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Simplified wafo.transform/models.py

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master
Per A Brodtkorb 8 years ago
parent 344e6cd97c
commit b01d58e987
3 changed files with 162 additions and 121 deletions
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11
wafo/bitwise.py
Unescape Escape View File

@ -77,21 +77,14 @@ def setbits(bitlist):
>>> setbits([1,0])
1
"""
# return bitlist[7]<<7 | bitlist[6]<<6 | bitlist[5]<<5 | bitlist[4]<<4 | \
# bitlist[3]<<3 | bitlist[2]<<2 | bitlist[1]<<1 | bitlist[0]
val = 0
for i, j in enumerate(bitlist):
val |= j << i
return val
def test_docstrings():
import doctest
print('Testing docstrings in %s' % __file__)
doctest.testmod(optionflags=doctest.NORMALIZE_WHITESPACE)
if __name__ == '__main__':
test_docstrings()
from wafo.testing import test_docstrings
test_docstrings(__file__)
# t = set(np.arange(8),1,1)
# t=get(0x84,np.arange(0,8))

271
wafo/transform/models.py
Unescape Escape View File

@ -15,6 +15,8 @@ import warnings
from .core import TrCommon, TrData
__all__ = ['TrHermite', 'TrLinear', 'TrOchi']
_EPS = np.finfo(float).eps
_example = '''
>>> import numpy as np
>>> import wafo.spectrum.models as sm
@ -34,6 +36,16 @@ _example = '''
'''
def _assert(cond, msg):
if not cond:
raise ValueError(msg)
def _assert_warn(cond, msg):
if not cond:
warnings.warn(msg)
class TrCommon2(TrCommon):
__doc__ = TrCommon.__doc__ # @ReservedAssignment
@ -132,91 +144,119 @@ class TrHermite(TrCommon2):
def __init__(self, *args, **kwds):
super(TrHermite, self).__init__(*args, **kwds)
self.pardef = kwds.get('pardef', 1)
self._c3 = None
self._c4 = None
self._forward = None
self._backward = None
self._x_limit = None
self.pardef = kwds.get('pardef', 1)
self.set_poly()
def _poly_par_from_stats(self):
skew = self.skew
ga2 = self.kurt - 3.0
if ga2 <= 0:
self._c4 = ga2 / 24.
self._c3 = skew / 6.
elif self.pardef == 2:
# Winterstein 1988 parametrization
if skew ** 2 > 8 * (ga2 + 3.) / 9.:
warnings.warn('Kurtosis too low compared to the skewness')
self._c4 = (sqrt(1. + 1.5 * ga2) - 1.) / 18.
self._c3 = skew / (6. * (1 + 6. * self._c4))
@property
def pardef(self):
return self._pardef
@pardef.setter
def pardef(self, pardef):
self._pardef = pardef
if pardef == 2:
self._softening_parameters = self._winterstein1988
else:
# Winterstein et. al. 1994 parametrization intended to
# apply for the range: 0 <= ga2 < 12 and 0<= skew^2 < 2*ga2/3
if skew ** 2 > 2 * (ga2) / 3:
warnings.warn('Kurtosis too low compared to the skewness')
if (ga2 < 0) or (12 < ga2):
warnings.warn('Kurtosis must be between 0 and 12')
self._c3 = skew / 6 * \
(1 - 0.015 * abs(skew) + 0.3 * skew ** 2) / (1 + 0.2 * ga2)
if ga2 == 0.:
self._c4 = 0.0
else:
expon = 1. - 0.1 * (ga2 + 3.) ** 0.8
c41 = (1. - 1.43 * skew ** 2. / ga2) ** (expon)
self._c4 = 0.1 * ((1. + 1.25 * ga2) ** (1. / 3.) - 1.) * c41
self._softening_parameters = self._winterstein1994
if not np.isfinite(self._c3) or not np.isfinite(self._c4):
raise ValueError('Unable to calculate the polynomial')
def _check_c3_c4(self, c3, c4):
_assert(np.isfinite(c3) and np.isfinite(c4),
'Unable to calculate the polynomial')
if abs(c4) < sqrt(_EPS):
c4 = 0.0
return c4
def set_poly(self):
'''
Set poly function from stats (i.e., mean, sigma, skew and kurt)
'''
def _winterstein1988(self, skew, excess_kurtosis):
"""Winterstein 1988 parametrization"""
if self._c3 is None:
self._poly_par_from_stats()
eps = np.finfo(float).eps
