private static void mltply_test()
//****************************************************************************80
//
// Purpose:
//
// MLTPLY_TEST tests MLTPLY, which multiplies two Chebyshev series.
//
// Licensing:
//
// This code is distributed under the GNU LGPL license.
//
// Modified:
//
// 24 September 2011
//
// Author:
//
// John Burkardt
//
{
int i;
const int nf = 5;
const int npl = 10;
Console.WriteLine("");
Console.WriteLine("MLTPLY_TEST");
Console.WriteLine(" MLTPLY computes the product of two Chebyshev series.");
Console.WriteLine("");
Console.WriteLine(" Multiply series for SIN(X) and COS(X)");
Console.WriteLine(" and compare with series for 1/2*SIN(2X).");
double[] x = Chebyshev.cheby(nf, npl, functn);
double[] x1 = new double[npl];
double[] x2 = new double[npl];
for (i = 0; i < npl; i++)
{
x1[i] = x[i + 0 * npl];
x2[i] = x[i + 1 * npl];
x[i + 2 * npl] = 0.5 * x[i + 2 * npl];
}
double[] x3 = ChebyshevSeries.mltply_new(x1, x2, npl);
Console.WriteLine("");
Console.WriteLine(" Sin(x) Cos(x) 1/2*Sin(2x) RESULT");
Console.WriteLine("");
for (i = 0; i < npl; i++)
{
Console.WriteLine(" " + x[i + 0 * npl].ToString(CultureInfo.InvariantCulture).PadLeft(14)
+ " " + x[i + 1 * npl].ToString(CultureInfo.InvariantCulture).PadLeft(14)
+ " " + x[i + 2 * npl].ToString(CultureInfo.InvariantCulture).PadLeft(14)
+ " " + x3[i].ToString(CultureInfo.InvariantCulture).PadLeft(14) + "");
}
}
private static void test01()
//****************************************************************************80
//
// Purpose:
//
// TEST01 considers an even Chebyshev series for EXP(X).
//
// Discussion:
//
// Table 5 is from Clenshaw, and contains 18 terms of the Chebyshev
// series for exp(x) over [-1,+1].
//
// Licensing:
//
// This code is distributed under the GNU LGPL license.
//
// Modified:
//
// 13 January 2014
//
// Author:
//
// Manfred Zimmer
//
// Reference:
//
// Charles Clenshaw,
// Mathematical Tables, Volume 5,
// Chebyshev series for mathematical functions,
// London, 1962.
//
{
double[] table5 =
{
2.53213175550401667120,
1.13031820798497005442,
0.27149533953407656237,
0.04433684984866380495,
0.00547424044209373265,
0.00054292631191394375,
0.00004497732295429515,
0.00000319843646240199,
0.00000019921248066728,
0.00000001103677172552,
0.00000000055058960797,
0.00000000002497956617,
0.00000000000103915223,
0.00000000000003991263,
0.00000000000000142376,
0.00000000000000004741,
0.00000000000000000148,
0.00000000000000000004
}
;
double s1 = 0;
double s2 = 0;
double s3 = 0;
Console.WriteLine("");
Console.WriteLine("TEST01:");
Console.WriteLine(" ECHEBSER3 computes a Chebyshev series approximation");
Console.WriteLine(" and the first three derivatives.");
Console.WriteLine("");
Console.WriteLine(" Errors of a Chebyshev series for exp(x)");
Console.WriteLine("");
Console.WriteLine(" x err(y) err(y') err(y\") err(y\"')");
Console.WriteLine("");
for (int i = -10; i <= 10; i++)
{
double x = i / 10.0;
double s = ChebyshevSeries.echebser3(x, table5, 18, ref s1, ref s2, ref s3);
double y = Math.Exp(x);
s -= y;
s1 -= y;
s2 -= y;
s3 -= y;
Console.WriteLine(x.ToString(CultureInfo.InvariantCulture).PadLeft(5)
+ s.ToString(CultureInfo.InvariantCulture).PadLeft(14)
+ s1.ToString(CultureInfo.InvariantCulture).PadLeft(14)
+ s2.ToString(CultureInfo.InvariantCulture).PadLeft(14)
+ s3.ToString(CultureInfo.InvariantCulture).PadLeft(14) + "");
}
}
private static void test03()
//****************************************************************************80
//
// Purpose:
//
// TEST03 considers an odd Chebyshev series for SINH(X).
