diff options
Diffstat (limited to 'numpy/polynomial/laguerre.py')
| -rw-r--r-- | numpy/polynomial/laguerre.py | 119 |
1 files changed, 59 insertions, 60 deletions
diff --git a/numpy/polynomial/laguerre.py b/numpy/polynomial/laguerre.py index 9d88162ce..8d2705d5d 100644 --- a/numpy/polynomial/laguerre.py +++ b/numpy/polynomial/laguerre.py @@ -66,17 +66,18 @@ import numpy.linalg as la from . import polyutils as pu from ._polybase import ABCPolyBase -__all__ = ['lagzero', 'lagone', 'lagx', 'lagdomain', 'lagline', - 'lagadd', 'lagsub', 'lagmulx', 'lagmul', 'lagdiv', 'lagpow', - 'lagval', 'lagder', 'lagint', 'lag2poly', 'poly2lag', 'lagfromroots', - 'lagvander', 'lagfit', 'lagtrim', 'lagroots', 'Laguerre', 'lagval2d', - 'lagval3d', 'laggrid2d', 'laggrid3d', 'lagvander2d', 'lagvander3d', - 'lagcompanion', 'laggauss', 'lagweight'] +__all__ = [ + 'lagzero', 'lagone', 'lagx', 'lagdomain', 'lagline', 'lagadd', + 'lagsub', 'lagmulx', 'lagmul', 'lagdiv', 'lagpow', 'lagval', 'lagder', + 'lagint', 'lag2poly', 'poly2lag', 'lagfromroots', 'lagvander', + 'lagfit', 'lagtrim', 'lagroots', 'Laguerre', 'lagval2d', 'lagval3d', + 'laggrid2d', 'laggrid3d', 'lagvander2d', 'lagvander3d', 'lagcompanion', + 'laggauss', 'lagweight'] lagtrim = pu.trimcoef -def poly2lag(pol) : +def poly2lag(pol): """ poly2lag(pol) @@ -117,12 +118,12 @@ def poly2lag(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 = lagadd(lagmulx(res), pol[i]) return res -def lag2poly(c) : +def lag2poly(c): """ Convert a Laguerre series to a polynomial. @@ -194,7 +195,7 @@ lagone = np.array([1]) lagx = np.array([1, -1]) -def lagline(off, scl) : +def lagline(off, scl): """ Laguerre series whose graph is a straight line. @@ -224,13 +225,13 @@ def lagline(off, scl) : 5.0 """ - if scl != 0 : + if scl != 0: return np.array([off + scl, -scl]) - else : + else: return np.array([off]) -def lagfromroots(roots) : +def lagfromroots(roots): """ Generate a Laguerre series with given roots. @@ -280,9 +281,9 @@ def lagfromroots(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 = [lagline(-r, 1) for r in roots] @@ -337,10 +338,10 @@ def lagadd(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) @@ -385,10 +386,10 @@ def lagsub(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 @@ -499,13 +500,13 @@ def lagmul(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 = lagsub(c[-i]*xs, (c1*(nd - 1))/nd) c1 = lagadd(tmp, lagsub((2*nd - 1)*c1, lagmulx(c1))/nd) return lagadd(c0, lagsub(c1, lagmulx(c1))) @@ -556,16 +557,16 @@ def lagdiv(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): @@ -576,7 +577,7 @@ def lagdiv(c1, c2): return quo, pu.trimseq(rem) -def lagpow(c, pow, maxpower=16) : +def lagpow(c, pow, maxpower=16): """Raise a Laguerre series to a power. Returns the Laguerre series `c` raised to the power `pow`. The @@ -613,24 +614,24 @@ def lagpow(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 = lagmul(prd, c) return prd -def lagder(c, m=1, scl=1, axis=0) : +def lagder(c, m=1, scl=1, axis=0): """ Differentiate a Laguerre series. @@ -708,7 +709,7 @@ def lagder(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 @@ -815,9 +816,9 @@ def lagint(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") @@ -831,7 +832,7 @@ def lagint(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 +925,21 @@ def lagval(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) - - 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*(nd - 1))/nd c1 = tmp + (c1*((2*nd - 1) - x))/nd return c0 + c1*(1 - x) @@ -1174,7 +1174,7 @@ def laggrid3d(x, y, z, c): return c -def lagvander(x, deg) : +def lagvander(x, deg): """Pseudo-Vandermonde matrix of given degree. Returns the pseudo-Vandermonde matrix of degree `deg` and sample points @@ -1229,14 +1229,14 @@ def lagvander(x, deg) : dtyp = x.dtype v = np.empty(dims, dtype=dtyp) v[0] = x*0 + 1 - if ideg > 0 : + if ideg > 0: v[1] = 1 - x - for i in range(2, ideg + 1) : + for i in range(2, ideg + 1): v[i] = (v[i-1]*(2*i - 1 - x) - v[i-2]*(i - 1))/i return np.rollaxis(v, 0, v.ndim) -def lagvander2d(x, y, deg) : +def lagvander2d(x, y, deg): """Pseudo-Vandermonde matrix of given degrees. Returns the pseudo-Vandermonde matrix of degrees `deg` and sample @@ -1299,7 +1299,7 @@ def lagvander2d(x, y, deg) : return v.reshape(v.shape[:-2] + (-1,)) -def lagvander3d(x, y, z, deg) : +def lagvander3d(x, y, z, deg): """Pseudo-Vandermonde matrix of given degrees. Returns the pseudo-Vandermonde matrix of degrees `deg` and sample @@ -1490,13 +1490,13 @@ def lagfit(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") @@ -1516,7 +1516,7 @@ def lagfit(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. @@ -1535,9 +1535,9 @@ def lagfit(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 @@ -1566,7 +1566,6 @@ def lagcompanion(c): .. versionadded::1.7.0 """ - accprod = np.multiply.accumulate # c is a trimmed copy [c] = pu.as_series([c]) if len(c) < 2: @@ -1634,9 +1633,9 @@ def lagroots(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([1 + c[0]/c[1]]) m = lagcompanion(c) @@ -1651,8 +1650,8 @@ def laggauss(deg): Computes the sample points and weights for Gauss-Laguerre quadrature. These sample points and weights will correctly integrate polynomials of - degree :math:`2*deg - 1` or less over the interval :math:`[0, \inf]` with the - weight function :math:`f(x) = \exp(-x)`. + degree :math:`2*deg - 1` or less over the interval :math:`[0, \inf]` + with the weight function :math:`f(x) = \exp(-x)`. Parameters ---------- |