package np

Get an attribute of this module as a Py.Object.t. This is useful to pass a Python function to another function.

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 array.

Parameters ---------- alist : 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.

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

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

Examples -------- >>> from numpy.polynomial import polyutils as pu >>> a = np.arange(4) >>> pu.as_series(a) array([0.]), array([1.]), array([2.]), array([3.]) >>> b = np.arange(6).reshape((2,3)) >>> pu.as_series(b) array([0., 1., 2.]), array([3., 4., 5.])

>>> pu.as_series((1, np.arange(3), np.arange(2, dtype=np.float16))) array([1.]), array([0., 1., 2.]), array([0., 1.])

>>> pu.as_series(2, [1.1, 0.]) array([2.]), array([1.1])

>>> pu.as_series(2, [1.1, 0.], trim=False) array([2.]), array([1.1, 0. ])

Return a domain suitable for given abscissae.

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

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

Returns ------- 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

Examples -------- >>> 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)

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`.

Parameters ---------- 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.

Returns ------- 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

Notes ----- Effectively, this implements:

.. math :: x\_out = new0 + m(x - old0)

where

.. math :: m = \fracnew[1]-new[0]

Examples -------- >>> from numpy.polynomial import polyutils as pu >>> 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 = pu.mapdomain(x, old_domain, new_domain); x_out array( 0. , 1.25663706, 2.51327412, 3.76991118, 5.02654825, # may vary 6.28318531) >>> x - pu.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(old0, old1, 6); z array(-1. -1.j , -0.6-0.6j, -0.2-0.2j, 0.2+0.2j, 0.6+0.6j, 1. +1.j ) >>> new_z = pu.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 ) # may vary

Linear map parameters between domains.

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

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

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

See Also -------- getdomain, mapdomain

Notes ----- 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.

Examples -------- >>> from numpy.polynomial import polyutils as pu >>> pu.mapparms((-1,1),(-1,1)) (0.0, 1.0) >>> pu.mapparms((1,-1),(-1,1)) (-0.0, -1.0) >>> i = complex(0,1) >>> pu.mapparms((-i,-1),(1,i)) ((1+1j), (1-0j))

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.'

Parameters ---------- 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.

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

Raises ------ ValueError If `tol` < 0

See Also -------- trimseq

Examples -------- >>> from numpy.polynomial import polyutils as pu >>> pu.trimcoef((0,0,3,0,5,0,0)) array(0., 0., 3., 0., 5.) >>> pu.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 >>> pu.trimcoef((3e-4,1e-3*(1-i),5e-4,2e-5*(1+i)), 1e-3) array(0.0003+0.j , 0.001 -0.001j)

Remove small Poly series coefficients.

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

Returns ------- 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.

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