private void buttonClearAll_Click(object sender, EventArgs e)
{
MainMatrix = null;
dataGridViewMatrix.Columns.Clear();
b = null;
dataGridViewVectorb.Columns.Clear();
}
public static Vector operator *(Vector A, double Scalar)
{
Vector B = new Vector(A.Elements.Length);
for (int i = 0; i < A.Elements.Length; ++i)
{
B[i] = A[i] * Scalar;
}
return B;
}
public static MMatrix CalculateArgumentMatrix(MMatrix CoefficientMatrix, Vector b)
{
//Form Argument matrix from CoefficientMatrix and b
MMatrix ArgumentMatrix = new MMatrix(CoefficientMatrix.row, CoefficientMatrix.col + 1);
for (int i = 0; i < CoefficientMatrix.row; ++i)
for (int j = 0; j < CoefficientMatrix.col; ++j)
ArgumentMatrix[i, j] = CoefficientMatrix[i, j];
for (int i = 0; i < CoefficientMatrix.row; ++i)
ArgumentMatrix[i, ArgumentMatrix.col - 1] = b[i];
return ArgumentMatrix;
}
public static string PrintSystemOfEquations(MMatrix CoefficientMatrix, Vector b)
{
StringBuilder sb = new StringBuilder("");
for (int i = 0; i < CoefficientMatrix.row; ++i)
{
for (int j = 0; j < CoefficientMatrix.col; ++j)
{
string sign = (CoefficientMatrix[i, j] >= 0) ? "+" : "";
sb.Append(sign);
sb.Append(CoefficientMatrix[i, j]);
sb.Append(" X");
sb.Append(j + 1);
sb.Append("\t\t");
}
sb.Append(" = ");
sb.Append(b[i]);
sb.Append("\r\n");
}
return sb.ToString();
}
private void button1_MouseClick(object sender, MouseEventArgs e)
{
ReadFromFile();
b = new DenseVector(n, n);
b = A.Multiply(s); // Punctul 1
Giv_R = new DenseMatrix(n, n);
Giv_Q = new DenseMatrix(n, n);
//Givens
Givens_Decomposition(A,b); // Punctul 2
dnAnalytics.LinearAlgebra.Decomposition.IQR t;
t = new Householder(A);
textBox1.AppendText("\r\nR\r\n\r\n");
print_matrix(t.R());
textBox1.AppendText("\r\nR\r\n\r\n");
print_matrix(Giv_R);
textBox1.AppendText("Q\r\n\r\n");
print_matrix(t.Q());
textBox1.AppendText("Q\r\n\r\n");
print_matrix(Giv_Q);
}
public static double DotProduct(Vector A, Vector B)
{
return A*B;
}
public static double L2Norm(Vector A)
{
return Math.Sqrt(A*A);
}
public static double SpectralRadius(MMatrix A)
{
Vector Eigenvalues = new Vector();
if (!A.IsSquared())
throw new MMatrixException("Matrix must be squared.");
Eigenvalues = A.QRIterationBasic(GlobalMath.MAXITER).DiagVector();
Eigenvalues.Sort(true);
return Math.Abs(Eigenvalues[0]);
}
public Vector DiagVector()
{
if (!this.IsSquared())
throw new MMatrixException("Cannot get diagonal of a non-square matrix.");
Vector v = new Vector(this.col);
for (int i = 0; i < this.col; ++i)
{
v[i] = this[i, i];
}
return v;
}
public static void Sort(Vector A, bool bDescending)
{
Array.Sort(A.Elements);
if (bDescending)
//Sort_Descending(A);
Array.Reverse(A.Elements);
//else
//Sort_Ascending(A);
}
public Vector Orthonormalize(Vector OrthonormalVector)
{
return Orthonormalize(this,OrthonormalVector);
}
