What causes "Matrix of equation coefficients is not square shaped." in TheAlgorithms/C-Sharp?

Ensure matrix is n x n and pass the right-hand side as the separate double[] coefficients argument.

TheAlgorithms/C-Sharp · error · ArgumentException

Matrix of equation coefficients is not square shaped.

Error message

Matrix of equation coefficients is not square shaped.

What it means

LU.Eliminate(matrix, coefficients) solves a linear system A*x = b via LU decomposition and requires the coefficient matrix to be square (n x n). It throws ArgumentException 'Matrix of equation coefficients is not square shaped.' when matrix.GetLength(0) != matrix.GetLength(1), before delegating to Decompose.

Solutions

Ensure matrix is n x n and pass the right-hand side as the separate double[] coefficients argument.
If your data is an augmented n x (n+1) matrix, copy the first n columns into a square array and the last column into the coefficients vector.
For non-square (over/underdetermined) systems use an appropriate solver (e.g. least squares), not LU.Eliminate.

Example fix

// before
lu.Eliminate(augmented, null); // augmented is n x (n+1): throws
// after
int n = augmented.GetLength(0);
var a = new double[n, n];
var b = new double[n];
for (int i = 0; i < n; i++)
{
    for (int j = 0; j < n; j++) a[i, j] = augmented[i, j];
    b[i] = augmented[i, n];
}
var x = lu.Eliminate(a, b);

Defensive patterns

Strategy: validation

Validate before calling

if (matrix.GetLength(0) != matrix.GetLength(1))
    throw new ArgumentException("Eliminate requires a square coefficient matrix");
if (coefficients == null || coefficients.Length != matrix.GetLength(0))
    throw new ArgumentException("coefficients length must match matrix size");

Type guard

static bool IsSquareSystem(double[,] m, double[] b) =>
    m != null && b != null && m.GetLength(0) == m.GetLength(1) && b.Length == m.GetLength(0);

Try / catch

try
{
    var x = LU.Eliminate(matrix, coefficients);
}
catch (ArgumentException ex) when (ex.Message.Contains("not square"))
{
    // split augmented matrix or reject input
}

Prevention

Pass the RHS as a separate vector, never as an extra matrix column.
Split augmented matrices before calling Eliminate.
Use least-squares solvers for non-square systems instead of LU.

When it happens

Trigger: Calling Eliminate with a rectangular matrix (e.g. an n x (n+1) augmented matrix passed as the matrix argument instead of splitting the last column into coefficients); passing a matrix whose dimensions were misread from file input.

Common situations: Loading an augmented matrix from CSV and passing the whole thing as 'matrix'; building a least-squares/overdetermined system (more equations than unknowns) and trying to solve it with LU instead of least squares.

Understand the failure class

Background: Tensor shape mismatch errors ("must have shape", "expected shape ... got ..."): when tensor dimensions disagree with what an op or layer was told to expect — this error's family across 6 libraries.

Related errors

AI-assisted analysis of TheAlgorithms/C-Sharp@96e2905cab (2026-09-13). Data as JSON: /api/errors/f66977d3d0b39f28. Report an issue: GitHub.

Appendix: source

Thrown at Algorithms/Numeric/Decomposition/LU.cs:77

            }
        }

        return (L: lower, U: upper);
    }

    /// <summary>
    ///     Eliminates linear equations system represented as A*x=b, using LU-decomposition,
    ///     where A - matrix of equation coefficients, b - vector of absolute terms of equations.
    /// </summary>
    /// <param name="matrix">Matrix of equation coefficients.</param>
    /// <param name="coefficients">Vector of absolute terms of equations.</param>
    /// <returns>Vector-solution for linear equations system.</returns>
    /// <exception cref="ArgumentException">Matrix of equation coefficients is not square shaped.</exception>
    public static double[] Eliminate(double[,] matrix, double[] coefficients)
    {
        if (matrix.GetLength(0) != matrix.GetLength(1))
        {
            throw new ArgumentException("Matrix of equation coefficients is not square shaped.");
        }

        var pivot = matrix.GetLength(0);
        var upperTransform = new double[pivot, 1]; // U * upperTransform = coefficients
        var solution = new double[pivot]; // L * solution = upperTransform
        (double[,] l, double[,] u) = Decompose(matrix);

        for (var i = 0; i < pivot; i++)
        {
            double pivotPointSum = 0;

            for (var j = 0; j < i; j++)
            {
                pivotPointSum += upperTransform[j, 0] * l[i, j];
            }

            upperTransform[i, 0] = (coefficients[i] - pivotPointSum) / l[i, i];
        }

View on GitHub (pinned to 96e2905cab)