//From now on, our comments will use latex syntax
public static int Test_ElementaryMatrix_Multiply_ElementaryMatrix()
{
/*
* E_{ij}E_{rs} = e_ie'_je_re'_s = \delta_{r j}e'_ie'_s = \delta_{j r}E_{is} \\
* if\;r = j \\
* E_{ij}E_{rs} = \delta_{j j}E_{is} = E_{is}
*
*/
StringBuilder sb = new StringBuilder();
ElementaryMatrix E12 = new ElementaryMatrix(4, 4, "E13"); // 4 x 4 ElementaryMatrix
ElementaryMatrix E13 = new ElementaryMatrix(4, 4, "E32"); // 4 x 4 ElementaryMatrix
sb.Append(@"E_{ij}E_{rs} = e_ie'_je_re'_s = \delta_{r j}e'_ie'_s = \delta_{j r}E_{is} \\");
sb.Append(@"if\;r = j \\");
sb.Append(@"E_{ij}E_{rs} = \delta_{j j}E_{is} = E_{is} \\");
sb.Append(@"Output\;is: \\");
//Test Elementary Matrix * Elementary Matrix
ElementaryMatrix em = E12 * E13;
sb.Append(em.ToLatex("F"));
HtmlOutputMethods.WriteLatexEqToHtmlAndLaunch(sb.ToString(), "Test_ElementaryMatrix_Multiply_ElementaryMatrix.html"); //display Latex via mathjax
return(0);
}
public static int Test_ElementaryMatrix_ElementaryMatrix()
{
ElementaryMatrix em = new ElementaryMatrix(4, 4, "E11");
HtmlOutputMethods.WriteLatexEqToHtmlAndLaunch(em.ToLatex("F"), "Test_ElementaryMatrix_ElementaryMatrix.html");
return(0);
}
public static int Test_UnitVectorProductTo_ElementaryMatrix()
{
UnitVectorSpace uvs = new UnitVectorSpace(4); //Order four Unit Vector Space
UnitVector e2 = uvs["e2"]; // order 4 e2 unit vector
UnitVector e1 = uvs["e1"]; //order 4 e1 unit operator
ElementaryMatrix em = e2 * e1; //product of Unit Vectors
HtmlOutputMethods.WriteLatexEqToHtmlAndLaunch(em.ToLatex("F"), "Test_UnitVectorProductTo_ElementaryMatrix.html"); //display Latex via mathjax
return(0);
}
/*TODO: remove this GPG
* public static UnitVector operator*(ElementaryMatrix em, UnitVector uv)
* {
* UnitVector uvOut = null;
* //using following realtionships
* //Eij * er = ei * e'j * er
* // = &jr * ei where & is the Kronecker Delta
* UnitVectorSpace uvp = new UnitVectorSpace(uv.Order);
* UnitVector ei = uvp["e" + em.Major.ToString()];
* UnitVector ej = uvp["e" + em.Minor.ToString()];
* RowColumn rc = ej.IsRowOrColumn;
* ej.IsRowOrColumn = RowColumn.Row;
*
* uvOut = ei * ej * uv;
* ej.IsRowOrColumn = rc; //Set it back to what it was
* return uvOut;
* }
*/
public static ElementaryMatrix operator*(UnitVector e1, UnitVector e2)
{
ElementaryMatrix em = null;
RowColumn rc = e2.IsRowOrColumn;
if (e1.IsRowOrColumn == RowColumn.Row) //Dot product
{
return((ElementaryMatrix)DotProduct(e1, e2));
}
e2.IsRowOrColumn = RowColumn.Row; //transpose
string emName = "E" + e1.Name[1].ToString() + e2.Name[1].ToString();
em = new ElementaryMatrix(e1.Order, e2.Order, emName);
em.FullRep = em.LatexName + " = " + e1.ToLatex() + e2.ToLatex() + " = " + em.ToLatex();
e2.IsRowOrColumn = rc; //set back to what it was
return(em);
}
public static ElementaryMatrix operator *(ElementaryMatrix a, ElementaryMatrix b)
{
ElementaryMatrix retVal = new ElementaryMatrix(a.Rows, a.Columns);
