diff options
Diffstat (limited to 'numpy/polynomial/hermite.py')
| -rw-r--r-- | numpy/polynomial/hermite.py | 117 |
1 files changed, 58 insertions, 59 deletions
diff --git a/numpy/polynomial/hermite.py b/numpy/polynomial/hermite.py index 43ede58ac..1fd49d774 100644 --- a/numpy/polynomial/hermite.py +++ b/numpy/polynomial/hermite.py @@ -66,18 +66,18 @@ import numpy.linalg as la from . import polyutils as pu from ._polybase import ABCPolyBase -__all__ = ['hermzero', 'hermone', 'hermx', 'hermdomain', 'hermline', - 'hermadd', 'hermsub', 'hermmulx', 'hermmul', 'hermdiv', 'hermpow', - 'hermval', 'hermder', 'hermint', 'herm2poly', 'poly2herm', - 'hermfromroots', 'hermvander', 'hermfit', 'hermtrim', 'hermroots', - 'Hermite', 'hermval2d', 'hermval3d', 'hermgrid2d', 'hermgrid3d', - 'hermvander2d', 'hermvander3d', 'hermcompanion', 'hermgauss', - 'hermweight'] +__all__ = [ + 'hermzero', 'hermone', 'hermx', 'hermdomain', 'hermline', 'hermadd', + 'hermsub', 'hermmulx', 'hermmul', 'hermdiv', 'hermpow', 'hermval', + 'hermder', 'hermint', 'herm2poly', 'poly2herm', 'hermfromroots', + 'hermvander', 'hermfit', 'hermtrim', 'hermroots', 'Hermite', + 'hermval2d', 'hermval3d', 'hermgrid2d', 'hermgrid3d', 'hermvander2d', + 'hermvander3d', 'hermcompanion', 'hermgauss', 'hermweight'] hermtrim = pu.trimcoef -def poly2herm(pol) : +def poly2herm(pol): """ poly2herm(pol) @@ -118,12 +118,12 @@ def poly2herm(pol) : [pol] = pu.as_series([pol]) deg = len(pol) - 1 res = 0 - for i in range(deg, -1, -1) : + for i in range(deg, -1, -1): res = hermadd(hermmulx(res), pol[i]) return res -def herm2poly(c) : +def herm2poly(c): """ Convert a Hermite series to a polynomial. @@ -174,7 +174,7 @@ def herm2poly(c) : c0 = c[-2] c1 = c[-1] # i is the current degree of c1 - for i in range(n - 1, 1, -1) : + for i in range(n - 1, 1, -1): tmp = c0 c0 = polysub(c[i - 2], c1*(2*(i - 1))) c1 = polyadd(tmp, polymulx(c1)*2) @@ -198,7 +198,7 @@ hermone = np.array([1]) hermx = np.array([0, 1/2]) -def hermline(off, scl) : +def hermline(off, scl): """ Hermite series whose graph is a straight line. @@ -228,13 +228,13 @@ def hermline(off, scl) : 5.0 """ - if scl != 0 : + if scl != 0: return np.array([off, scl/2]) - else : + else: return np.array([off]) -def hermfromroots(roots) : +def hermfromroots(roots): """ Generate a Hermite series with given roots. @@ -284,9 +284,9 @@ def hermfromroots(roots) : array([ 0.+0.j, 0.+0.j]) """ - if len(roots) == 0 : + if len(roots) == 0: return np.ones(1) - else : + else: [roots] = pu.as_series([roots], trim=False) roots.sort() p = [hermline(-r, 1) for r in roots] @@ -340,10 +340,10 @@ def hermadd(c1, c2): """ # c1, c2 are trimmed copies [c1, c2] = pu.as_series([c1, c2]) - if len(c1) > len(c2) : + if len(c1) > len(c2): c1[:c2.size] += c2 ret = c1 - else : + else: c2[:c1.size] += c1 ret = c2 return pu.trimseq(ret) @@ -388,10 +388,10 @@ def hermsub(c1, c2): """ # c1, c2 are trimmed copies [c1, c2] = pu.as_series([c1, c2]) - if len(c1) > len(c2) : + if len(c1) > len(c2): c1[:c2.size] -= c2 ret = c1 - else : + else: c2 = -c2 c2[:c1.size] += c1 ret = c2 @@ -501,13 +501,13 @@ def hermmul(c1, c2): elif len(c) == 2: c0 = c[0]*xs c1 = c[1]*xs - else : + else: nd = len(c) c0 = c[-2]*xs c1 = c[-1]*xs - for i in range(3, len(c) + 1) : + for i in range(3, len(c) + 1): tmp = c0 - nd = nd - 1 + nd = nd - 1 c0 = hermsub(c[-i]*xs, c1*(2*(nd - 1))) c1 = hermadd(tmp, hermmulx(c1)*2) return hermadd(c0, hermmulx(c1)*2) @@ -560,16 +560,16 @@ def hermdiv(c1, c2): """ # c1, c2 are trimmed copies [c1, c2] = pu.as_series([c1, c2]) - if c2[-1] == 0 : + if c2[-1] == 0: raise ZeroDivisionError() lc1 = len(c1) lc2 = len(c2) - if lc1 < lc2 : + if lc1 < lc2: return c1[:1]*0, c1 - elif lc2 == 1 : + elif lc2 == 1: return c1/c2[-1], c1[:1]*0 - else : + else: quo = np.empty(lc1 - lc2 + 1, dtype=c1.dtype) rem = c1 for i in range(lc1 - lc2, - 1, -1): @@ -580,7 +580,7 @@ def hermdiv(c1, c2): return quo, pu.trimseq(rem) -def hermpow(c, pow, maxpower=16) : +def hermpow(c, pow, maxpower=16): """Raise a Hermite series to a power. Returns the Hermite series `c` raised to the power `pow`. The @@ -617,24 +617,24 @@ def hermpow(c, pow, maxpower=16) : # c is a trimmed copy [c] = pu.as_series([c]) power = int(pow) - if power != pow or power < 0 : + if power != pow or power < 0: raise ValueError("Power must be a non-negative integer.") - elif maxpower is not None and power > maxpower : + elif maxpower is not None and power > maxpower: raise ValueError("Power is too large") - elif power == 0 : + elif power == 0: return np.array([1], dtype=c.dtype) - elif power == 1 : + elif power == 1: return c - else : + else: # This can be made more efficient by using powers of two # in the usual way. prd = c - for i in range(2, power + 1) : + for i in range(2, power + 1): prd = hermmul(prd, c) return prd -def hermder(c, m=1, scl=1, axis=0) : +def hermder(c, m=1, scl=1, axis=0): """ Differentiate a Hermite series. @@ -712,7 +712,7 @@ def hermder(c, m=1, scl=1, axis=0) : n = len(c) if cnt >= n: c = c[:1]*0 - else : + else: for i in range(cnt): n = n - 1 c *= scl @@ -816,9 +816,9 @@ def hermint(c, m=1, k=[], lbnd=0, scl=1, axis=0): if cnt != m: raise ValueError("The order of integration must be integer") - if cnt < 0 : + if cnt < 0: raise ValueError("The order of integration must be non-negative") - if len(k) > cnt : + if len(k) > cnt: raise ValueError("Too many integration constants") if iaxis != axis: raise ValueError("The axis must be integer") @@ -832,7 +832,7 @@ def hermint(c, m=1, k=[], lbnd=0, scl=1, axis=0): c = np.rollaxis(c, iaxis) k = list(k) + [0]*(cnt - len(k)) - for i in range(cnt) : + for i in range(cnt): n = len(c) c *= scl if n == 1 and np.all(c[0] == 0): @@ -924,22 +924,22 @@ def hermval(x, c, tensor=True): if