private void factorLUToolStripMenuItem_Click(object sender, EventArgs e)
{
try
{
if (OutputMatrix != null)
{
OutputMatrix.FactorLU_withP();
MMatrix P = new MMatrix(OutputMatrix.LU_P);
MMatrix L = new MMatrix(OutputMatrix.LU_L);
MMatrix U = new MMatrix(OutputMatrix.LU_U);
string s = "\n\n\nFactor LU:\n";
s += "\nP=\n" + P.PrintToString();
s += "\nL=\n" + L.PrintToString();
s += "\nU=\n" + U.PrintToString();
s += "\nA=P*LU\n" + (P.Transpose()*L*U).PrintToString();
RichText_Display(s);
}
}
catch (MMatrixException exp)
{
MessageBox.Show("INFO: " + exp.Message, sProjectTile, MessageBoxButtons.OK, MessageBoxIcon.Warning);
}
}
private void buttonGenerateMatrix_Click(object sender, EventArgs e)
{
Random rand = new Random();
int rows = (int)numericUpDownRow.Value;
int cols = (int)numericUpDownCol.Value;
min = (int)numericUpDownMin.Value;
max = (int)numericUpDownMax.Value;
if (radioButtonRandom.Checked)
MainMatrix = MMatrix.RandomMatrix(rows, cols, min, max);
else if (radioButtonDiagonal.Checked)
{
MainMatrix = MMatrix.DiagonalMatrix(rows, rand.Next(max));
cols = rows;
}
else if (radioButtonIdentity.Checked)
{
MainMatrix = MMatrix.DiagonalMatrix(rows, 1);
cols = rows;
}
else if (radioButtonSymetric.Checked)
{
MainMatrix = MMatrix.RandomMatrix(rows, cols, min, (int)Math.Sqrt(max));
MainMatrix = MainMatrix * MainMatrix.Transpose();
cols = rows;
}
//Matrix A
this.dataGridViewMatrix.ColumnHeadersHeightSizeMode = DataGridViewColumnHeadersHeightSizeMode.DisableResizing;
dataGridViewMatrix.SuspendLayout();
dataGridViewMatrix.Columns.Clear();
DataGridViewColumn[] DCS = new DataGridViewColumn[cols];
for (int i = 0; i < cols; ++i)
{
DataGridViewColumn column = new DataGridViewTextBoxColumn();
column.HeaderText = string.Concat("A", (i + 1).ToString());
DCS[i] = column;
}
this.dataGridViewMatrix.Columns.AddRange(DCS);
dataGridViewMatrix.Rows.Add(rows);
//for DataGrid: [column, row]
for (int j = 0; j < MainMatrix.col; ++j)
for (int i = 0; i < MainMatrix.row; ++i)
dataGridViewMatrix[j,i].Value = MainMatrix[i, j];
//this.dataGridViewMatrix.AutoSizeColumnsMode = DataGridViewAutoSizeColumnsMode.DisplayedCells;
dataGridViewMatrix.ResumeLayout();
numericUpDownCol.Value = cols;
//Vector b
b = Vector.RandomVector(rows, min, max);
dataGridViewVectorb.SuspendLayout();
dataGridViewVectorb.Columns.Clear();
dataGridViewVectorb.Columns.Add("b","b");
dataGridViewVectorb.Columns[0].Width = ColWidth;
dataGridViewVectorb.Rows.Add(rows);
for (int i = 0; i < b.Elements.Length; ++i)
dataGridViewVectorb[0, i].Value = b[i];
dataGridViewVectorb.ResumeLayout();
}
public void MatrixTest()
{
double[,] Arr1 = new double[4, 4] { { 1, 1, 0, 3 }, { 2, 1, -1, 1 }, { 3, -1, -1, 2 }, { -1, 2, 3, -1 } };
double[,] Arr2 = new double[3, 3] { { 4, -1, 1 }, { -1, 4.25, 2.75 }, { 1, 2.75, 3.5 } };
MMatrix A = new MMatrix(Arr1);
MMatrix B = new MMatrix();
MMatrix C = new MMatrix();
string s = "";
try
{
//A = MMatrix.RandomMatrix(size,0,10);
s += "\nMatrix A=\n" + A.PrintToString();
s += "\nDet (A)= \n" + Convert.ToString(A.Determinant()) + "\n";
s += "\nA^-1= \n" + A.Inverse().PrintToString();
s += "\nA*A^-1= \n" + (A * A.Inverse()).PrintToString();
C = A * A.Transpose();
s += "\nC=A*A^T=\n" + C.PrintToString();
/////////////////Factor A = LDL*
MMatrix.FactorLDLt(C);
s += "\nFactor LDL*(C): L=\n" + (new MMatrix(C.LDL_L)).PrintToString();
s += "\nFactor LDL*(C): D=\n" + (new MMatrix(C.LDL_D)).PrintToString();
B = (new MMatrix(C.LDL_L)) * (new MMatrix(C.LDL_D)) * (new MMatrix(C.LDL_L)).Transpose();
