def standard_pade_approximants(pols, sols, idx=1, numdeg=2, dendeg=2, \
nbr=4, verbose=True):
r"""
Computes Pade approximants based on the series in standard double
precision for the polynomials in *pols*, where the leading
coefficients of the series are the solutions in *sols*.
On entry are the following seven parameters:
*pols*: a list of string representations of polynomials,
*sols*: a list of solutions of the polynomials in *pols*,
*idx*: index of the series parameter, by default equals 1,
*numdeg*: the degree of the numerator,
*dendeg*: the degree of the denominator,
*nbr*: number of steps with Newton's method,
*verbose*: whether to write intermediate output to screen or not.
On return is a list of lists of strings. Each lists of strings
represents the series solution for the variables in the list *pols*.
"""
from phcpy.solver import number_of_symbols
from phcpy.interface import store_standard_solutions
from phcpy.interface import store_standard_system, load_standard_system
from phcpy.phcpy2c3 \
import py2c_standard_Pade_approximant as Pade_approximants
from phcpy.phcpy2c3 import py2c_syspool_standard_size as poolsize
from phcpy.phcpy2c3 import py2c_syspool_copy_to_standard_container
from phcpy.phcpy2c3 import py2c_syspool_standard_clear
nbsym = number_of_symbols(pols)
if verbose:
print("the polynomials :")
for pol in pols:
print(pol)
print("Number of variables :", nbsym)
store_standard_system(pols, nbvar=nbsym)
store_standard_solutions(nbsym, sols)
fail = Pade_approximants(idx, numdeg, dendeg, nbr, int(verbose))
size = (-1 if fail else poolsize())
if verbose:
if size == -1:
print("An error occurred in the Pade constructor.")
else:
print("Computed %d Pade approximants." % size)
result = []
for k in range(1, size + 1):
py2c_syspool_copy_to_standard_container(k)
sersol = load_standard_system()
substsersol = substitute_symbol(sersol, idx)
result.append(make_fractions(substsersol))
py2c_syspool_standard_clear()
return result
def standard_newton_power_series(pols, lser, idx=1, nbr=4, verbose=True):
r"""
Computes series in standard double precision for the polynomials
in *pols*, where the leading terms are given in the list *lser*.
On entry are the following five parameters:
*pols*: a list of string representations of polynomials,
*lser*: a list of polynomials in the series parameter (e.g.: t),
for use as start terms in Newton's method,
*idx*: index of the series parameter, by default equals 1,
*nbr*: number of steps with Newton's method,
*verbose*: whether to write intermediate output to screen or not.
On return is a list of lists of strings. Each lists of strings
represents the series solution for the variables in the list *pols*.
"""
from phcpy.solver import number_of_symbols
from phcpy.interface import store_standard_system, load_standard_system
from phcpy.phcpy2c3 import py2c_standard_Newton_power_series as newton
from phcpy.phcpy2c3 import py2c_syspool_standard_init
from phcpy.phcpy2c3 import py2c_syspool_standard_create
from phcpy.phcpy2c3 import py2c_syspool_standard_size as poolsize
from phcpy.phcpy2c3 import py2c_syspool_copy_to_standard_container
from phcpy.phcpy2c3 import py2c_syspool_standard_clear
nbsym = number_of_symbols(pols)
if verbose:
print("the polynomials :")
for pol in pols:
print(pol)
print("Number of variables :", nbsym)
store_standard_system(lser, nbvar=1)
py2c_syspool_standard_init(1)
py2c_syspool_standard_create(1)
store_standard_system(pols, nbvar=nbsym)
fail = newton(idx, nbr, int(verbose))
size = (-1 if fail else poolsize())
if verbose:
if size == -1:
print("An error occurred in the execution of Newton's method.")
else:
print("Computed one series solution.")
py2c_syspool_copy_to_standard_container(1)
result = load_standard_system()
result = substitute_symbol(result, idx)
py2c_syspool_standard_clear()
return result
def standard_newton_power_series(pols, lser, idx=1, nbr=4, verbose=True):
r"""
Computes series in standard double precision for the polynomials
in *pols*, where the leading terms are given in the list *lser*.
On entry are the following five parameters:
*pols*: a list of string representations of polynomials,
*lser*: a list of polynomials in the series parameter (e.g.: t),
for use as start terms in Newton's method,
*idx*: index of the series parameter, by default equals 1,
*nbr*: number of steps with Newton's method,
*verbose*: whether to write intermediate output to screen or not.
On return is a list of lists of strings. Each lists of strings
represents the series solution for the variables in the list *pols*.
"""
from phcpy.solver import number_of_symbols
from phcpy.interface import store_standard_system, load_standard_system
from phcpy.phcpy2c3 import py2c_standard_Newton_power_series as newton
from phcpy.phcpy2c3 import py2c_syspool_standard_init
from phcpy.phcpy2c3 import py2c_syspool_standard_create
from phcpy.phcpy2c3 import py2c_syspool_standard_size as poolsize
from phcpy.phcpy2c3 import py2c_syspool_copy_to_standard_container
from phcpy.phcpy2c3 import py2c_syspool_standard_clear
nbsym = number_of_symbols(pols)
if verbose:
print("the polynomials :")
for pol in pols:
print(pol)
print("Number of variables :", nbsym)
store_standard_system(lser, nbvar=1)
py2c_syspool_standard_init(1);
py2c_syspool_standard_create(1);
store_standard_system(pols, nbvar=nbsym)
fail = newton(idx, nbr, int(verbose))
size = (-1 if fail else poolsize())
if verbose:
if size == -1:
print("An error occurred in the execution of Newton's method.")
else:
print("Computed one series solution.")
py2c_syspool_copy_to_standard_container(1)
result = load_standard_system()
result = substitute_symbol(result, idx)
py2c_syspool_standard_clear()
return result