Removed duplicated dea3 from integrate and misc.py import from numdifftools.extrapolate.dea3 instead

pepified

wafo/integrate.py

@@ -8,6 +8,8 @@ from scipy import special as sp
 from .plotbackend import plotbackend as plt
 from scipy.integrate import simps, trapz
 from .demos import humps
+from .misc import dea3
+from .dctpack import dct
 # from pychebfun import Chebfun
 
 _EPS = np.finfo(float).eps
@@ -18,79 +20,6 @@ __all__ = ['dea3', 'clencurt', 'romberg',
            'gaussq', 'richardson', 'quadgr', 'qdemo']
 
 
-def dea3(v0, v1, v2):
-    '''
-    Extrapolate a slowly convergent sequence
-
-    Parameters
-    ----------
-    v0,v1,v2 : array-like
-        3 values of a convergent sequence to extrapolate
-
-    Returns
-    -------
-    result : array-like
-        extrapolated value
-    abserr : array-like
-        absolute error estimate
-
-    Description
-    -----------
-    DEA3 attempts to extrapolate nonlinearly to a better estimate
-    of the sequence's limiting value, thus improving the rate of
-    convergence. The routine is based on the epsilon algorithm of
-    P. Wynn, see [1]_.
-
-     Example
-     -------
-     # integrate sin(x) from 0 to pi/2
-
-     >>> import numpy as np
-     >>> Ei= np.zeros(3)
-     >>> linfun = lambda k : np.linspace(0, np.pi/2., 2.**(k+5)+1)
-     >>> for k in np.arange(3):
-     ...     x = linfun(k)
-     ...     Ei[k] = np.trapz(np.sin(x),x)
-     >>> En, err = dea3(Ei[0],Ei[1],Ei[2])
-     >>> En, err
-     (array([ 1.]), array([ 0.0002008]))
-     >>> TrueErr = Ei-1.
-     >>> TrueErr
-     array([ -2.0080568e-04,  -5.0199908e-05,  -1.2549882e-05])
-
-     See also
-     --------
-     dea
-
-     Reference
-     ---------
-     .. [1] C. Brezinski (1977)
-            "Acceleration de la convergence en analyse numerique",
-            "Lecture Notes in Math.", vol. 584,
-            Springer-Verlag, New York, 1977.
-    '''
-    E0, E1, E2 = np.atleast_1d(v0, v1, v2)
-    abs = np.abs  # @ReservedAssignment
-    max = np.maximum  # @ReservedAssignment
-    delta2, delta1 = E2 - E1, E1 - E0
-    err2, err1 = abs(delta2), abs(delta1)
-    tol2, tol1 = max(abs(E2), abs(E1)) * _EPS, max(abs(E1), abs(E0)) * _EPS
-
-    with warnings.catch_warnings():
-        warnings.simplefilter("ignore")  # ignore division by zero and overflow
-        ss = 1.0 / delta2 - 1.0 / delta1
-        smalle2 = (abs(ss * E1) <= 1.0e-3).ravel()
-
-    result = 1.0 * E2
-    abserr = err1 + err2 + abs(E2) * _EPS * 10.0
-    converged = (err1 <= tol1) & (err2 <= tol2).ravel() | smalle2
-    k4, = (1 - converged).nonzero()
-    if k4.size > 0:
-        result[k4] = E1[k4] + 1.0 / ss[k4]
-        abserr[k4] = err1[k4] + err2[k4] + abs(result[k4] - E2[k4])
-    return result, abserr
-
-
 def clencurt(fun, a, b, n0=5, trace=False, args=()):
     '''
     Numerical evaluation of an integral, Clenshaw-Curtis method.
@@ -183,13 +112,11 @@ def clencurt(fun, a, b, n0=5, trace=False, args=()):
     fft = np.fft.fft
     tmp = np.real(fft(f[:n, :], axis=0))
     c = 2 / n * (tmp[0:n / 2 + 1, :] + np.cos(np.pi * s2) * f[n, :])
-# % old call
-# %  c = 2/n * cos(s2*s'*pi/n) * f
     c[0, :] = c[0, :] / 2
     c[n / 2, :] = c[n / 2, :] / 2
 
 # % alternative call
-# % c = dct(f)
+    # c2 = dct(f)
 
     c = c[0:n / 2 + 1, :] / ((s2 - 1) * (s2 + 1))
     Q = (af - bf) * np.sum(c, axis=0)

wafo/interpolate.py

@@ -1102,10 +1102,10 @@ def test_smoothing_spline():
     dy1 = pp1(x1)
     y01 = pp0(x1)
     # dy = y-y1
-    import matplotlib.pyplot as plb
+    import matplotlib.pyplot as plt
 
-    plb.plot(x, y, x1, y1, '.', x1, dy1, 'ro', x1, y01, 'r-')
+    plt.plot(x, y, x1, y1, '.', x1, dy1, 'ro', x1, y01, 'r-')
-    plb.show('hold')
+    plt.show('hold')
     pass
     # tck = interpolate.splrep(x, y, s=len(x))
 
