private void buttonClearAll_Click(object sender, EventArgs e)
{
MainMatrix = null;
dataGridViewMatrix.Columns.Clear();
b = null;
dataGridViewVectorb.Columns.Clear();
}
public MMatrix(MMatrix A)
{
if (A != null)
{
this.row = A.row;
this.col = A.col;
if (A.MArray != null)
this.MArray = (double[,])A.MArray.Clone();
}
}
public MMatrix(MMatrix A, int row, int column)
{
if ((row > A.row) || (column > A.col))
throw new MMatrixException("Cannot create matrix. Exceed the number of row and/or column.");
this.row = row;
this.col = column;
this.MArray = new double[row, column];
for (int i = 0; i < row; ++i)
for (int j = 0; j < col; ++j)
this.MArray[i, j] = A.MArray[i, j];
}
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;
}
//Trunkcate a matrix
public MMatrix(MMatrix A, int FromRow, int ToRow, int FromColumn, int ToColumn)
{
if ((FromRow > A.row) || (FromColumn > A.col))
throw new MMatrixException("Cannot create matrix. Wrong indices");
if (ToRow > A.row)
ToRow = A.row;
if (ToColumn > A.col)
ToColumn = A.col;
if ((FromRow > ToRow) || (FromColumn > ToColumn))
throw new MMatrixException("Cannot create matrix. Wrong indices");
this.row = ToRow - FromRow;
this.col = ToColumn - FromColumn;
this.MArray = new double[this.row, this.col];
for (int i = FromRow; i < ToRow; ++i)
for (int j = FromColumn; j < ToColumn; ++j)
this.MArray[i - FromRow, j - FromColumn] = A.MArray[i, j];
}
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();
}
//After solving the system, Argument Matrix will contain the reduced system
public static string PrintSystemOfEquations(MMatrix AugmentedMatrix)
{
StringBuilder sb = new StringBuilder("");
for (int i = 0; i < AugmentedMatrix.row; ++i)
{
for (int j = 0; j < AugmentedMatrix.col - 1; ++j)
{
string sign = (AugmentedMatrix[i, j] >= 0) ? "+" : "";
sb.Append(sign);
sb.Append(Math.Round(AugmentedMatrix[i, j], GlobalMath.DIGITS));
sb.Append(" X");
sb.Append(j + 1);
sb.Append("\t\t");
}
sb.Append(" = ");
sb.Append(Math.Round(AugmentedMatrix[i, AugmentedMatrix.col - 1], GlobalMath.DIGITS));
sb.Append("\r\n");
}
return sb.ToString();
}
public void QRTest()
{
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[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(Arr2);
string s = "";
try
{
s += "\nA=\n" + A.PrintToString();
A.Householder();
s += "\nHouseholder (A): A(n-1)=\n" + A.PrintToString();
s += "\nEigenvalues approximation: " + A.Eigenvalues().PrintToString();
s += "\nEigenvalues: " + B.Eigenvalues().PrintToString();
this.RichText_Display(s);
}
catch (MMatrixException exp)
{
MessageBox.Show("INFO: " + exp.Message, sProjectTile, MessageBoxButtons.OK, MessageBoxIcon.Warning);
}
}
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);
}
}
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);
}
}
private void newToolStripMenuItem_Click(object sender, EventArgs e)
{
if (this.pictureBox1.Image != null)
{
pictureBox1.Image.Dispose();
pictureBox1.Image = null;
hScrollBar1.Visible = false;
vScrollBar1.Visible = false;
}
this.richTextBox1.Text = "";
argumentMatrix = null;
if (OutputImage != null)
{
OutputImage.Dispose();
OutputImage = null;
}
if (InputImage != null)
{
InputImage.Dispose();
InputImage = null;
}
}
private void factorSVDToolStripMenuItem_Click(object sender, EventArgs e)
{
try
{
if (OutputMatrix != null)
{
OutputMatrix.FactorSVD();
MMatrix U = new MMatrix(OutputMatrix.SVD_U);
MMatrix S = new MMatrix(OutputMatrix.SVD_S);