isinstance(x, (tuple, list)): x = np.asarray(x) if isinstance(x, np.ndarray) and tensor: - c = c.reshape(c.shape + (1,)*x.ndim) + c = c.reshape(c.shape + (1,)*x.ndim) x2 = x*2 - if len(c) == 1 : + if len(c) == 1: c0 = c[0] c1 = 0 - elif len(c) == 2 : + elif len(c) == 2: c0 = c[0] c1 = c[1] - else : + else: nd = len(c) c0 = c[-2] c1 = c[-1] - for i in range(3, len(c) + 1) : + for i in range(3, len(c) + 1): tmp = c0 - nd = nd - 1 + nd = nd - 1 c0 = c[-i] - c1*(2*(nd - 1)) c1 = tmp + c1*x2 return c0 + c1*x2 @@ -1174,7 +1174,7 @@ def hermgrid3d(x, y, z, c): return c -def hermvander(x, deg) : +def hermvander(x, deg): """Pseudo-Vandermonde matrix of given degree. Returns the pseudo-Vandermonde matrix of degree `deg` and sample points @@ -1229,15 +1229,15 @@ def hermvander(x, deg) : dtyp = x.dtype v = np.empty(dims, dtype=dtyp) v[0] = x*0 + 1 - if ideg > 0 : + if ideg > 0: x2 = x*2 v[1] = x2 - for i in range(2, ideg + 1) : + for i in range(2, ideg + 1): v[i] = (v[i-1]*x2 - v[i-2]*(2*(i - 1))) return np.rollaxis(v, 0, v.ndim) -def hermvander2d(x, y, deg) : +def hermvander2d(x, y, deg): """Pseudo-Vandermonde matrix of given degrees. Returns the pseudo-Vandermonde matrix of degrees `deg` and sample @@ -1300,7 +1300,7 @@ def hermvander2d(x, y, deg) : return v.reshape(v.shape[:-2] + (-1,)) -def hermvander3d(x, y, z, deg) : +def hermvander3d(x, y, z, deg): """Pseudo-Vandermonde matrix of given degrees. Returns the pseudo-Vandermonde matrix of degrees `deg` and sample @@ -1491,13 +1491,13 @@ def hermfit(x, y, deg, rcond=None, full=False, w=None): y = np.asarray(y) + 0.0 # check arguments. - if deg < 0 : + if deg < 0: raise ValueError("expected deg >= 0") if x.ndim != 1: raise TypeError("expected 1D vector for x") if x.size == 0: raise TypeError("expected non-empty vector for x") - if y.ndim < 1 or y.ndim > 2 : + if y.ndim < 1 or y.ndim > 2: raise TypeError("expected 1D or 2D array for y") if len(x) != len(y): raise TypeError("expected x and y to have same length") @@ -1517,7 +1517,7 @@ def hermfit(x, y, deg, rcond=None, full=False, w=None): rhs = rhs * w # set rcond - if rcond is None : + if rcond is None: rcond = len(x)*np.finfo(x.dtype).eps # Determine the norms of the design matrix columns. @@ -1536,9 +1536,9 @@ def hermfit(x, y, deg, rcond=None, full=False, w=None): msg = "The fit may be poorly conditioned" warnings.warn(msg, pu.RankWarning) - if full : + if full: return c, [resids, rank, s, rcond] - else : + else: return c @@ -1568,7 +1568,6 @@ def hermcompanion(c): .. versionadded::1.7.0 """ - accprod = np.multiply.accumulate # c is a trimmed copy [c] = pu.as_series([c]) if len(c) < 2: @@ -1636,9 +1635,9 @@ def hermroots(c): """ # c is a trimmed copy [c] = pu.as_series([c]) - if len(c) <= 1 : + if len(c) <= 1: return np.array([], dtype=c.dtype) - if len(c) == 2 : + if len(c) == 2: return np.array([-.5*c[0]/c[1]]) m = hermcompanion(c) |