# A class for solving a system of linear equations using Gaussian Elimination

class LinearEquationSolver
{
List<LinearEquation> rows = new List<LinearEquation>();
decimal[] solution;

public void AddLinearEquation(decimal result, params decimal[] coefficients)
{
}

public IList<decimal> Solve()       //Returns a list of coefficients for the variables in the same order they were entered
{
solution = new decimal[rows[0].Coefficients.Count()];

for (int pivotM = 0; pivotM < rows.Count() - 1; pivotM++)
{
int pivotN = rows[pivotM].IndexOfFirstNonZero;

for (int i = pivotN + 1; i < rows.Count(); i++)
{
LinearEquation rowToReduce = rows[i];
decimal pivotFactor = rowToReduce[pivotN] / -rows[pivotM][pivotN];
}
}

while (rows.Any(r => r.Result != 0))
{
LinearEquation row = rows.FirstOrDefault(r => r.NonZeroCount == 1);
if (row == null)
{
break;
}

int solvedIndex = row.IndexOfFirstNonZero;
decimal newSolution = row.Result / row[solvedIndex];

}

return solution;
}

private void AddToSolution(int index, decimal value)
{
foreach (LinearEquation row in rows)
{
decimal coefficient = row[index];
row[index] -= coefficient;
row.Result -= coefficient * value;
}

solution[index] = value;
}

private class LinearEquation
{
public decimal[] Coefficients;
public decimal Result;

public LinearEquation(decimal result, params decimal[] coefficients)
{
this.Coefficients = coefficients;
this.Result = result;
}

public decimal this[int i]
{
get { return Coefficients[i]; }
set { Coefficients[i] = value; }
}

public void AddCoefficients(LinearEquation pivotEquation, decimal factor)
{
for (int i = 0; i < this.Coefficients.Count(); i++)
{
this[i] += pivotEquation[i] * factor;
if (Math.Abs(this[i]) < 0.000000001M)    //Because sometimes rounding errors mean it's not quite zero, and it needs to be
{
this[i] = 0;
}
}

this.Result += pivotEquation.Result * factor;
}

public int IndexOfFirstNonZero
{
get
{
for (int i = 0; i < Coefficients.Count(); i++)
{
if (this[i] != 0) return i;
}
return -1;
}
}

public int NonZeroCount
{
get
{
int count = 0;
for (int i = 0; i < Coefficients.Count(); i++)
{
if (this[i] != 0) count++;
}
return count;
}
}
}
}


Are there any edge-cases I've missed? Is there a better way to handle potential rounding errors than just checking if a value is close to zero and zeroing it if it is? Is it overkill to use Decimals like this?

Here's a test program:

class Program
{
static void Main(string[] args)
{
LinearEquationSolver test = new LinearEquationSolver();

var result = test.Solve();

foreach (var asdf in result)
{
Console.Write(asdf);
}

}
}

• In my opinion even when testing you should give variables meaningful names, otherwise you will develop a bad habit which might be hard to overcome. – Mihai-Daniel Virna Jul 8 '16 at 7:42

## Enumerable.Count() vs count access

One problem that slows your program's performance is that you call

Coefficients.Count()


In a few places while you are using array instead of an IEnumerable<T> where this is the only way to count the elements and as you can see this is a method rather than being a property. Instead you should simply call Coefficients.Length.

Edit

As @t3chb0t pointed in the comments and discussed here C# will simply return the Count property of the collection even when you call the method .Count() which means Coefficients.Count() & Coefficients.Length are almost equivalent in performance since the method has to do a type checking.

Nevertheless when possible, you should always prefer using your collection's specific functions and properties, rather than the generic ones. In your case Coefficients.Length.

## Properties vs fields

Ideally you should always use properties instead of fields

public decimal[] Coefficients;
public decimal Result;


Can become

public decimal[] Coefficients { get; }
public decimal Result { get; set; }


You properties should be as restrictive as possible the less your class exposes the better.

## Indexer with public backing collection ?

This doesn't makes much sense. Usually when a class has a indexer it's used internally with a private backing collection, but you have an iterator + a public collection.

In your case I don't see any reason why would you use an indexer here the public array Coefficients is more than enough and it's a lot more readable, so you should remove that indexer and just access the array like this :

public void AddCoefficients(LinearEquation pivotEquation, decimal factor)
{
for (int i = 0; i < this.Coefficients.Length; i++)
{
Coefficients[i] += pivotEquation.Coefficients[i]*factor;
if (Math.Abs(Coefficients[i]) < 0.000000001M)
//Because sometimes rounding errors mean it's not quite zero, and it needs to be
{
Coefficients[i] = 0;
}
}
this.Result += pivotEquation.Result*factor;
}


## Redundant this qualifier

While I do agree that this is up to a personal preference I don't like it. You don't need a single this qualifier in your code it would be better to remove it it's just extra text to read..

## Expression bodied properties + LINQ

public int IndexOfFirstNonZero
{
get
{
for (int i = 0; i < Coefficients.Length; i++)
{
if (Coefficients[i] != 0)
{
return i;
}
}
return -1;
}
}

public int NonZeroCount
{
get
{
int count = 0;
for (int i = 0; i < Coefficients.Length; i++)
{
if (Coefficients[i] != 0) count++;
}
return count;
}
}


You can really shorten those get only properties using LINQ :

public int IndexOfFirstNonZero
{
get
{
int value = (int) Coefficients.FirstOrDefault(x => x != 0);
return value == default(int) ? -1 : value;
}
}

public int NonZeroCount => Coefficients.Count(t => t != 0);

• One correction. The Count extension is smart enough to not enumerate a collection if it implements the ICollection interface, see Enumerable.Count<TSource> Method If the type of source implements ICollection<T>, that implementation is used to obtain the count of elements. Otherwise, this method determines the count. – t3chb0t Dec 25 '16 at 12:50
• And a tip: I suggest qouting the OP's code in the answer. This way it's easier to distinquish it from the review ;-) – t3chb0t Dec 25 '16 at 12:52
• Thanks for the edit @t3chb0t I will make sure to apply that to my future answer, I will update the answer with the correction you mentioned. – Denis Dec 25 '16 at 12:59