//Orthonormalize all eigenvectors based on the first one
public static MMatrix Orthonormalize(MMatrix Eigenvectors)
{
MMatrix A = new MMatrix(Eigenvectors);
Vector v1 = new Vector(Eigenvectors.row);
Vector v = new Vector(Eigenvectors.row);
for (int i = 0; i < v1.Elements.Length; ++i)
v1[i] = A[i, 0];
v1 = v1.Normalize();
for (int i = 0; i < v1.Elements.Length; ++i)
A[i, 0] = v1[i];
for (int i = 1; i < Eigenvectors.col; ++i)
{
for (int j = 0; j < Eigenvectors.row; ++j)
v[j] = Eigenvectors[j,i];
v = v.Orthonormalize(v1);
for (int j = 0; j < v.Elements.Length; ++j)
A[j, i] = v[j];
}
return A;
}
public static Vector Orthonormalize(Vector A, Vector OrthonormalVector)
{
Vector B = new Vector();
B = A - OrthonormalVector * A * OrthonormalVector;
B = B.Normalize();
return B;
}
//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 = 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;
}
//Find eigenvalues, eigenvectors (each column is a vector)
private static void Jacobi_Cyclic_Method(ref Vector eigenvalues, ref MMatrix eigenvectors, MMatrix A, int n)
{
int i, j, k, m;
MMatrix pAk, pAm, p_r, p_e;
double threshold_norm;
double threshold;
double tan_phi, sin_phi, cos_phi, tan2_phi, sin2_phi, cos2_phi;
double sin_2phi, cos_2phi, cot_2phi;
double dum1;
double dum2;
double dum3;
double max;
eigenvalues = new Vector(n);
eigenvectors = DiagonalMatrix(n, 1);
pAk = new MMatrix();
pAm = new MMatrix();
p_r = new MMatrix();
p_e = eigenvectors;
// Take care of trivial cases
if (n < 1)
return;
if (n == 1)
{
eigenvalues[0] = A[0, 0];
eigenvectors[0, 0] = 1.0;
return;
}
// Initialize the eigenvalues to the identity matrix.
/*for (p_e = eigenvectors, i = 0; i < n; ++i)
for (j = 0; j < n; ++j)
p_e[i, j] = (i == j) ? 1.0 : 0.0; */
// Calculate the threshold and threshold_norm.
for (threshold = 0.0, pAk = A, i = 0; i < (n - 1); ++i)
for (j = i + 1; j < n; ++j)
threshold += pAk[i, j] * pAk[i, j];
threshold = Math.Sqrt(threshold + threshold);
threshold_norm = threshold * GlobalMath.EPSILON;
max = threshold + 1.0;
while (threshold > threshold_norm)
{
threshold /= 10.0;
if (max < threshold)
continue;
max = 0.0;
pAk = A;
pAm = pAk;
for (k = 0; k < (n - 1); ++k)
{
for (m = k + 1; m < n; ++m)
{
if (Math.Abs(pAk[k, m]) < threshold)
continue;
// Calculate the sin and cos of the rotation angle which annihilates A[k][m].
cot_2phi = 0.5 * (pAk[k, k] - pAm[m, m]) / pAk[k, m];
dum1 = Math.Sqrt(cot_2phi * cot_2phi + 1.0);
if (cot_2phi < 0.0)
dum1 = -dum1;
tan_phi = -cot_2phi + dum1;
tan2_phi = tan_phi * tan_phi;
sin2_phi = tan2_phi / (1.0 + tan2_phi);
cos2_phi = 1.0 - sin2_phi;
sin_phi = Math.Sqrt(sin2_phi);
if (tan_phi < 0.0)
sin_phi = -sin_phi;
cos_phi = Math.Sqrt(cos2_phi);
sin_2phi = 2.0 * sin_phi * cos_phi;
cos_2phi = cos2_phi - sin2_phi;
// Rotate columns k and m for both the matrix A and the matrix of eigenvectors.
