C#盤算矩陣的逆矩陣辦法實例剖析。本站提示廣大學習愛好者:(C#盤算矩陣的逆矩陣辦法實例剖析)文章只能為提供參考,不一定能成為您想要的結果。以下是C#盤算矩陣的逆矩陣辦法實例剖析正文
本文實例講述了C#盤算矩陣的逆矩陣辦法。分享給年夜家供年夜家參考。詳細以下:
1.代碼思緒
1)對矩陣停止正當性檢討:矩陣必需為方陣
2)盤算矩陣行列式的值(Determinant函數)
3)只要滿秩矩陣才有逆矩陣,是以假如行列式的值為0(在代碼中以相對值小於1E-6做斷定),則終止函數,報出異常
4)求出隨同矩陣(AdjointMatrix函數)
5)逆矩陣各元素即其隨同矩陣各元素除以矩陣行列式的商
2.函數代碼
(注:本段代碼只完成了一個思緒,能夠其實不是該成績的最優解)
/// <summary> /// 求矩陣的逆矩陣 /// </summary> /// <param name="matrix"></param> /// <returns></returns> public static double[][] InverseMatrix(double[][] matrix) { //matrix必需為非空 if (matrix == null || matrix.Length == 0) { return new double[][] { }; } //matrix 必需為方陣 int len = matrix.Length; for (int counter = 0; counter < matrix.Length; counter++) { if (matrix[counter].Length != len) { throw new Exception("matrix 必需為方陣"); } } //盤算矩陣行列式的值 double dDeterminant = Determinant(matrix); if (Math.Abs(dDeterminant) <= 1E-6) { throw new Exception("矩陣弗成逆"); } //制造一個隨同矩陣年夜小的矩陣 double[][] result = AdjointMatrix(matrix); //矩陣的每項除以矩陣行列式的值,即為所求 for (int i = 0; i < matrix.Length; i++) { for (int j = 0; j < matrix.Length; j++) { result[i][j] = result[i][j] / dDeterminant; } } return result; } /// <summary> /// 遞歸盤算行列式的值 /// </summary> /// <param name="matrix">矩陣</param> /// <returns></returns> public static double Determinant(double[][] matrix) { //二階及以下行列式直接盤算 if (matrix.Length == 0) return 0; else if (matrix.Length == 1) return matrix[0][0]; else if (matrix.Length == 2) { return matrix[0][0] * matrix[1][1] - matrix[0][1] * matrix[1][0]; } //對第一行應用“加邊法”遞歸盤算行列式的值 double dSum = 0, dSign = 1; for (int i = 0; i < matrix.Length; i++) { double[][] matrixTemp = new double[matrix.Length - 1][]; for (int count = 0; count < matrix.Length - 1; count++) { matrixTemp[count] = new double[matrix.Length - 1]; } for (int j = 0; j < matrixTemp.Length; j++) { for (int k = 0; k < matrixTemp.Length; k++) { matrixTemp[j][k] = matrix[j + 1][k >= i ? k + 1 : k]; } } dSum += (matrix[0][i] * dSign * Determinant(matrixTemp)); dSign = dSign * -1; } return dSum; } /// <summary> /// 盤算方陣的隨同矩陣 /// </summary> /// <param name="matrix">方陣</param> /// <returns></returns> public static double[][] AdjointMatrix(double [][] matrix) { //制造一個隨同矩陣年夜小的矩陣 double[][] result = new double[matrix.Length][]; for (int i = 0; i < result.Length; i++) { result[i] = new double[matrix[i].Length]; } //生成隨同矩陣 for (int i = 0; i < result.Length; i++) { for (int j = 0; j < result.Length; j++) { //存儲代數余子式的矩陣(行、列數都比原矩陣少1) double[][] temp = new double[result.Length - 1][]; for (int k = 0; k < result.Length - 1; k++) { temp[k] = new double[result[k].Length - 1]; } //生成代數余子式 for (int x = 0; x < temp.Length; x++) { for (int y = 0; y < temp.Length; y++) { temp[x][y] = matrix[x < i ? x : x + 1][y < j ? y : y + 1]; } } //Console.WriteLine("代數余子式:"); //PrintMatrix(temp); result[j][i] = ((i + j) % 2 == 0 ? 1 : -1) * Determinant(temp); } } //Console.WriteLine("隨同矩陣:"); //PrintMatrix(result); return result; } /// <summary> /// 打印矩陣 /// </summary> /// <param name="matrix">待打印矩陣</param> private static void PrintMatrix(double[][] matrix, string title = "") { //1.題目值為空則不顯示題目 if (!String.IsNullOrWhiteSpace(title)) { Console.WriteLine(title); } //2.打印矩陣 for (int i = 0; i < matrix.Length; i++) { for (int j = 0; j < matrix[i].Length; j++) { Console.Write(matrix[i][j] + "\t"); //留意不克不及寫為:Console.Write(matrix[i][j] + '\t'); } Console.WriteLine(); } //3.空行 Console.WriteLine(); }
3.Main函數挪用
static void Main(string[] args) { double[][] matrix = new double[][] { new double[] { 1, 2, 3 }, new double[] { 2, 2, 1 }, new double[] { 3, 4, 3 } }; PrintMatrix(matrix, "原矩陣"); PrintMatrix(AdjointMatrix(matrix), "隨同矩陣"); Console.WriteLine("行列式的值為:" + Determinant(matrix) + '\n'); PrintMatrix(InverseMatrix(matrix), "逆矩陣"); Console.ReadLine(); }
4.履行成果
願望本文所述對年夜家的C#法式設計有所贊助。