def test_correlated_scatter(self):
n = 50
r = (sp.arange(n, dtype=float) + 10.0 * n) / 10.0 * n
data = sp.sin(sp.arange(n)) * r
amp = 25.0
theory = data / amp
# Generate correlated matrix.
C = random.rand(n, n) # [0, 1)
# Raise to high power to make values near 1 rare.
C = (C**10) * 0.2
C = (C + C.T) / 2.0
C += sp.identity(n)
C *= r[:, None] / 2.0
C *= r[None, :] / 2.0
# Generate random numbers in diagonal frame.
h, R = linalg.eigh(C)
self.assertTrue(sp.alltrue(h > 0))
rand_vals = random.normal(size=n) * sp.sqrt(h)
# Rotate back.
data += sp.dot(R.T, rand_vals)
out = utils.ampfit(data, C, theory)
a, s = out['amp'], out['error']
self.assertTrue(sp.allclose(a, amp, atol=5.0 * s, rtol=0))
# Expect the next line to fail 1/100 trials.
self.assertFalse(sp.allclose(a, amp, atol=0.01 * s, rtol=0))
def test_uncorrelated_noscatter(self):
data = sp.arange(10, dtype=float)
theory = data / 2.0
C = sp.identity(10)
out = utils.ampfit(data, C, theory)
a, s = out['amp'], out['error']
self.assertAlmostEqual(a, 2)
def test_correlated_scatter(self) :
n = 50
r = (sp.arange(n, dtype=float) + 10.0*n)/10.0*n
data = sp.sin(sp.arange(n)) * r
amp = 25.0
theory = data/amp
# Generate correlated matrix.
C = random.rand(n, n) # [0, 1)
# Raise to high power to make values near 1 rare.
C = (C**10) * 0.2
C = (C + C.T)/2.0
C += sp.identity(n)
C *= r[:, None]/2.0
C *= r[None, :]/2.0
# Generate random numbers in diagonal frame.
h, R = linalg.eigh(C)
self.assertTrue(sp.alltrue(h>0))
rand_vals = random.normal(size=n)*sp.sqrt(h)
# Rotate back.
data += sp.dot(R.T, rand_vals)
out = utils.ampfit(data, C, theory)
a, s = out['amp'], out['error']
self.assertTrue(sp.allclose(a, amp, atol=5.0*s, rtol=0))
# Expect the next line to fail 1/100 trials.
self.assertFalse(sp.allclose(a, amp, atol=0.01*s, rtol=0))
def test_uncorrelated_noscatter(self):
data = sp.arange(10, dtype=float)
theory = data/2.0
C = sp.identity(10)
out = utils.ampfit(data, C, theory)
a, s = out['amp'], out['error']
self.assertAlmostEqual(a, 2)
def test_uncorrelated_noscatter_error(self):
data = sp.arange(10, dtype=float) + 1.0
amp = 5.0
theory = data/amp
C = sp.diag((sp.arange(10, dtype=float) + 1.0)**2)
a, s = utils.ampfit(data, C, theory)
self.assertAlmostEqual(a, amp)
self.assertAlmostEqual(s/a, 1.0/sp.sqrt(10))
def test_uncorrelated_noscatter_error(self):
data = sp.arange(10, dtype=float) + 1.0
amp = 5.0
theory = data / amp
C = sp.diag((sp.arange(10, dtype=float) + 1.0)**2)
out = utils.ampfit(data, C, theory)
a, s = out['amp'], out['error']
self.assertAlmostEqual(a, amp)
self.assertAlmostEqual(s / a, 1.0 / sp.sqrt(10))
def test_uncorrelated_scatter_error(self):
n = 1000
data = sp.arange(n, dtype=float) + 1.0
amp = 5.0
theory = data/amp
C = sp.diag((sp.arange(n, dtype=float) + 1.0)**2)
data += random.normal(size=n)*data
a, s = utils.ampfit(data, C, theory)
self.assertTrue(sp.allclose(a, amp, rtol=5.0/sp.sqrt(n), atol=0))
# Expect the next line to fail 1/100 trials.
self.assertFalse(sp.allclose(a, amp, rtol=0.01/sp.sqrt(n), atol=0))
self.assertAlmostEqual(s, amp/sp.sqrt(1000))
def test_uncorrelated_scatter_error(self):
n = 1000
data = sp.arange(n, dtype=float) + 1.0
amp = 5.0
theory = data / amp
C = sp.diag((sp.arange(n, dtype=float) + 1.0)**2)
data += random.normal(size=n) * data
out = utils.ampfit(data, C, theory)
a, s = out['amp'], out['error']
self.assertTrue(sp.allclose(a, amp, rtol=5.0 / sp.sqrt(n), atol=0))
# Expect the next line to fail 1/100 trials.
self.assertFalse(sp.allclose(a, amp, rtol=0.01 / sp.sqrt(n), atol=0))
self.assertAlmostEqual(s, amp / sp.sqrt(1000))