public static RationalCoFactorInfo GetCoFactor(RationalSquareMatrix symIn, int Column)
{
RationalCoFactorInfo cfi = new RationalCoFactorInfo();
cfi.Sign = (int)Math.Pow(-1, Column + 1);
RationalVector col = symIn[Column - 1];
cfi.CoFactor = col[0];
List <Rational> symList = new List <Rational>();
for (int i = 1; i < symIn.Rows; i++)
{
for (int j = 0; j < symIn.Columns; j++)
{
if (j + 1 != Column)
{
symList.Add(symIn[i, j]);
}
}
}
cfi.Minor = new RationalSquareMatrix(symIn.Rows - 1, symIn.Columns - 1, symList);
cfi.Minor.MinorName = symIn.MinorName;
return(cfi);
}
public static RationalSquareMatrix FaddevasMethod(RationalSquareMatrix AIn, out RationalVector CharacteristicEquation)
{
RationalSquareMatrix A = AIn.Clone();
CharacteristicEquation = new RationalVector();
RationalSquareMatrix A_n = A;
Rational b_n = 1;
RationalSquareMatrix B_n = null;
RationalSquareMatrix I = null;
RationalSquareMatrix AInv = null;
int i = 0;
for (i = 1; i < A.Rows; i++)
{
b_n = -A_n.Trace() / (i);
CharacteristicEquation.Add(b_n);
I = RationalSquareMatrix.IdentityMatrix(A.Rows);
B_n = A_n + b_n * I;
A_n = A * B_n;
}
b_n = -A_n.Trace() / (i);
CharacteristicEquation.Add(b_n);
AInv = -1 / b_n * B_n;
AInv.FullRep = A.ToLatex() + "^{-1} = " + AInv.ToLatex();
return(AInv);
}
public static int Test_CramersRule()
{
RationalFactory rf = new RationalFactory(); //Create rational factory
RationalSquareMatrix ACopy = rf[3, 3, //Matrix to solve
"1", "2", "-2",
"-1", "1", "3",
"2", "-1", "2"
];
RationalVector rv = new RationalVector {
-7, 3, 8
}; //values to solve for
StringBuilder sb = new StringBuilder(); //Start building latex
sb.Append(@"\begin{aligned}");
//Start system of linear equations
sb.AppendFormat(@"&x_1 + 2x_2 - 2x_3 = -7 \\ \\");
sb.AppendFormat(@"&-x_1 + x_2 + 3x_3 = 3 \\ \\");
sb.AppendFormat(@"&2x_1 - x_2 + 2x_3 = 8 \\ \\");
RationalVector rvSolved = ACopy.CramersRule(rv); //solve system of linear equations
sb.AppendFormat(@"&x_1 = {0}, x_2 = {1}, x_3 = {2}", rvSolved[0].ToLatex(), rvSolved[1].ToLatex(), rvSolved[2].ToLatex()); //output values
sb.Append(@"\end{aligned}");
HtmlOutputMethods.WriteLatexEqToHtmlAndLaunch(sb.ToString(), "Test_CramersRule.html"); //display Latex via mathjax
return(0);
}
public static int Test_RationalSquareMatrix()
{
RationalFactory rf = new RationalFactory();
RealFactory rff = new RealFactory();
RationalSquareMatrix A = rf[3, 3,
"1", "2", "-2",
"-1", "1", "3",
"2", "-1", "2"
];
SquareRealMatrix SA = rff[3, 3,
7, 2, -2,
3, 1, 3,
8, -1, 2
];
RationalVector rv = rf["7", "3", "8"];
StringBuilder sb = new StringBuilder();//Start building latex
sb.Append(@"\begin{aligned}");
sb.AppendFormat(@"&A = {0}", A.ToLatex() + @" \\ \\"); //display A matrix
A[0] = rv;
sb.AppendFormat(@"&Ab = {0}", A.ToLatex()); //display Vec A
sb.AppendFormat(@"&Det = {0}", SA.Determinant()); //display Vec A
sb.Append(@"\end{aligned}");
HtmlOutputMethods.WriteLatexEqToHtmlAndLaunch(sb.ToString(), "Test_VecOperator.html"); //display Latex via mathjax
return(0);
}
public RationalSquareMatrix Inverse()
{
RationalSquareMatrix Inv = null;
RationalVector rv = new RationalVector();
Inv = FaddevasMethod(this, out rv);
return(Inv);
}
public static RationalVector operator +(Rational value, RationalVector v)
{
RationalVector vM = new RationalVector();
for (int i = 0; i < v.Count; i++)
{
vM.Add(value + v[i]);
}
return(vM);
}
public static RationalVector operator /(RationalVector v, Rational value)
{
RationalVector vM = new RationalVector();
for (int i = 0; i < v.Count; i++)
{
vM.Add(v[i] / value);
}
return(vM);
}
public static RationalVector operator -(RationalVector v1, RationalVector v2)