c3 = self._c3
c4 = self._c4
ma = self.mean
sa = self.sigma
if abs(c4) < sqrt(eps):
c4 = 0.0
_assert_warn(skew ** 2 <= 8 * (excess_kurtosis + 3.) / 9,
'Kurtosis too low compared to the skewness')
c4 = (sqrt(1. + 1.5 * excess_kurtosis) - 1.) / 18.
c3 = skew / (6. * (1 + 6. * c4))
c4 = self._check_c3_c4(c3, c4)
return c3, c4
def _winterstein1994(self, skew, excess_kurtosis):
"""Winterstein et. al. 1994 parametrization
# gdef = self.kurt-3.0
if self.kurt < 3.0:
p = np.poly1d([-c4, -c3, 1. + 3. * c4, c3]) # forward, g
self._forward = p
self._backward = None
intended to apply for the range:
0 <= excess_kurtosis < 12 and 0<= skew^2 < 2*excess_kurtosis/3
"""
_assert_warn(skew ** 2 <= 2 * (excess_kurtosis) / 3,
'Kurtosis too low compared to the skewness')
_assert_warn(0 <= excess_kurtosis < 12,
'Kurtosis must be between 0 and 12')
c3 = (skew / 6 * (1 - 0.015 * abs(skew) + 0.3 * skew ** 2) /
(1 + 0.2 * excess_kurtosis))
if excess_kurtosis == 0.:
c4 = 0.0
else:
Km1 = np.sqrt(1. + 2. * c3 ** 2 + 6 * c4 ** 2)
# backward G
p = np.poly1d(np.r_[c4, c3, 1. - 3. * c4, -c3] / Km1)
self._forward = None
self._backward = p
expon = 1. - 0.1 * (excess_kurtosis + 3.) ** 0.8
c41 = (1. - 1.43 * skew ** 2. / excess_kurtosis) ** (expon)
c4 = 0.1 * ((1. + 1.25 * excess_kurtosis) ** (1. / 3.) - 1.) * c41
c4 = self._check_c3_c4(c3, c4)
return c3, c4
def _hardening_parameters(self, skew, excess_kurtosis):
c4 = excess_kurtosis / 24.
c3 = skew / 6.
c4 = self._check_c3_c4(c3, c4)
return c3, c4
def _set_x_limit(self, root, polynom):
"""Compute where it is possible to invert the polynomial"""
if self.kurt <= 3.:
self._x_limit = root
else:
self._x_limit = self.sigma * polynom(root) + self.mean
txt1 = '''
The polynomial is not a strictly increasing function.
The derivative of g(x) is infinite at x = %g''' % self._x_limit
warnings.warn(txt1)
def _check_monotonicity(self, p):
dp = p.deriv(m=1) # derivative
roots = dp.r # roots of the derivative
roots = roots[where(abs(imag(roots)) < _EPS)] # Keep only real roots
if roots.size > 0:
self._set_x_limit(roots, p)
def _set_hardening_model(self):
skew, excess_kurtosis = self.skew, self.kurt - 3.0
c3, c4 = self._hardening_parameters(skew, excess_kurtosis)
p = np.poly1d([-c4, -c3, 1. + 3. * c4, c3])
self._forward = p
self._backward = lambda yn: self._poly_inv(self._forward, yn)
# Check if it is a strictly increasing function.
self._check_monotonicity(p)
def _set_softening_model(self):
skew, excess_kurtosis = self.skew, self.kurt - 3.0
c3, c4 = self._softening_parameters(skew, excess_kurtosis)
Km1 = np.sqrt(1. + 2. * c3 ** 2 + 6 * c4 ** 2)
# backward G
p = np.poly1d(np.r_[c4, c3, 1. - 3. * c4, -c3] / Km1)
self._backward = p
self._forward = lambda yn: self._poly_inv(self._backward, yn)
# Check if it is a strictly increasing function.
dp = p.deriv(m=1) # % Derivative
r = dp.r # % Find roots of the derivative
r = r[where(abs(imag(r)) < eps)] # Keep only real roots
if r.size > 0:
# Compute where it is possible to invert the polynomial
if self.kurt < 3.:
self._x_limit = r
else:
self._x_limit = sa * p(r) + ma
txt1 = '''
The polynomial is not a strictly increasing function.
The derivative of g(x) is infinite at x = %g''' % self._x_limit
warnings.warn(txt1)
return
self._check_monotonicity(p)
def set_poly(self):
'''
Set poly function from stats (i.e., mean, sigma, skew and kurt)
'''
if self.kurt <= 3.0:
self._set_hardening_model()
else:
self._set_softening_model()
def check_forward(self, x):
