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import unittest 

import numpy as np 

import numbers 

 

import lsst.utils.tests 

 

from lsst.sims.utils import _FactorialGenerator 

from lsst.sims.utils import ZernikePolynomialGenerator 

 

 

def setup_module(module): 

lsst.utils.tests.init() 

 

 

class FactorialTestCase(unittest.TestCase): 

 

def test_factorial(self): 

gen = _FactorialGenerator() 

ii = gen.evaluate(9) 

ans = 9*8*7*6*5*4*3*2 

self.assertEqual(ii, ans) 

 

ii = gen.evaluate(15) 

ans = 15*14*13*12*11*10*9*8*7*6*5*4*3*2 

self.assertEqual(ii, ans) 

 

ii = gen.evaluate(3) 

ans = 6 

self.assertEqual(ii, ans) 

 

self.assertEqual(gen.evaluate(0), 1) 

self.assertEqual(gen.evaluate(1), 1) 

 

 

class ZernikeTestCase(unittest.TestCase): 

 

longMessage = True 

 

@classmethod 

def setUpClass(cls): 

cls.d_r = 0.01 

cls.d_phi = 0.005*np.pi 

r_grid = np.arange(0.0, 1.0, cls.d_r) 

phi_grid = np.arange(0.0, 2.0*np.pi, cls.d_phi) 

mesh = np.meshgrid(r_grid, phi_grid) 

cls.r_grid = mesh[0].flatten() 

cls.phi_grid = mesh[1].flatten() 

 

r_grid = np.arange(0.0, 1.0, 0.1) 

phi_grid =np.arange(0.0, 2.0*np.pi, 0.05*np.pi) 

mesh=np.meshgrid(r_grid, phi_grid) 

cls.r_grid_small = mesh[0].flatten() 

cls.phi_grid_small = mesh[1].flatten() 

 

def test_orthogonality(self): 

""" 

Test that ZernikePolynomialGenerator returns 

polynomials that are orthogonal on the unit disc 

""" 

 

polynomials = {} 

z_gen = ZernikePolynomialGenerator() 

 

for n in range(3): 

for m in range(-n, n+1, 2): 

vals = np.zeros(len(self.r_grid), dtype=float) 

for ii, (rr, pp) in enumerate(zip(self.r_grid, self.phi_grid)): 

vals[ii] = z_gen.evaluate(rr, pp, n, m) 

nm_tuple = (n,m) 

polynomials[nm_tuple] = vals 

 

p_keys = list(polynomials.keys()) 

for ii in range(len(p_keys)): 

p1_name = p_keys[ii] 

p1 = polynomials[p1_name] 

integral = (p1*p1*self.r_grid*self.d_r*self.d_phi).sum() 

normed_integral = integral/z_gen.norm(p1_name[0], p1_name[1]) 

self.assertLess(np.abs(normed_integral-1.0), 0.04) 

for jj in range(ii+1, len(p_keys)): 

p2_name = p_keys[jj] 

p2 = polynomials[p2_name] 

dot = (p1*p2*self.r_grid*self.d_r*self.d_phi).sum() 

msg = '\n%s norm %e\n dot %e\n' % (p1_name, integral, dot) 

self.assertLess(np.abs(dot/integral), 0.01, msg=msg) 

 

def test_zeros(self): 

""" 

Test that ZernikePolynomialGenerator returns zero 

when values of n and m require it. 

""" 

rng = np.random.RandomState(88) 

z_gen = ZernikePolynomialGenerator() 

for n in range(4): 

for m in range(-(n-1), n, 2): 

r = rng.random_sample() 

phi = rng.random_sample()*2.0*np.pi 

self.assertAlmostEqual(0.0, z_gen.evaluate(r, phi, n, m), 10) 

 

def test_r_greater_than_one(self): 

""" 

Test that the expected error is raised if we try to evaluate 

the Zernike polynomial with r>1 

""" 

z_gen = ZernikePolynomialGenerator() 

vv = z_gen.evaluate(1.2, 2.1, 2, 0) 

self.assertTrue(np.isnan(vv)) 

vv = z_gen.evaluate(np.array([0.1, 0.5, 1.2]), 

np.array([0.1, 0.2, 0.3]), 

2, -2) 

self.assertTrue(np.isnan(vv[2])) 

self.assertFalse(np.isnan(vv[0])) 

self.assertFalse(np.isnan(vv[1])) 

vv = z_gen.evaluate_xy(1.1, 1.2, 4, -2) 

self.assertTrue(np.isnan(vv)) 

vv = z_gen.evaluate_xy(np.array([0.1, 0.2, 0.3]), 

np.array([0.1, 1.0, 0.1]), 

4, 2) 

self.assertTrue(np.isnan(vv[1])) 

self.assertFalse(np.isnan(vv[0])) 

self.assertFalse(np.isnan(vv[2])) 

