static void Main(string[] args)
{
try {
EllipticFunction ell = new EllipticFunction(0.1, 1.0); // parameter m = 0.1
// See Abramowitz and Stegun, table 17.1
Console.WriteLine( String.Format( "{0} {1}", ell.K(), ell.E()));
double phi = 20 * Math.Acos(-1.0) / 180.0;;
// See Abramowitz and Stegun, table 17.6 with
// alpha = asin(sqrt(m)) = 18.43 deg and phi = 20 deg
Console.WriteLine( String.Format("{0} {1}", ell.E(phi),
ell.E(Math.Sin(phi), Math.Cos(phi),
Math.Sqrt(1 - ell.k2 * Math.Sin(phi) * Math.Sin(phi))) ) );
// See Carlson 1995, Sec 3.
Console.WriteLine(String.Format("RF(1,2,0) = {0}", EllipticFunction.RF(1,2)));
Console.WriteLine(String.Format("RF(2,3,4) = {0}", EllipticFunction.RF(2,3,4)));
Console.WriteLine(String.Format("RC(0,1/4) = {0}", EllipticFunction.RC(0,0.25)));
Console.WriteLine(String.Format("RC(9/4,2) = {0}", EllipticFunction.RC(2.25,2)));
Console.WriteLine(String.Format("RC(1/4,-2) = {0}", EllipticFunction.RC(0.25,-2)));
Console.WriteLine(String.Format("RJ(0,1,2,3) = {0}", EllipticFunction.RJ(0,1,2,3)));
Console.WriteLine(String.Format("RJ(2,3,4,5) = {0}", EllipticFunction.RJ(2,3,4,5)));
Console.WriteLine(String.Format("RD(0,2,1) = {0}", EllipticFunction.RD(0,2,1)));
Console.WriteLine(String.Format("RD(2,3,4) = {0}", EllipticFunction.RD(2,3,4)));
Console.WriteLine(String.Format("RG(0,16,16) = {0}", EllipticFunction.RG(16,16)));
Console.WriteLine(String.Format("RG(2,3,4) = {0}", EllipticFunction.RG(2,3,4)));
Console.WriteLine(String.Format("RG(0,0.0796,4) = {0}", EllipticFunction.RG(0.0796, 4)));
}
catch (GeographicErr e) {
Console.WriteLine( String.Format( "Caught exception: {0}", e.Message ) );
}
}
private void OnSet(object sender, EventArgs e)
{
try
{
double k2 = Double.Parse(m_k2TextBox.Text);
double alpha2 = Double.Parse(m_alpha2TextBox.Text);
if (m_constructorComboBox.SelectedIndex == 0)
{
m_func = new EllipticFunction(k2, alpha2);
}
else
{
double kp2 = Double.Parse(m_kp2TextBox.Text);
double alphap2 = Double.Parse(m_alphap2TextBox.Text);
m_func = new EllipticFunction(k2, alpha2, kp2, alphap2);
}
m_KtextBox.Text = m_func.K().ToString();
m_EtextBox.Text = m_func.E().ToString();
m_DtextBox.Text = m_func.D().ToString();
m_KEtextBox.Text = m_func.KE().ToString();
m_PItextBox.Text = m_func.Pi().ToString();
m_GtextBox.Text = m_func.G().ToString();
m_HtextBox.Text = m_func.H().ToString();
}
catch (Exception xcpt)
{
MessageBox.Show(xcpt.Message, "Error", MessageBoxButtons.OK, MessageBoxIcon.Error);
}
}
static void Main(string[] args)
{
try {
EllipticFunction ell = new EllipticFunction(0.1, 1.0); // parameter m = 0.1
// See Abramowitz and Stegun, table 17.1
Console.WriteLine(String.Format("{0} {1}", ell.K(), ell.E()));
double phi = 20 * Math.Acos(-1.0) / 180.0;;
// See Abramowitz and Stegun, table 17.6 with
// alpha = asin(sqrt(m)) = 18.43 deg and phi = 20 deg
Console.WriteLine(String.Format("{0} {1}", ell.E(phi),
ell.E(Math.Sin(phi), Math.Cos(phi),
Math.Sqrt(1 - ell.k2 * Math.Sin(phi) * Math.Sin(phi)))));
// See Carlson 1995, Sec 3.