p_r = A;
dum1 = pAk[k, k];
dum2 = pAm[m, m];
dum3 = pAk[k, m];
pAk[k, k] = dum1 * cos2_phi + dum2 * sin2_phi + dum3 * sin_2phi;
pAm[m, m] = dum1 * sin2_phi + dum2 * cos2_phi - dum3 * sin_2phi;
pAk[k, m] = 0.0;
pAm[m, k] = 0.0;
for (i = 0; i < n; ++i)
{
if ((i == k) || (i == m))
continue;
if (i < k)
dum1 = p_r[i, k];
else
dum1 = pAk[k, i];
if (i < m)
dum2 = p_r[i, m];
else
dum2 = pAm[m, i];
dum3 = dum1 * cos_phi + dum2 * sin_phi;
if (i < k)
p_r[i, k] = dum3;
else
pAk[k, i] = dum3;
dum3 = -dum1 * sin_phi + dum2 * cos_phi;
if (i < m)
p_r[i, m] = dum3;
else
pAm[m, i] = dum3;
}
for (p_e = eigenvectors, i = 0; i < n; ++i)
{
dum1 = p_e[i, k];
dum2 = p_e[i, m];
p_e[i, k] = dum1 * cos_phi + dum2 * sin_phi;
p_e[i, m] = -dum1 * sin_phi + dum2 * cos_phi;
}
}
for (i = 0; i < n; ++i)
if (i == k)
continue;
else if (max < Math.Abs(pAk[k, i]))
max = Math.Abs(pAk[k, i]);
}
}
for (pAk = A, k = 0; k < n; ++k)
eigenvalues[k] = pAk[k, k];
}
public void Jacobi_Cyclic_Method(ref Vector eigenvalues, ref MMatrix eigenvectors)
{
if (!this.IsSquared())
throw new MMatrixException("Matrix must be squared.");
Jacobi_Cyclic_Method(ref eigenvalues, ref eigenvectors, this, this.row);
}
//Jacobi Cyclic Method is not correct enough
public Vector Eigenvalues_JacobiCyclic()
{
Vector Eigenvalues = new Vector();
MMatrix Eigenvectors = new MMatrix();
MMatrix temp = this.Clone();
if (!this.IsSquared())
throw new MMatrixException("Matrix must be squared.");
temp.Jacobi_Cyclic_Method(ref Eigenvalues, ref Eigenvectors);
return Eigenvalues;
}
public static double LInfinitiveNorm(Vector A)
{
Vector B = A.Abs();
double Max = B[0];
for (int j = 1; j < B.Elements.Length; ++j)
if (Max < B[j])
Max = B[j];
return Max;
}
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 Vector Normalize(Vector A)
{
return A / L2Norm(A);
}
private void eigenvectorsToolStripMenuItem_Click(object sender, EventArgs e)
{
try
{
StringBuilder sb = new StringBuilder("");
Vector eigenvalues = new Vector();
MMatrix eigenvectors = new MMatrix();
if (OutputMatrix != null)
{
MMatrix temp = OutputMatrix.Clone();
temp.Jacobi_Cyclic_Method(ref eigenvalues, ref eigenvectors);
sb.Append("\n\n\nEigenvectors (A) = \n");
for (int i = 0; i < eigenvectors.col; ++i)
{
sb.Append("V");
sb.Append(i + 1);
sb.Append("\t\t");
}
sb.Append("\n");
sb.Append(eigenvectors.PrintToString());
RichText_Display(sb.ToString());
}
}
catch (MMatrixException exp)
{
MessageBox.Show("INFO: " + exp.Message, sProjectTile, MessageBoxButtons.OK, MessageBoxIcon.Warning);
}
}
public static Vector RandomVector(int NumElements, int minvalue, int maxvalue)
{
Vector A = new Vector(NumElements);
Random ranobj = new Random();
for (int i = 0; i < NumElements; ++i)
A[i] = ranobj.Next(minvalue, maxvalue);
return A;
}
public static double SpectralRadius_Jacobi(MMatrix A)
{
Vector Eigenvalues = new Vector();
MMatrix Eigenvectors = new MMatrix();
MMatrix temp = A.Clone();
temp.Jacobi_Cyclic_Method(ref Eigenvalues, ref Eigenvectors);
Eigenvalues.Sort(true);
return Math.Abs(Eigenvalues[0]);
}
public static void Sort_Descending(Vector A)
{
int m = A.Elements.Length;
double temp;
for (int i = 0; i < m; ++i)
for (int j = i + 1; j < m; ++j)
{
if (A[i] < A[j])
{
temp = A[i];
A[i] = A[j];
A[j] = temp;
}
}
}
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 Vector(Vector A)
{
Elements = (double[])A.Elements.Clone();
}
public static Vector Abs(Vector A)
{
Vector B = new Vector(A.Elements.Length);
for (int i = 0; i < A.Elements.Length; ++i)
B[i] = Math.Abs(A[i]);
return B;
}
public static Vector operator +(Vector A, Vector B)
{
if (A.Elements.Length != B.Elements.Length)
throw new MMatrixException("Two vectors are different size.");
Vector C = new Vector(A.Elements.Length);
for (int i = 0; i < A.Elements.Length; ++i)
{
C[i] = A[i] + B[i];
}
return C;
}
public Vector Column(int j)
{
Vector v = new Vector(this.row);
for (int i = 0; i < this.row; ++i)
{
v[i] = this[i, j];
}
return v;
}