MMatrix Vt = new MMatrix(OutputMatrix.SVD_Vt);
string s = "\n\n\n";
s += "Factor SVD:\n";
s += "\nU=\n" + U.PrintToString();
s += "\nS=\n" + S.PrintToString();
s += "\nV'=\n" + Vt.PrintToString();
//s += "\nA=USV*\n" + (U * S * Vt.Transpose()).PrintToString();
RichText_Display(s);
}
}
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);
}
}
private void addToolStripMenuItem_Click(object sender, EventArgs e)
{
if (InputMatrixForm.ShowDialog() == DialogResult.OK)
{
if (InputMatrixForm.MainMatrix != null)
{
string s = "\n\n\n";
s += "Matrix B = \n" + InputMatrixForm.MainMatrix.PrintToString();
RichText_Display(s);
argumentMatrix = InputMatrixForm.MainMatrix;
}
}
try
{
if ((OutputMatrix != null) && (argumentMatrix!=null))
{
string s = "\n\n\n";
s += "A + B = \n" + (OutputMatrix + argumentMatrix).PrintToString();
RichText_Display(s);
}
}
catch (MMatrixException exp)
{
MessageBox.Show("INFO: " + exp.Message, sProjectTile, MessageBoxButtons.OK, MessageBoxIcon.Warning);
}
}
public void SaveMatrixText(MMatrix matrix)
{
SaveFileDialog saveDlg = new SaveFileDialog();
saveDlg.Title = "Save Output Matrix";
saveDlg.Filter = "Rich Text Format (*.rtf)|*.rtf|Text files (*.txt)|*.txt|All files (*.*)|*.*";
string FileName = "";
bSaveDone = false;
//if(matrix != null)
if (saveDlg.ShowDialog() == DialogResult.OK)
{
FileName = saveDlg.FileName;
}
if (FileName != "")
{
richTextBox1.SaveFile(FileName);
/*
string[] FileNamePart = new string[2];
string FileExtension = ".txt";
FileNamePart = FileName.Split('.');
if (FileNamePart.Length > 1)
FileExtension = "." + FileNamePart[1];
SaveText(FileName, matrix.PrintToString(), false);
//SVD
if (matrix.SVD_U != null)
SaveText(FileNamePart[0] + "_SVD_U" + FileExtension, (new MMatrix(matrix.SVD_U)).PrintToString(), false);
if (matrix.SVD_S != null)
SaveText(FileNamePart[0] + "_SVD_S" + FileExtension, (new MMatrix(matrix.SVD_S)).PrintToString(), false);
if (matrix.SVD_Vt != null)
SaveText(FileNamePart[0] + "_SVD_Vt" + FileExtension, (new MMatrix(matrix.SVD_Vt)).PrintToString(), false);
//LU
if (matrix.LU_P != null)
SaveText(FileNamePart[0] + "_LU_P" + FileExtension, (new MMatrix(matrix.LU_P)).PrintToString(), false);
if (matrix.LU_L != null)
SaveText(FileNamePart[0] + "_LU_L" + FileExtension, (new MMatrix(matrix.LU_L)).PrintToString(), false);
if (matrix.LU_U != null)
SaveText(FileNamePart[0] + "_LU_U" + FileExtension, (new MMatrix(matrix.LU_U)).PrintToString(), false);
//LDL*
if (matrix.LDL_L != null)
SaveText(FileNamePart[0] + "_LDL*_L" + FileExtension, (new MMatrix(matrix.LDL_L)).PrintToString(), false);
if (matrix.LDL_D != null)
SaveText(FileNamePart[0] + "_LDL*_D" + FileExtension, (new MMatrix(matrix.LDL_D)).PrintToString(), false);
if (matrix.LDL_L != null)
SaveText(FileNamePart[0] + "_LDL*_Lt" + FileExtension, (new MMatrix(matrix.LDL_L)).Transpose().PrintToString(), false);
* */
}
bSaveDone = true;
}
public static string PrintToString(MMatrix A)
{
StringBuilder sb = new StringBuilder("");
for (int i = 0; i < A.row; ++i)
{
for (int j = 0; j < A.col; ++j)
{
sb.Append(Math.Round(A[i, j], GlobalMath.DIGITS));
sb.Append("\t\t");
}
sb.Append("\r\n");
}
return sb.ToString();
}
public static MMatrix PowEntry(MMatrix A, double pow)
{
return PowEntry(A, A.row, A.col, pow);
}
//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;
}
//Orthonormalize all eigenvectors based on the first one
