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 RationalSquareMatrix operator *(RationalSquareMatrix a, RationalSquareMatrix b)
{
RationalSquareMatrix retVal = new RationalSquareMatrix(a.Rows, a.Columns);
for (int rowCount = 0; rowCount < retVal.Rows; rowCount++)
{
for (int colCount = 0; colCount < retVal.Columns; colCount++)
{
for (int retColCount = 0; retColCount < retVal.Columns; retColCount++)
{
retVal.InternalRep[rowCount, colCount] += a.InternalRep[rowCount, retColCount] * b.InternalRep[retColCount, colCount];
}
}
}
StringBuilder sb = new StringBuilder();
sb.Append(a.ToLatex());
sb.Append(b.ToLatex());
sb.Append(" = ");
sb.Append(retVal.ToLatex());
retVal.FullRep = sb.ToString();
return(retVal);
}
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 Rational Det2X2(RationalSquareMatrix rsm2X2, string CoFactor = "1")
{
Rational rCoFactor = Rational.Parse(CoFactor);
Rational ret = (rsm2X2[0, 0] * rsm2X2[1, 1] - rsm2X2[0, 1] * rsm2X2[1, 0]) * rCoFactor;
return(ret);
}
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 int Test_EMatrix()
{
RationalFactory rf = new RationalFactory();
RationalSquareMatrix I = RationalSquareMatrix.IdentityMatrix(3);
RationalSquareMatrix ACopy = rf[3, 3,
"1", "2", "-2",
"-1", "1", "3",
"2", "-1", "2"
];
RationalSquareMatrix ACopy2 = rf[3, 3,
"-7", "2", "-2",
"-3", "1", "3",
"8", "-1", "2"
];
RationalSquareMatrix ACopy3 = rf[4, 4,
"4", "7", "2", "3",
"1", "3", "1", "2",
"2", "5", "3", "4",
"1", "4", "2", "3"
];
string ll = RationalSquareMatrix.DetFullRep(ACopy);
HtmlOutputMethods.WriteLatexEqToHtmlAndLaunch(ll, "Test_EMatrix.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 static string DetFullRep(RationalSquareMatrix A)
{
StringBuilder sb = new StringBuilder();//Start building latex
Rational ret = 1;
RationalSquareMatrix I = IdentityMatrix(A.Rows);
int i = 0;
int j = 0;
sb.Append(@"\begin{aligned}");
sb.AppendFormat(@"&A = {0} I = {1}", A.ToLatex(), I.ToLatex() + @"\textrm{Initial matrix and identity matrix} \\ \\");//display A and I matrices before
List <int[]> inds = LowerEchelonIndexes(I);
foreach (int[] arr in inds)
{
i = arr[0];
j = arr[1];
Rational r = Rational.Abs(A[i, j]) / Rational.Abs(A[j, j]);
if (A[i, j] > 0 && A[j, j] > 0)
{
r = r * -1;
}
if (A[i, j] < 0 && A[j, j] < 0)
{
r = r * -1;
}
string comment = string.Format(@"R_{0} \rightarrow R_{0} + {1}R_{2}", (i + 1), r.ToLatex(), (j + 1));
I[i, j] = r;
sb.AppendFormat(@"&{0}{1} = ", A.ToLatex(), I.ToLatex());//display A matrix and augmented I matrix
A = I * A;
sb.AppendFormat(@"{0}", A.ToLatex() + comment + @" \\ \\");//display A matrix after elementary operation
I[i, j] = 0;
}
string combo = string.Empty;
for (i = 0; i < A.Rows; i++)
{
for (j = 0; j < A.Columns; j++)
{
if (i == j)
{
combo += A[i, j].ToLatex() + @"\cdot";
ret *= A[i, j];
}
}
}
sb.AppendFormat(@"&Det = {0} = {1}", combo.Substring(0, combo.Length - 5), ret.ToLatex());//display det of A matrix
sb.Append(@"\end{aligned}");
return(sb.ToString());
}
public RationalSquareMatrix Inverse()
{
RationalSquareMatrix Inv = null;
RationalVector rv = new RationalVector();
Inv = FaddevasMethod(this, out rv);
return(Inv);
}
public static int Test_Rational_Determinant()
{
RationalFactory rf = new RationalFactory();
RationalSquareMatrix A = rf[3, 3,
"1", "2", "-2",
"-1", "1", "3",
"2", "-1", "2"
];
RationalSquareMatrix ACopy3 = rf[4, 4,
"4", "7", "2", "3",
"1", "3", "1", "2",
"2", "5", "3", "4",
"1", "4", "2", "3"