for (int rowCount = 0; rowCount < retVal.Rows; rowCount++)
{
for (int colCount = 0; colCount < retVal.Columns; colCount++)
{
for (int k = 0; k < retVal.Columns; k++)
{
retVal.InternalRep[rowCount, colCount] += a.InternalRep[rowCount, k] * b.InternalRep[k, colCount];
if (retVal.InternalRep[rowCount, colCount] == 1)
{
retVal.Major = rowCount + 1;
retVal.Minor = colCount + 1;
retVal.Name = $"E{retVal.Major.ToString()}{retVal.Minor.ToString()}";
retVal.m_LatexName = $"E_{{{(retVal.Major).ToString() + (retVal.Minor).ToString()}}}";
}
}
}
}
StringBuilder sb = new StringBuilder();
sb.Append(a.LatexName + b.LatexName + " = ");
sb.Append(a.ToLatex());
sb.Append(b.ToLatex());
sb.Append(" = ");
sb.Append(retVal.LatexName + " = ");
sb.Append(retVal.ToLatex());
retVal.FullRep = sb.ToString();
return(retVal);
}
public static int Test_UnitVector_Multiply_ElementaryMatrix()
{
/*
* e'r * Eij = e'r * ei * e'j = &ri *e'j where & = Kronecker delta
*
*/
StringBuilder sb = new StringBuilder();
ElementaryMatrix E12 = new ElementaryMatrix(4, 4, "E12"); // 4 x 4 ElementaryMatrix
UnitVector e1 = new UnitVector("e1", 4); //Order four unit vector e1
UnitVector e2 = new UnitVector("e2", 4, RowColumn.Row); //Order four row unit vector e2
UnitVector er = new UnitVector("e3", 4, RowColumn.Row); //Order four unit row vector e3 our er above
/*
* i = 1, j = 2, r = 3
*/
sb.Append(@"e'_rE_{ij} = e'_re_ie'_j = \delta_{r j}e'j \\");
//Test matrix unit vector * Elementary Matrix, er * Eij
UnitVector uvE1 = er * E12;
sb.Append(@"e'_3E_{12} = " + uvE1.ToLatex() + @"\;");
//Test e'r * ei * e'j
UnitVector uvE2 = er * e1 * e2;
sb.Append(@"e'_3e_1e'_2 = " + uvE2.ToLatex() + @"\;");
//Test &ri * e'j
UnitVector uvE3 = UnitVector.KroneckerDelta(3, 1) * e2;
sb.Append(@" \delta_{3 1}e_2 = " + uvE3.ToLatex() + @" \tag{1}");
HtmlOutputMethods.WriteLatexEqToHtmlAndLaunch(sb.ToString(), "Test_UnitVector_Multiply_ElementaryMatrix.html"); //display Latex via mathjax
return(0);
}
public static int Test_ElementaryMatrix_Multiply_UnitVector()
{
/*
* Eij * er = ei*e'j*er = &jr *ei where & = Kronecker delta
*
*/
StringBuilder sb = new StringBuilder();
ElementaryMatrix E12 = new ElementaryMatrix(4, 4, "E12"); // 4 x 4 ElementaryMatrix
UnitVector e1 = new UnitVector("e1", 4); //Order four unit vector e1
UnitVector e2 = new UnitVector("e2", 4, RowColumn.Row); //Order four row unit vector e2
UnitVector er = new UnitVector("e3", 4); //Order four unit vector e3 our er above
/*
* i = 1, j = 2, r = 3
*/
//Test matrix * unit vector, Eij * er
UnitVector uvE1 = E12 * er;
sb.Append(@"E_{12}e_3 = " + uvE1.ToLatex() + @"\;");
//Test e1* e'j * er
UnitVector uvE2 = e1 * e2 * er;
sb.Append(@"e_1e'_2e_3 = " + uvE2.ToLatex() + @"\;");
//Test &jr * ei
UnitVector uvE3 = UnitVector.KroneckerDelta(2, 3) * e1;
sb.Append(@" \delta_{2 3}e_1 = " + uvE3.ToLatex());
HtmlOutputMethods.WriteLatexEqToHtmlAndLaunch(sb.ToString(), "Test_ElementaryMatrix_Multiply_UnitVector.html"); //display Latex via mathjax
return(0);
}
