def test_invalid_acc_raises_exception(self):
with self.assertRaises(ValueError):
coefficients(deriv=1, acc=3)
with self.assertRaises(ValueError):
coefficients(deriv=1, acc=0)
with self.assertRaises(ValueError):
coefficients_non_uni(1, 3, None, None)
with self.assertRaises(ValueError):
coefficients_non_uni(1, 0, None, None)
def _setup_der_coef(self):
self._derwindow_ = self.par["acc"] + 1
if self.par["der"] > 0:
self._dercoef_ = findiff.coefficients(
deriv=self.par["der"],
acc=self.par["acc"])["backward"]["coefficients"]
else:
self._dercoef_ = np.array(self._derwindow_ *
[1 / self._derwindow_])
self._ylist_ = deque(self._derwindow_ * [np.NAN])
def test_non_uniform(self):
x = np.linspace(0, 10, 100)
dx = x[1] - x[0]
c_uni = coefficients(deriv=2, acc=2)
coefs_uni = c_uni["center"]["coefficients"] / dx**2
c_non_uni = coefficients_non_uni(deriv=2, acc=2, coords=x, idx=5)
coefs_non_uni = c_non_uni["coefficients"]
np.testing.assert_array_almost_equal(coefs_non_uni, coefs_uni)
def trendln(self, mintrend, maxtrend):
mom, momacc = self.momentum()
self.df['Mom Acc'] = np.round(momacc, 2)
self.df['Mom'] = np.round(mom, 2)
coeff = findiff.coefficients(deriv=1, acc=1)
slope_support = mintrend[-1][1][0]
intercept_support = mintrend[-1][1][1]
slope_resistance = maxtrend[-1][1][0]
intercept_resistance = maxtrend[-1][1][1]
df = self.get_trend_line(slope_support, intercept_support,
slope_resistance, intercept_resistance)
return df
def make_central_diffs ( order ) :
"""Helper function to get table for central differences
"""
import findiff
from ostap.math.base import lcm
from math import fsum, sqrt
from ostap.math.finitediffs import calc_dot
def fact ( n ) :
return 1 if 0 == n else n * fact ( n - 1 )
D = order
for I in range ( 0 , 26 ) :
## for I in range ( 0 , 10 ) :
r = findiff.coefficients(deriv=D, offsets=tuple ( k for k in range (-I-D, I+D+1 ) ), symbolic=True)
c = r['coefficients']
## print ( 'offsets' , r['offsets'] )
denom = lcm ( *[ i.q for i in c ] )
coeffs = [ denom*i for i in c ]
e = ( fsum ( ( 1.0 * k * k for k in coeffs ) ) ** 0.5 ) / ( denom * sqrt ( 12.0 ) )
if all ( [ float(i) == i for i in coeffs ] ) :
n = r['accuracy']
d = D
stencil = tuple ( range ( -I - D , I + D + 1 ) )
fun = lambda x : x**(n+d)
ff = fact ( n + d )
a = denom * ff
b = calc_dot ( fun , 0.0 , 1.0 , stencil , coeffs )
term = a / b
to = topt ( d , n )
line = ' RuleConf ( %d , darray ( %s ) , %s , %d , darray ( range ( %s , %s ) ) , %.10g , %.1f , %.4f ) , ' % ( D , coeffs , denom , n , - I - D , I + D + 1 , e , term , to )
roff = r['offsets']
assert roff == stencil , 'forward invalid stencil!'