public static MMatrix Orthonormalize(Queue<Vector> Eigenvectors)
{
MMatrix A = new MMatrix(Eigenvectors.ElementAt(0).Elements.Length, Eigenvectors.Count);
Vector v1, v;
int column = 0;
v1 = Eigenvectors.ElementAt(0);
v1 = v1.Normalize();
for (int i = 0; i < v1.Elements.Length; ++i)
{
A[i, 0] = v1[i];
}
for (int j = 1; j < Eigenvectors.Count; ++j)
{
v = Eigenvectors.ElementAt(j);
v = v.Orthonormalize(v1);
column++;
for (int i = 0; i < v.Elements.Length; ++i)
{
A[i, column] = v[i];
}
}
return A;
}
public static MMatrix Minor(MMatrix A, int row, int col)
{
MMatrix minor = new MMatrix(A.row - 1, A.col - 1);
int m = 0, n = 0;
for (int i = 0; i < A.row; ++i)
{
if (i == row)
continue;
n = 0;
for (int j = 0; j < A.col; ++j)
{
if (j == col)
continue;
minor[m, n] = A[i, j];
n++;
}
m++;
}
return minor;
}
public void SVDMatrixTest()
{
double[,] Arr1 = new double[3, 3] { { 4, -1, 1 }, { -1, 4.25, 2.75 }, { 1, 2.75, 3.5 } };
double[,] Arr2 = new double[4, 4] { { 1, 1, 0, 3 }, { 2, 1, -1, 1 }, { 3, -1, -1, 2 }, { -1, 2, 3, -1 } };
double[,] Arr3 = new double[2, 3] { { 3, 1, 1 }, { -1, 3, 1 } };
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 = "";
try
{
//A = MMatrix.RandomMatrix(size,0,255);
A.FactorSVD();
s = "Factor SVD:\n";
s += "\nMatrix A=\n" + A.PrintToString();
s += "\nU=\n" + (new MMatrix(A.SVD_U)).PrintToString();
s += "\nS=\n" + (new MMatrix(A.SVD_S)).PrintToString();
s += "\nVt=\n" + (new MMatrix(A.SVD_Vt)).PrintToString();
B = (new MMatrix(A.SVD_U)) * (new MMatrix(A.SVD_S)) * (new MMatrix(A.SVD_Vt));
s += "\nA=USV*\n" + B.PrintToString();
this.RichText_Display(s);
OutputMatrix = A;
}
catch (MMatrixException exp)
{
MessageBox.Show("INFO: " + exp.Message, sProjectTile, MessageBoxButtons.OK, MessageBoxIcon.Warning);
}
}
//Matrix must be trigdiagonal (using Householder)
//This routine cannot find exactly eigenvalues
public static Queue<double> QR(MMatrix matrix, double TOL, int MaxIterations)
{
int n = matrix.row;
int M = MaxIterations;
int k;
double SHIFT, lamda,b,c,d,m1,m2,lamda1,lamda2,min,sigma;
double[] A = new double[n];
double[] B = new double[n];
double[] C = new double[n];
double[] D = new double[n];
double[] Q = new double[n];
double[] R = new double[n];
double[] S = new double[n];
double[] X = new double[n];
double[] Y = new double[n];
double[] Z = new double[n];
double[] Sig = new double[n];
Queue<double> QLamda=new Queue<double>();
for (int i = 0; i < n; ++i)
A[i] = matrix[i, i];
for (int i = 1; i < n; ++i)
B[i] = matrix[i,i-1];
k = 1;
SHIFT = 0;
while (k <= M)
{
if (Math.Abs(B[n - 1]) <= TOL)
{
lamda = A[n - 1] + SHIFT;
QLamda.Enqueue(lamda);
n = n - 1;
}
if (B[1] <= TOL)
{
lamda = A[0] + SHIFT;
QLamda.Enqueue(lamda);
n = n - 1;
A[0] = A[1];
for (int j = 1; j < n; ++j)
{
A[j] = A[j + 1];
B[j] = B[j + 1];
}
}
if (n == 0)
return QLamda;
if (n == 1)
{
lamda = A[0] + SHIFT;
QLamda.Enqueue(lamda);
return QLamda;
}
/*
for (int j = 2; j < n - 1; ++j)
{
if (Math.Abs(B[j]) <= TOL)
{
throw new MMatrixException("Split into A[0]..A[j-1], B[1]..B[j-1] and A[j]..A[n-1], B[j+1]..B[n-1]"+SHIFT.ToString());
}
}
*/
b = -(A[n - 2] + A[n - 1]);
c = A[n - 1] * A[n - 2] - B[n - 1]* B[n - 1];
d = Math.Sqrt(b * b - 4 * c);
if(b > 0)
{
m1 = -2*c/(b+d);
m2 = -(b+d)/2;
}
else
{
m1 = (d-b)/2;
m2 = 2*c/(d-b);
}
if (n == 2)
{
lamda1 = m1 + SHIFT;
lamda2 = m2 + SHIFT;
QLamda.Enqueue(lamda1);
QLamda.Enqueue(lamda2);
return QLamda;
}
min = Math.Min(Math.Abs(m1 - A[n - 1]), Math.Abs(m2 - A[n - 1]));
