def permute_quaddobl_system(pols):
"""
Permutes the equations in the list of polynomials in pols
with coefficients in quad double precision,
along the permutation used in the mixed volume computation.
"""
from phcpy.phcpy2c2 import py2c_celcon_permute_quaddobl_system
from phcpy.interface import store_quaddobl_system, load_quaddobl_system
store_quaddobl_system(pols)
py2c_celcon_permute_quaddobl_system()
return load_quaddobl_system()
def quaddobl_scale_system(pols):
"""
Applies equation and variable scaling in quad double precision
to the polynomials in the list pols.
On return is the list of scaled polynomials and the scaling coefficients.
"""
from phcpy.interface import store_quaddobl_system, load_quaddobl_system
from phcpy.phcpy2c2 import py2c_scale_quaddobl_system
store_quaddobl_system(pols)
cffs = py2c_scale_quaddobl_system(2)
spol = load_quaddobl_system()
return (spol, cffs)
def quaddobl_usolve(pol, mxi, eps):
"""
Applies the method of Durand-Kerner (aka Weierstrass)
to the polynomial in the string pol, in quad double precision
The maximum number of iterations is in mxi,
the requirement on the accuracy in eps.
"""
from phcpy.phcpy2c2 import py2c_usolve_quaddobl
from phcpy.interface import store_quaddobl_system, load_quaddobl_solutions
store_quaddobl_system([pol])
nit = py2c_usolve_quaddobl(mxi, eps)
rts = load_quaddobl_solutions()
return (nit, rts)
def newton_step(system, solutions, precision='d', decimals=100):
"""
Applies one Newton step to the solutions of the system.
For each solution, prints its last line of diagnostics.
Four levels of precision are supported:
d : standard double precision (1.1e-15 or 2^(-53)),
dd : double double precision (4.9e-32 or 2^(-104)),
qd : quad double precision (1.2e-63 or 2^(-209)).
mp : arbitrary precision, where the number of decimal places
in the working precision is determined by decimals.
"""
if(precision == 'd'):
from interface import store_standard_system
from interface import store_standard_solutions, load_standard_solutions
store_standard_system(system)
store_standard_solutions(len(system), solutions)
from phcpy.phcpy2c2 import py2c_standard_Newton_step
py2c_standard_Newton_step()
result = load_standard_solutions()
elif(precision == 'dd'):
from interface import store_dobldobl_system
from interface import store_dobldobl_solutions, load_dobldobl_solutions
store_dobldobl_system(system)
store_dobldobl_solutions(len(system), solutions)
from phcpy.phcpy2c2 import py2c_dobldobl_Newton_step
py2c_dobldobl_Newton_step()
result = load_dobldobl_solutions()
elif(precision == 'qd'):
from interface import store_quaddobl_system
from interface import store_quaddobl_solutions, load_quaddobl_solutions
store_quaddobl_system(system)
store_quaddobl_solutions(len(system), solutions)
from phcpy.phcpy2c2 import py2c_quaddobl_Newton_step
py2c_quaddobl_Newton_step()
result = load_quaddobl_solutions()
elif(precision == 'mp'):
from interface import store_multprec_system
from interface import store_multprec_solutions, load_multprec_solutions
store_multprec_system(system, decimals)
store_multprec_solutions(len(system), solutions)
from phcpy.phcpy2c2 import py2c_multprec_Newton_step
py2c_multprec_Newton_step(decimals)
result = load_multprec_solutions()
else:
print 'wrong argument for precision'
return None
for sol in result:
strsol = sol.split('\n')
print strsol[-1]
return result
def quaddobl_deflate(system, solutions):
"""
The deflation method augments the given system with
derivatives to restore the quadratic convergence of
Newton's method at isolated singular solutions,
in quad double precision.
After application of deflation with default settings,
the new approximate solutions are returned.
"""
from phcpy.phcpy2c2 import py2c_quaddobl_deflate
from phcpy.interface import store_quaddobl_system
from phcpy.interface import store_quaddobl_solutions
from phcpy.interface import load_quaddobl_solutions
store_quaddobl_system(system)
store_quaddobl_solutions(len(system), solutions)
py2c_quaddobl_deflate()
result = load_quaddobl_solutions()
return result