Zo zadanej štvorcovej matice 3x3 program vypočita pomocou metódy determinantov inverznú maticu 3x3 (ak existuje). Podmienka existencie inverznej matice je daná determinantom vstupnej (zadanej) matice. V prílohe sa nachádza DLL a jednoduchá Windows form aplikácia.

A - štovrcová matica veľkosti 3x3

|A| - determinant matice

A^-1 - inverzná matica

Pričom, ak |A| = 0 k matici A neexistuje inverzná matica.

Zdrojový kód:

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
namespace MathOperations
{
    public class Matrix
    {
        public bool InverseMatrixCalc(out string errorMessage, double[,] inputMatrix, out double[,] inverseMatrix)
        {
            errorMessage = "";
            //|inputMatrix[0,0] inputMatrix[0,1] inputMatrix[0,2]|-1
            //|inputMatrix[1,0] inputMatrix[1,1] inputMatrix[1,2]|
            //|inputMatrix[2,0] inputMatrix[2,1] inputMatrix[2,2]|
            inverseMatrix = new double[3, 3];
            try
            {
                if (inputMatrix.Length != 9 || inputMatrix.Rank != 2)
                {
                    errorMessage = "Vstupna matica ma nespravnu velkost.";
                    return false;
                }
                //DET  =  a11(a33a22-a32a23)-a21(a33a12-a32a13)+a31(a23a12-a22a13)
                double DET = inputMatrix[0,0] * (inputMatrix[2,2] * inputMatrix[1,1]
                            - inputMatrix[2,1] * inputMatrix[1,2])
                            - inputMatrix[1,0] * (inputMatrix[2,2] * inputMatrix[0,1]
                            - inputMatrix[2,1] * inputMatrix[0,2])
                            + inputMatrix[2,0] * (inputMatrix[1,2] * inputMatrix[0,1]
                            - inputMatrix[1,1] * inputMatrix[0,2]);
                //podmienka pre vypocet inverznej matice
                if (DET == 0)
                {
                    errorMessage = "K zadanej vstupnej matici neexistuje inverzna matica.";
                    return false;
                }
                DET = 1 / DET;
                //| a11 a12 a13 |-1             |   a33a22-a32a23  -(a33a12-a32a13)   a23a12-a22a13 |
                //| a21 a22 a23 |    =  1/DET * | -(a33a21-a31a23)   a33a11-a31a13  -(a23a11-a21a13)|
                //| a31 a32 a33 |               |   a32a21-a31a22  -(a32a11-a31a12)   a22a11-a21a12 |
                inverseMatrix[0, 0] = DET * (inputMatrix[2, 2] * inputMatrix[1, 1]
                                    - inputMatrix[2, 1] * inputMatrix[1, 2]);
                inverseMatrix[0, 1] = DET * (-1 * (inputMatrix[2, 2] * inputMatrix[0, 1]
                                    - inputMatrix[2, 1] * inputMatrix[0, 2]));
                inverseMatrix[0, 2] = DET * (inputMatrix[1, 2] * inputMatrix[0, 1]
                                    - inputMatrix[1, 1] * inputMatrix[0, 2]);
                inverseMatrix[1, 0] = DET * (-1 * (inputMatrix[2, 2] * inputMatrix[1, 0]
                                    - inputMatrix[2, 0] * inputMatrix[1, 2]));
                inverseMatrix[1, 1] = DET * (inputMatrix[2, 2] * inputMatrix[0, 0]
                                    - inputMatrix[2, 0] * inputMatrix[0, 2]);
                inverseMatrix[1, 2] = DET * (-1 * (inputMatrix[1, 2] * inputMatrix[0, 0]
                                    - inputMatrix[1, 0] * inputMatrix[0, 2]));
                inverseMatrix[2, 0] = DET * (inputMatrix[2, 1] * inputMatrix[1, 0]
                                    - inputMatrix[2, 0] * inputMatrix[1, 1]);
                inverseMatrix[2, 1] = DET * (-1 * (inputMatrix[2, 1] * inputMatrix[0, 0]
                                    - inputMatrix[2, 0] * inputMatrix[0, 1]));
                inverseMatrix[2, 2] = DET * (inputMatrix[1, 1] * inputMatrix[0, 0]
                                    - inputMatrix[1, 0] * inputMatrix[0, 1]);
            }
            catch (Exception ex)
            {
                errorMessage = ex.Message;
                return false;
            }
            return true;
        }
    }
}