static private void TestPiecewise()
{
var x = new double[] { -2.0, 0, 2 };
var p1 = new Polynomial(new double[] { -4 });
var p2 = new Polynomial(new double[] { 4 });
var myPoly = new Piecewise(x, new Polynomial[] { p1, p2 });
Debug.Assert(myPoly.Evaluate(-2) == -4);
Debug.Assert(myPoly.Evaluate(-1) == -4);
Debug.Assert(myPoly.Evaluate(0) == -4);
Debug.Assert(myPoly.Evaluate(1) == 4);
Debug.Assert(myPoly.Evaluate(2) == 4);
myPoly = myPoly * 2;
Debug.Assert(myPoly.Evaluate(-2) == -8);
Debug.Assert(myPoly.Evaluate(-1) == -8);
Debug.Assert(myPoly.Evaluate(0) == -8);
Debug.Assert(myPoly.Evaluate(1) == 8);
Debug.Assert(myPoly.Evaluate(2) == 8);
myPoly = myPoly * myPoly;
Debug.Assert(myPoly.Evaluate(-2) == 64);
Debug.Assert(myPoly.Evaluate(-1) == 64);
Debug.Assert(myPoly.Evaluate(0) == 64);
Debug.Assert(myPoly.Evaluate(1) == 64);
Debug.Assert(myPoly.Evaluate(2) == 64);
var myPoly2 = new Piecewise(-4, 2, p1);
var myPoly3 = new Piecewise(-2, 4, p2);
var myPoly4 = myPoly2 + myPoly3;
Debug.Assert(myPoly4.Evaluate(-100) == 0);
Debug.Assert(myPoly4.Evaluate(100) == 0);
Debug.Assert(myPoly4.Evaluate(0) == 0);
Debug.Assert(myPoly4.Evaluate(-3) == -4);
Debug.Assert(myPoly4.Evaluate(3) == 4);
}
// using Cox-de Boor formula to calculate basis functions
// This forms a triangular dependence, see pp 51 An Introduction to NURBS by Rogers
// This is tricky to implement since adjacent elements of the knot vector can be equal to each other
public BSpline_Basis_Function(double[] x, int K)
{
Polys = new Piecewise[x.Length - 1];
for (int i = 0; i < Polys.Length; i++)
{
Polys[i] = new Piecewise(x[i], x[i + 1], new Polynomial(new double[] { 1 }));
}
int Length = Polys.Length - 1;
for (int iLevel = 2; iLevel < K + 1; iLevel++)
{
for (int i = 0; i < Length; i++)
{
var mpoly1 = new Polynomial(new double[] { -x[i], 1 });
var mult1 = x[i + iLevel - 1] - x[i];
if (mult1 != 0)
{
mult1 = 1.0 / mult1;
}
mpoly1 = mpoly1 * mult1;
var mpoly2 = new Polynomial(new double[] { x[i + iLevel], -1 });
var mult2 = x[i + iLevel] - x[i + 1];
if (mult2 != 0)
{
mult2 = 1.0 / mult2;
}
mpoly2 = mpoly2 * mult2;
Polys[i] = Polys[i] * mpoly1 + Polys[i + 1] * mpoly2;
}
Length--;
}
Array.Resize(ref Polys, Polys.Length - K + 1);
}
private void FormEditEquation_Load(object sender, EventArgs e)
{
richTextBoxEquation.SelectionTabs = new int[] { 25, 50, 75, 100 };
Global.Attributes.Clear();
Global.LoadAttributes();
List <String> listAttribute = new List <String>();
if (m_bArea)
{
listBoxAttribute.Items.Add("AREA");
listBoxAttribute.Items.Add("LENGTH");
}
richTextBoxEquation.Text = m_strEquation;
if (m_isPiecewise)
{
Piecewise pw = new Piecewise(richTextBoxEquation.Text);
foreach (AgeValue ageValue in pw.AgeValueList)
{
dgvPerformance.Rows.Add(ageValue.Age, ageValue.Value);
}
}
checkBoxAsFunction.Checked = m_isFunction;
ReloadAttributes();
m_hashFunction.Add("E", "Represents the natural logarithmic base, specified by the constant, e.");
m_hashFunction.Add("PI", "Represents the ratio of the circumference of a circle to its diameter, specified by the constant, pi.");
m_hashFunction.Add("Abs(x)", "Returns the absolute value of a specified number.");
m_hashFunction.Add("Acos(x)", "Returns the angle whose cosine is the specified number.");
m_hashFunction.Add("Asin(x)", "Returns the angle whose sine is the specified number.");
m_hashFunction.Add("Atan(x)", "Returns the angle whose tangent is the specified number.");
m_hashFunction.Add("Atan(x,y)", "Returns the angle whose tangent is the quotient of two specified numbers.");
m_hashFunction.Add("Ceiling(x)", "Returns the smallest whole number greater than or equal to the specified number.");
m_hashFunction.Add("Cos(x)", "Returns the cosine of the specified angle.");
m_hashFunction.Add("Cosh(x)", "Returns the hyperbolic cosine of the specified angle.");
m_hashFunction.Add("Exp(x)", "Returns e raised to the specified power.");
m_hashFunction.Add("Floor(x)", "Returns the largest whole number less than or equal to the specified number.");
m_hashFunction.Add("IEEERemainder(x,y)", "Returns the remainder resulting from the division of a specified number by another specified number.");
m_hashFunction.Add("Log(x)", "Returns the logarithm of a specified number.");
m_hashFunction.Add("Log10(x)", "Returns the base 10 logarithm of a specified number.");
m_hashFunction.Add("Max(x,y)", "Returns the larger of two specified numbers.");
m_hashFunction.Add("Min(x,y)", "Returns the smaller of two numbers.");
m_hashFunction.Add("Pow(x,y)", "Returns a specified number raised to the specified power.");
m_hashFunction.Add("Round(x)", "Returns the number nearest the specified value.");
m_hashFunction.Add("Sign(x)", "Returns a value indicating the sign of a number.");
m_hashFunction.Add("Sin(x)", "Returns the sine of the specified angle.");
m_hashFunction.Add("Sinh(x)", "Returns the hyperbolic sine of the specified angle.");
m_hashFunction.Add("Sqrt(x)", "Returns the square root of a specified number.");
m_hashFunction.Add("Tan(x)", "Returns the tangent of the specified angle.");
m_hashFunction.Add("Tanh(x)", "Returns the hyperbolic tangent of the specified angle.");
FillDefault();
}
private static double u_x1_01(double t)
//****************************************************************************80
//
// Purpose:
//
// U_X1_01 evaluates U at the boundary X1.
//
// Licensing:
//
// This code is distributed under the GNU LGPL license.
//
// Modified:
//
// 24 January 2012
//
// Author:
//
// John Burkardt
//
// Parameters:
//
// Input, double T, the time.
//
// Output, double U, the value of U(T,X1).
//
{
int nd = 6;
double[] td =
{
0.0, 0.10, 0.20, 0.30, 0.40, 0.50
}
;
double[] tv = new double[1];
double[] ud =
{
0.0, 2.0, 10.0, 8.0, 5.0, 0.0
}
;
tv[0] = t;
double[] uv = Piecewise.piecewise_linear(nd, td, ud, 1, tv);
double u = uv[0];
return(u);
}
