Matrix without new instance

using MatrixCalculations.Exceptions;
using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Threading.Tasks;

namespace MatrixCalculations
{
    public class Matrix
    {
        //private properties
        private int _width;
        private int _heigth;
        private List<MatrixRow> _matrix = new List<MatrixRow>();
        private List<MatrixRow> _echelonForm = new List<MatrixRow>();

        public Matrix(int h, int w)
        {
            _width = w;
            Heigth = h;
        }



        //Row and Column operations
        public Matrix AddRow(MatrixRow r)
        {
            //Throw Exception if we want to add a row which is not the proper length
            if (r.Length() != Width)
                throw new FaultyRowSizeException(string.Format("ROW SIZE WRONG. ALLOWED: {0}, GIVEN: {1}", Width, r.Length()));

            //Throw an exception if we want to add a row to a full matrix
            if (Heigth > _matrix.Count)
            {
                _matrix.Add(r);
                return this;
            }
            else
            {
                throw new MatrixFullException("MATRIX IS FULL, NOT ABLE TO INSERT");
            }
        }
        public Matrix SwapRows(int i, int k)
        {
            if (i > (Heigth - 1))
                throw new RowIndexOutOfBounds(string.Format("ROW INDEX WAS OUT OF BOUNDS. GIVEN {0}, MATRIXHEIGHT {1}", i, Heigth));
            if (k > (Heigth - 1))
                throw new RowIndexOutOfBounds(string.Format("ROW INDEX WAS OUT OF BOUNDS. GIVEN {0}, MATRIXHEIGHT {1}", k, Heigth));

            var temp = _matrix[i];
            _matrix[i] = _matrix[k];
            _matrix[k] = temp;
            return this;
        }

        //Echelon form
        public Matrix Rref()
        {
            var done = false;
            var nonzerocoord = new Coordinate(0, 0);
            while (!done)
            {

                //Step 1: Find the first non-zero column
                for (int ci = nonzerocoord.Column; ci < _width; ci++)
                {
                    if (!IsZeroColumn(ci))
                    {
                        nonzerocoord.Column = ci;
                        break;
                    }
                }
                //Step 2: Find the pivot-value, make it one, and put it on top
                SetPivotOneAndOnTop(nonzerocoord);

                //We have a pivot element, we need to make every element below the pivot zero.
                SetElementsZeroBelowPivot(nonzerocoord);

                //We need to repeat these steps disregarding the previous pivot
                //We repeat with next column
                nonzerocoord.Column++;
                nonzerocoord.Row++;
                if (nonzerocoord.Column == _width || nonzerocoord.Row == _heigth)
                    done = true;
            }
            //AT this point we are only in echelonform
            //To get to row reduced echelonform we need to substract from the bottom up
            for (int ri = 0; ri < _heigth; ri++)
            {
                SetElementsZeroAbovePivot(new Coordinate(ri, 0));
            }
            return this;
        }
        public Matrix Transpose()
        {
            Matrix transposed = new Matrix(Width, Heigth);
            for (int ci = 0; ci < Width; ci++)
            {
                var values = new List<double>();

                for (int ri = 0; ri < Heigth; ri++)
                {
                    values.Add(GetRow(ri).GetVal(ci));
                }
                transposed.AddRow(new MatrixRow(values.ToArray()));
            }
            return transposed;
        }



        //Value Manipulation
        public double GetVal(int ri, int ci)
        {
            //Throw Exceptions accordingly.
            if (ri > (Heigth - 1))
                throw new RowIndexOutOfBounds(string.Format("ROW INDEX WAS OUT OF BOUNDS. GIVEN {0}, MATRIXHEIGHT {1}", ri, Heigth));
            if (ci > (Width - 1))
                throw new ColumnOutOfBoundsException(string.Format("COLUMN INDEX WAS OUT OF BOUNDS. GIVEN {0}, MATRIXHEIGHT {1}", ci, Width));

            //Get the value from the row
            return this.GetRow(ri).GetVal(ci);
        }
        public double GetVal(Coordinate c)
        {
            //Throw Exceptions accordingly.
            if (c.Row > (Heigth - 1))
                throw new RowIndexOutOfBounds(string.Format("ROW INDEX WAS OUT OF BOUNDS. GIVEN {0}, MATRIXHEIGHT {1}", c.Row, Heigth));
            if (c.Column > (Width - 1))
                throw new ColumnOutOfBoundsException(string.Format("COLUMN INDEX WAS OUT OF BOUNDS. GIVEN {0}, MATRIXHEIGHT {1}", c.Column, Width));