//
// Discussion:
//
// TABLE5ODD contains the odd Chebyshev series coefficients for
// sinh(x) over -1 <= x <= 1.
//
// Licensing:
//
// This code is distributed under the GNU LGPL license.
//
// Modified:
//
// 26 January 2014
//
// Author:
//
// Manfred Zimmer
//
// Reference:
//
// Charles Clenshaw,
// Mathematical Tables, Volume 5,
// Chebyshev series for mathematical functions,
// London, 1962.
//
{
double s1 = 0;
double s2 = 0;
double[] table5odd =
{
1.13031820798497005442,
0.04433684984866380495,
0.00054292631191394375,
0.00000319843646240199,
0.00000001103677172552,
0.00000000002497956617,
0.00000000000003991263,
0.00000000000000004741,
0.00000000000000000004
}
;
Console.WriteLine("");
Console.WriteLine("TEST03:");
Console.WriteLine(" ODDCHEBSER2 computes an odd Chebyshev series approximation.");
Console.WriteLine(" and its first two derivatives.");
Console.WriteLine("");
Console.WriteLine(" Errors of an odd Chebyshev series y(x) approximating sinh(x):");
Console.WriteLine("");
Console.WriteLine(" x err(y) err(y') err(y\")");
Console.WriteLine("");
for (int i = 0; i <= 10; i++)
{
double x = i / 10.0;
double s = ChebyshevSeries.oddchebser2(x, table5odd, 9, ref s1, ref s2);
double y = Math.Sinh(x);
double y1 = Math.Cosh(x);
s -= y;
s1 -= y1;
s2 -= y;
Console.WriteLine(x.ToString(CultureInfo.InvariantCulture).PadLeft(5)
+ s.ToString(CultureInfo.InvariantCulture).PadLeft(14)
+ s1.ToString(CultureInfo.InvariantCulture).PadLeft(14)
+ s2.ToString(CultureInfo.InvariantCulture).PadLeft(14) + "");
}
}
private static void test02()
//****************************************************************************80
//
// Purpose:
//
// TEST02 considers an even Chebyshev series for COS(PI*X/2).
//
// Discussion:
//
// TABLE1 contains the even Chebyshev series coefficients for
// cos(pi*x/2) over [-1,+1].
//
// Licensing:
//
// This code is distributed under the GNU LGPL license.
//
// Modified:
//
// 26 January 2014
//
// Author:
//
// Manfred Zimmer
//
// Reference:
//
// Charles Clenshaw,
// Mathematical Tables, Volume 5,
// Chebyshev series for mathematical functions,
// London, 1962.
//
{
double s1 = 0;
double s2 = 0;
double[] table1 =
{
+0.94400243153646953490,
-0.49940325827040708740,
+0.02799207961754761751,
-0.00059669519654884650,
+0.00000670439486991684,
-0.00000004653229589732,
+0.00000000021934576590,
-0.00000000000074816487,
+0.00000000000000193230,
-0.00000000000000000391,
+0.00000000000000000001
}
;
double y = 0;
double y1 = 0;
Console.WriteLine("");
Console.WriteLine("TEST02:");
Console.WriteLine(" EVENCHEBSER2 computes an even Chebyshev series");
Console.WriteLine(" and its first two derivatives.");
Console.WriteLine("");
Console.WriteLine(" Errors of an even Chebyshev series for cos(pi*x/2):");
Console.WriteLine("");
Console.WriteLine(" x err(y) err(y') err(y\")");
Console.WriteLine("");
for (int i = 0; i <= 10; i++)
{
double x = i / 10.0;
double s = ChebyshevSeries.evenchebser2(x, table1, 11, ref s1, ref s2);
Helpers.sincos(Math.PI / 2 * x, ref y1, ref y);
y1 = -y1 * Math.PI / 2;
double y2 = -y * (Math.PI / 2 * Math.PI / 2);
s -= y;
s1 -= y1;
s2 -= y2;
Console.WriteLine(x.ToString(CultureInfo.InvariantCulture).PadLeft(5)
+ s.ToString(CultureInfo.InvariantCulture).PadLeft(14)
+ s1.ToString(CultureInfo.InvariantCulture).PadLeft(14)
+ s2.ToString(CultureInfo.InvariantCulture).PadLeft(14) + "");
}
}
private static void dfrnt_test()
//****************************************************************************80
//
// Purpose:
//
// DFRNT_TEST tests DFRNT, which computes the Chebyshev series of a derivative.