Console.WriteLine(String.Format("RF(1,2,0) = {0}", EllipticFunction.RF(1, 2)));
Console.WriteLine(String.Format("RF(2,3,4) = {0}", EllipticFunction.RF(2, 3, 4)));
Console.WriteLine(String.Format("RC(0,1/4) = {0}", EllipticFunction.RC(0, 0.25)));
Console.WriteLine(String.Format("RC(9/4,2) = {0}", EllipticFunction.RC(2.25, 2)));
Console.WriteLine(String.Format("RC(1/4,-2) = {0}", EllipticFunction.RC(0.25, -2)));
Console.WriteLine(String.Format("RJ(0,1,2,3) = {0}", EllipticFunction.RJ(0, 1, 2, 3)));
Console.WriteLine(String.Format("RJ(2,3,4,5) = {0}", EllipticFunction.RJ(2, 3, 4, 5)));
Console.WriteLine(String.Format("RD(0,2,1) = {0}", EllipticFunction.RD(0, 2, 1)));
Console.WriteLine(String.Format("RD(2,3,4) = {0}", EllipticFunction.RD(2, 3, 4)));
Console.WriteLine(String.Format("RG(0,16,16) = {0}", EllipticFunction.RG(16, 16)));
Console.WriteLine(String.Format("RG(2,3,4) = {0}", EllipticFunction.RG(2, 3, 4)));
Console.WriteLine(String.Format("RG(0,0.0796,4) = {0}", EllipticFunction.RG(0.0796, 4)));
}
catch (GeographicErr e) {
Console.WriteLine(String.Format("Caught exception: {0}", e.Message));
}
}
private void OnValidate(object sender, EventArgs e)
{
try
{
double phi = 0.8;
EllipticFunction f = new EllipticFunction(0.3, 0.4, 0.7, 0.6);
f.Reset(0.2, 0.3, 0.8, 0.7);
f = new EllipticFunction(0.3, 0.4);
f.Reset(0.2, 0.3);
double cn, sn, dn;
f.sncndn(0.3, out sn, out cn, out dn);
f.Delta(sn, cn);
f.D();
f.D(phi);
f.D(sn, cn, dn);
f.Pi();
f.Pi(phi);
f.Pi(sn, cn, dn);
f.KE();
f.K();
f.H();
f.H(phi);
f.H(sn, cn, dn);
f.G();
f.G(phi);
f.G(sn, cn, dn);
f.F(phi);
f.F(sn, cn, dn);
f.Einv(0.75);
f.Ed(60.0);
f.E();
f.E(phi);
f.E(sn, cn, dn);
double tau = 3.1415927 / 10.0;
f.deltaEinv(Math.Sin(tau), Math.Cos(tau));
f.deltaD(sn, cn, dn);
f.deltaE(sn, cn, dn);
f.deltaF(sn, cn, dn);
f.deltaG(sn, cn, dn);
f.deltaH(sn, cn, dn);
f.deltaPi(sn, cn, dn);
}
catch (Exception xcpt)
{
MessageBox.Show(xcpt.Message, "Error", MessageBoxButtons.OK, MessageBoxIcon.Error);
}
MessageBox.Show("No errors detected", "OK", MessageBoxButtons.OK, MessageBoxIcon.Information);
}
private bool ZetaInv0(double psi, double lam, out double u, out double v)
{
bool retval = false;
if (psi < -_e * PI / 4 &&
lam > (1 - 2 * _e) * PI / 2 &&
psi < lam - (1 - _e) * PI / 2)
{
// N.B. this branch is normally not taken because psi < 0 is converted
// psi > 0 by Forward.