s += "\nFactor LDL*: C=L*D*L^T\n" + B.PrintToString();
B = (new MMatrix(C.LDL_L)) * (new MMatrix(C.LDL_L)).Transpose();
s += "\nFactor LDL*: C=L*L^T\n" + B.PrintToString();
/////////////////Factor A = LU
C.FactorLU();
s += "\nFactor LU(C): L=\n" + (new MMatrix(C.LU_L)).PrintToString();
s += "\nFactor LU(C): U=\n" + (new MMatrix(C.LU_U)).PrintToString();
s += "\nFactor LU: C=L*U\n" + ((new MMatrix(C.LU_L)) * (new MMatrix(C.LU_U))).PrintToString();
///////////////////Factor A = PLU
A.FactorLU_withP();
s += "\nFactor LU (A): P=\n" + (new MMatrix(A.LU_P)).PrintToString();
s += "\nFactor LU (A): L=\n" + (new MMatrix(A.LU_L)).PrintToString();
s += "\nFactor LU (A): U=\n" + (new MMatrix(A.LU_U)).PrintToString();
s += "\nFactor LU: A=PLU\n" + ((new MMatrix(A.LU_P)).Transpose() * (new MMatrix(A.LU_L)) * (new MMatrix(A.LU_U))).PrintToString();
this.RichText_Display(s);
OutputMatrix = C;
}
catch (MMatrixException exp)
{
MessageBox.Show("INFO: " + exp.Message, sProjectTile, MessageBoxButtons.OK, MessageBoxIcon.Warning);
}
}
private void factorLDLtToolStripMenuItem_Click(object sender, EventArgs e)
{
try
{
if (OutputMatrix != null)
{
OutputMatrix.FactorLDLt();
MMatrix L = new MMatrix(OutputMatrix.LDL_L);
MMatrix D = new MMatrix(OutputMatrix.LDL_D);
string s = "\n\n\nFactor LDL*:\n";
s += "\nL=\n" + L.PrintToString();
s += "\nD=\n" + D.PrintToString();
s += "\nA=LDL*\n" + (L*D*L.Transpose()).PrintToString();
RichText_Display(s);
}
}
catch (MMatrixException exp)
{
MessageBox.Show("INFO: " + exp.Message, sProjectTile, MessageBoxButtons.OK, MessageBoxIcon.Warning);
}
}
public static double L2Norm(MMatrix A)
{
return Math.Sqrt(MMatrix.SpectralRadius(A.Transpose() * A));
}
public void EigenvectorTest()
{
double[,] Arr1 = new double[4, 4] { { 4, 1, -2, 2 }, { 1, 2, 0, 1 }, { -2, 0, 3, -2 }, { 2, 1, -2, -1 } };
double[,] Arr2 = new double[2, 3] { { 3,1,1 }, { -1, 3,1 }};
double[,] Arr3 = new double[5, 5] { { 2, 0, 8, 6, 0 }, { 1, 6, 0, 1, 7 }, { 5, 0, 7, 4, 0 }, { 7, 0, 8, 5, 0 }, { 0, 10, 0, 0, 7 } };
double[,] Arr4 = new double[4, 4] { { 3, 1, 0, 1 }, { 1, 3, 1, 1 }, { 0, 1, 3, 1 }, { 1, 1, 1, 3 } };
MMatrix A = new MMatrix(Arr2);
MMatrix B = new MMatrix();
string s = "";
Vector v = new Vector();
MMatrix Eigenvectors = new MMatrix();
try
{
//A = MMatrix.RandomMatrix(3,0,255);
B = A*A.Transpose();
s += "\nAA*=\n" + B.PrintToString();
B.Jacobi_Cyclic_Method(ref v, ref Eigenvectors);
s += "\nBefore sort:";
s += "\nEigenvalues of(A*At)=" + v.PrintToString();
s += "\nEigenvectors of A*At:\n" + Eigenvectors.PrintToString();
MMatrix.SortEigen(ref v, ref Eigenvectors);
s += "\nAfter sort:";
s += "\nEigenvalues of(A*At)=" + v.PrintToString();
s += "\nEigenvectors of A*At:\n" + Eigenvectors.PrintToString();
//This is not neccesary anymore since the eigenvectors are already orthonomalized
s += "\nOrthonormalize eigenvectors(Ax = 0)\n" + MMatrix.Orthonormalize(Eigenvectors).PrintToString();
this.RichText_Display(s);
}
catch (MMatrixException exp)
{
MessageBox.Show("INFO: " + exp.Message, sProjectTile, MessageBoxButtons.OK, MessageBoxIcon.Warning);
}
}
public static bool IsOrthogonal(MMatrix matrix)
{
MMatrix I = MMatrix.DiagonalMatrix(matrix.row, 1);
return (matrix * matrix.Transpose() == I);
}
//A = U*S*Vt
//A*At = U*S^2*Ut
//At*A = V*S^2*Vt
//A*At = (At*A)t
//This method is not right
public static void FactorSVD_LDLt(MMatrix A)
{
MMatrix AA = new MMatrix();
MMatrix Eigenvectors = new MMatrix();
Vector Eigenvalues = new Vector();
int index = A.row;
if (A.row > A.col)