 

def test_array(self): 

""" 

Test that ZernikePolynomialGenerator can handle arrays of inputs 

""" 

z_gen = ZernikePolynomialGenerator() 

n = 2 

m = -2 

val_arr = z_gen.evaluate(self.r_grid_small, self.phi_grid_small, n, m) 

self.assertEqual(len(val_arr), len(self.r_grid_small)) 

for ii, (rr, pp) in enumerate(zip(self.r_grid_small, 

self.phi_grid_small)): 

 

vv = z_gen.evaluate(rr, pp, n, m) 

self.assertAlmostEqual(vv, val_arr[ii], 14) 

 

def test_xy(self): 

""" 

Test that ZernikePolynomialGenerator can handle Cartesian coordinates 

""" 

n = 4 

m = 2 

z_gen = ZernikePolynomialGenerator() 

x = self.r_grid_small*np.cos(self.phi_grid_small) 

y = self.r_grid_small*np.sin(self.phi_grid_small) 

val_arr = z_gen.evaluate_xy(x, y, n, m) 

self.assertGreater(np.abs(val_arr).max(), 1.0e-6) 

for ii, (rr, pp) in enumerate(zip(self.r_grid_small, 

self.phi_grid_small)): 

vv = z_gen.evaluate(rr, pp, n, m) 

self.assertAlmostEqual(vv, val_arr[ii], 14) 

 

def test_xy_one_at_a_time(self): 

""" 

Test that ZernikePolynomialGenerator can handle 

scalar Cartesian coordinates (as opposed to arrays 

of Cartesian coordinates) 

""" 

n = 4 

m = 2 

z_gen = ZernikePolynomialGenerator() 

x = self.r_grid_small*np.cos(self.phi_grid_small) 

y = self.r_grid_small*np.sin(self.phi_grid_small) 

 

for ii in range(len(self.r_grid_small)): 

vv_r = z_gen.evaluate(self.r_grid_small[ii], 

self.phi_grid_small[ii], n, m) 

vv_xy = z_gen.evaluate_xy(x[ii], y[ii], n, m) 

self.assertAlmostEqual(vv_r, vv_xy, 14) 

self.assertIsInstance(vv_xy, numbers.Number) 

 

def test_Zernike_origin(self): 

""" 

Test that ZernikePolynomialGenerator is well-behaved 

at r=0 

""" 

n = 4 

m = 2 

z_gen = ZernikePolynomialGenerator() 

ans = z_gen.evaluate(0.0, 1.2, n, m) 

self.assertEqual(ans, 0.0) 

ans = z_gen.evaluate(np.array([0.0, 0.0]), 

np.array([1.2, 2.1]), 

n, m) 

 

np.testing.assert_array_equal(ans, np.zeros(2, dtype=float)) 

ans = z_gen.evaluate_xy(0.0, 0.0, n, m) 

self.assertEqual(ans, 0.0) 

ans = z_gen.evaluate_xy(np.zeros(2, dtype=float), 

np.zeros(2, dtype=float), 

n, m) 

np.testing.assert_array_equal(ans, np.zeros(2, dtype=float)) 

 

n = 0 

m = 0 

ans = z_gen.evaluate(0.0, 1.2, n, m) 

self.assertEqual(ans, 1.0) 

ans = z_gen.evaluate(np.array([0.0, 0.0]), 

np.array([1.2, 2.1]), 

n, m) 

 

np.testing.assert_array_equal(ans, np.ones(2, dtype=float)) 

ans = z_gen.evaluate_xy(0.0, 0.0, n, m) 

self.assertEqual(ans, 1.0) 

ans = z_gen.evaluate_xy(np.zeros(2, dtype=float), 

np.zeros(2, dtype=float), 

n, m) 

np.testing.assert_array_equal(ans, np.ones(2, dtype=float)) 

 

 

class MemoryTestClass(lsst.utils.tests.MemoryTestCase): 

pass 

 

 

215 ↛ 216line 215 didn't jump to line 216, because the condition on line 215 was never trueif __name__ == "__main__": 

lsst.utils.tests.init() 

unittest.main()