def leg2poly(cs) :
"""
Convert a Legendre series to a polynomial.
Convert an array representing the coefficients of a Legendre series,
ordered from lowest degree to highest, to an array of the coefficients
of the equivalent polynomial (relative to the "standard" basis) ordered
from lowest to highest degree.
Parameters
----------
cs : array_like
1-d array containing the Legendre series coefficients, ordered
from lowest order term to highest.
Returns
-------
pol : ndarray
1-d array containing the coefficients of the equivalent polynomial
(relative to the "standard" basis) ordered from lowest order term
to highest.
See Also
--------
poly2leg
Notes
-----
The easy way to do conversions between polynomial basis sets
is to use the convert method of a class instance.
Examples
--------
>>> c = P.Legendre(range(4))
>>> c
Legendre([ 0., 1., 2., 3.], [-1., 1.])
>>> p = c.convert(kind=P.Polynomial)
>>> p
Polynomial([-1. , -3.5, 3. , 7.5], [-1., 1.])
>>> P.leg2poly(range(4))
array([-1. , -3.5, 3. , 7.5])
"""
from polynomial import polyadd, polysub, polymulx
[cs] = pu.as_series([cs])
n = len(cs)
if n < 3:
return cs
else:
c0 = cs[-2]
c1 = cs[-1]
# i is the current degree of c1
for i in range(n - 1, 1, -1) :
tmp = c0
c0 = polysub(cs[i - 2], (c1*(i - 1))/i)
c1 = polyadd(tmp, (polymulx(c1)*(2*i - 1))/i)
return polyadd(c0, polymulx(c1))
def cheb2poly(cs):
"""
Convert a Chebyshev series to a polynomial.
Convert an array representing the coefficients of a Chebyshev series,
ordered from lowest degree to highest, to an array of the coefficients
of the equivalent polynomial (relative to the "standard" basis) ordered
from lowest to highest degree.
Parameters
----------
cs : array_like
1-d array containing the Chebyshev series coefficients, ordered
from lowest order term to highest.
Returns
-------
pol : ndarray
1-d array containing the coefficients of the equivalent polynomial
(relative to the "standard" basis) ordered from lowest order term
to highest.
See Also
--------
poly2cheb
Notes
-----
The easy way to do conversions between polynomial basis sets
is to use the convert method of a class instance.
Examples
--------
>>> from numpy import polynomial as P
>>> c = P.Chebyshev(range(4))
>>> c
Chebyshev([ 0., 1., 2., 3.], [-1., 1.])
>>> p = c.convert(kind=P.Polynomial)
>>> p
Polynomial([ -2., -8., 4., 12.], [-1., 1.])
>>> P.cheb2poly(range(4))
array([ -2., -8., 4., 12.])
"""
from polynomial import polyadd, polysub, polymulx
[cs] = as_series([cs])
n = len(cs)
if n < 3:
return cs
else:
c0 = cs[-2]
c1 = cs[-1]
# i is the current degree of c1
for i in range(n - 1, 1, -1):
tmp = c0
c0 = polysub(cs[i - 2], c1)
c1 = polyadd(tmp, polymulx(c1) * 2)
return polyadd(c0, polymulx(c1))
def leg2poly(cs) :
"""
Convert a Legendre series to a polynomial.
Convert an array representing the coefficients of a Legendre series,
ordered from lowest degree to highest, to an array of the coefficients
of the equivalent polynomial (relative to the "standard" basis) ordered
from lowest to highest degree.
Parameters
----------
cs : array_like
1-d array containing the Legendre series coefficients, ordered
from lowest order term to highest.
Returns
-------
pol : ndarray
1-d array containing the coefficients of the equivalent polynomial
(relative to the "standard" basis) ordered from lowest order term
to highest.
See Also
--------
poly2leg
Notes
-----
The easy way to do conversions between polynomial basis sets
is to use the convert method of a class instance.
