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.phcpy2c3 import py2c_copy_standard_container_to_start_system
from phcpy.phcpy2c3 import py2c_copy_standard_container_to_start_solutions
from phcpy.phcpy2c3 import py2c_standard_cascade_homotopy
from phcpy.phcpy2c3 import py2c_solve_by_standard_homotopy_continuation
from phcpy.phcpy2c3 import py2c_solcon_clear_standard_solutions
from phcpy.phcpy2c3 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_track(target, start, sols, gamma=0, tasks=0):
r"""
Does path tracking with standard 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.
The number of tasks in the multithreading is defined by *tasks*.
The default zero value for *tasks* indicates no multithreading.
On return are the string representations of the solutions
computed at the end of the paths.
"""
from phcpy.phcpy2c3 import py2c_copy_standard_container_to_target_system
from phcpy.phcpy2c3 import py2c_copy_standard_container_to_start_system
from phcpy.phcpy2c3 import py2c_copy_standard_container_to_start_solutions
from phcpy.phcpy2c3 import py2c_create_standard_homotopy
from phcpy.phcpy2c3 import py2c_create_standard_homotopy_with_gamma
from phcpy.phcpy2c3 import py2c_solve_by_standard_homotopy_continuation
from phcpy.phcpy2c3 import py2c_solcon_clear_standard_solutions
from phcpy.phcpy2c3 import py2c_copy_standard_target_solutions_to_container
from phcpy.interface import store_standard_system
from phcpy.interface import store_standard_solutions
from phcpy.interface import load_standard_solutions
from phcpy.solver import number_of_symbols
dim = number_of_symbols(start)
store_standard_system(target, nbvar=dim)
py2c_copy_standard_container_to_target_system()
store_standard_system(start, nbvar=dim)
py2c_copy_standard_container_to_start_system()
# py2c_clear_standard_homotopy()
if(gamma == 0):
py2c_create_standard_homotopy()
else:
py2c_create_standard_homotopy_with_gamma(gamma.real, gamma.imag)
store_standard_solutions(dim, sols)
py2c_copy_standard_container_to_start_solutions()
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_track(target, start, sols, gamma=0, tasks=0):
"""
Does path tracking with standard 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.phcpy2c3 import py2c_copy_standard_container_to_target_system
from phcpy.phcpy2c3 import py2c_copy_standard_container_to_start_system
from phcpy.phcpy2c3 import py2c_copy_standard_container_to_start_solutions
from phcpy.phcpy2c3 import py2c_create_standard_homotopy
from phcpy.phcpy2c3 import py2c_create_standard_homotopy_with_gamma
from phcpy.phcpy2c3 import py2c_solve_by_standard_homotopy_continuation
from phcpy.phcpy2c3 import py2c_solcon_clear_standard_solutions
from phcpy.phcpy2c3 import py2c_copy_standard_target_solutions_to_container
from phcpy.interface import store_standard_system
from phcpy.interface import store_standard_solutions
from phcpy.interface import load_standard_solutions
from phcpy.solver import number_of_symbols
dim = number_of_symbols(start)
store_standard_system(target, nbvar=dim)
py2c_copy_standard_container_to_target_system()
store_standard_system(start, nbvar=dim)
py2c_copy_standard_container_to_start_system()
# py2c_clear_standard_homotopy()
if (gamma == 0):
py2c_create_standard_homotopy()
else:
py2c_create_standard_homotopy_with_gamma(gamma.real, gamma.imag)
store_standard_solutions(dim, sols)
py2c_copy_standard_container_to_start_solutions()
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_diagonal_homotopy(dim1, sys1, esols1, dim2, sys2, esols2):
r"""
Defines a diagonal homotopy to intersect the witness sets defined
by (*sys1*, *esols1*) and (*sys2*, *esols2*), respectively of dimensions
*dim1* and *dim2*. The systems *sys1* and *sys2* are assumed to be square
and with as many slack variables as the dimension of the solution sets.
The data is stored in standard double precision.
"""
from phcpy.interface import store_standard_system as storesys
from phcpy.interface import store_standard_solutions as storesols
from phcpy.phcpy2c3 import py2c_copy_standard_container_to_target_system
from phcpy.phcpy2c3 import py2c_copy_standard_container_to_target_solutions
from phcpy.phcpy2c3 import py2c_copy_standard_container_to_start_system
from phcpy.phcpy2c3 import py2c_copy_standard_container_to_start_solutions
from phcpy.phcpy2c3 import py2c_standard_diagonal_homotopy
from phcpy.phcpy2c3 import py2c_syscon_number_of_symbols
from phcpy.phcpy2c3 import py2c_syscon_string_of_symbols
from phcpy.phcpy2c3 import py2c_diagonal_symbols_doubler
storesys(sys1)
symbols = py2c_syscon_string_of_symbols()
nbsymbs = py2c_syscon_number_of_symbols()
print('number of symbols :', nbsymbs)
print('names of variables :', symbols)
storesols(len(sys1), esols1)
if(dim1 >= dim2):
py2c_copy_standard_container_to_target_system()
py2c_copy_standard_container_to_target_solutions()
else:
py2c_copy_standard_container_to_start_system()
py2c_copy_standard_container_to_start_solutions()
storesys(sys2)
storesols(len(sys2), esols2)
if(dim1 >= dim2):
py2c_copy_standard_container_to_start_system()
py2c_copy_standard_container_to_start_solutions()
else:
py2c_copy_standard_container_to_target_system()
py2c_copy_standard_container_to_target_solutions()
if(dim1 >= dim2):
py2c_standard_diagonal_homotopy(dim1, dim2)
else:
py2c_standard_diagonal_homotopy(dim2, dim1)
py2c_diagonal_symbols_doubler(nbsymbs-dim1, dim1, len(symbols), symbols)
def standard_track(target, start, sols, filename="", verbose=False):
"""
Wraps the tracker for Pade continuation in standard double precision.
On input are a target system, a start system with solutions,
optionally: a string *filename* and the *verbose* flag.
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.
On return are the string representations of the solutions
computed at the end of the paths.
"""
from phcpy.phcpy2c3 import py2c_copy_standard_container_to_target_system
from phcpy.phcpy2c3 import py2c_copy_standard_container_to_start_system
from phcpy.phcpy2c3 import py2c_copy_standard_container_to_start_solutions
from phcpy.phcpy2c3 import py2c_create_standard_homotopy_with_gamma
from phcpy.phcpy2c3 import py2c_clear_standard_operations_data
from phcpy.interface import store_standard_system
from phcpy.interface import store_standard_solutions
from phcpy.interface import load_standard_solutions
from phcpy.solver import number_of_symbols
from phcpy.phcpy2c3 import py2c_padcon_standard_track
dim = number_of_symbols(start)
store_standard_system(target, nbvar=dim)
py2c_copy_standard_container_to_target_system()
store_standard_system(start, nbvar=dim)
py2c_copy_standard_container_to_start_system()
store_standard_solutions(dim, sols)
py2c_copy_standard_container_to_start_solutions()
(regamma, imgamma) = get_homotopy_continuation_parameter(1)
py2c_create_standard_homotopy_with_gamma(regamma, imgamma)
nbc = len(filename)
fail = py2c_padcon_standard_track(nbc, filename, int(verbose))
# py2c_clear_standard_operations_data()
return load_standard_solutions()