private void Approximation()
{
LinearLeastSquares approx = new LinearLeastSquares(GetGraphicPoints());
_rSquare = approx.RSquares;
_approxLine = approx.Line;
_relativeEstimation = approx.RelativeEstimation;
}
public void LinearAlgebraLLS()
{
//using DotNumerics.LinearAlgebra;
//using DotNumerics;
Matrix A = new Matrix(3, 2);
A[0, 0] = 2; A[0, 1] = 5;
A[1, 0] = 1; A[1, 1] = 5;
A[2, 0] = 8; A[2, 1] = 2;
Matrix B = new Matrix(3, 1);
B[0, 0] = 5;
B[1, 0] = 3;
B[2, 0] = 8;
LinearLeastSquares leastSquares = new LinearLeastSquares();
Matrix Xcof = leastSquares.COFSolve(A, B);
Matrix Xqr = leastSquares.QRorLQSolve(A, B);
Matrix Xsvd = leastSquares.SVDdcSolve(A, B);
ObjectDumper.Write("A=");
ObjectDumper.Write(A.MatrixToString("0.000"));
ObjectDumper.Write("B=");
ObjectDumper.Write(B.MatrixToString("0.000"));
ObjectDumper.Write("Using a omplete orthogonal factorization of A. X =");
ObjectDumper.Write(Xcof.MatrixToString("0.000"));
ObjectDumper.Write("Using a QR or LQ factorization of A. X = ");
ObjectDumper.Write(Xqr.MatrixToString("0.000"));
ObjectDumper.Write("Using the singular value decomposition of A. X = ");
ObjectDumper.Write(Xsvd.MatrixToString("0.000"));
}
private static void test01()
//****************************************************************************80
//
// Purpose:
//
// TEST01 calls LLSQ to match 15 data values.
//
// Licensing:
//
// This code is distributed under the GNU LGPL license.
//
// Modified:
//
// 17 July 2011
//
// Author:
//
// John Burkardt
//
{
double a = 0;
double b = 0;
int i;
int n = 15;
double[] x =
{
1.47, 1.50, 1.52, 1.55, 1.57, 1.60, 1.63, 1.65, 1.68, 1.70,
1.73, 1.75, 1.78, 1.80, 1.83
};
double[] y =
{
52.21, 53.12, 54.48, 55.84, 57.20, 58.57, 59.93, 61.29, 63.11, 64.47,
66.28, 68.10, 69.92, 72.19, 74.46
};
Console.WriteLine("");
Console.WriteLine("TEST01");
Console.WriteLine(" LLSQ can compute the formula for a line of the form");
Console.WriteLine(" y = A * x + B");
Console.WriteLine(" which minimizes the RMS error to a set of N data values.");
LinearLeastSquares.llsq(n, x, y, ref a, ref b);
Console.WriteLine("");
Console.WriteLine(" Estimated relationship is y = " + a + " * x + " + b + "");
Console.WriteLine(" Expected value is y = 61.272 * x - 39.062");
Console.WriteLine("");
Console.WriteLine(" I X Y B+A*X |error|");
Console.WriteLine("");
double error = 0.0;
for (i = 0; i < n; i++)
{
Console.WriteLine(" " + i.ToString(CultureInfo.InvariantCulture).PadLeft(4)
+ " " + x[i].ToString(CultureInfo.InvariantCulture).PadLeft(7)
+ " " + y[i].ToString(CultureInfo.InvariantCulture).PadLeft(7)
+ " " + (b + a * x[i]).ToString(CultureInfo.InvariantCulture).PadLeft(7)
+ " " + (b + a * x[i] - y[i]).ToString(CultureInfo.InvariantCulture).PadLeft(7) + "");
error += Math.Pow(b + a * x[i] - y[i], 2);
}
error = Math.Sqrt(error / n);
Console.WriteLine("");
Console.WriteLine(" RMS error = " + error + "");
}
private static void test02()
//****************************************************************************80
//
// Purpose:
//
// TEST02 calls LLSQ0 to match 14 data values.
//
// Licensing:
//
// This code is distributed under the GNU LGPL license.
//
// Modified:
//
// 15 January 2019
//
// Author:
//
// John Burkardt
//
{
double a = 0;
int i;
int n = 14;
double[] x =
{
0.00, 0.10, 0.15, 0.20, 0.25,
0.30, 0.35, 0.40, 0.45, 0.50,
0.55, 0.60, 0.65, 0.70
};
double[] y =
{
0.0000, 0.0865, 0.1015, 0.1106, 0.1279,
0.1892, 0.2695, 0.2888, 0.2425, 0.3465,
0.3225, 0.3764, 0.4263, 0.4562
};
Console.WriteLine("");
Console.WriteLine("TEST02");
Console.WriteLine(" LLSQ0 can compute the formula for a line of the form");
Console.WriteLine(" y = A * x");
Console.WriteLine(" which minimizes the RMS error to a set of N data values.");
LinearLeastSquares.llsq0(n, x, y, ref a);
Console.WriteLine("");
Console.WriteLine(" Estimated relationship is y = " + a + " * x");
Console.WriteLine("");
Console.WriteLine(" I X Y A*X |error|");
Console.WriteLine("");
double error = 0.0;
for (i = 0; i < n; i++)
{
Console.WriteLine(" " + i.ToString(CultureInfo.InvariantCulture).PadLeft(4)
+ " " + x[i]
+ " " + y[i]
+ " " + a * x[i]
+ " " + (a * x[i] - y[i]) + "");
error += Math.Pow(a * x[i] - y[i], 2);
}
error = Math.Sqrt(error / n);
Console.WriteLine("");
Console.WriteLine(" RMS error = " + error + "");
}
