private static void vandermonde_matrix_1d_test() //****************************************************************************80 // // Purpose: // // VANDERMONDE_MATRIX_1D_TEST tests VANDERMONDE_MATRIX_1D. // // Licensing: // // This code is distributed under the GNU LGPL license. // // Modified: // // 04 July 2015 // // Author: // // John Burkardt // { const int nd = 4; double[] xd = { -1.0, 2.0, 3.0, 5.0 }; Console.WriteLine(""); Console.WriteLine("VANDERMONDE_MATRIX_1D_TEST"); Console.WriteLine(" VANDERMONDE_MATRIX_1D sets the Vandermonde matrix for 1D interpolation."); double[] ad = Vandermonde.vandermonde_matrix_1d(nd, xd); typeMethods.r8mat_print(nd, nd, ad, " Vandermonde matrix:"); }
private static void test02(int prob) //****************************************************************************80 // // Purpose: // // TEST02 tests VANDERMONDE_INTERP_1D_MATRIX. // // Licensing: // // This code is distributed under the GNU LGPL license. // // Modified: // // 02 June 2013 // // Author: // // John Burkardt // // Parameters: // // Input, int PROB, the problem index. // { List <string> command_unit = new(); List <string> data_unit = new(); int i; List <string> interp_unit = new(); int j; Console.WriteLine(""); Console.WriteLine("TEST02:"); Console.WriteLine(" VANDERMONDE_INTERP_1D_MATRIX sets the Vandermonde linear system"); Console.WriteLine(" for the interpolating polynomial."); Console.WriteLine(" Interpolate data from TEST_INTERP problem #" + prob + ""); int nd = TestInterp.p00_data_num(prob); Console.WriteLine(" Number of data points = " + nd + ""); double[] xy = TestInterp.p00_data(prob, 2, nd); typeMethods.r8mat_transpose_print(2, nd, xy, " Data array:"); double[] xd = new double[nd]; double[] yd = new double[nd]; for (i = 0; i < nd; i++) { xd[i] = xy[0 + 2 * i]; yd[i] = xy[1 + 2 * i]; } // // Compute Vandermonde matrix and get condition number. // double[] ad = Vandermonde.vandermonde_matrix_1d(nd, xd); // // Solve linear system. // double[] cd = QRSolve.qr_solve(nd, nd, ad, yd); // // Create data file. // string data_filename = "data" + prob + ".txt"; for (j = 0; j < nd; j++) { data_unit.Add(" " + xd[j] + " " + yd[j] + ""); } File.WriteAllLines(data_filename, data_unit); Console.WriteLine(""); Console.WriteLine(" Created graphics data file \"" + data_filename + "\"."); // // Create interp file. // int ni = 501; double xmin = typeMethods.r8vec_min(nd, xd); double xmax = typeMethods.r8vec_max(nd, xd); double[] xi = typeMethods.r8vec_linspace_new(ni, xmin, xmax); double[] yi = Vandermonde.vandermonde_value_1d(nd, cd, ni, xi); string interp_filename = "interp" + prob + ".txt"; for (j = 0; j < ni; j++) { interp_unit.Add(" " + xi[j] + " " + yi[j] + ""); } File.WriteAllLines(interp_filename, interp_unit); Console.WriteLine(" Created graphics interp file \"" + interp_filename + "\"."); // // Plot the data and the interpolant. // string command_filename = "commands" + prob + ".txt"; string output_filename = "plot" + prob + ".png"; command_unit.Add("# " + command_filename + ""); command_unit.Add("#"); command_unit.Add("# Usage:"); command_unit.Add("# gnuplot < " + command_filename + ""); command_unit.Add("#"); command_unit.Add("set term png"); command_unit.Add("set output '" + output_filename + "'"); command_unit.Add("set xlabel '<---X--->'"); command_unit.Add("set ylabel '<---Y--->'"); command_unit.Add("set title 'Data versus Vandermonde polynomial interpolant'"); command_unit.Add("set grid"); command_unit.Add("set style data lines"); command_unit.Add("plot '" + data_filename + "' using 1:2 with points pt 7 ps 2 lc rgb 'blue',\\"); command_unit.Add(" '" + interp_filename + "' using 1:2 lw 3 linecolor rgb 'red'"); File.WriteAllLines(command_filename, command_unit); Console.WriteLine(" Created graphics command file \"" + command_filename + "\"."); }
private static void test01(int prob) //****************************************************************************80 // // Purpose: // // TEST01 tests VANDERMONDE_INTERP_1D. // // Licensing: // // This code is distributed under the GNU LGPL license. // // Modified: // // 07 October 2012 // // Author: // // John Burkardt // { const bool debug = false; int i; Console.WriteLine(""); Console.WriteLine("TEST01:"); Console.WriteLine(" Interpolate data from TEST_INTERP problem #" + prob + ""); int nd = TestInterp.p00_data_num(prob); Console.WriteLine(" Number of data points = " + nd + ""); double[] xy = TestInterp.p00_data(prob, 2, nd); switch (debug) { case true: typeMethods.r8mat_transpose_print(2, nd, xy, " Data array:"); break; } double[] xd = new double[nd]; double[] yd = new double[nd]; for (i = 0; i < nd; i++) { xd[i] = xy[0 + i * 2]; yd[i] = xy[1 + i * 2]; } // // Compute Vandermonde matrix and get condition number. // double[] ad = Vandermonde.vandermonde_matrix_1d(nd, xd); double condition = Matrix.condition_hager(nd, ad); Console.WriteLine(""); Console.WriteLine(" Condition of Vandermonde matrix is " + condition + ""); // // Solve linear system. // double[] cd = QRSolve.qr_solve(nd, nd, ad, yd); // // #1: Does interpolant match function at interpolation points? // int ni = nd; double[] xi = typeMethods.r8vec_copy_new(ni, xd); double[] yi = Vandermonde.vandermonde_value_1d(nd, cd, ni, xi); double int_error = typeMethods.r8vec_norm_affine(ni, yi, yd) / ni; Console.WriteLine(""); Console.WriteLine(" L2 interpolation error averaged per interpolant node = " + int_error + ""); // // #2: Compare estimated curve length to piecewise linear (minimal) curve length. // Assume data is sorted, and normalize X and Y dimensions by (XMAX-XMIN) and // (YMAX-YMIN). // double xmin = typeMethods.r8vec_min(nd, xd); double xmax = typeMethods.r8vec_max(nd, xd); double ymin = typeMethods.r8vec_min(nd, yd); double ymax = typeMethods.r8vec_max(nd, yd); ni = 501; xi = typeMethods.r8vec_linspace_new(ni, xmin, xmax); yi = Vandermonde.vandermonde_value_1d(nd, cd, ni, xi); double ld = 0.0; for (i = 0; i < nd - 1; i++) { ld += Math.Sqrt(Math.Pow((xd[i + 1] - xd[i]) / (xmax - xmin), 2) + Math.Pow((yd[i + 1] - yd[i]) / (ymax - ymin), 2)); } double li = 0.0; for (i = 0; i < ni - 1; i++) { li += Math.Sqrt(Math.Pow((xi[i + 1] - xi[i]) / (xmax - xmin), 2) + Math.Pow((yi[i + 1] - yi[i]) / (ymax - ymin), 2)); } Console.WriteLine(""); Console.WriteLine(" Normalized length of piecewise linear interpolant = " + ld + ""); Console.WriteLine(" Normalized length of polynomial interpolant = " + li + ""); }