def laurent_cascade_filter(dim, embpols, nonsols, tol, \
nbtasks=0, prc='d', verbose=True):
r"""
Runs one step in the cascade homotopy defined by the embedding of
Laurent polynomials in *embpols*, starting at the solutions in *nonsols*,
removing the last hyperplane from *embpols* at dimension *dim*.
The tolerance *tol* is used to split filter the solutions.
By default, the precision *prc* is double ('d'). Other valid values
for *prc* are 'dd' (for double double) and 'qd' (for quad double).
If *verbose*, then some output is written to screen.
"""
if (prc == 'd'):
from phcpy.sets \
import drop_variable_from_standard_laurent_polynomials as drop1poly
from phcpy.sets \
import drop_coordinate_from_standard_solutions as drop1sols
elif (prc == 'dd'):
from phcpy.sets \
import drop_variable_from_dobldobl_laurent_polynomials as drop1poly
from phcpy.sets \
import drop_coordinate_from_dobldobl_solutions as drop1sols
elif (prc == 'qd'):
from phcpy.sets \
import drop_variable_from_quaddobl_laurent_polynomials as drop1poly
from phcpy.sets \
import drop_coordinate_from_quaddobl_solutions as drop1sols
else:
print 'invalid value for precision as argument for prc'
return
if verbose:
print 'running a cascade with %d paths ...' % len(nonsols)
sols = laurent_cascade_step\
(dim, embpols, nonsols, precision=prc, tasks=nbtasks)
dimslackvar = 'zz' + str(dim)
embdown = drop1poly(embpols, dimslackvar)
solsdrop = drop1sols(sols, len(embpols), dimslackvar)
if dim <= 1:
return (embdown[:-1], solsdrop)
else:
(sols0, sols1) = split_filter(solsdrop, dim - 1, tol, verbose)
return (embdown[:-1], sols0, sols1)
def laurent_cascade_filter(dim, embpols, nonsols, tol, \
nbtasks=0, prc='d', verbose=True):
r"""
Runs one step in the cascade homotopy defined by the embedding of
Laurent polynomials in *embpols*, starting at the solutions in *nonsols*,
removing the last hyperplane from *embpols* at dimension *dim*.
The tolerance *tol* is used to split filter the solutions.
By default, the precision *prc* is double ('d'). Other valid values
for *prc* are 'dd' (for double double) and 'qd' (for quad double).
If *verbose*, then some output is written to screen.
"""
if(prc == 'd'):
from phcpy.sets \
import drop_variable_from_standard_laurent_polynomials as drop1poly
from phcpy.sets \
import drop_coordinate_from_standard_solutions as drop1sols
elif(prc == 'dd'):
from phcpy.sets \
import drop_variable_from_dobldobl_laurent_polynomials as drop1poly
from phcpy.sets \
import drop_coordinate_from_dobldobl_solutions as drop1sols
elif(prc == 'qd'):
from phcpy.sets \
import drop_variable_from_quaddobl_laurent_polynomials as drop1poly
from phcpy.sets \
import drop_coordinate_from_quaddobl_solutions as drop1sols
else:
print 'invalid value for precision as argument for prc'
return
if verbose:
print 'running a cascade with %d paths ...' % len(nonsols)
sols = laurent_cascade_step\
(dim, embpols, nonsols, precision=prc, tasks=nbtasks)
dimslackvar = 'zz' + str(dim)
embdown = drop1poly(embpols, dimslackvar)
solsdrop = drop1sols(sols, len(embpols), dimslackvar)
if dim <= 1:
return (embdown[:-1], solsdrop)
else:
(sols0, sols1) = split_filter(solsdrop, dim-1, tol, verbose)
return (embdown[:-1], sols0, sols1)