@@ -1250,10 +1250,10 @@ def test_pp():
     pp(1)
     pp(1.5)
     dpp = pp.derivative()
-    import pylab as plb
+    import matplotlib.pyplot as plt
-    x = plb.linspace(-1, 3)
+    x = np.linspace(-1, 3)
-    plb.plot(x, pp(x), x, dpp(x), '.')
+    plt.plot(x, pp(x), x, dpp(x), '.')
-    plb.show()
+    plt.show()
 
 
 def test_docstrings():

wafo/misc.py

@@ -17,6 +17,7 @@ from scipy.special import gammaln
 from scipy.integrate import trapz, simps
 import warnings
 from time import strftime, gmtime
+from numdifftools.extrapolation import dea3
 from .plotbackend import plotbackend
 from collections import OrderedDict
 try:
@@ -33,7 +34,7 @@ __all__ = ['now', 'spaceline', 'narg_smallest', 'args_flat', 'is_numlike',
            'parse_kwargs', 'detrendma', 'ecross', 'findcross', 'findextrema',
            'findpeaks', 'findrfc', 'rfcfilter', 'findtp', 'findtc',
            'findoutliers', 'common_shape', 'argsreduce', 'stirlerr',
-           'getshipchar',
+           'getshipchar', 'dea3',
            'betaloge', 'gravity', 'nextpow2', 'discretize', 'polar2cart',
            'cart2polar', 'meshgrid', 'ndgrid', 'trangood', 'tranproc',
            'plot_histgrm', 'num2pistr', 'test_docstrings', 'lazywhere',
@@ -2107,79 +2108,6 @@ def gravity(phi=45):
                       0.0000059 * sin(2 * phir) ** 2.)
 
 
-def dea3(v0, v1, v2):
-    '''
-    Extrapolate a slowly convergent sequence
-
-    Parameters
-    ----------
-    v0, v1, v2 : array-like
-        3 values of a convergent sequence to extrapolate
-
-    Returns
-    -------
-    result : array-like
-        extrapolated value
-    abserr : array-like
-        absolute error estimate
-
-    Description
-    -----------
-    DEA3 attempts to extrapolate nonlinearly to a better estimate
-    of the sequence's limiting value, thus improving the rate of
-    convergence. The routine is based on the epsilon algorithm of
-    P. Wynn, see [1]_.
-
-     Example
-     -------
-     # integrate sin(x) from 0 to pi/2
-
-     >>> import numpy as np
-     >>> import numdifftools as nd
-     >>> Ei= np.zeros(3)
-     >>> linfun = lambda k : np.linspace(0,np.pi/2.,2.**(k+5)+1)
-     >>> for k in np.arange(3):
-     ...    x = linfun(k)
-     ...    Ei[k] = np.trapz(np.sin(x),x)
-     >>> [En, err] = nd.dea3(Ei[0], Ei[1], Ei[2])
-     >>> truErr = Ei-1.
-     >>> (truErr, err, En)
-     (array([ -2.00805680e-04,  -5.01999079e-05,  -1.25498825e-05]),
-     array([ 0.00020081]), array([ 1.]))
-
-     See also
-     --------
-     dea
-
-     Reference
-     ---------
-     .. [1] C. Brezinski (1977)
-            "Acceleration de la convergence en analyse numerique",
-            "Lecture Notes in Math.", vol. 584,
-            Springer-Verlag, New York, 1977.
-    '''
-    E0, E1, E2 = np.atleast_1d(v0, v1, v2)
-    abs = np.abs  # @ReservedAssignment
-    max = np.maximum  # @ReservedAssignment
-    delta2, delta1 = E2 - E1, E1 - E0
-    err2, err1 = abs(delta2), abs(delta1)
-    tol2, tol1 = max(abs(E2), abs(E1)) * _EPS, max(abs(E1), abs(E0)) * _EPS
-
-    with warnings.catch_warnings():
-        warnings.simplefilter("ignore")  # ignore division by zero and overflow
-        ss = 1.0 / delta2 - 1.0 / delta1
-        smallE2 = (abs(ss * E1) <= 1.0e-3).ravel()
-
-    result = 1.0 * E2
-    abserr = err1 + err2 + abs(E2) * _EPS * 10.0
-    converged = (err1 <= tol1) & (err2 <= tol2).ravel() | smallE2
-    k4, = (1 - converged).nonzero()
-    if k4.size > 0:
-        result[k4] = E1[k4] + 1.0 / ss[k4]
-        abserr[k4] = err1[k4] + err2[k4] + abs(result[k4] - E2[k4])
-    return result, abserr
-
-
 def nextpow2(x):
     '''
     Return next higher power of 2

wafo/polynomial.py

@@ -724,7 +724,7 @@ def poly2str(p, variable='x'):
 
     N = len(coeffs) - 1
 
-    for k in range(len(coeffs)):
+    for k in range(N+1):
         coefstr = '%.4g' % abs(coeffs[k])
         if coefstr[-4:] == '0000':
             coefstr = coefstr[:-5]
@@ -733,21 +733,18 @@ def poly2str(p, variable='x'):
             if coefstr != '0':
                 newstr = '%s' % (coefstr,)
             else:
-                if k == 0:
+                newstr = '0' if k == 0 else ''
-                    newstr = '0'
-                else:
-                    newstr = ''
         elif power == 1:
             if coefstr == '0':
                 newstr = ''
-            elif coefstr == 'b' or coefstr == '1':
+            elif coefstr in ['b', '1']:
                 newstr = var
             else:
                 newstr = '%s*%s' % (coefstr, var)
         else:
             if coefstr == '0':
                 newstr = ''
-            elif coefstr == 'b' or coefstr == '1':
+            elif coefstr in ['b', '1']:
                 newstr = '%s**%d' % (var, power,)
             else:
                 newstr = '%s*%s**%d' % (coefstr, var, power)

wafo/spectrum/core.py

@@ -1811,7 +1811,7 @@ class SpecData1D(PlotData):
         rind = Rind(**options)
         if (Nx > 1):
             # (M,m) or (M,m)v distribution wanted
-            if ((def_nr == 0 or def_nr == 2)):
+            if def_nr in [0, 2]:
                 asize = [Nx1, Nx1]
             else:
                 # (M,m,TMm), (M,m,TMm)v  (M,m,TMd)v or (M,M,Tdm)v