public double FindPoints(double x, double y, Mapack.Matrix coef) { double p = 0; double[][] xArray = new double[1][]; for (int i = 0; i < xArray.Length; i++) { xArray[i] = new double[4]; } xArray[0][0] = 1; xArray[0][1] = x; xArray[0][2] = Math.Pow(x, 2); xArray[0][3] = Math.Pow(x, 3); double[][] yArray = new double[4][]; for (int i = 0; i < yArray.Length; i++) { yArray[i] = new double[1]; } yArray[0][0] = 1; yArray[1][0] = y; yArray[2][0] = Math.Pow(y, 2); yArray[3][0] = Math.Pow(y, 3); Mapack.Matrix xMatrix = new Mapack.Matrix(xArray); Mapack.Matrix yMatrix = new Mapack.Matrix(yArray); Mapack.Matrix res = Mapack.Matrix.Multiply(xMatrix, coef); res = Mapack.Matrix.Multiply(res, yMatrix); p = res.Determinant; return(p); }
//function public override double[] propagate(double[] Bids) { Mapack.Matrix BidM = new Matrix(new double[][] { Bids }); //sanity check try{ if (Bids.Length != W1.Rows) { throw new Exception("The number of bids and weights does not match"); } } catch (Exception e) { Console.WriteLine(e.Message); } Mapack.Matrix ProtoProbs = BidM * W1; double SigmaSum = 0; for (int i = 0; i < ProtoProbs.Columns; i++) { double d = Math.Exp(ProtoProbs[0, i]); ProtoProbs[0, i] = d; SigmaSum += d; } double[] Probabilities = new double[ProtoProbs.Columns]; for (int i = 0; i < ProtoProbs.Columns; i++) { Probabilities[i] = ProtoProbs[0, i] / (1 + SigmaSum); } return(Probabilities); }
//*function public void CSVtoMAT(ref StreamReader SR, ref Mapack.Matrix W) { string line = " "; List <string[]> LineList = new List <string[]>(); while (!SR.EndOfStream && !line.Contains("nextmatrix")) { line = SR.ReadLine(); if (line.Contains(",")) { LineList.Add(line.Split(',')); } } int Row = LineList.Count; int Col = LineList[0].Length; W = new Matrix(Row, Col); int R = 0; int C = 0; foreach (string[] ln in LineList) { foreach (string cell in ln) { W[R, C] = Double.Parse(cell); C++; } R++; C = 0; } }
public BicubicInterpolator() { fixedArray[0] = new double[] { 1, 0, 0, 0 }; fixedArray[1] = new double[] { 0, 0, 1, 0 }; fixedArray[2] = new double[] { -3, 3, -2, -1 }; fixedArray[3] = new double[] { 2, -2, 1, 1 }; fixed1 = new Mapack.Matrix(fixedArray); fixed2 = fixed1.Transpose(); coefficient = new Mapack.Matrix(4, 4); }
public int[,] constructFourByFour(int[,] pixelArray) { bool start_new_row = false; bool sec_iteration_new_row = false; int row_index = 0; int col_index = 0; int new_row = 0; int new_col = 0; int[,] doubled_image = new int[2 * pixelArray.GetLength(0), 2 * pixelArray.GetLength(1)];; while (row_index + fourGrid.GetLength(0) <= pixelArray.GetLength(0)) { while (col_index + fourGrid.GetLength(1) <= pixelArray.GetLength(1)) { for (int i = 0; i < fourGrid.GetLength(0); i++) { for (int j = 0; j < fourGrid.GetLength(1); j++) { fourGrid[i, j] = pixelArray[i + row_index, j + col_index]; } } //gridCount++; //Console.WriteLine("Grid " + gridCount + " :"); //printArray(fourGrid); //Console.WriteLine(""); double[][] complex = constrComplexMatrix(fourGrid); Mapack.Matrix comp = new Mapack.Matrix(complex); coefficient = Mapack.Matrix.Multiply(fixed1, comp); coefficient = Mapack.Matrix.Multiply(coefficient, fixed2); // Console.WriteLine("Fixed 1:\n " + fixed1.ToString()); //Console.WriteLine("Complex : \n" + comp.ToString()); //Console.WriteLine("Fixed 2: \n" + fixed2.ToString());//; coefficient.ToString()); //Console.WriteLine("Coefficients:\n " + coefficient.ToString()); //if(new_row >= 39 || new_col >= 39){ // break; //} if (sec_iteration_new_row && start_new_row) { doubled_image[new_row, new_col] = check_range((int)Math.Ceiling(FindPoints(0.5, 0.5, coefficient))); doubled_image[new_row + 1, new_col] = check_range((int)Math.Ceiling(FindPoints(0.5, 1, coefficient))); doubled_image[new_row, new_col + 1] = check_range((int)Math.Ceiling(FindPoints(1, 0.5, coefficient))); doubled_image[new_row + 1, new_col + 1] = fourGrid[2, 2]; new_col += 2; } else if ((new_row == 0 && new_col == 0) || start_new_row) { if (start_new_row) { doubled_image[new_row, new_col] = check_range((int)Math.Ceiling(FindPoints(0, 0.5, coefficient))); doubled_image[new_row + 1, new_col] = fourGrid[2, 1]; doubled_image[new_row, new_col + 1] = check_range((int)Math.Ceiling(FindPoints(0.5, 0.5, coefficient))); doubled_image[new_row + 1, new_col + 1] = check_range((int)Math.Ceiling(FindPoints(0.5, 1, coefficient))); doubled_image[new_row, new_col + 2] = check_range((int)Math.Ceiling(FindPoints(1, 0.5, coefficient))); doubled_image[new_row + 1, new_col + 2] = fourGrid[2, 2]; new_col += 3; sec_iteration_new_row = true; } else { doubled_image[new_row, new_col] = fourGrid[1, 1]; doubled_image[new_row + 1, new_col] = check_range((int)Math.Ceiling(FindPoints(0, 0.5, coefficient))); doubled_image[new_row + 2, new_col] = fourGrid[2, 1]; doubled_image[new_row, new_col + 1] = check_range((int)Math.Ceiling(FindPoints(0.5, 0, coefficient))); doubled_image[new_row + 1, new_col + 1] = check_range((int)Math.Ceiling(FindPoints(0.5, 0.5, coefficient))); doubled_image[new_row + 2, new_col + 1] = check_range((int)Math.Ceiling(FindPoints(0.5, 1, coefficient))); doubled_image[new_row, new_col + 2] = fourGrid[1, 2]; doubled_image[new_row + 1, new_col + 2] = check_range((int)Math.Ceiling(FindPoints(1, 0.5, coefficient))); doubled_image[new_row + 2, new_col + 2] = fourGrid[2, 2]; new_col += 3; } // start_new_row = false; } else { doubled_image[new_row, new_col] = check_range((int)Math.Ceiling(FindPoints(0.5, 0, coefficient))); doubled_image[new_row + 1, new_col] = check_range((int)Math.Ceiling(FindPoints(0.5, 0.5, coefficient))); doubled_image[new_row + 2, new_col] = check_range((int)Math.Ceiling(FindPoints(0.5, 1, coefficient))); doubled_image[new_row, new_col + 1] = fourGrid[1, 2]; doubled_image[new_row + 1, new_col + 1] = check_range((int)Math.Ceiling(FindPoints(1, 0.5, coefficient))); doubled_image[new_row + 2, new_col + 1] = fourGrid[2, 2]; new_col += 2; } col_index++; } row_index++; if (start_new_row) { new_row += 2; } else { new_row += 3; } start_new_row = true; sec_iteration_new_row = false; col_index = 0; new_col = 0; } return(doubled_image); }
/// <summary>Construct singular value decomposition.