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#include <stdio.h> |
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#include <cmath> |
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#include "SHFunc.hpp" |
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|
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SHFunc::SHFunc() { |
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} |
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|
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double SHFunc::getValueAt(double costheta, double phi) { |
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|
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double f, p, phase; |
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|
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// incredibly inefficient way to get the normalization, but |
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// we use a lookup table in the factorial code: |
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|
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// normalization factor: |
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f = sqrt( (2*L+1)/(4.0*M_PI) * Fac(L-M) / Fac(L+M) ); |
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// associated Legendre polynomial |
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p = LegendreP(L,M,costheta); |
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|
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if (funcType == SH_SIN) { |
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phase = sin((double)M * phi); |
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} else { |
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phase = cos((double)M * phi); |
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} |
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|
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|
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return coefficient*f*p*phase; |
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|
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} |
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//-----------------------------------------------------------------------------// |
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// |
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// double LegendreP (int l, int m, double x); |
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// |
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// Computes the value of the associated Legendre polynomial P_lm (x) |
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// of order l at a given point. |
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// |
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// Input: |
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// l = degree of the polynomial >= 0 |
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// m = parameter satisfying 0 <= m <= l, |
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// x = point in which the computation is performed, range -1 <= x <= 1. |
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// Returns: |
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// value of the polynomial in x |
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// |
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//-----------------------------------------------------------------------------// |
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|
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double SHFunc::LegendreP (int l, int m, double x) { |
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// check parameters |
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if (m < 0 || m > l || fabs(x) > 1.0) { |
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printf("LegendreP got a bad argument\n"); |
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return NAN; |
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} |
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|
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double pmm = 1.0; |
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if (m > 0) { |
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double h = sqrt((1.0-x)*(1.0+x)), |
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f = 1.0; |
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for (int i = 1; i <= m; i++) { |
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pmm *= -f * h; |
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f += 2.0; |
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} |
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} |
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if (l == m) |
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return pmm; |
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else { |
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double pmmp1 = x * (2 * m + 1) * pmm; |
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if (l == (m+1)) |
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return pmmp1; |
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else { |
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double pll = 0.0; |
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for (int ll = m+2; ll <= l; ll++) { |
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pll = (x * (2 * ll - 1) * pmmp1 - (ll + m - 1) * pmm) / (ll - m); |
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pmm = pmmp1; |
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pmmp1 = pll; |
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} |
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return pll; |
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} |
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} |
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} |
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|
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double SHFunc::Fac (int n) { |
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|
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static double facn[31] = { |
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1.0, |
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1.0, |
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2.0, |
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6.0, |
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24.0, |
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120.0, |
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720.0, |
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5040.0, |
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40320.0, |
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362880.0, |
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3628800.0, |
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39916800.0, |
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479001600.0, |
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6227020800.0, |
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87178291200.0, |
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1.307674368e12, |
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2.0922789888e13, |
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3.55687428096e14, |
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6.402373705728e15, |
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1.21645100408832e17, |
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2.43290200817664e18, |
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5.109094217170944e19, |
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1.12400072777760768e21, |
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2.585201673888497664e22, |
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6.2044840173323943936e23, |
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1.5511210043330985984e25, |
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4.03291461126605635584e26, |
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1.0888869450418352160768e28, |
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3.04888344611713860501504e29, |
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8.841761993739701954543616e30, |
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2.6525285981219105863630848e32 |
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}; |
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|
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|
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static int nmax = 0; |
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static double xmin, xmax; |
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|
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if (n < 0) { |
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printf("factorial of negative integer undefined\n"); |
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return NAN; |
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} |
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|
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if (n <= 30) return facn[n]; |
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else { |
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printf("n is so large that Fac(n) will overflow\n"); |
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return NAN; |
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} |
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} |