if self._x_limit is not None:
@ -262,6 +302,18 @@ class TrHermite(TrCommon2):
xn = self._backward(yn)
return self.sigma * xn + self.mean
def _solve_quadratic(self, p, xn):
# Quadratic: Solve a*u**2+b*u+c = xn
coefs = p.coeffs
a = coefs[0]
b = coefs[1]
c = coefs[2] - xn
t = 0.5 * (b + sign(b) * sqrt(b ** 2 - 4 * a * c))
# so1 = t/a # largest solution
so2 = -c / t # smallest solution
return so2
def _poly_inv(self, p, xn):
'''
Invert polynomial
@ -269,32 +321,27 @@ class TrHermite(TrCommon2):
if p.order < 2:
return xn
elif p.order == 2:
# Quadratic: Solve a*u**2+b*u+c = xn
coefs = p.coeffs
a = coefs[0]
b = coefs[1]
c = coefs[2] - xn
t = 0.5 * (b + sign(b) * sqrt(b ** 2 - 4 * a * c))
# so1 = t/a # largest solution
so2 = -c / t # smallest solution
return so2
return self._solve_quadratic(p, xn)
elif p.order == 3:
# Solve
# K*(c4*u^3+c3*u^2+(1-3*c4)*u-c3) = xn = (x-ma)/sa
# -c4*xn^3-c3*xn^2+(1+3*c4)*xn+c3 = u
coefs = p.coeffs[1::] / p.coeffs[0]
a = coefs[0]
b = coefs[1]
c = coefs[2] - xn / p.coeffs[0]
x0 = a / 3.
# substitue xn = z-x0 and divide by c4 => z^3 + 3*p1*z+2*q0 = 0
p1 = b / 3 - x0 ** 2
# p1 = (b-a**2/3)/3
# q0 = (c + x0*(2.*x0/3.-b))/2.
# q0 = x0**3 -a*b/6 +c/2
q0 = x0 * (x0 ** 2 - b / 2) + c / 2
return self._solve_third_order(p, xn)
def _solve_third_order(self, p, xn):
# Solve
# K*(c4*u^3+c3*u^2+(1-3*c4)*u-c3) = xn = (x-ma)/sa
# -c4*xn^3-c3*xn^2+(1+3*c4)*xn+c3 = u
coefs = p.coeffs[1::] / p.coeffs[0]
a = coefs[0]
b = coefs[1]
c = coefs[2] - xn / p.coeffs[0]
x0 = a / 3.
# substitue xn = z-x0 and divide by c4 => z^3 + 3*p1*z+2*q0 = 0
p1 = b / 3 - x0 ** 2
# p1 = (b-a**2/3)/3
# q0 = (c + x0*(2.*x0/3.-b))/2.
# q0 = x0**3 -a*b/6 +c/2
q0 = x0 * (x0 ** 2 - b / 2) + c / 2
# z^3+3*p1*z+2*q0=0
# c3 = self._c3
@ -305,23 +352,23 @@ class TrHermite(TrCommon2):
# p1 = b1-1.-x0**2.
# Km1 = np.sqrt(1.+2.*c3**2+6*c4**2)
# q0 = x0**3-1.5*b1*(x0+xn*Km1)
# q0 = x0**3-1.5*b1*(x0+xn)
if self._x_limit is not None: # % Three real roots
d = sqrt(-p1)
theta1 = arccos(-q0 / d ** 3) / 3
th2 = np.r_[0, -2 * pi / 3, 2 * pi / 3]
x1 = abs(2 * d * cos(theta1[ceil(len(xn) / 2)] + th2) - x0)
ix = x1.argmin() # % choose the smallest solution
return 2. * d * cos(theta1 + th2[ix]) - x0
else: # %Only one real root exist
q1 = sqrt((q0) ** 2 + p1 ** 3)
# Find the real root of the monic polynomial
A0 = (q1 - q0) ** (1. / 3.)
B0 = -(q1 + q0) ** (1. / 3.)
return A0 + B0 - x0 # % real root
# The other complex roots are given by
# x= -(A0+B0)/2+(A0-B0)*sqrt(3)/2-x0
# x=-(A0+B0)/2+(A0-B0)*sqrt(-3)/2-x0
# q0 = x0**3-1.5*b1*(x0+xn)
if self._x_limit is not None: # % Three real roots
d = sqrt(-p1)
theta1 = arccos(-q0 / d ** 3) / 3
th2 = np.r_[0, -2 * pi / 3, 2 * pi / 3]
x1 = abs(2 * d * cos(theta1[ceil(len(xn) / 2)] + th2) - x0)
ix = x1.argmin() # choose the smallest solution
return 2. * d * cos(theta1 + th2[ix]) - x0
else: # Only one real root exist
q1 = sqrt((q0) ** 2 + p1 ** 3)
# Find the real root of the monic polynomial
A0 = (q1 - q0) ** (1. / 3.)
B0 = -(q1 + q0) ** (1. / 3.)
return A0 + B0 - x0 # real root
# The other complex roots are given by
# x= -(A0+B0)/2+(A0-B0)*sqrt(3)/2-x0
# x=-(A0+B0)/2+(A0-B0)*sqrt(-3)/2-x0
class TrLinear(TrCommon2):

1
wafo/transform/tests/test_models.py
Unescape Escape View File

@ -2,6 +2,7 @@ from wafo.transform.models import TrHermite, TrOchi, TrLinear
import numpy as np
from numpy.testing import assert_array_almost_equal
def test_trhermite():
std = 7. / 4

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