sigma = min + A[n - 1];
SHIFT += sigma;
for (int j = 0; j < n; ++j)
D[j] = A[j] - sigma;
X[0] = D[0];
Y[0] = B[1];
for (int j = 1; j < n; ++j)
{
Z[j - 1] = Math.Sqrt(X[j-1]*X[j-1]+B[j]*B[j]);
C[j] = X[j-1] / Z[j-1];
Sig[j] = B[j] / Z[j - 1];
Q[j - 1] = C[j] * Y[j - 1] + S[j] * D[j];
X[j] = -Sig[j] * Y[j - 1] + C[j] * D[j];
if (j != n - 1)
{
R[j - 1] = Sig[j] * B[j + 1];
Y[j] = C[j] * B[j + 1];
}
}
Z[n - 1] = X[n - 1];
A[0] = Sig[1] * Q[0] + C[1] * Z[0];
B[1] = Sig[1] * Z[1];
for (int j = 1; j < n - 1; ++j)
{
A[j] = Sig[j + 1] * Q[j] + C[j] * C[j + 1] * Z[j];
B[j + 1] = Sig[j + 1] * Z[j + 1];
}
A[n - 1] = C[n - 1] * Z[n - 1];
k++;
}
throw new MMatrixException("Maximum number of iterations exceeded.");
}
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 MMatrix RandomMatrix(int row, int column, int minvalue, int maxvalue)
{
MMatrix A = new MMatrix(row, column);
Random ranobj = new Random();
for (int i = 0; i < A.row; ++i)
for (int j = 0; j < A.col; ++j)
A[i, j] = ranobj.Next(minvalue, maxvalue);
return A;
}
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);
}
}
public static int Rank(MMatrix A)
{
MMatrix temp = A.EchelonForm();
int index = Math.Min(temp.row, temp.col);
int rank = 0;
for (int i = 0; i < index; ++i)
{
if (temp[i, i] != 0)
rank++;
}
return rank;
}
private void inputMatrixToolStripMenuItem_Click(object sender, EventArgs e)
{
if (InputMatrixForm.ShowDialog() == DialogResult.OK)
{
if (InputMatrixForm.MainMatrix != null)
{
string s = string.Concat("\n\n\nMatrix A = \n", InputMatrixForm.MainMatrix.PrintToString());
RichText_Display(s);
OutputMatrix = InputMatrixForm.MainMatrix;
}
}
}
public static MMatrix ReducedEchelonForm(MMatrix matrix)
{
try
{
MMatrix ReducedEchelonMatrix = new MMatrix(matrix);
for (int i = 0; i < matrix.row; ++i)
{
if (i < ReducedEchelonMatrix.col)
{
if (ReducedEchelonMatrix[i, i] == 0) // if diagonal entry is zero,
for (int j = i + 1; j < ReducedEchelonMatrix.row; ++j)
if (ReducedEchelonMatrix[j, i] != 0) //check if some below entry is non-zero
ReducedEchelonMatrix.InterchangeRow(i, j); // then interchange the two rows
if (ReducedEchelonMatrix[i, i] == 0) // if not found any non-zero diagonal entry
continue; // increment i;
if (ReducedEchelonMatrix[i, i] != 1) // if diagonal entry is not 1 ,
for (int j = i + 1; j < ReducedEchelonMatrix.row; ++j)
if (ReducedEchelonMatrix[j, i] == 1) //check if some below entry is 1
ReducedEchelonMatrix.InterchangeRow(i, j); // then interchange the two rows
ReducedEchelonMatrix.MultiplyRow(i, 1 / (ReducedEchelonMatrix[i, i]));
for (int j = i + 1; j < ReducedEchelonMatrix.row; ++j)
ReducedEchelonMatrix.AddRow(j, i, -ReducedEchelonMatrix[j, i]);
for (int j = i - 1; j >= 0; j--)
ReducedEchelonMatrix.AddRow(j, i, -ReducedEchelonMatrix[j, i]);
}
}
return ReducedEchelonMatrix;
}
catch (Exception)
{
throw new MMatrixException("MMatrix can not be reduced to Echelon form");
}
}
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 static double RootMeanSquareError(MMatrix MActual,MMatrix MApproximate)
{
double err = 0;
//err = MMatrix.LInfinitiveNorm(MActual - MApproximate) / MMatrix.LInfinitiveNorm(MActual);
double sum = 0;
double diff;
for (int i = 0; i < MActual.row; ++i)
for (int j = 0; j < MActual.col; ++j)
{
diff = MActual[i, j] - MApproximate[i, j];
sum += diff * diff;
}
err = Math.Sqrt(sum / (MActual.row * MActual.col));
return err;
}