PyNeb  1.1.2
PyNeb Reference Manua
pyneb.utils.polyutils Namespace Reference


class  PolyBase
class  PolyDomainError
class  PolyError
class  RankWarning


def any (iterable)
def trimseq (seq)
def as_series
def trimcoef
def getdomain (x)
def mapparms (old, new)
def mapdomain (x, old, new)


list __all__

Detailed Description

Utililty objects for the polynomial modules.

This module provides: error and warning objects; a polynomial base class;
and some routines used in both the `polynomial` and `chebyshev` modules.

Error objects
- `PolyError` -- base class for this sub-package's errors.
- `PolyDomainError` -- raised when domains are "mismatched."

Warning objects
- `RankWarning` -- raised by a least-squares fit when a rank-deficient
  matrix is encountered.

Base class
- `PolyBase` -- The base class for the `Polynomial` and `Chebyshev`

- `as_series` -- turns a list of array_likes into 1-D arrays of common
- `trimseq` -- removes trailing zeros.
- `trimcoef` -- removes trailing coefficients that are less than a given
  magnitude (thereby removing the corresponding terms).
- `getdomain` -- returns a domain appropriate for a given set of abscissae.
- `mapdomain` -- maps points between domains.
- `mapparms` -- parameters of the linear map between domains.

Function Documentation

def pyneb.utils.polyutils.any (   iterable)
def pyneb.utils.polyutils.as_series (   alist,
  trim = True 
Return argument as a list of 1-d arrays.

The returned list contains array(s) of dtype double, complex double, or
object.  A 1-d argument of shape ``(N,)`` is parsed into ``N`` arrays of
size one; a 2-d argument of shape ``(M,N)`` is parsed into ``M`` arrays
of size ``N`` (i.e., is "parsed by row"); and a higher dimensional array
raises a Value Error if it is not first reshaped into either a 1-d or 2-d

a : array_like
    A 1- or 2-d array_like
trim : boolean, optional
    When True, trailing zeros are removed from the inputs.
    When False, the inputs are passed through intact.

[a1, a2,...] : list of 1d-arrays
    A copy of the input data as a list of 1-d arrays.

ValueError :
    Raised when `as_series` cannot convert its input to 1-d arrays, or at
    least one of the resulting arrays is empty.

>>> from numpy import polynomial as P
>>> a = np.arange(4)
>>> P.as_series(a)
[array([ 0.]), array([ 1.]), array([ 2.]), array([ 3.])]
>>> b = np.arange(6).reshape((2,3))
>>> P.as_series(b)
[array([ 0.,  1.,  2.]), array([ 3.,  4.,  5.])]
def pyneb.utils.polyutils.getdomain (   x)
Return a domain suitable for given abscissae.

Find a domain suitable for a polynomial or Chebyshev series
defined at the values supplied.

x : array_like
    1-d array of abscissae whose domain will be determined.

domain : ndarray
    1-d array containing two values.  If the inputs are complex, then
    the two returned points are the lower left and upper right corners
    of the smallest rectangle (aligned with the axes) in the complex
    plane containing the points `x`. If the inputs are real, then the
    two points are the ends of the smallest interval containing the
    points `x`.

See Also
mapparms, mapdomain

>>> from numpy.polynomial import polyutils as pu
>>> points = np.arange(4)**2 - 5; points
array([-5, -4, -1,  4])
>>> pu.getdomain(points)
array([-5.,  4.])
>>> c = np.exp(complex(0,1)*np.pi*np.arange(12)/6) # unit circle
>>> pu.getdomain(c)
array([-1.-1.j,  1.+1.j])
def pyneb.utils.polyutils.mapdomain (   x,
Apply linear map to input points.

The linear map ``offset + scale*x`` that maps the domain `old` to
the domain `new` is applied to the points `x`.

x : array_like
    Points to be mapped. If `x` is a subtype of ndarray the subtype
    will be preserved.
old, new : array_like
    The two domains that determine the map.  Each must (successfully)
    convert to 1-d arrays containing precisely two values.

x_out : ndarray
    Array of points of the same shape as `x`, after application of the
    linear map between the two domains.

