def double_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 double 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_dobldobl_container_to_start_system
from phcpy.phcpy2c2 import py2c_copy_dobldobl_container_to_start_solutions
from phcpy.phcpy2c2 import py2c_dobldobl_cascade_homotopy
from phcpy.phcpy2c2 import py2c_solve_by_dobldobl_homotopy_continuation
from phcpy.phcpy2c2 import py2c_solcon_clear_dobldobl_solutions
from phcpy.phcpy2c2 import py2c_copy_dobldobl_target_solutions_to_container
from phcpy.interface import store_dobldobl_witness_set
from phcpy.interface import load_dobldobl_solutions
store_dobldobl_witness_set(len(embsys), dim, embsys, esols)
py2c_copy_dobldobl_container_to_start_system()
py2c_copy_dobldobl_container_to_start_solutions()
py2c_dobldobl_cascade_homotopy()
py2c_solve_by_dobldobl_homotopy_continuation(tasks)
py2c_solcon_clear_dobldobl_solutions()
py2c_copy_dobldobl_target_solutions_to_container()
return load_dobldobl_solutions()
def double_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 double 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_dobldobl_container_to_start_system
from phcpy.phcpy2c2 import py2c_copy_dobldobl_container_to_start_solutions
from phcpy.phcpy2c2 import py2c_dobldobl_cascade_homotopy
from phcpy.phcpy2c2 import py2c_solve_by_dobldobl_homotopy_continuation
from phcpy.phcpy2c2 import py2c_solcon_clear_dobldobl_solutions
from phcpy.phcpy2c2 import py2c_copy_dobldobl_target_solutions_to_container
from phcpy.interface import store_dobldobl_witness_set
from phcpy.interface import load_dobldobl_solutions
store_dobldobl_witness_set(len(embsys), dim, embsys, esols)
py2c_copy_dobldobl_container_to_start_system()
py2c_copy_dobldobl_container_to_start_solutions()
py2c_dobldobl_cascade_homotopy()
py2c_solve_by_dobldobl_homotopy_continuation(tasks)
py2c_solcon_clear_dobldobl_solutions()
py2c_copy_dobldobl_target_solutions_to_container()
return load_dobldobl_solutions()
def dobldobl_start_diagonal_cascade(gamma=0, tasks=0):
r"""
Does the path tracking to start a diagonal cascade in double double
precision. For this to work, the functions dobldobl_diagonal_homotopy
and dobldobl_diagonal_cascade_solutions must be executed successfully.
If *gamma* equals 0 on input, then a random *gamma* constant is generated,
otherwise, the given complex *gamma* will be used in the homotopy.
Multitasking is available, and activated by the *tasks* parameter.
Returns the target (system and its corresponding) solutions.
"""
from phcpy.phcpy2c2 import py2c_create_dobldobl_homotopy
from phcpy.phcpy2c2 import py2c_create_dobldobl_homotopy_with_gamma
from phcpy.phcpy2c2 import py2c_solve_by_dobldobl_homotopy_continuation
from phcpy.phcpy2c2 import py2c_solcon_clear_dobldobl_solutions
from phcpy.phcpy2c2 import py2c_syscon_clear_dobldobl_system
from phcpy.phcpy2c2 import py2c_copy_dobldobl_target_solutions_to_container
from phcpy.phcpy2c2 import py2c_copy_dobldobl_target_system_to_container
from phcpy.interface import load_dobldobl_solutions
from phcpy.interface import load_dobldobl_system
if (gamma == 0):
py2c_create_dobldobl_homotopy()
else:
py2c_create_dobldobl_homotopy_with_gamma(gamma.real, gamma.imag)
py2c_solve_by_dobldobl_homotopy_continuation(tasks)
py2c_solcon_clear_dobldobl_solutions()
py2c_syscon_clear_dobldobl_system()
py2c_copy_dobldobl_target_solutions_to_container()
# from phcpy.phcpy2c2 import py2c_write_dobldobl_target_system
# print 'the dobldobl target system :'
# py2c_write_dobldobl_target_system()
py2c_copy_dobldobl_target_system_to_container()
tsys = load_dobldobl_system()
sols = load_dobldobl_solutions()
return (tsys, sols)
def dobldobl_start_diagonal_cascade(gamma=0, tasks=0):
r"""
Does the path tracking to start a diagonal cascade in double double
precision. For this to work, the functions dobldobl_diagonal_homotopy
and dobldobl_diagonal_cascade_solutions must be executed successfully.
If *gamma* equals 0 on input, then a random *gamma* constant is generated,
otherwise, the given complex *gamma* will be used in the homotopy.
Multitasking is available, and activated by the *tasks* parameter.
Returns the target (system and its corresponding) solutions.
