public static SquareRealMatrix operator *(SquareRealMatrix a, SquareRealMatrix b)
{
SquareRealMatrix retVal = new SquareRealMatrix(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];
double sens = retVal.InternalRep[rowCount, colCount];
if (Math.Abs(sens) < 1.0e-8d) //f**ked up value set to zero // TODO: tell us how you really feel about it, Brad. GPG
{
retVal.InternalRep[rowCount, colCount] = 0;
}
}
}
}
StringBuilder sb = new StringBuilder();
sb.Append("$$");
sb.Append(a.ToLatex());
sb.Append(" \\cdot ");
sb.Append(b.ToLatex());
sb.Append(" = ");
sb.Append(retVal.ToLatex());
sb.Append("$$");
retVal.m_FullRep = sb.ToString();
return(retVal);
}
public static SquareRealMatrix operator +(SquareRealMatrix a, SquareRealMatrix b)
{
SquareRealMatrix retVal = new SquareRealMatrix(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.InternalRep[i, j];
}
}
StringBuilder sb = new StringBuilder();
sb.Append("$$");
sb.Append(a.ToLatex());
sb.Append(" + ");
sb.Append(b.ToLatex());
sb.Append(" = ");
sb.Append(retVal.ToLatex());
sb.Append("$$");
retVal.m_FullRep = sb.ToString();
return(retVal);
}
public static SquareRealMatrix operator -(double b, SquareRealMatrix a)
{
SquareRealMatrix retVal = new SquareRealMatrix(a.Rows, a.Columns);
for (int rowCount = 0; rowCount < retVal.Rows; rowCount++)
{
for (int colCount = 0; colCount < retVal.Columns; colCount++)
{
retVal.InternalRep[rowCount, colCount] = b - a.InternalRep[rowCount, colCount];
}
}
StringBuilder sb = new StringBuilder();
sb.Append("$$");
sb.Append(b.ToString());
sb.Append(" - ");
sb.Append(a.ToLatex());
sb.Append(" = ");
sb.Append(retVal.ToLatex());
sb.Append("$$");
retVal.m_FullRep = sb.ToString();
return(retVal);
}
public static int Test_KroneckerSum()
{
RealFactory rf = new RealFactory();
SquareRealMatrix A = rf[2, 2,
1, -1,
0, 2
];
SquareRealMatrix B = rf[2, 2,
1, 0,
2, -1
];
StringBuilder sb = new StringBuilder();//Start building latex
sb.Append(@"\begin{aligned}");
sb.AppendFormat(@"&A = {0}\;B = {1}", A.ToLatex(), B.ToLatex() + @" \\ \\");
sb.AppendFormat(@"&C = A\;\oplus\;B = {0}", SquareRealMatrix.KroneckerSum(A, B).ToLatex());
sb.Append(@"\end{aligned}");
HtmlOutputMethods.WriteLatexEqToHtmlAndLaunch(sb.ToString(), "Test_KroneckerSum.html"); //display Latex via mathjax
return(0);
}
public static int Test_UnitVector_Col_Row_Accessors()
{
List <double> initer = new List <double> {
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16
}; //init matrix vector
SquareRealMatrix A = new SquareRealMatrix(4, 4, initer); //create 4X4 matrix
A.Name = "A"; //give it a name
UnitVectorSpace uvs = new UnitVectorSpace(4); //Create unit vector space to use
UnitVector e2 = new UnitVector("e2", 4, RowColumn.Column);
UnitVector e2_p = new UnitVector("e2", 4, RowColumn.Row);
RealVector rv = A * e2;
StringBuilder sb = new StringBuilder();//Start building latex
sb.Append(@"\begin{aligned}");
sb.AppendFormat(@"&A = &{0} \\ \\", A.ToLatex()); //Display Original A matrix
sb.Append(@"&A_{.2} = &" + rv.ToLatex() + @" \\ \\");
RealVector rvRow = e2_p * A;
sb.Append(@"&A_{2.}' = &" + rvRow.ToLatex());
sb.Append(@"\end{aligned}");
HtmlOutputMethods.WriteLatexEqToHtmlAndLaunch(sb.ToString(), "Test_UnitVector_Col_Row_Accessors.html"); //display Latex via mathjax
return(0);
}
public static int Test_Partioned_Matrix()
{
List <double> initer = new List <double> {
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16
}; //init matrix vector
SquareRealMatrix A = new SquareRealMatrix(4, 4, initer); //create 4X4 matrix
A.Name = "A"; //give it a name
SquareRealMatrix AColumns = new SquareRealMatrix(new List <RealVector> {
A[".1"], A[".2"], A[".3"], A[".4"]
}); //Create partioned matrix from columns
SquareRealMatrix ARows = new SquareRealMatrix(new List <RealVector> {
A["1."], A["2."], A["3."], A["4."]