See Also
getdomain, mapparms

Effectively, this implements:

.. math ::
    x\\_out = new[0] + m(x - old[0])


.. math ::
    m = \\frac{new[1]-new[0]}{old[1]-old[0]}

>>> from numpy import polynomial as P
>>> old_domain = (-1,1)
>>> new_domain = (0,2*np.pi)
>>> x = np.linspace(-1,1,6); x
array([-1. , -0.6, -0.2,  0.2,  0.6,  1. ])
>>> x_out = P.mapdomain(x, old_domain, new_domain); x_out
array([ 0.        ,  1.25663706,  2.51327412,  3.76991118,  5.02654825,
>>> x - P.mapdomain(x_out, new_domain, old_domain)
array([ 0.,  0.,  0.,  0.,  0.,  0.])

Also works for complex numbers (and thus can be used to map any line in
the complex plane to any other line therein).

>>> i = complex(0,1)
>>> old = (-1 - i, 1 + i)
>>> new = (-1 + i, 1 - i)
>>> z = np.linspace(old[0], old[1], 6); z
array([-1.0-1.j , -0.6-0.6j, -0.2-0.2j,  0.2+0.2j,  0.6+0.6j,  1.0+1.j ])
>>> new_z = P.mapdomain(z, old, new); new_z
array([-1.0+1.j , -0.6+0.6j, -0.2+0.2j,  0.2-0.2j,  0.6-0.6j,  1.0-1.j ])
def pyneb.utils.polyutils.mapparms (   old,
Linear map parameters between domains.

Return the parameters of the linear map ``offset + scale*x`` that maps
`old` to `new` such that ``old[i] -> new[i]``, ``i = 0, 1``.

old, new : array_like
    Domains. Each domain must (successfully) convert to a 1-d array
    containing precisely two values.

offset, scale : scalars
    The map ``L(x) = offset + scale*x`` maps the first domain to the

See Also
getdomain, mapdomain

Also works for complex numbers, and thus can be used to calculate the
parameters required to map any line in the complex plane to any other
line therein.

>>> from numpy import polynomial as P
>>> P.mapparms((-1,1),(-1,1))
(0.0, 1.0)
>>> P.mapparms((1,-1),(-1,1))
(0.0, -1.0)
>>> i = complex(0,1)
>>> P.mapparms((-i,-1),(1,i))
((1+1j), (1+0j))
def pyneb.utils.polyutils.trimcoef (   c,
  tol = 0 
Remove "small" "trailing" coefficients from a polynomial.

"Small" means "small in absolute value" and is controlled by the
parameter `tol`; "trailing" means highest order coefficient(s), e.g., in
``[0, 1, 1, 0, 0]`` (which represents ``0 + x + x**2 + 0*x**3 + 0*x**4``)
both the 3-rd and 4-th order coefficients would be "trimmed."

c : array_like
    1-d array of coefficients, ordered from lowest order to highest.
tol : number, optional
    Trailing (i.e., highest order) elements with absolute value less
    than or equal to `tol` (default value is zero) are removed.

trimmed : ndarray
    1-d array with trailing zeros removed.  If the resulting series
    would be empty, a series containing a single zero is returned.

    If `tol` < 0

See Also

>>> from numpy import polynomial as P
>>> P.trimcoef((0,0,3,0,5,0,0))
array([ 0.,  0.,  3.,  0.,  5.])
>>> P.trimcoef((0,0,1e-3,0,1e-5,0,0),1e-3) # item == tol is trimmed
array([ 0.])
>>> i = complex(0,1) # works for complex
>>> P.trimcoef((3e-4,1e-3*(1-i),5e-4,2e-5*(1+i)), 1e-3)
array([ 0.0003+0.j   ,  0.0010-0.001j])
def pyneb.utils.polyutils.trimseq (   seq)
Remove small Poly series coefficients.

seq : sequence
    Sequence of Poly series coefficients. This routine fails for
    empty sequences.

series : sequence
    Subsequence with trailing zeros removed. If the resulting sequence
    would be empty, return the first element. The returned sequence may
    or may not be a view.

Do not lose the type info if the sequence contains unknown objects.

Variable Documentation

list __all__
Initial value:
1 = ['RankWarning', 'PolyError', 'PolyDomainError', 'PolyBase',
2  'as_series', 'trimseq', 'trimcoef', 'getdomain', 'mapdomain',
3  'mapparms']