Examples
--------
>>> c = P.Legendre(range(4))
>>> c
Legendre([ 0., 1., 2., 3.], [-1., 1.])
>>> p = c.convert(kind=P.Polynomial)
>>> p
Polynomial([-1. , -3.5, 3. , 7.5], [-1., 1.])
>>> P.leg2poly(range(4))
array([-1. , -3.5, 3. , 7.5])
"""
from polynomial import polyadd, polysub, polymulx
[cs] = pu.as_series([cs])
n = len(cs)
if n < 3:
return cs
else:
c0 = cs[-2]
c1 = cs[-1]
# i is the current degree of c1
for i in range(n - 1, 1, -1) :
tmp = c0
c0 = polysub(cs[i - 2], (c1*(i - 1))/i)
c1 = polyadd(tmp, (polymulx(c1)*(2*i - 1))/i)
return polyadd(c0, polymulx(c1))
def cheb2poly(cs) :
"""
Convert a Chebyshev series to a polynomial.
Convert an array representing the coefficients of a Chebyshev series,
ordered from lowest degree to highest, to an array of the coefficients
of the equivalent polynomial (relative to the "standard" basis) ordered
from lowest to highest degree.
Parameters
----------
cs : array_like
1-d array containing the Chebyshev series coefficients, ordered
from lowest order term to highest.
Returns
-------
pol : ndarray
1-d array containing the coefficients of the equivalent polynomial
(relative to the "standard" basis) ordered from lowest order term
to highest.
See Also
--------
poly2cheb
Notes
-----
The easy way to do conversions between polynomial basis sets
is to use the convert method of a class instance.
Examples
--------
>>> from numpy import polynomial as P
>>> c = P.Chebyshev(range(4))
>>> c
Chebyshev([ 0., 1., 2., 3.], [-1., 1.])
>>> p = c.convert(kind=P.Polynomial)
>>> p
Polynomial([ -2., -8., 4., 12.], [-1., 1.])
>>> P.cheb2poly(range(4))
array([ -2., -8., 4., 12.])
"""
from polynomial import polyadd, polysub, polymulx
[cs] = pu.as_series([cs])
n = len(cs)
if n < 3:
return cs
else:
c0 = cs[-2]
c1 = cs[-1]
for i in range(n - 3, -1, -1) :
tmp = c0
c0 = polysub(cs[i], c1)
c1 = polyadd(tmp, polymulx(c1)*2)
return polyadd(c0, polymulx(c1))
def herm2poly(cs) :
"""
Convert a Hermite series to a polynomial.
Convert an array representing the coefficients of a Hermite series,
ordered from lowest degree to highest, to an array of the coefficients
of the equivalent polynomial (relative to the "standard" basis) ordered
from lowest to highest degree.
Parameters
----------
cs : array_like
1-d array containing the Hermite series coefficients, ordered
from lowest order term to highest.
Returns
-------
pol : ndarray
1-d array containing the coefficients of the equivalent polynomial
(relative to the "standard" basis) ordered from lowest order term
to highest.
See Also
--------
poly2herm
Notes
-----
The easy way to do conversions between polynomial basis sets
is to use the convert method of a class instance.
Examples
--------
>>> from numpy.polynomial.hermite import herm2poly
>>> herm2poly([ 1. , 2.75 , 0.5 , 0.375])
array([ 0., 1., 2., 3.])
"""
from polynomial import polyadd, polysub, polymulx
[cs] = pu.as_series([cs])
n = len(cs)
if n == 1:
return cs
if n == 2:
cs[1] *= 2
return cs
else:
c0 = cs[-2]
c1 = cs[-1]
# i is the current degree of c1
for i in range(n - 1, 1, -1) :
tmp = c0
c0 = polysub(cs[i - 2], c1*(2*(i - 1)))
c1 = polyadd(tmp, polymulx(c1)*2)
return polyadd(c0, polymulx(c1)*2)