}); //Create partioned matrix from rows
StringBuilder sb = new StringBuilder(); //Start building latex
sb.Append(@"\begin{aligned}");
sb.AppendFormat(@"&A = &{0} \\ \\", A.ToLatex()); //Display Original A matrix
sb.Append(@"&A = \left[ A_{.1}\;A_{.2}\;A_{.3}\;A_{.4} \right] = \;\;" + "&" + AColumns.ToLatex() + @" \\ \\"); //partioned matrix via columns of A
sb.Append(@"&\left[ A_{1.}\;A_{2.}\;A_{3.}\;A_{4.} \right] = \;\;" + "&" + ARows.ToLatex() + @" \\ \\"); //partioned matrix via rows of A
sb.Append(@"&A = \left[ A_{1.}\;A_{2.}\;A_{3.}\;A_{4.} \right]' = \;\;" + "&" + ARows.Transpose().ToLatex() + @" \\ \\"); //transpose to get A
sb.Append(@"\end{aligned}");
HtmlOutputMethods.WriteLatexEqToHtmlAndLaunch(sb.ToString(), "Test_Partioned_Matrix.html"); //display Latex via mathjax
return(0);
}
public static SquareRealMatrix KroneckerSum(SquareRealMatrix a, SquareRealMatrix b)
{
SquareRealMatrix retVal = null;
SquareRealMatrix id = IdentityMatrix(a.Rows);
retVal = KroneckerProduct(a, id) + KroneckerProduct(id, b);
retVal.FullRep = a.ToLatex() + @"\;\oplus\;" + b.ToLatex() + " = " + retVal.ToLatex(); //produce latex string
return(retVal);
}
public static string MultipliedVectorLatex(SquareRealMatrix A, double[] VectorIn, double[] VectorOut)
{
StringBuilder sb = new StringBuilder();
sb.Append(A.ToLatex());
sb.Append(VectorToLatex(VectorIn));
sb.Append(" = ");
sb.Append(VectorToLatex(VectorOut));
return(sb.ToString());
}
public static int Test_Rows_Of_Matrix()
{
List <double> initer = new List <double> {
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16
}; //init matrix vector
SquareRealMatrix A = new SquareRealMatrix(4, 4, initer); //create 4X4 matrix
A.Name = "A"; //give it a name
RealVector rvRow = A["2."]; //use accessor to get row 2 of matrix
string outR = @"\begin{aligned}&A = " + A.ToLatex() + @" \\ \\" + "&" + rvRow.ToLatex("F") + @"\end{aligned}"; //use row accessor A2. which returns row 2.
HtmlOutputMethods.WriteLatexEqToHtmlAndLaunch(outR, "TestRows_Of_Matrix.html"); //display Latex via mathjax
return(0);
}
public static SquareRealMatrix KroneckerProduct(SquareRealMatrix a, SquareRealMatrix 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
SquareRealMatrix retVal = new SquareRealMatrix(Rows, Columns);
int rowCount = 0;
int colCount = 0;
double exp = 0;
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++)
{
exp = a[incAMR, incAMC] * b[incR, incC];
incC++;
if (incC > b.Columns - 1)////reached end of columns of b matrix
{
incC = 0;
incAMC++;
}
retVal[rowCount, colCount] = exp;
}
incR++;
}
retVal.FullRep = a.ToLatex() + @"\;\otimes\;" + b.ToLatex() + " = " + retVal.ToLatex(); //produce latex string
return(retVal);
}
public static int Test_VecOperator()
{
RealFactory rf = new RealFactory(); //create a real factory
SquareRealMatrix A = rf[2, 2, //create a 2 X 2 real matrix
1, 2,
3, 4
];
RealVector VecA = A.Vec("A"); //use Vec operator giving the matrix a name
StringBuilder sb = new StringBuilder(); //Start building latex
sb.Append(@"\begin{aligned}");
sb.AppendFormat(@"&A = {0}", A.ToLatex() + @" \\ \\"); //display A matrix
sb.AppendFormat(@"&{0}", VecA.ToLatex("F")); //display Vec A
sb.Append(@"\end{aligned}");
HtmlOutputMethods.WriteLatexEqToHtmlAndLaunch(sb.ToString(), "Test_VecOperator.html"); //display Latex via mathjax
return(0);
}
public static int Test_TraceFunction()
{
RealFactory rf = new RealFactory(); //create a real factory
SquareRealMatrix A = rf[3, 3, //create a 3 X 3 real matrix
1, 2, 3,
7, 8, 9,
6, 5, 4
];
StringBuilder sb = new StringBuilder();//Start building latex
sb.Append(@"\begin{aligned}");
sb.AppendFormat(@"&A = {0}", A.ToLatex() + @" \\ \\"); //display A matrix
sb.AppendFormat(@"&tr A = {0}", A.Trace() + @" \\ \\"); //display trace
sb.Append(@"\end{aligned}");
HtmlOutputMethods.WriteLatexEqToHtmlAndLaunch(sb.ToString(), "Test_TraceFunction.html"); //display Latex via mathjax
return(0);
}
public static SquareRealMatrix ElementaryMatrix(int rows, int columns, string Name)
{
SquareRealMatrix retVal = new SquareRealMatrix(rows, columns);
retVal.Name = Name;
if (retVal.Name[0] != 'E')
{
throw new Exception("Name of ElementaryMatrix must begin with a capital E followed by two number indices");
}
int oI1 = 0;
int oI2 = 0;
try
{
if (!int.TryParse(retVal.Name[1].ToString(), out oI1))
{
throw new Exception("Name of ElementaryMatrix must begin with a capital E followed by two number indices, index 1 bad.");
}
if (!int.TryParse(retVal.Name[2].ToString(), out oI2))
{
throw new Exception("Name of ElementaryMatrix must begin with a capital E followed by two number indices, index 2 bad");
}
retVal[oI1 - 1, oI2 - 1] = 1;
retVal.LatexName = @"E_{" + (oI1).ToString() + (oI2).ToString() + "}";
}
catch (Exception)
{
throw new Exception("Name of ElementaryMatrix must begin with a capital E followed by two number indices. Could not parse indices.");
}
retVal.FullRep = retVal.LatexName + @"\;=\;" + retVal.ToLatex();
return(retVal);
}