</summary> public SingularValueDecomposition(Matrix value) { if (value == null) { throw new ArgumentNullException("value"); } Matrix copy = (Matrix) value.Clone(); double[][] a = copy.Array; m = value.Rows; n = value.Columns; int nu = Math.Min(m,n); s = new double [Math.Min(m+1,n)]; U = new Matrix(m, nu); V = new Matrix(n, n); double[][] u = U.Array; double[][] v = V.Array; double[] e = new double [n]; double[] work = new double [m]; bool wantu = true; bool wantv = true; // Reduce A to bidiagonal form, storing the diagonal elements in s and the super-diagonal elements in e. int nct = Math.Min(m-1,n); int nrt = Math.Max(0,Math.Min(n-2,m)); for (int k = 0; k < Math.Max(nct,nrt); k++) { if (k < nct) { // Compute the transformation for the k-th column and place the k-th diagonal in s[k]. // Compute 2-norm of k-th column without under/overflow. s[k] = 0; for (int i = k; i < m; i++) { s[k] = Hypotenuse(s[k],a[i][k]); } if (s[k] != 0.0) { if (a[k][k] < 0.0) { s[k] = -s[k]; } for (int i = k; i < m; i++) { a[i][k] /= s[k]; } a[k][k] += 1.0; } s[k] = -s[k]; } for (int j = k+1; j < n; j++) { if ((k < nct) & (s[k] != 0.0)) { // Apply the transformation. double t = 0; for (int i = k; i < m; i++) t += a[i][k]*a[i][j]; t = -t/a[k][k]; for (int i = k; i < m; i++) a[i][j] += t*a[i][k]; } // Place the k-th row of A into e for the subsequent calculation of the row transformation. e[j] = a[k][j]; } if (wantu & (k < nct)) { // Place the transformation in U for subsequent back // multiplication. for (int i = k; i < m; i++) u[i][k] = a[i][k]; } if (k < nrt) { // Compute the k-th row transformation and place the k-th super-diagonal in e[k]. // Compute 2-norm without under/overflow. e[k] = 0; for (int i = k+1; i < n; i++) { e[k] = Hypotenuse(e[k],e[i]); } if (e[k] != 0.0) { if (e[k+1] < 0.0) e[k] = -e[k]; for (int i = k+1; i < n; i++) e[i] /= e[k]; e[k+1] += 1.0; } e[k] = -e[k]; if ((k+1 < m) & (e[k] != 0.0)) { // Apply the transformation. for (int i = k+1; i < m; i++) work[i] = 0.0; for (int j = k+1; j < n; j++) for (int i = k+1; i < m; i++) work[i] += e[j]*a[i][j]; for (int j = k+1; j < n; j++) { double t = -e[j]/e[k+1]; for (int i = k+1; i < m; i++) a[i][j] += t*work[i]; } } if (wantv) { // Place the transformation in V for subsequent back multiplication. for (int i = k+1; i < n; i++) v[i][k] = e[i]; } } } // Set up the final bidiagonal matrix or order p. int p = Math.Min(n,m+1); if (nct < n) s[nct] = a[nct][nct]; if (m < p) s[p-1] = 0.0; if (nrt+1 < p) e[nrt] = a[nrt][p-1]; e[p-1] = 0.0; // If required, generate U. if (wantu) { for (int j = nct; j < nu; j++) { for (int i = 0; i < m; i++) u[i][j] = 0.0; u[j][j] = 1.0; } for (int k = nct-1; k >= 0; k--) { if (s[k] != 0.0) { for (int j = k+1; j < nu; j++) { double t = 0; for (int i = k; i < m; i++) t += u[i][k]*u[i][j]; t = -t/u[k][k]; for (int i = k; i < m; i++) u[i][j] += t*u[i][k]; } for (int i = k; i < m; i++ ) u[i][k] = -u[i][k]; u[k][k] = 1.0 + u[k][k]; for (int i = 0; i < k-1; i++) u[i][k] = 0.0; } else { for (int i = 0; i < m; i++) u[i][k] = 0.0; u[k][k] = 1.0; } } } // If required, generate V. if (wantv) { for (int k = n-1; k >= 0; k--) { if ((k < nrt) & (e[k] != 0.0)) { for (int j = k+1; j < nu; j++) { double t = 0; for (int i = k+1; i < n; i++) t += v[i][k]*v[i][j]; t = -t/v[k+1][k]; for (int i = k+1; i < n; i++) v[i][j] += t*v[i][k]; } } for (int i = 0; i < n; i++) v[i][k] = 0.0; v[k][k] = 1.0; } } // Main iteration loop for the singular values. int pp = p-1; int iter = 0; double eps = Math.Pow(2.0,-52.0); while (p > 0) { int k,kase; // Here is where a test for too many iterations would go. // This section of the program inspects for // negligible elements in the s and e arrays. On // completion the variables kase and k are set as follows. // kase = 