def my_moments(potential, df, point):
# create an action finder to transform from position+velocity to actions
af = agama.ActionFinder(potential)
# function to be integrated over [scaled] velocity
def integrand(scaledv):
# input is a Nx3 array of velocity values in polar coordinates (|v|, theta, phi)
sintheta = numpy.sin(scaledv[:, 1])
posvel = numpy.column_stack(( \
numpy.tile(point, len(scaledv)).reshape(-1,3), \
scaledv[:,0] * sintheta * numpy.cos(scaledv[:,2]), \
scaledv[:,0] * sintheta * numpy.sin(scaledv[:,2]), \
scaledv[:,0] * numpy.cos(scaledv[:,1]) ))
jacobian = scaledv[:,
0]**2 * sintheta # jacobian of the above transformation
actions = af(posvel) # compute actions at the given points
return df(
actions
) * jacobian # and return the values of DF times the jacobian
# integration region: |v| from 0 to escape velocity, theta and phi are angles of spherical coords
v_esc = (-2 * potential.potential(point))**0.5
result, error, neval = agama.integrateNdim(integrand, [0, 0, 0],
[v_esc, numpy.pi, 2 * numpy.pi],
toler=1e-5)
return result
#!/usr/bin/python
### shows a pretty checkerboard picture - samples drawn from the given function
import agama, numpy, matplotlib.pyplot as plt
# the user-defined function must take a single argument which is a 2d array MxN,
# where N is the dimension of the space and M is the number of points where
# the function should be evaluated simultaneously (for performance reasons),
# i.e., it should operate with columns of the input array x[:,0], x[:,1], etc.
def fnc(x):
return numpy.maximum(
0,
numpy.sin(11 * numpy.pi * x[:, 0]) *
numpy.sin(15 * numpy.pi * x[:, 1]))
valI, errI, _ = agama.integrateNdim(fnc, 2, maxeval=50000)
exact = (2 / numpy.pi)**2 * 83. / 165
print "N-dimensional integration: result =", valI, "+-", errI, " (exact value:", exact, ")"
arr, valS, errS, _ = agama.sampleNdim(fnc, 50000, [-1, 1], [0, 2])
print "N-dimensional sampling: result =", valS, "+-", errS
plt.plot(arr[:, 0], arr[:, 1], ',')
plt.show()
if abs(valI - exact) < errI and abs(
valS - exact) < errS and errI < 1e-3 and errS < 1e-3:
print "\033[1;32mALL TESTS PASSED\033[0m"
else:
print "\033[1;31mSOME TESTS FAILED\033[0m"
#!/usr/bin/python
### shows a pretty checkerboard picture - samples drawn from the given function
import agama, numpy, matplotlib.pyplot as plt
# the user-defined function must take a single argument which is a 2d array MxN,
# where N is the dimension of the space and M is the number of points where
# the function should be evaluated simultaneously (for performance reasons),
# i.e., it should operate with columns of the input array x[:,0], x[:,1], etc.
def fnc(x):
return numpy.maximum(0, numpy.sin(11*numpy.pi*x[:,0]) * numpy.sin(15*numpy.pi*x[:,1]))
valI,errI,_ = agama.integrateNdim(fnc, 2, maxeval=50000)
exact = (2/numpy.pi)**2 * 83./165
print "N-dimensional integration: result =", valI, "+-", errI, " (exact value:", exact, ")"
arr,valS,errS,_ = agama.sampleNdim(fnc, 50000, [-1,1], [0,2])
print "N-dimensional sampling: result =", valS, "+-", errS
plt.plot(arr[:,0], arr[:,1], ',')
plt.show()
if abs(valI-exact)<errI and abs(valS-exact)<errS and errI<1e-3 and errS<1e-3:
print "\033[1;32mALL TESTS PASSED\033[0m"
else:
print "\033[1;31mSOME TESTS FAILED\033[0m"