def standard_double_cascade_step(dim, embsys, esols, tasks=0):
r"""
Given in *embsys* an embedded polynomial system and
solutions with nonzero slack variables in *esols*, does one step
in the homotopy cascade, with standard double precision arithmetic.
The dimension of the solution set represented by *embsys*
and *esols* is the value of *dim*.
The number of tasks in multithreaded path tracking is given by *tasks*.
The default zero value of *tasks* indicates no multithreading.
The list on return contains witness points on
lower dimensional solution components.
"""
from phcpy.phcpy2c2 import py2c_copy_standard_container_to_start_system
from phcpy.phcpy2c2 import py2c_copy_standard_container_to_start_solutions
from phcpy.phcpy2c2 import py2c_standard_cascade_homotopy
from phcpy.phcpy2c2 import py2c_solve_by_standard_homotopy_continuation
from phcpy.phcpy2c2 import py2c_solcon_clear_standard_solutions
from phcpy.phcpy2c2 import py2c_copy_standard_target_solutions_to_container
from phcpy.interface import store_standard_witness_set
from phcpy.interface import load_standard_solutions
store_standard_witness_set(len(embsys), dim, embsys, esols)
py2c_copy_standard_container_to_start_system()
py2c_copy_standard_container_to_start_solutions()
py2c_standard_cascade_homotopy()
py2c_solve_by_standard_homotopy_continuation(tasks)
py2c_solcon_clear_standard_solutions()
py2c_copy_standard_target_solutions_to_container()
return load_standard_solutions()
def standard_double_cascade_step(dim, embsys, esols, tasks=0):
r"""
Given in *embsys* an embedded polynomial system and
solutions with nonzero slack variables in *esols*, does one step
in the homotopy cascade, with standard double precision arithmetic.
The dimension of the solution set represented by *embsys*
and *esols* is the value of *dim*.
The number of tasks in multithreaded path tracking is given by *tasks*.
The default zero value of *tasks* indicates no multithreading.
The list on return contains witness points on
lower dimensional solution components.
"""
from phcpy.phcpy2c2 import py2c_copy_standard_container_to_start_system
from phcpy.phcpy2c2 import py2c_copy_standard_container_to_start_solutions
from phcpy.phcpy2c2 import py2c_standard_cascade_homotopy
from phcpy.phcpy2c2 import py2c_solve_by_standard_homotopy_continuation
from phcpy.phcpy2c2 import py2c_solcon_clear_standard_solutions
from phcpy.phcpy2c2 import py2c_copy_standard_target_solutions_to_container
from phcpy.interface import store_standard_witness_set
from phcpy.interface import load_standard_solutions
store_standard_witness_set(len(embsys), dim, embsys, esols)
py2c_copy_standard_container_to_start_system()
py2c_copy_standard_container_to_start_solutions()
py2c_standard_cascade_homotopy()
py2c_solve_by_standard_homotopy_continuation(tasks)
py2c_solcon_clear_standard_solutions()
py2c_copy_standard_target_solutions_to_container()
return load_standard_solutions()
def standard_monodromy_breakup(embsys, esols, dim, \
islaurent=0, verbose=True, nbloops=0):
r"""
Applies the monodromy breakup algorithm in standard double precision
to factor the *dim*-dimensional algebraic set represented by the
embedded system *embsys* and its solutions *esols*.
If the embedded polynomial system is a Laurent system,
then islaurent must equal one, the default is zero.
If *verbose* is False, then no output is written.
If *nbloops* equals zero, then the user is prompted to give
the maximum number of loops.
