コード例 #1
0
        private void buttonClearAll_Click(object sender, EventArgs e)
        {
            MainMatrix = null;
            dataGridViewMatrix.Columns.Clear();

            b = null;
            dataGridViewVectorb.Columns.Clear();
        }
コード例 #2
0
        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;
        }
コード例 #3
0
        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;
        }
コード例 #4
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        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();
        }
コード例 #5
0
ファイル: Form1.cs プロジェクト: alexflorea/CN
        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);
        }
コード例 #6
0
 public static double DotProduct(Vector A, Vector B)
 {
     return A*B;
 }
コード例 #7
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 public static double L2Norm(Vector A)
 {
     return Math.Sqrt(A*A);
 }
コード例 #8
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        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]);
        }
コード例 #9
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        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;
        }
コード例 #10
0
 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);
 }
コード例 #11
0
 public Vector Orthonormalize(Vector OrthonormalVector)
 {
     return Orthonormalize(this,OrthonormalVector);
 }
コード例 #12
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        //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;
        }
コード例 #13
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        public static Vector Orthonormalize(Vector A, Vector OrthonormalVector)
        {
            Vector B = new Vector();

            B = A - OrthonormalVector * A * OrthonormalVector;
            B = B.Normalize();

            return B;
        }
コード例 #14
0
        //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;
        }
コード例 #15
0
        //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;
        }
コード例 #16
0
        //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];
        }
コード例 #17
0
 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);
 }
コード例 #18
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        //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;
        }
コード例 #19
0
        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;
        }
コード例 #20
0
        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);
            }
        }
コード例 #21
0
 public static Vector Normalize(Vector A)
 {
     return A / L2Norm(A);
 }
コード例 #22
0
 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);
     }
 }
コード例 #23
0
        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;
        }
コード例 #24
0
        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]);
        }
コード例 #25
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;
                    }
                }
        }
コード例 #26
0
        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();
        }
コード例 #27
0
 public Vector(Vector A)
 {
     Elements = (double[])A.Elements.Clone();
 }
コード例 #28
0
        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;
        }
コード例 #29
0
        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;
        }
コード例 #30
0
        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;
        }