//
// Licensing:
//
// This code is distributed under the GNU LGPL license.
//
// Modified:
//
// 24 September 2011
//
// Author:
//
// John Burkardt
//
{
int i;
int j;
const int nf = 5;
const int npl = 10;
Console.WriteLine("");
Console.WriteLine("DFRNT_TEST");
Console.WriteLine(" DFRNT computes the Chebyshev series for the derivative");
Console.WriteLine(" of several functions.");
double[] x = Chebyshev.cheby(nf, npl, functn);
double[] x2 = new double[npl];
for (j = 0; j < nf; j++)
{
for (i = 0; i < npl; i++)
{
x2[i] = x[i + j * npl];
}
double[] x3 = ChebyshevSeries.dfrnt(x2, npl);
for (i = 0; i < npl; i++)
{
x[i + j * npl] = x3[i];
}
}
Console.WriteLine("");
Console.WriteLine(" Chebyshev series for d/dx of:");
Console.WriteLine("");
Console.WriteLine(" Sin(x) Cos(x) Sin(2x) Cos(2x) X^5");
Console.WriteLine("");
for (i = 0; i < npl; i++)
{
string cout = "";
for (j = 0; j < nf; j++)
{
cout += " " + x[i + j * npl].ToString(CultureInfo.InvariantCulture).PadLeft(14);
}
Console.WriteLine(cout);
}
}
private static void edcheb_test()
//****************************************************************************80
//
// Purpose:
//
// EDCHEB_TEST tests EDCHEB, which evaluates the derivative of a Chebyshev series.
//
// Licensing:
//
// This code is distributed under the GNU LGPL license.
//
// Modified:
//
// 24 September 2011
//
// Author:
//
// John Burkardt
//
{
int j;
const int nf = 5;
const int npl = 10;
const int nx = 6;
Console.WriteLine("");
Console.WriteLine("EDCHEB_TEST");
Console.WriteLine(" EDCHEB evaluates the derivative of a Chebyshev series.");
double[] x = Chebyshev.cheby(nf, npl, functn);
double[] x2 = new double[npl];
for (j = 0; j < nf; j++)
{
int i;
for (i = 0; i < npl; i++)
{
x2[i] = x[i + j * npl];
}
Console.WriteLine("");
switch (j)
{
case 0:
Console.WriteLine(" Sin(x)");
break;
case 1:
Console.WriteLine(" Cos(x)");
break;
case 2:
Console.WriteLine(" Sin(2x)");
break;
case 3:
Console.WriteLine(" Cos(2x)");
break;
case 4:
Console.WriteLine(" x^5");
break;
}
Console.WriteLine("");
int k;
for (k = 0; k < nx; k++)
{
double xval = 2.0 * k / (nx - 1) - 1.0;
double[] fxj = functn_d(xval);
double fval = ChebyshevSeries.edcheb(xval, x2, npl);
Console.WriteLine(" " + xval.ToString(CultureInfo.InvariantCulture).PadLeft(14)
+ " " + fxj[j].ToString(CultureInfo.InvariantCulture).PadLeft(14)
+ " " + fval.ToString(CultureInfo.InvariantCulture).PadLeft(14) + "");
}
}
}