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Linear Equation Solver - Gaussian Elimination (C#)

, 22 May 2012 CPOL 29.3K 11
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Linear equation solver - Gaussian Elimination.

Introduction 

This code implements the Gaussian elimination algorithm in C#.

Background

Since I was unable to find this algo in C#, I wrote it on my own.

Using the code

Simply copy and paste the code to your project. If you prefer double precision, replace all occurances of "float" with "double".

public static class LinearEquationSolver
{
    /// <summary>Computes the solution of a linear equation system.</summary>
    /// <param name="M">
    /// The system of linear equations as an augmented matrix[row, col] where (rows + 1 == cols).
    /// It will contain the solution in "row canonical form" if the function returns "true".
    /// </param>
    /// <returns>Returns whether the matrix has a unique solution or not.</returns>
    public static bool Solve(float[,] M)
    {
        // input checks
        int rowCount = M.GetUpperBound(0) + 1;
        if (M == null || M.Length != rowCount * (rowCount + 1))
          throw new ArgumentException("The algorithm must be provided with a (n x n+1) matrix.");
        if (rowCount < 1)
          throw new ArgumentException("The matrix must at least have one row.");

        // pivoting
        for (int col = 0; col + 1 < rowCount; col++) if (M[col, col] == 0)
        // check for zero coefficients
        {
            // find non-zero coefficient
            int swapRow = col + 1;
            for (;swapRow < rowCount; swapRow++) if (M[swapRow, col] != 0) break;

            if (M[swapRow, col] != 0) // found a non-zero coefficient?
            {
                // yes, then swap it with the above
                float[] tmp = new float[rowCount + 1];
                for (int i = 0; i < rowCount + 1; i++)
                  { tmp[i] = M[swapRow, i]; M[swapRow, i] = M[col, i]; M[col, i] = tmp[i]; }
            }
            else return false; // no, then the matrix has no unique solution
        }

        // elimination
        for (int sourceRow = 0; sourceRow + 1 < rowCount; sourceRow++)
        {
            for (int destRow = sourceRow + 1; destRow < rowCount; destRow++)
            {
                float df = M[sourceRow, sourceRow];
                float sf = M[destRow, sourceRow];
                for (int i = 0; i < rowCount + 1; i++)
                  M[destRow, i] = M[destRow, i] * df - M[sourceRow, i] * sf;
            }
        }

        // back-insertion
        for (int row = rowCount - 1; row >= 0; row--)
        {
            float f = M[row,row];
            if (f == 0) return false;

            for (int i = 0; i < rowCount + 1; i++) M[row, i] /= f;
            for (int destRow = 0; destRow < row; destRow++)
              { M[destRow, rowCount] -= M[destRow, row] * M[row, rowCount]; M[destRow, row] = 0; }
        }
        return true;
    }
}

Changes

License

This article, along with any associated source code and files, is licensed under The Code Project Open License (CPOL)

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About the Author

janismac
Germany Germany
No Biography provided

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Comments and Discussions

 
QuestionProblem with search for non-zero pivot element Pin
Member 1035586924-Jan-14 17:47
memberMember 1035586924-Jan-14 17:47 
NewsSolving a System of Linear Equation Pin
WiiMaxx15-Jul-13 2:58
memberWiiMaxx15-Jul-13 2:58 
BugIncorrect calculation Pin
elw00d12325-Sep-12 3:11
memberelw00d12325-Sep-12 3:11 
SuggestionFurther C# packages on Gaussian Elimination and Linear Matrix Algebra in general Pin
akemper21-May-12 11:33
memberakemper21-May-12 11:33 
QuestionPInvoke and ACML is a solid solution Pin
Jonathan Langdon21-May-12 7:04
memberJonathan Langdon21-May-12 7:04 
QuestionSuggestion Pin
jarvisa21-May-12 0:14
memberjarvisa21-May-12 0:14 
QuestionMost of us use 3rd party libraries... Pin
Andreas Gieriet20-May-12 22:10
memberAndreas Gieriet20-May-12 22:10 

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