index = A.col;
AA = A * A.Transpose();
AA.FactorLDLt();
Eigenvectors = new MMatrix(AA.LDL_L);
Eigenvalues = new Vector(AA.row);
for (int i = 0; i < index; ++i)
Eigenvalues[i] = AA.LDL_D[i, i];
SortEigen(ref Eigenvalues, ref Eigenvectors);
A.SVD_U = Eigenvectors.MArray;
if (A.SVD_S == null)
A.SVD_S = new double[A.row, A.col];
for (int i = 0; i < index; ++i)
A.SVD_S[i, i] = Math.Sqrt(Eigenvalues[i]);
AA = AA.Transpose();
AA.FactorLDLt();
Eigenvectors = new MMatrix(AA.LDL_L);
Eigenvalues = new Vector(AA.row);
for (int i = 0; i < index; ++i)
Eigenvalues[i] = AA.LDL_D[i, i];
SortEigen(ref Eigenvalues, ref Eigenvectors);
A.SVD_Vt = Eigenvectors.Transpose().MArray;
}
//A = U*S*Vt
//This method is not right
public static void FactorSVD(MMatrix A)
{
MMatrix B = new MMatrix();
Vector Eigenvalues = new Vector();
MMatrix Eigenvectors = new MMatrix();
int index;
//U
B = A * A.Transpose();
B.Jacobi_Cyclic_Method(ref Eigenvalues,ref Eigenvectors);
SortEigen(ref Eigenvalues,ref Eigenvectors);
A.SVD_U = Eigenvectors.MArray;
//S
A.SVD_S = new double[A.row, A.col];
index = (A.row < A.col) ? (A.row) : (A.col);
for (int i = 0; i < index; ++i)
A.SVD_S[i, i] = Math.Sqrt(Eigenvalues[i]);
//V
B = B.Transpose();
B.Jacobi_Cyclic_Method(ref Eigenvalues,ref Eigenvectors);
SortEigen(ref Eigenvalues,ref Eigenvectors);
A.SVD_Vt = Eigenvectors.Transpose().MArray;
}
//A = L*D*Lt
private static void FactorLDLt(MMatrix A, int size)
{
A.FactorLU();
A.LDL_L = (double[,])A.LU_L.Clone();
MMatrix MU = new MMatrix(A.LU_U);
MU = MU.Transpose();
MU.FactorLU();
A.LDL_D = (double[,])MU.LU_U.Clone();
}
private void buttonGenerateMatrix_Click(object sender, EventArgs e)
{
Random rand = new Random();
int rows = (int)numericUpDownRow.Value;
int cols = (int)numericUpDownCol.Value;
min = (int)numericUpDownMin.Value;
max = (int)numericUpDownMax.Value;
if (radioButtonRandom.Checked)
MainMatrix = MMatrix.RandomMatrix(rows, cols, min, max);
else if (radioButtonDiagonal.Checked)
{
MainMatrix = MMatrix.DiagonalMatrix(rows, rand.Next(max));
cols = rows;
}
else if (radioButtonIdentity.Checked)
{
MainMatrix = MMatrix.DiagonalMatrix(rows, 1);
cols = rows;
}
else if (radioButtonSymetric.Checked)
{
MainMatrix = MMatrix.RandomMatrix(rows, cols, min, (int)Math.Sqrt(max));
MainMatrix = MainMatrix * MainMatrix.Transpose();
cols = rows;
}
else if (radioButtonGaussian.Checked)
{
double std = 1.4;
double theta = 0;
MainMatrix = MMatrix.D2Gauss(rows, std, rows, std, theta);
//MainMatrix = MMatrix.D2Gauss_Canny(rows, std, rows, std, theta); //Sobel kernel
cols = rows;
}
this.dataGridViewMatrix.ColumnHeadersHeightSizeMode = DataGridViewColumnHeadersHeightSizeMode.DisableResizing;
dataGridViewMatrix.SuspendLayout();
dataGridViewMatrix.Columns.Clear();
/*
int ColCount = dataGridViewMatrix.Columns.Count;
for (int i = 0; i < ColCount; ++i)
dataGridViewMatrix.Columns.RemoveAt(0);
*/
DataGridViewColumn[] DCS = new DataGridViewColumn[cols];
for (int i = 0; i < cols; ++i)
{
DataGridViewColumn column = new DataGridViewTextBoxColumn();
column.HeaderText = string.Concat("A", (i + 1).ToString());
DCS[i] = column;
}
this.dataGridViewMatrix.Columns.AddRange(DCS);
dataGridViewMatrix.Rows.Add(rows);
//for DataGrid: [column, row]
for (int j = 0; j < MainMatrix.col; ++j)
for (int i = 0; i < MainMatrix.row; ++i)
dataGridViewMatrix[j,i].Value = MainMatrix[i, j];
//this.dataGridViewMatrix.AutoSizeColumnsMode = DataGridViewAutoSizeColumnsMode.DisplayedCells;
dataGridViewMatrix.ResumeLayout();
numericUpDownCol.Value = cols;
}