//
// There's a log singularity at w = w0 = Eu.K() + i * Ev.K(),
// corresponding to the south pole, where we have, approximately
//
// psi = _e + i * pi/2 - _e * atanh(cos(i * (w - w0)/(1 + _mu/2)))
//
// Inverting this gives:
double
psix = 1 - psi / _e,
lamx = (PI / 2 - lam) / _e;
u = Asinh(Sin(lamx) / Hypot(Cos(lamx), Sinh(psix))) *
(1 + _mu / 2);
v = Atan2(Cos(lamx), Sinh(psix)) * (1 + _mu / 2);
u = _Eu.K() - u;
v = _Ev.K() - v;
}
else if (psi < _e * PI / 2 &&
lam > (1 - 2 * _e) * PI / 2)
{
// At w = w0 = i * Ev.K(), we have
//
// zeta = zeta0 = i * (1 - _e) * pi/2
// zeta' = zeta'' = 0
//
// including the next term in the Taylor series gives:
//
// zeta = zeta0 - (_mv * _e) / 3 * (w - w0)^3
//
// When inverting this, we map arg(w - w0) = [-90, 0] to
// arg(zeta - zeta0) = [-90, 180]
double
dlam = lam - (1 - _e) * PI / 2,
rad = Hypot(psi, dlam),
// atan2(dlam-psi, psi+dlam) + 45d gives arg(zeta - zeta0) in range
// [-135, 225). Subtracting 180 (since multiplier is negative) makes
// range [-315, 45). Multiplying by 1/3 (for cube root) gives range
// [-105, 15). In particular the range [-90, 180] in zeta space maps
// to [-90, 0] in w space as required.
ang = Atan2(dlam - psi, psi + dlam) - 0.75 * PI;
// Error using this guess is about 0.21 * (rad/e)^(5/3)
retval = rad < _e * taytol_;
rad = Cbrt(3 / (_mv * _e) * rad);
ang /= 3;
u = rad * Cos(ang);
v = rad * Sin(ang) + _Ev.K();
}
else
{
// Use spherical TM, Lee 12.6 -- writing atanh(sin(lam) / cosh(psi)) =
// asinh(sin(lam) / hypot(cos(lam), sinh(psi))). This takes care of the
// log singularity at zeta = Eu.K() (corresponding to the north pole)
v = Asinh(Sin(lam) / Hypot(Cos(lam), Sinh(psi)));
u = Atan2(Sinh(psi), Cos(lam));
// But scale to put 90,0 on the right place
u *= _Eu.K() / (PI / 2);
v *= _Eu.K() / (PI / 2);
}
return(retval);
}
private void OnValidate(object sender, EventArgs e)
{
try
{
double phi = 0.8;
EllipticFunction f = new EllipticFunction(0.3, 0.4, 0.7, 0.6);
f.Reset(0.2, 0.3, 0.8, 0.7);
f = new EllipticFunction(0.3, 0.4);
f.Reset(0.2, 0.3);
double cn, sn, dn;
f.sncndn(0.3, out sn, out cn, out dn);
f.Delta(sn, cn);
f.D();
f.D(phi);
f.D(sn, cn, dn);
f.Pi();
f.Pi(phi);
f.Pi(sn, cn, dn);
f.KE();
f.K();
f.H();
f.H(phi);
f.H(sn, cn, dn);
f.G();
f.G(phi);
f.G(sn, cn, dn);
f.F(phi);
f.F(sn, cn, dn);
f.Einv(0.75);
f.Ed(60.0);
f.E();
f.E(phi);
f.E(sn, cn, dn);
double tau = 3.1415927 / 10.0;
f.deltaEinv(Math.Sin(tau), Math.Cos(tau));
f.deltaD(sn, cn, dn);
f.deltaE(sn, cn, dn);
f.deltaF(sn, cn, dn);
f.deltaG(sn, cn, dn);
f.deltaH(sn, cn, dn);
f.deltaPi(sn, cn, dn);
}
catch (Exception xcpt)
{
MessageBox.Show(xcpt.Message, "Error", MessageBoxButtons.OK, MessageBoxIcon.Error);
}
MessageBox.Show("No errors detected", "OK", MessageBoxButtons.OK, MessageBoxIcon.Information);
}