"""
from phcpy.phcpy2c3 import py2c_factor_set_standard_to_mute
from phcpy.phcpy2c3 import py2c_factor_set_standard_to_verbose
from phcpy.phcpy2c3 import py2c_factor_standard_assign_labels
from phcpy.phcpy2c3 import py2c_factor_initialize_standard_monodromy
from phcpy.phcpy2c3 import py2c_factor_initialize_standard_sampler
from phcpy.phcpy2c3 import py2c_factor_initialize_standard_Laurent_sampler
from phcpy.phcpy2c3 import py2c_factor_standard_trace_grid_diagnostics
from phcpy.phcpy2c3 import py2c_factor_set_standard_trace_slice
from phcpy.phcpy2c3 import py2c_factor_store_standard_gammas
from phcpy.phcpy2c3 import py2c_factor_standard_track_paths
from phcpy.phcpy2c3 import py2c_factor_store_standard_solutions
from phcpy.phcpy2c3 import py2c_factor_restore_standard_solutions
from phcpy.phcpy2c3 import py2c_factor_new_standard_slices
from phcpy.phcpy2c3 import py2c_factor_swap_standard_slices
from phcpy.phcpy2c3 import py2c_factor_permutation_after_standard_loop
from phcpy.phcpy2c3 import py2c_factor_number_of_standard_components
from phcpy.phcpy2c3 import py2c_factor_update_standard_decomposition
from phcpy.phcpy2c3 import py2c_solcon_write_standard_solutions
from phcpy.phcpy2c3 import py2c_solcon_clear_standard_solutions
from phcpy.interface import store_standard_witness_set
from phcpy.interface import store_standard_laurent_witness_set
if(verbose):
print('... applying monodromy factorization with standard doubles ...')
py2c_factor_set_standard_to_verbose()
else:
py2c_factor_set_standard_to_mute()
deg = len(esols)
nvar = len(embsys)
if(verbose):
print('dim =', dim)
if(islaurent == 1):
store_standard_laurent_witness_set(nvar, dim, embsys, esols)
py2c_factor_standard_assign_labels(nvar, deg)
py2c_factor_initialize_standard_Laurent_sampler(dim)
else:
store_standard_witness_set(nvar, dim, embsys, esols)
py2c_factor_standard_assign_labels(nvar, deg)
py2c_factor_initialize_standard_sampler(dim)
if(verbose):
py2c_solcon_write_standard_solutions()
if(nbloops == 0):
strnbloops = input('give the maximum number of loops : ')
nbloops = int(strnbloops)
py2c_factor_initialize_standard_monodromy(nbloops, deg, dim)
py2c_factor_store_standard_solutions()
if(verbose):
print('... initializing the grid in standard double precision ...')
for i in range(1, 3):
py2c_factor_set_standard_trace_slice(i)
py2c_factor_store_standard_gammas(nvar)
py2c_factor_standard_track_paths(islaurent)
py2c_factor_store_standard_solutions()
py2c_factor_restore_standard_solutions()
py2c_factor_swap_standard_slices()
(err, dis) = py2c_factor_standard_trace_grid_diagnostics()
if(verbose):
print('The diagnostics of the trace grid :')
print(' largest error on the samples :', err)
print(' smallest distance between the samples :', dis)
for i in range(1, nbloops+1):
if(verbose):
print('... starting loop %d ...' % i)
py2c_factor_new_standard_slices(dim, nvar)
py2c_factor_store_standard_gammas(nvar)
py2c_factor_standard_track_paths(islaurent)
py2c_solcon_clear_standard_solutions()
py2c_factor_store_standard_gammas(nvar)
py2c_factor_standard_track_paths(islaurent)
py2c_factor_store_standard_solutions()
sprm = py2c_factor_permutation_after_standard_loop(deg)
if(verbose):
perm = eval(sprm)
print('the permutation :', perm)
nb0 = py2c_factor_number_of_standard_components()
done = py2c_factor_update_standard_decomposition(deg, len(sprm), sprm)
nb1 = py2c_factor_number_of_standard_components()
if(verbose):
print('number of factors : %d -> %d' % (nb0, nb1))
deco = decomposition(deg)
print('decomposition :', deco)
if(done == 1):
break
py2c_factor_restore_standard_solutions()
def standard_monodromy_breakup(embsys, esols, dim, \
islaurent=0, verbose=True, nbloops=0):
r"""
Applies the monodromy breakup algorithm in standard double precision
to factor the *dim*-dimensional algebraic set represented by the
embedded system *embsys* and its solutions *esols*.
If the embedded polynomial system is a Laurent system,
then islaurent must equal one, the default is zero.
If *verbose* is False, then no output is written.
If *nbloops* equals zero, then the user is prompted to give
the maximum number of loops.