];
RationalSquareMatrix ACopy3_2 = rf[3, 3,
1, 2, 3,
4, 1, 6,
7, 8, 1
];
List <RationalCoFactorInfo> cfList = RationalSquareMatrix.GetAllMatrixCoFactors(ACopy3);
StringBuilder sb = new StringBuilder();//Start building latex
sb.Append(@"\begin{aligned}");
sb.AppendFormat(@"&{0} \\ \\", ACopy3.ToLatex());
//foreach(IGrouping<string, RationalCoFactorInfo> funk in q.ToList())
foreach (RationalCoFactorInfo ci in cfList)
{
sb.AppendFormat(@"&{0} \\ \\", ci.Minor.MinorName + " = " + ((ci.Sign < 0) ? "-" : "") + ci.CoFactor.ToLatex() + ci.Minor.ToLatex());
foreach (List <RationalCoFactorInfo> lstChild in ci.ListOfLists)
{
foreach (RationalCoFactorInfo ci2 in lstChild)
{
//if (ci2.Minor.Rows == 4)
{
sb.AppendFormat(@"&{0} \\ \\", ci.Minor.MinorName + " = " + ((ci.Sign < 0) ? "-" : "") + ci.CoFactor.ToLatex() + ci2.CoFactor.ToLatex() + ci2.Minor.ToLatex());
}
}
}
}
sb.Append(@"&Det = " + RationalSquareMatrix.Det(ACopy3_2));
sb.Append(@"\end{aligned}");
HtmlOutputMethods.WriteLatexEqToHtmlAndLaunch(sb.ToString(), "Test_Rational_Determinant.html"); //display Latex via mathjax
return(0);
}
public static List <RationalCoFactorInfo> GetCoFactors(RationalSquareMatrix ParentMatrix)
{
List <RationalCoFactorInfo> cfiL = new List <RationalCoFactorInfo>();
int Order = ParentMatrix.Rows;
for (int i = 0; i < ParentMatrix.Columns; i++)
{
cfiL.Add(GetCoFactor(ParentMatrix, i + 1));
}
return(cfiL);
}
public RationalSquareMatrix Clone()
{
RationalSquareMatrix ret = new RationalSquareMatrix(this.Rows, this.Columns);
for (int i = 0; i < Rows; i++)
{
for (int j = 0; j < Columns; j++)
{
ret.InternalRep[i, j] = this.InternalRep[i, j];
}
}
ret.Name = this.Name;
ret.LatexName = this.LatexName;
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 static RationalSquareMatrix IdentityMatrix(int Order)
{
RationalSquareMatrix retVal = new RationalSquareMatrix(Order, Order);
for (int rowCount = 0; rowCount < retVal.Rows; rowCount++)
{
for (int colCount = 0; colCount < retVal.Columns; colCount++)
{
if (rowCount == colCount)
{
retVal[rowCount, colCount] = 1;
}
}
}
return(retVal);
}
public static Rational Det(RationalSquareMatrix A)
{
Rational ret = 1;
RationalSquareMatrix I = IdentityMatrix(A.Rows);
int i = 0;
int j = 0;
List <int[]> inds = LowerEchelonIndexes(I);
foreach (int[] arr in inds)
{
i = arr[0];
j = arr[1];
Rational r = Rational.Abs(A[i, j]) / Rational.Abs(A[j, j]);
if (A[i, j] > 0 && A[j, j] > 0)
{
r = r * -1;
}
if (A[i, j] < 0 && A[j, j] < 0)
{
r = r * -1;
}
I[i, j] = r;
A = I * A;
I[i, j] = 0;
}
for (i = 0; i < A.Rows; i++)
{
for (j = 0; j < A.Columns; j++)
{
if (i == j)
{
ret *= A[i, j];
}
}
}
return(ret);
}
public RationalSquareMatrix this[int Rows, int Columns, params string[] exps]
{
get
{
RationalSquareMatrix ret = new RationalSquareMatrix(Rows, Columns);
ret.Parent = this;
int cnt = 0;
for (int i = 0; i < Rows; i++)
{
for (int j = 0; j < Columns; j++)
{
ret[i, j] = Rational.Parse(exps[cnt++]);
}
}
return(ret);
}
}
public static List <int[]> UpperEchelonIndexes(RationalSquareMatrix A)
{
List <int[]> Indexes = new List <int[]>();
for (int i = 0; i < A.Rows; i++)
{
for (int j = 1; j < A.Columns; j++)
{
if (i == j)
{
int ind = j + 1;
while (ind < A.Columns)
{
Indexes.Add(new int[] { i, ind });
ind++;
}
}
}
}
return(Indexes);
}
public static RationalSquareMatrix KroneckerProduct(RationalSquareMatrix a, RationalSquareMatrix b)
{
int Rows = a.Rows * b.Rows; // calculate number of rows.