1 if s(p) and e[k-1] are negligible and k<p // kase = 2 if s(k) is negligible and k<p // kase = 3 if e[k-1] is negligible, k<p, and s(k), ..., s(p) are not negligible (qr step). // kase = 4 if e(p-1) is negligible (convergence). for (k = p-2; k >= -1; k--) { if (k == -1) break; if (Math.Abs(e[k]) <= eps*(Math.Abs(s[k]) + Math.Abs(s[k+1]))) { e[k] = 0.0; break; } } if (k == p-2) { kase = 4; } else { int ks; for (ks = p-1; ks >= k; ks--) { if (ks == k) break; double t = (ks != p ? Math.Abs(e[ks]) : 0.0) + (ks != k+1 ? Math.Abs(e[ks-1]) : 0.0); if (Math.Abs(s[ks]) <= eps*t) { s[ks] = 0.0; break; } } if (ks == k) kase = 3; else if (ks == p-1) kase = 1; else { kase = 2; k = ks; } } k++; // Perform the task indicated by kase. switch (kase) { // Deflate negligible s(p). case 1: { double f = e[p-2]; e[p-2] = 0.0; for (int j = p-2; j >= k; j--) { double t = Hypotenuse(s[j],f); double cs = s[j]/t; double sn = f/t; s[j] = t; if (j != k) { f = -sn*e[j-1]; e[j-1] = cs*e[j-1]; } if (wantv) { for (int i = 0; i < n; i++) { t = cs*v[i][j] + sn*v[i][p-1]; v[i][p-1] = -sn*v[i][j] + cs*v[i][p-1]; v[i][j] = t; } } } } break; // Split at negligible s(k). case 2: { double f = e[k-1]; e[k-1] = 0.0; for (int j = k; j < p; j++) { double t = Hypotenuse(s[j],f); double cs = s[j]/t; double sn = f/t; s[j] = t; f = -sn*e[j]; e[j] = cs*e[j]; if (wantu) { for (int i = 0; i < m; i++) { t = cs*u[i][j] + sn*u[i][k-1]; u[i][k-1] = -sn*u[i][j] + cs*u[i][k-1]; u[i][j] = t; } } } } break; // Perform one qr step. case 3: { // Calculate the shift. double scale = Math.Max(Math.Max(Math.Max(Math.Max(Math.Abs(s[p-1]),Math.Abs(s[p-2])),Math.Abs(e[p-2])), Math.Abs(s[k])),Math.Abs(e[k])); double sp = s[p-1]/scale; double spm1 = s[p-2]/scale; double epm1 = e[p-2]/scale; double sk = s[k]/scale; double ek = e[k]/scale; double b = ((spm1 + sp)*(spm1 - sp) + epm1*epm1)/2.0; double c = (sp*epm1)*(sp*epm1); double shift = 0.0; if ((b != 0.0) | (c != 0.0)) { shift = Math.Sqrt(b*b + c); if (b < 0.0) shift = -shift; shift = c/(b + shift); } double f = (sk + sp)*(sk - sp) + shift; double g = sk*ek; // Chase zeros. for (int j = k; j < p-1; j++) { double t = Hypotenuse(f,g); double cs = f/t; double sn = g/t; if (j != k) e[j-1] = t; f = cs*s[j] + sn*e[j]; e[j] = cs*e[j] - sn*s[j]; g = sn*s[j+1]; s[j+1] = cs*s[j+1]; if (wantv) { for (int i = 0; i < n; i++) { t = cs*v[i][j] + sn*v[i][j+1]; v[i][j+1] = -sn*v[i][j] + cs*v[i][j+1]; v[i][j] = t; } } t = Hypotenuse(f, g); cs = f/t; sn = g/t; s[j] = t; f = cs*e[j] + sn*s[j+1]; s[j+1] = -sn*e[j] + cs*s[j+1]; g = sn*e[j+1]; e[j+1] = cs*e[j+1]; if (wantu && (j < m-1)) { for (int i = 0; i < m; i++) { t = cs*u[i][j] + sn*u[i][j+1]; u[i][j+1] = -sn*u[i][j] + cs*u[i][j+1]; u[i][j] = t; } } } e[p-2] = f; iter = iter + 1; } break; // Convergence. case 4: { // Make the singular values positive. if (s[k] <= 0.0) { s[k] = (s[k] < 0.0 ? -s[k] : 0.0); if (wantv) for (int i = 0; i <= pp; i++) v[i][k] = -v[i][k]; } // Order the singular values. while (k < pp) { if (s[k] >= s[k+1]) break; double t = s[k]; s[k] = s[k+1]; s[k+1] = t; if (wantv && (k < n-1)) for (int i = 0; i < n; i++) { t = v[i][k+1]; v[i][k+1] = v[i][k]; v[i][k] = t; } if (wantu && (k < m-1)) for (int i = 0; i < m; i++) { t = u[i][k+1]; u[i][k+1] = u[i][k]; u[i][k] = t; } k++; } iter = 0; p--; } break; } } }