"""
from phcpy.phcpy2c3 import py2c_factor_set_standard_to_mute
from phcpy.phcpy2c3 import py2c_factor_set_standard_to_verbose
from phcpy.phcpy2c3 import py2c_factor_standard_assign_labels
from phcpy.phcpy2c3 import py2c_factor_initialize_standard_monodromy
from phcpy.phcpy2c3 import py2c_factor_initialize_standard_sampler
from phcpy.phcpy2c3 import py2c_factor_initialize_standard_Laurent_sampler
from phcpy.phcpy2c3 import py2c_factor_standard_trace_grid_diagnostics
from phcpy.phcpy2c3 import py2c_factor_set_standard_trace_slice
from phcpy.phcpy2c3 import py2c_factor_store_standard_gammas
from phcpy.phcpy2c3 import py2c_factor_standard_track_paths
from phcpy.phcpy2c3 import py2c_factor_store_standard_solutions
from phcpy.phcpy2c3 import py2c_factor_restore_standard_solutions
from phcpy.phcpy2c3 import py2c_factor_new_standard_slices
from phcpy.phcpy2c3 import py2c_factor_swap_standard_slices
from phcpy.phcpy2c3 import py2c_factor_permutation_after_standard_loop
from phcpy.phcpy2c3 import py2c_factor_number_of_standard_components
from phcpy.phcpy2c3 import py2c_factor_update_standard_decomposition
from phcpy.phcpy2c3 import py2c_solcon_write_standard_solutions
from phcpy.phcpy2c3 import py2c_solcon_clear_standard_solutions
from phcpy.interface import store_standard_witness_set
from phcpy.interface import store_standard_laurent_witness_set
if (verbose):
print('... applying monodromy factorization with standard doubles ...')
py2c_factor_set_standard_to_verbose()
else:
py2c_factor_set_standard_to_mute()
deg = len(esols)
nvar = len(embsys)
if (verbose):
print('dim =', dim)
if (islaurent == 1):
store_standard_laurent_witness_set(nvar, dim, embsys, esols)
py2c_factor_standard_assign_labels(nvar, deg)
py2c_factor_initialize_standard_Laurent_sampler(dim)
else:
store_standard_witness_set(nvar, dim, embsys, esols)
py2c_factor_standard_assign_labels(nvar, deg)
py2c_factor_initialize_standard_sampler(dim)
if (verbose):
py2c_solcon_write_standard_solutions()
if (nbloops == 0):
strnbloops = input('give the maximum number of loops : ')
nbloops = int(strnbloops)
py2c_factor_initialize_standard_monodromy(nbloops, deg, dim)
py2c_factor_store_standard_solutions()
if (verbose):
print('... initializing the grid in standard double precision ...')
for i in range(1, 3):
py2c_factor_set_standard_trace_slice(i)
py2c_factor_store_standard_gammas(nvar)
py2c_factor_standard_track_paths(islaurent)
py2c_factor_store_standard_solutions()
py2c_factor_restore_standard_solutions()
py2c_factor_swap_standard_slices()
(err, dis) = py2c_factor_standard_trace_grid_diagnostics()
if (verbose):
print('The diagnostics of the trace grid :')
print(' largest error on the samples :', err)
print(' smallest distance between the samples :', dis)
for i in range(1, nbloops + 1):
if (verbose):
print('... starting loop %d ...' % i)
py2c_factor_new_standard_slices(dim, nvar)
py2c_factor_store_standard_gammas(nvar)
py2c_factor_standard_track_paths(islaurent)
py2c_solcon_clear_standard_solutions()
py2c_factor_store_standard_gammas(nvar)
py2c_factor_standard_track_paths(islaurent)
py2c_factor_store_standard_solutions()
sprm = py2c_factor_permutation_after_standard_loop(deg)
if (verbose):
perm = eval(sprm)
print('the permutation :', perm)
nb0 = py2c_factor_number_of_standard_components()
done = py2c_factor_update_standard_decomposition(deg, len(sprm), sprm)
nb1 = py2c_factor_number_of_standard_components()
if (verbose):
print('number of factors : %d -> %d' % (nb0, nb1))
deco = decomposition(deg)
print('decomposition :', deco)
if (done == 1):
break
py2c_factor_restore_standard_solutions()