + vector2[i];
}
return new Vector(v);
}
/// <summary>ベクトル減算</summary>
public static Vector operator -(Vector vector1, Vector vector2) {
if(vector1.Dim != vector2.Dim) {
throw new ArgumentException();
}
int size = vector1.Dim;
double[] v = new double[size];
for(int i = 0; i < size; i++) {
v[i] = vector1[i] - vector2[i];
}
return new Vector(v);
}
/// <summary>スカラー倍</summary>
public static Vector operator *(double r, Vector vector) {
double[] v = new double[vector.Dim];
for(int i = 0; i < vector.Dim; i++) {
v[i] = vector[i] * r;
}
return new Vector(v);
}
/// <summary>スカラー倍</summary>
public static Vector operator *(Vector vector, double r) {
return r * vector;
}
/// <summary>スカラー逆数倍</summary>
public static Vector operator /(Vector vector, double r) {
return (1 / r) * vector;
}
/// <summary>ベクトル間距離</summary>
public static double Distance(Vector vector1, Vector vector2) {
return (vector1 - vector2).Norm;
}
/// <summary>ベクトル間距離2乗</summary>
public static double SquareDistance(Vector vector1, Vector vector2) {
return (vector1 - vector2).SquareNorm;
}
/// <summary>ベクトル内積</summary>
public static double InnerProduct(Vector vector1, Vector vector2) {
if(vector1.Dim != vector2.Dim) {
throw new ArgumentException();
}
double sum = 0;
for(int i = 0, dim = vector1.Dim; i < dim; i++) {
sum += vector1[i] * vector2[i];
}
return sum;
}
/// <summary>ゼロベクトル</summary>
public static Vector Zero(int size) {
return new Vector(new double[size]);
}
/// <summary>ゼロベクトルか判定</summary>
public static bool IsZero(Vector vector) {
for(int i = 0; i < vector.Dim; i++) {
if(vector[i] != 0) {
return false;
}
}
return true;
}
/// <summary>不正なベクトル</summary>
public static Vector Invalid(int size) {
double[] v = new double[size];
for(int i = 0; i < size; i++) {
v[i] = double.NaN;
}
return new Vector(v);
}
/// <summary>有効なベクトルか判定</summary>
public static bool IsValid(Vector vector) {
for(int i = 0; i < vector.Dim; i++) {
if(double.IsNaN(vector[i]) || double.IsInfinity(vector[i])) {
return false;
}
}
return true;
}
/// <summary>ベクトルが等しいか</summary>
public static bool operator ==(Vector vector1, Vector vector2) {
if(ReferenceEquals(vector1, vector2)) {
return true;
}
if((object)vector1 == null || (object)vector2 == null) {
return false;
}
return vector1.v.SequenceEqual(vector2.v);
}
/// <summary>ベクトルが異なるか判定</summary>
public static bool operator !=(Vector vector1, Vector vector2) {
return !(vector1 == vector2);
}
/// <summary>等しいか判定</summary>
public override bool Equals(object obj) {
return obj is Vector ? (Vector)obj == this : false;
}
/// <summary>ハッシュ値</summary>
public override int GetHashCode() {
return Dim > 0 ? v[0].GetHashCode() : 0;
}
/// <summary>クローン</summary>
public object Clone() {
return new Vector(v);
}
/// <summary>コピー</summary>
public Vector Copy() {
return new Vector(v);
}
/// <summary>文字列化</summary>
public override string ToString() {
if(Dim <= 0) {
return string.Empty;
}
string str = $"{v[0]}";
for(int i = 1; i < Dim; i++) {
str += $",{v[i]}";
}
return str;
}
}
}
関連項目
ベクトルクラス単体テスト
