public MyMatrix Clone()
{
MyMatrix newmatrix = new MyMatrix(n, m);
for (int i = 0; i < n; i++)
{
for (int j = 0; j < m; j++)
{
newmatrix[i, j] = values[i, j].Clone();
}
}
return(newmatrix);
}
public static MyMatrix operator *(Rational a, MyMatrix B)
{
MyMatrix aB = B.Clone();
for (int i = 0; i < B.n; i++)
{
for (int j = 0; j < B.m; j++)
{
aB[i, j] *= a;
}
}
return(aB);
}
public static MyMatrix operator -(MyMatrix A, MyMatrix B)
{
if (A.n != B.n || A.m != B.m)
{
throw new InvalidOperationException("Dimension mismatch!");
}
MyMatrix subt = new MyMatrix(A.n, A.m);
for (int i = 0; i < subt.n; i++)
{
for (int j = 0; j < subt.m; j++)
{
subt[i, j] = A[i, j] - B[i, j];
}
}
return(subt);
}
public MyMatrix Adjunct()
{
if (n != m)
{
throw new InvalidOperationException("Dimension mismatch!");
}
MyMatrix adjunct = new MyMatrix(n);
for (int i = 0; i < n; i++)
{
for (int j = 0; j < n; j++)
{
adjunct[i, j] = Adjunct(i, j);
}
}
return(adjunct);
}
public MyMatrix Apply(MyMatrix vector)
{
MyMatrix output = new MyMatrix(n, 1);
if (vector.N != n || vector.M != 1)
{
throw new InvalidOperationException("Dimension mismatch!");
}
for (int i = 0; i < n; i++)
{
for (int j = 0; j < m; j++)
{
output[i, 0] += values[i, j] * vector[j, 0];
}
}
return(output);
}
public static MyMatrix FromWolfram(string input)
{
string[] lines = input.Replace("\n", "").Replace("\r", "").Replace(" ", "").Split(new string[] { "},{" }, StringSplitOptions.None);
lines[0] = lines[0].Replace("{", "");
lines[lines.Length - 1] = lines.Last().Replace("}", "");
MyMatrix tmp = new MyMatrix(lines.Length, lines[0].Split(',').Length);
for (int i = 0; i < lines.Length; i++)
{
string[] args = lines[i].Split(',');
for (int j = 0; j < args.Length; j++)
{
tmp[i, j] = new Rational(args[j]);
}
}
return(tmp);
}
public bool Equals(MyMatrix other)
{
if (n != other.n || m != other.m)
{
return(false);
}
for (int i = 0; i < n; i++)
{
for (int j = 0; j < m; j++)
{
if (values[i, j] != other[i, j])
{
return(false);
}
}
}
return(true);
}
public string KerBasis()
{
MyMatrix row_echelon = Clone();
string output = row_echelon.GaussLaTeX() + '\n';
LaTeXExport export = new LaTeXExport(1, ",", 1, false, "$$\\ker\\ \\text{basis}:\\ ");
List <int> pivots = new List <int>();
for (int i = 0; i < n; i++)
{
int j_s = 0;
for (; j_s < m && row_echelon[i, j_s] == 0; j_s++)
{
;
}
if (j_s >= m)
{
break;
}
pivots.Add(j_s);
}
int j_free = 0;
for (int j = 0; j < m - pivots.Count; j++, j_free++)
{
for (; pivots.Contains(j_free); j_free++)
{
;
}
MyMatrix basis_el = new MyMatrix(m, 1);
basis_el[j_free, 0] = 1;
for (int i = 0; i < pivots.Count; i++)
{
basis_el[pivots[i], 0] = -row_echelon[i, j_free];
}
export.Add(basis_el.GetLaTeX());
}
if (export.Empty)
{
export.Add(new MyMatrix(m, 1).GetLaTeX());
}
return(output + export.Result);
}
public static MyMatrix operator *(MyMatrix A, MyMatrix B)
{
if (A.m != B.n)
{
throw new InvalidOperationException("Dimension mismatch!");
}
MyMatrix AB = new MyMatrix(A.n, B.m);
for (int i = 0; i < AB.n; i++)
{
for (int j = 0; j < AB.m; j++)
{
for (int l = 0; l < A.m; l++)
{
AB[i, j] += A[i, l] * B[l, j];
}
}
}
return(AB);
}
public static MyMatrix FromLaTeX(string input)
{
string[] lines = input.Replace("\n", "").Replace("\r", "").Replace(" ", "").Split(new string[] { "\\\\" }, StringSplitOptions.None);
if (lines[0].Contains("begin"))
{
lines[0] = lines[0].Substring(lines[0].IndexOf('}') + 1);
if (lines[0][0] == '{')
{
lines[0] = lines[0].Substring(lines[0].IndexOf('}') + 1);
}
}
if (lines.Last().Contains("end"))
{
lines[lines.Length - 1] = lines.Last().Substring(0, lines.Last().IndexOf("\\end"));
}
int end_empty = 0;
if (lines.Last().Length == 0)
{
end_empty = 1;
}
MyMatrix tmp = new MyMatrix(lines.Length - end_empty, lines[0].Split('&').Length);
for (int i = 0; i < tmp.N; i++)
{
string[] args = lines[i].Split('&');
for (int j = 0; j < args.Length; j++)
{
if (args[j].Contains("frac"))
{
tmp[i, j] = ParseFrac(args[j]);
}
else
{
tmp[i, j] = new Rational(args[j]);
}
}
}
return(tmp);
}
public static Rational ScalarProduct(MyMatrix a, MyMatrix b)
{
MyMatrix a_n, b_n;
if (a.m == 1)
{
a_n = a.Transposed();
}
else
{
a_n = a;
}
if (b.m == 1)
{
b_n = b;
}
else
{
b_n = b.Transposed();
}
return((a_n * b_n).Sum());
}
public string InverseLaTeX()
{
if (!IsSquare)
{
throw new InvalidOperationException("Matrix is not square!");
}
if (Determinant == 0)
{
throw new DivideByZeroException("Determinant zero!");
}
MyMatrix tmp = new MyMatrix(n, n * 2);
tmp.Set(this);
for (int i = 0; i < n; i++)
{
tmp[i, i + n] = 1;
}
string output = tmp.GaussLaTeX(n);
for (int i = 0; i < n; i++)
{
for (int j = 0; j < n; j++)
{
tmp[i, j] = tmp[i, j + n];
}
}
tmp.M = n;
/*try
* {
* if (!(tmp * this).Equals(Id))
* throw new Exception();
* }
* catch { throw new ArithmeticException("Cannot find inverse matrix!"); }*/
values = tmp.values;
return(output);
}