def newton_laurent_step(system, solutions, precision='d', decimals=100):
"""
Applies one Newton step to the solutions of the Laurent 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_laurent_system
from interface import store_standard_solutions, load_standard_solutions
store_standard_laurent_system(system)
store_standard_solutions(len(system), solutions)
from phcpy.phcpy2c2 import py2c_standard_Newton_Laurent_step
py2c_standard_Newton_Laurent_step()
result = load_standard_solutions()
elif(precision == 'dd'):
from interface import store_dobldobl_laurent_system
from interface import store_dobldobl_solutions, load_dobldobl_solutions
store_dobldobl_laurent_system(system)
store_dobldobl_solutions(len(system), solutions)
from phcpy.phcpy2c2 import py2c_dobldobl_Newton_Laurent_step
py2c_dobldobl_Newton_Laurent_step()
result = load_dobldobl_solutions()
elif(precision == 'qd'):
from interface import store_quaddobl_laurent_system
from interface import store_quaddobl_solutions, load_quaddobl_solutions
store_quaddobl_laurent_system(system)
store_quaddobl_solutions(len(system), solutions)
from phcpy.phcpy2c2 import py2c_quaddobl_Newton_Laurent_step
py2c_quaddobl_Newton_Laurent_step()
result = load_quaddobl_solutions()
elif(precision == 'mp'):
from interface import store_multprec_laurent_system
from interface import store_multprec_solutions, load_multprec_solutions
store_multprec_laurent_system(system, decimals)
store_multprec_solutions(len(system), solutions)
from phcpy.phcpy2c2 import py2c_multprec_Newton_Laurent_step
py2c_multprec_Newton_Laurent_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 newton_steps(system, solutions, accuracy=8, maxsteps=4, maxprec=256):
"""
Runs a sequence of variable precision Newton steps to approximate
solutions accurate up to a specified number of decimal places.
In addition to the system and solutions, there are three parameters:
accuracy : number of decimal places wanted to be accurate,
maxsteps : maximum number of Newton steps,
maxprec : maximum number of decimal places in the precision used
to estimate the condition numbers.
"""
from phcpy.phcpy2c2 import py2c_varbprec_Newton_Laurent_steps as vmpnewt
from phcpy.interface import store_multprec_solutions
from phcpy.interface import load_multprec_solutions
dim = len(system)
store_multprec_solutions(dim, solutions)
pols = ""
for polynomial in system:
pols = pols + polynomial
vmpnewt(dim, accuracy, maxsteps, maxprec, len(pols), pols)
result = load_multprec_solutions()
return result