int Columns = a.Columns * b.Rows; // calculate number of columns
int incC = 0; // increment variable for column of b matrix
int incR = 0; // increment variable for row of b matrix
int incAMC = 0; // increment variable for column of a matrix
int incAMR = 0; // increment variable for row of a matrix
RationalSquareMatrix retVal = new RationalSquareMatrix(Rows, Columns);
int rowCount;
int colCount;
string exp = string.Empty;
for (rowCount = 0; rowCount < retVal.Rows; rowCount++)
{
if (incR > b.Rows - 1) // reached end of rows of b matrix
{
incR = 0;
incAMR++;
}
incAMC = 0;
for (colCount = 0; colCount < retVal.Columns; colCount++)
{
incC++;
if (incC > b.Columns - 1) // reached end of columns of b matrix
{
incC = 0;
incAMC++;
}
retVal[rowCount, colCount] = a[incAMR, incAMC] * b[incR, incC];
}
incR++;
}
retVal.FullRep = a.ToLatex() + @"\;\otimes\;" + b.ToLatex() + " = " + retVal.ToLatex(); //produce latex string
return(retVal);
}
public static RationalSquareMatrix operator *(RationalSquareMatrix a, Rational b)
{
RationalSquareMatrix retVal = new RationalSquareMatrix(a.Rows, a.Columns);
for (int i = 0; i < retVal.Rows; i++)
{
for (int j = 0; j < retVal.Columns; j++)
{
retVal.InternalRep[i, j] = a.InternalRep[i, j] * b;
}
}
StringBuilder sb = new StringBuilder();
sb.Append(b.ToLatex());
sb.Append(a.ToLatex());
sb.Append(" = ");
sb.Append(retVal.ToLatex());
retVal.FullRep = sb.ToString();
return(retVal);
}
public static List <RationalCoFactorInfo> GetAllMatrixCoFactors(RationalSquareMatrix ParentMatrix)
{
List <RationalCoFactorInfo> cfList = RationalSquareMatrix.GetCoFactors(ParentMatrix);
ParentMatrix.MinorName = "M1";
if (cfList[0].Minor.Rows == 2) //At two go back
{
return(cfList);
}
int inc = 0;
RationalCoFactorInfo cfi = null;
RationalCoFactorInfo cfiChild = null;
List <RationalCoFactorInfo> cfListChild = null;
string TopMinorName = string.Empty;
while (inc < cfList.Count)
{
if (cfi == null)
{
cfi = cfList[inc];
TopMinorName = "M" + (inc + 1).ToString();
cfi.Minor.MinorName = TopMinorName;
}
else if (cfi != null && cfi.ListOfLists.Count == 0) //init value
{
List <RationalCoFactorInfo> cfListTmp = RationalSquareMatrix.GetCoFactors(cfi.Minor);
cfi.ListOfLists.Add(cfListTmp);
cfListChild = new List <RationalCoFactorInfo>(cfListTmp);
if (cfListChild[0].Minor.Rows == 2) //end of line
{
cfList[inc] = cfi;
cfi = null;
inc++;
}
}
else if (cfi != null && cfi.ListOfLists.Count > 0) //have value
{
List <RationalCoFactorInfo> cfListTmp = null;
cfiChild = new RationalCoFactorInfo();
foreach (RationalCoFactorInfo cfiC in cfListChild)
{
cfListTmp = RationalSquareMatrix.GetCoFactors(cfiC.Minor);
cfi.ListOfLists.Add(cfListTmp);
cfiChild.ListOfLists.Add(cfListTmp);
}
cfListChild = new List <RationalCoFactorInfo>();
foreach (List <RationalCoFactorInfo> cfl in cfiChild.ListOfLists)
{
foreach (RationalCoFactorInfo cfiC in cfl)
{
cfListChild.Add(cfiC);
}
}
cfiChild = null;
if (cfListChild[0].Minor.Rows == 2) //end of line
{
cfList[inc] = cfi;
cfi = null;
inc++;
}
}
}
return(cfList);
}
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);
}