            //Get the value from the row
            return this.GetRow(c.Row).GetVal(c.Column);
        }
        public Matrix SetVal(int ri, int ci, double val)
        {
            if (ri > (Heigth - 1))
                throw new RowIndexOutOfBounds(string.Format("ROW INDEX WAS OUT OF BOUNDS. GIVEN {0}, MATRIXHEIGHT {1}", ri, Heigth));
            if (ci > (Width - 1))
                throw new ColumnOutOfBoundsException(string.Format("COLUMN INDEX WAS OUT OF BOUNDS. GIVEN {0}, MATRIXHEIGHT {1}", ci, Width));
            _matrix[ri].SetVal(ci, val);
            return this;
        }

        //Public properties
        public int RowCount()
        {
            return _matrix.Count;
        }
        public int Width
        {
            get { return _width; }
        }
        public int Heigth
        {
            get { return _heigth; }
            set { _heigth = value; }
        }

        //Row Manipulation
        public MatrixRow GetRow(int ri)
        {
            return _matrix[ri];
        }
        public void SetRow(int ri, MatrixRow row)
        {
            if (ri > (Heigth - 1))
                throw new RowIndexOutOfBounds(string.Format("ROW INDEX WAS OUT OF BOUNDS. GIVEN {0}, MATRIXHEIGHT {1}", ri, Heigth));
            if (row.Length() > Width)
                throw new FaultyRowSizeException(string.Format("ROW SIZE WRONG. ALLOWED: {0}, GIVEN: {1}", Width, row.Length()));

            _matrix[ri] = row;
        }


        //Debug
        public void PrintMatrix()
        {
            Console.WriteLine("Matrix: " + Heigth + " x " + Width);
            foreach (var row in _matrix)
            {
                row.PrintRow();
                Console.WriteLine();
            }
        }

        //Utilities
        private bool IsZeroColumn(int columnIndex)
        {
            bool foundNonZero = false;
            //Iterate through each row to find a non-zero alue
            foreach (MatrixRow r in _matrix)
            {
                if (!r.GetVal(columnIndex).Equals(0.0))
                {
                    foundNonZero = true;
                    break;
                }

            }
            return !foundNonZero;
        }
        private void SetPivotOneAndOnTop(Coordinate coord)
        {
            //We will check each row on the corresponding column value
            for (int ri = coord.Row; ri < _heigth; ri++)
            {
                var currentRow = GetRow(ri);
                //If the value is non-zero make it one by scaling
                //break;
                if (!currentRow.GetVal(coord.Column).Equals(0.00))
                {
                    SetRow(ri, currentRow.GetMultipliedInstance((1 / currentRow.GetVal(coord.Column))));

                    //We need to set this row to the first row
                    SwapRows(coord.Row, ri);
                    break;
                }
            }
        }
        private void SetElementsZeroBelowPivot(Coordinate pivotposition)
        {
            //Get the pivotrow and extract the pivotvalue
            var pivotRow = GetRow(pivotposition.Row);
            var pitvotValue = pivotRow.GetVal(pivotposition.Column);

            //We will change each row below the pivotrow
            //We will substract the pivotrow divided by the value of the current row
            //This makes every value zero below the pivot
            if (!pitvotValue.Equals(0.00))
            {
                for (int ri = (pivotposition.Row + 1); ri < _heigth; ri++)
                {
                    //Get the current row and determine the pivotvalue
                    //So we can determine the factor we need to multiply the pivotrow to get an instance to substract
                    var currentRow = GetRow(ri);
                    var valueBelowPivot = currentRow.GetVal(pivotposition.Column);

                    var factor = valueBelowPivot / pitvotValue;
                    SetRow(ri, currentRow.SubstractRow(pivotRow.GetMultipliedInstance(factor)));
                }
            }
        }
        private void SetElementsZeroAbovePivot(Coordinate pivotposition)
        {
            //Get the pivotrow and extract the pivotvalue
            //Get the pivotrow and extract the pivotvalue
            var pivotRow = GetRow(pivotposition.Row);
            var pivotValue = pivotRow.GetLeadingEntryValue();
            var pivotIndex = pivotRow.GetLeadingEntryIndex();


            if (!pivotValue.Equals(-1))
            {
                for (int ri = pivotposition.Row - 1; ri >= 0; ri--)
                {
                    var pivotColVal = GetRow(ri).GetVal(pivotIndex);
                    var factor = pivotColVal / pivotValue;
                    SetRow(ri, GetRow(ri).SubstractRow(pivotRow.GetMultipliedInstance(factor)));
                }
            }
        }
    }
}