print ( line )
def test_order2_acc2(self):
c = coefficients(deriv=2, acc=2)
coefs = c["center"]["coefficients"]
np.testing.assert_array_almost_equal(np.array([1., -2., 1.]), coefs)
offs = c["center"]["offsets"]
np.testing.assert_array_almost_equal(np.array([-1, 0, 1]), offs)
coefs = c["forward"]["coefficients"]
np.testing.assert_array_almost_equal(np.array([2, -5, 4, -1]), coefs)
offs = c["forward"]["offsets"]
np.testing.assert_array_almost_equal(np.array([0, 1, 2, 3]), offs)
coefs = c["backward"]["coefficients"]
np.testing.assert_array_almost_equal(np.array(([2, -5, 4, -1])[::-1]),
coefs)
offs = c["backward"]["offsets"]
np.testing.assert_array_almost_equal(np.array([-3, -2, -1, 0]), offs)
def test_order1_acc2(self):
c = coefficients(deriv=1, acc=2)
coefs = c["center"]["coefficients"]
np.testing.assert_array_almost_equal(np.array([-0.5, 0, 0.5]), coefs)
offs = c["center"]["offsets"]
np.testing.assert_array_almost_equal(np.array([-1, 0, 1]), offs)
coefs = c["forward"]["coefficients"]
np.testing.assert_array_almost_equal(np.array([-1.5, 2, -0.5]), coefs)
offs = c["forward"]["offsets"]
np.testing.assert_array_almost_equal(np.array([0, 1, 2]), offs)
coefs = c["backward"]["coefficients"]
np.testing.assert_array_almost_equal(-np.array([-1.5, 2, -0.5])[::-1],
coefs)
offs = c["backward"]["offsets"]
np.testing.assert_array_almost_equal(np.array([-2, -1, 0]), offs)
def getCenteredWeights(self, window, coefficients="gaussian", std=5):
"""
returns the coefficient and the indexes
"""
offsets = range(-window // 2, window // 2)
if coefficients == "findiff":
coefs = findiff.coefficients(1, window)["center"]
return (coefs["coefficients"], coefs["offsets"])
elif coefficients == "gaussian":
coefs = signal.gaussian(window, std,
sym=True) # get the guaussien filters
coefs = coefs * 2 / np.sum(
coefs) # scale them to sum to one for each side
coefs = [
coef if i >= window // 2 else -coef
for i, coef in enumerate(coefs)
] # invert the first weights
return coefs, offsets
else:
coefs = [
1 / window if i >= window // 2 else -1 / window
for i in range(window)
]
offsets = [range(-window // 2, window // 2)]
return (coefs, offsets)
# import matplotlib.pyplot as plt
# d = Derivative()
# w1, _ = d.getCenteredWeights(16, std=4)
# plt.plot(_, w1, label="std 4")
# w1, _ = d.getCenteredWeights(16, std=100)
# plt.plot(_, w1, label="std 100")
# w1, _ = d.getCenteredWeights(16, std=16//3)
# plt.plot(_, w1, label="std 16/3")
# plt.legend()
# plt.show()
def test_order1_acc4(self):
c = coefficients(deriv=1, acc=4)
coefs = c["center"]["coefficients"]
np.testing.assert_array_almost_equal(
np.array([1 / 12, -2 / 3, 0, 2 / 3, -1 / 12]), coefs)
offs = c["center"]["offsets"]
np.testing.assert_array_almost_equal(np.array([-2, -1, 0, 1, 2]), offs)
coefs = c["forward"]["coefficients"]
np.testing.assert_array_almost_equal(
np.array([-25 / 12, 4, -3, 4 / 3, -1 / 4]), coefs)
offs = c["forward"]["offsets"]
np.testing.assert_array_almost_equal(np.array([0, 1, 2, 3, 4]), offs)
coefs = c["backward"]["coefficients"]
np.testing.assert_array_almost_equal(
-np.array([-25 / 12, 4, -3, 4 / 3, -1 / 4])[::-1], coefs)
offs = c["backward"]["offsets"]
np.testing.assert_array_almost_equal(-np.array([0, 1, 2, 3, 4])[::-1],
offs)
def test_order2_acc4(self):
c = coefficients(deriv=2, acc=4)
coefs = c["center"]["coefficients"]
np.testing.assert_array_almost_equal(
np.array([-1 / 12, 4 / 3, -2.5, 4 / 3, -1 / 12]), coefs)
offs = c["center"]["offsets"]
np.testing.assert_array_almost_equal(np.array([-2, -1, 0, 1, 2]), offs)
coefs = c["forward"]["coefficients"]
np.testing.assert_array_almost_equal(
np.array([15 / 4, -77 / 6, 107 / 6, -13, 61 / 12, -5 / 6]), coefs)
offs = c["forward"]["offsets"]
np.testing.assert_array_almost_equal(np.array([0, 1, 2, 3, 4, 5]),
offs)
coefs = c["backward"]["coefficients"]
np.testing.assert_array_almost_equal(
np.array([15 / 4, -77 / 6, 107 / 6, -13, 61 / 12, -5 / 6])[::-1],
coefs)
offs = c["backward"]["offsets"]
np.testing.assert_array_almost_equal(
-np.array([0, 1, 2, 3, 4, 5])[::-1], offs)
def test_high_accuracy_results_in_type_error(self):
# in issue 25 the following line resulted in a TypeError
findiff.coefficients(deriv=1, acc=15)
def derkern(size = 5):
""" Difference kernel (derivative approximation )"""
if size == 0:
return [-1, 1]
size = size * 2
return findiff.coefficients(deriv = 1, acc = size)['center']['coefficients']
def test_invalid_deriv_raises_exception(self):
with self.assertRaises(ValueError):
coefficients(-1, 2)
with self.assertRaises(ValueError):
coefficients_non_uni(-1, 2, None, None)
def test_calc_accuracy_from_offsets_symbolic(self):
coefs = coefficients(1, offsets=[-4, -2, 0, 2, 4], symbolic=True)
self.assertEqual(4, coefs["accuracy"])