{
RationalVector vM = new RationalVector();
for (int i = 0; i < v1.Count; i++)
{
vM.Add(v1[i] - v2[i]);
}
return(vM);
}
public RationalVector this[params string[] exps]
{
get
{
RationalVector rv = new RationalVector();
foreach (string r in exps)
{
rv.Add(Rational.Parse(r));
}
return(rv);
}
}
public static Rational DotProduct(RationalVector v1, RationalVector v2)
{
Rational ret = 0;
if (v1.Count != v2.Count)
{
throw new Exception("Vectors must be equal in length");
}
for (int i = 0; i < v1.Count; i++)
{
ret += (v1[i] * v2[i]);
}
return(ret);
}
public RationalVector CramersRule(RationalVector VectorToSolve)
{
RationalVector Deltas = new RationalVector();
RationalSquareMatrix A = this.Clone();
Rational Delta = RationalSquareMatrix.Det(A);
for (int i = 0; i < this.Rows; i++)
{
RationalVector rvSave = A[i];
A[i] = VectorToSolve;
Deltas.Add(RationalSquareMatrix.Det(A) / Delta);
A[i] = rvSave;
}
return(Deltas);
}
public RationalVector this[int Column]
{
get
{
RationalVector ret = new RationalVector();
for (int i = 0; i < this.Rows; i++)
{
ret.Add(this[i, Column]);
}
return(ret);
}
set
{
for (int i = 0; i < this.Rows; i++)
{
this[i, Column] = value[i];
}
}
}
public static RationalVector Normalize(RationalVector v)
{
return(v / new Rational(Math.Sqrt(DotProduct(v, v).ToDouble())));
}
public static int Test_FaddevasMethod()
{
RationalFactory rf = new RationalFactory();
RationalSquareMatrix A = rf[3, 3,
"1", "0", "-2",
"4", "1", "0",
"0", "2", "1"
];
RationalVector rv = new RationalVector();
RationalSquareMatrix AInv = RationalSquareMatrix.FaddevasMethod(A, out rv);
StringBuilder sb = new StringBuilder();//Start building latex
sb.Append(@"A^{-1} = " + AInv.ToLatex());
HtmlOutputMethods.WriteLatexEqToHtmlAndLaunch(AInv.ToString("F"), "Test_FaddevasMethod_Determinant.html"); //display Latex via mathjax
/*
* RationalSquareMatrix A1 = A.Clone();
* StringBuilder sb = new StringBuilder();//Start building latex
* sb.Append(@"\begin{aligned}");
* sb.AppendFormat(@"&A1 = {0} \\ \\", A1.ToLatex());
*
* Rational b1 = -A1.Trace();
* sb.AppendFormat(@"&b1 = {0} \\ \\", b1.ToLatex());
* RationalSquareMatrix I = RationalSquareMatrix.IdentityMatrix(A.Rows);
*
* RationalSquareMatrix B1 = A1 + (b1 * I);
* sb.AppendFormat(@"&B1 = {0} \\ \\", B1.ToLatex());
*
* RationalSquareMatrix A2 = A * B1;
* sb.AppendFormat(@"&A2 = {0} \\ \\", A2.ToLatex());
*
* Rational b2 = A2.Trace() / -2;
* sb.AppendFormat(@"&b2 = {0} \\ \\", b2.ToLatex());
*
* I = RationalSquareMatrix.IdentityMatrix(A.Rows);
* RationalSquareMatrix B2 = A2 + b2 * I;
* sb.AppendFormat(@"&B2 = {0} \\ \\", B2.ToLatex());
*
* RationalSquareMatrix A3 = A * B2;
* sb.AppendFormat(@"&A3 = {0} \\ \\", A3.ToLatex());
*
* Rational b3 = A3.Trace() / -3;
* sb.AppendFormat(@"&b3 = {0} \\ \\", b3.ToLatex());
*
* RationalSquareMatrix AInv = 1/b3 * B2;
* sb.Append(@"&A^{-1} = " + AInv.ToLatex() + @" \\ \\");
*
*
* RationalSquareMatrix A_n = A;
* Rational b_n = 1;
* RationalSquareMatrix B_n = null;
* int i = 0;
* for(i = 0; i < A.Rows - 1; i++)
* {
* b_n = -A_n.Trace() / (i + 1);
* I = RationalSquareMatrix.IdentityMatrix(A.Rows);
*
* B_n = A_n + b_n * I;
* sb.Append(@"&Bn = " + B_n.ToLatex() + @" \\ \\");
*
* A_n = A * B_n;
* sb.Append(@"&An = " + A_n.ToLatex() + @" \\ \\");
* }
*
* b_n = -A_n.Trace() / (i + 1);
* sb.Append(@"&bn = " + b_n.ToLatex() + @" \\ \\");
*
* AInv = 1/b_n * B_n;
* sb.Append(@"&A^{-1} = " + AInv.ToLatex() + @" \\ \\");
*
* sb.Append(@"\end{aligned}");
* HtmlOutputMethods.WriteLatexEqToHtmlAndLaunch(sb.ToString(), "Test_FaddevasMethod_Determinant.html"); //display Latex via mathjax
*/
return(0);
}