public string GramSchmidt()
{
string output = "\\begin{align*}\n&" + GetRow(0).GetLaTeXLine() + "\\\\\n";
for (int i = 1; i < n; i++)
{
MyMatrix row = GetRow(i);
LaTeXExport export = new LaTeXExport(m + 1, "-", 1, begin: "&", end: (i < n - 1 ? "\\\\\n" : "\n"), new_line: "\\\\\n&");
export.Add(row.GetLaTeXLine());
for (int j = 0; j < i; j++)
{
MyMatrix j_row = GetRow(j);
if (j_row.IsZero)
{
continue;
}
Rational scalar = ScalarProduct(GetRow(i), j_row),
square = ScalarProduct(j_row, j_row);
Rational.RemoveDivisor(ref scalar, ref square);
export.Add($"\\frac{{{scalar}}}{{{square}}}" + j_row.GetLaTeXLine());
row -= (scalar / square) * j_row;
}
export.Add(row.GetLaTeXLine(), "=", 1);
output += export.Result;
SetRow(i, row);
}
return(output + "\\end{align*}");
}
public string ImBasis()
{
MyMatrix row_echelon = Clone();
string output = row_echelon.GaussLaTeX(revert: false) + '\n';
LaTeXExport export = new LaTeXExport(1, ",", 1, false, "$$\\text{Im basis}:\\ ");
for (int i = 0; i < n; i++)
{
int j_s = 0;
for (; j_s < m && row_echelon[i, j_s] == 0; j_s++)
{
;
}
if (j_s >= m)
{
break;
}
export.Add(GetColumn(j_s).GetLaTeX());
}
if (export.Empty)
{
export.Add(GetColumn(0).GetLaTeX());
}
return(output + export.Result);
}
public string KerBasis()
{
MyMatrix row_echelon = Clone();
string output = row_echelon.GaussLaTeX() + '\n';
LaTeXExport export = new LaTeXExport(1, ",", 1, false, "$$\\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 string GaussLaTeX(int max_m = -1, bool revert = true)
{
if (max_m == -1)
{
max_m = m;
}
LaTeXExport export = new LaTeXExport(m);
export.Add(GetLaTeX(max_m));
bool need_entry = false;
for (int i = 0; i < Math.Min(n, max_m); i++)
{
int j_start = i - 1, i_start;
do
{
j_start++;
for (i_start = i; i_start < n &&
values[i_start, j_start] == 0; i_start++)
{
;
}
} while (j_start < max_m - 1 && i_start == n);
if (i_start == n && j_start == max_m - 1)
{
break;
}
ElementarySwap(i, i_start);
if (values[i, j_start] != 1)
{
need_entry = true;
}
ElementaryProd(i, 1 / values[i, j_start]);
if (i != i_start)
{
export.Add(GetLaTeX(max_m));
need_entry = false;
}
bool done_sum = false;
for (int i_down = i + 1; i_down < n; i_down++)
{
if (values[i_down, j_start] != 0)
{
ElementarySum(i_down, i, -values[i_down, j_start] / values[i, j_start]);
done_sum = true;
}
}
if (done_sum)
{
export.Add(GetLaTeX(max_m));
need_entry = false;
}
}
if (revert)
{
for (int i = n - 1; i >= 0; i--)
{
int j_s = 0;
for (; j_s < max_m && values[i, j_s] == 0; j_s++)
{
;
}
if (j_s >= max_m)
{
continue;
}
bool done_sum = false;
for (int i_up = i - 1; i_up >= 0; i_up--)
{
if (values[i_up, j_s] != 0)
{
ElementarySum(i_up, i, -values[i_up, j_s] / values[i, j_s]);
done_sum = true;
}
}
if (done_sum)
{
export.Add(GetLaTeX(max_m));
need_entry = false;
}
}
}
if (need_entry)
{
export.Add(GetLaTeX(max_m));
}
return(export.Result);
}
public string SymmetricGauss()
{
if (!IsSquare)
{
throw new InvalidOperationException("Matrix is not square!");
}
if (!CheckSymmetry())
{
throw new InvalidOperationException("Matrix is not symmetric!");
}
LaTeXExport export = new LaTeXExport(m);
export.Add(GetLaTeX());
for (int i = 0; i < n; i++)
{
int i_start = i;
for (; i_start < n && values[i_start, i_start] == 0; i_start++)
{
;
}
if (i_start == n)
{
int j = i;
for (; j < n - 1; j++)
{
for (i_start = j + 1; i_start < n &&
values[i_start, j] == 0; i_start++)
{
;
}
if (i_start < n)
{
break;
}
}
if (j == n - 1 && i_start == n)
{
break;
}
ElementarySum(j, i_start, 1);
ElementarySum(j, i_start, 1, false);
export.Add(GetLaTeX());
i_start = j;
}
if (i_start != i)
{
ElementarySwap(i, i_start);
ElementarySwap(i, i_start, false);
export.Add(GetLaTeX());
}
for (int i_down = i + 1; i_down < n; i_down++)
{
if (values[i_down, i] != 0)
{
ElementarySum(i_down, i, -values[i_down, i] / values[i, i]);
ElementarySum(i_down, i, -values[i, i_down] / values[i, i], false);
export.Add(GetLaTeX());
}
}
}
bool need_entry = false;
for (int i = 0; i < n; i++)
{
if (values[i, i] != 1 && values[i, i] != -1 && values[i, i] != 0)
{
need_entry = true;
values[i, i] /= values[i, i].Abs();
}
}
if (need_entry)
{
export.Add(GetLaTeX());
}
return(export.Result);
}