"""
from phcpy.phcpy2c2 import py2c_create_dobldobl_homotopy
from phcpy.phcpy2c2 import py2c_create_dobldobl_homotopy_with_gamma
from phcpy.phcpy2c2 import py2c_solve_by_dobldobl_homotopy_continuation
from phcpy.phcpy2c2 import py2c_solcon_clear_dobldobl_solutions
from phcpy.phcpy2c2 import py2c_syscon_clear_dobldobl_system
from phcpy.phcpy2c2 import py2c_copy_dobldobl_target_solutions_to_container
from phcpy.phcpy2c2 import py2c_copy_dobldobl_target_system_to_container
from phcpy.interface import load_dobldobl_solutions
from phcpy.interface import load_dobldobl_system
if(gamma == 0):
py2c_create_dobldobl_homotopy()
else:
py2c_create_dobldobl_homotopy_with_gamma(gamma.real, gamma.imag)
py2c_solve_by_dobldobl_homotopy_continuation(tasks)
py2c_solcon_clear_dobldobl_solutions()
py2c_syscon_clear_dobldobl_system()
py2c_copy_dobldobl_target_solutions_to_container()
# from phcpy.phcpy2c2 import py2c_write_dobldobl_target_system
# print 'the dobldobl target system :'
# py2c_write_dobldobl_target_system()
py2c_copy_dobldobl_target_system_to_container()
tsys = load_dobldobl_system()
sols = load_dobldobl_solutions()
return (tsys, sols)
def double_double_track(target, start, sols, gamma=0, tasks=0):
r"""
Does path tracking in double double precision.
On input are a target system, a start system with solutions,
optionally a (random) gamma constant and the number of tasks.
The default value zero for *tasks* indicates no multithreading.
The number of tasks in the multithreading is given by *tasks*.
The *target* is a list of strings representing the polynomials
of the target system (which has to be solved).
The *start* is a list of strings representing the polynomials
of the start system with known solutions in *sols*.
The *sols* is a list of strings representing start solutions.
By default, a random *gamma* constant is generated,
otherwise *gamma* must be a nonzero complex constant.
On return are the string representations of the solutions
computed at the end of the paths.
"""
from phcpy.phcpy2c2 import py2c_copy_dobldobl_container_to_target_system
from phcpy.phcpy2c2 import py2c_copy_dobldobl_container_to_start_system
from phcpy.phcpy2c2 import py2c_copy_dobldobl_container_to_start_solutions
from phcpy.phcpy2c2 import py2c_create_dobldobl_homotopy
from phcpy.phcpy2c2 import py2c_create_dobldobl_homotopy_with_gamma
from phcpy.phcpy2c2 import py2c_solve_by_dobldobl_homotopy_continuation
from phcpy.phcpy2c2 import py2c_solcon_clear_dobldobl_solutions
from phcpy.phcpy2c2 import py2c_copy_dobldobl_target_solutions_to_container
from phcpy.interface import store_dobldobl_system
from phcpy.interface import store_dobldobl_solutions
from phcpy.interface import load_dobldobl_solutions
from phcpy.solver import number_of_symbols
dim = number_of_symbols(start)
store_dobldobl_system(target, nbvar=dim)
py2c_copy_dobldobl_container_to_target_system()
store_dobldobl_system(start, nbvar=dim)
py2c_copy_dobldobl_container_to_start_system()
# py2c_clear_dobldobl_homotopy()
if(gamma == 0):
py2c_create_dobldobl_homotopy()
else:
py2c_create_dobldobl_homotopy_with_gamma(gamma.real, gamma.imag)
store_dobldobl_solutions(dim, sols)
py2c_copy_dobldobl_container_to_start_solutions()
py2c_solve_by_dobldobl_homotopy_continuation(tasks)
py2c_solcon_clear_dobldobl_solutions()
py2c_copy_dobldobl_target_solutions_to_container()
return load_dobldobl_solutions()
def double_double_track(target, start, sols, gamma=0, tasks=0):
"""
Does path tracking in double double precision.
On input are a target system, a start system with solutions,
optionally a (random) gamma constant and the number of tasks.
The target is a list of strings representing the polynomials
of the target system (which has to be solved).
The start is a list of strings representing the polynomials
of the start system with known solutions in sols.
The sols is a list of strings representing start solutions.
By default, a random gamma constant is generated,
otherwise gamma must be a nonzero complex constant.
On return are the string representations of the solutions
computed at the end of the paths.
"""
from phcpy.phcpy2c2 import py2c_copy_dobldobl_container_to_target_system
from phcpy.phcpy2c2 import py2c_copy_dobldobl_container_to_start_system
from phcpy.phcpy2c2 import py2c_copy_dobldobl_container_to_start_solutions
from phcpy.phcpy2c2 import py2c_create_dobldobl_homotopy
from phcpy.phcpy2c2 import py2c_create_dobldobl_homotopy_with_gamma
from phcpy.phcpy2c2 import py2c_solve_by_dobldobl_homotopy_continuation
from phcpy.phcpy2c2 import py2c_solcon_clear_dobldobl_solutions
from phcpy.phcpy2c2 import py2c_copy_dobldobl_target_solutions_to_container
from phcpy.interface import store_dobldobl_system
from phcpy.interface import store_dobldobl_solutions
from phcpy.interface import load_dobldobl_solutions
from phcpy.solver import number_of_symbols
dim = number_of_symbols(start)
store_dobldobl_system(target, nbvar=dim)
py2c_copy_dobldobl_container_to_target_system()
store_dobldobl_system(start, nbvar=dim)
py2c_copy_dobldobl_container_to_start_system()
# py2c_clear_dobldobl_homotopy()
if(gamma == 0):
py2c_create_dobldobl_homotopy()
else:
py2c_create_dobldobl_homotopy_with_gamma(gamma.real, gamma.imag)
store_dobldobl_solutions(dim, sols)
py2c_copy_dobldobl_container_to_start_solutions()
py2c_solve_by_dobldobl_homotopy_continuation(tasks)
py2c_solcon_clear_dobldobl_solutions()
py2c_copy_dobldobl_target_solutions_to_container()
return load_dobldobl_solutions()