Example #1
0
def multiprecision_track(target, start, sols, gamma=0, decimals=80):
    """
    Does path tracking with multiprecision.
    On input are a target system, a start system with solutions,
    and optionally a (random) gamma constant.
    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 decimal places in the working precision is
    given by the value of decimals.
    On return are the string representations of the solutions
    computed at the end of the paths.
    """
    from phcpy.phcpy2c3 import py2c_copy_multprec_container_to_target_system
    from phcpy.phcpy2c3 import py2c_copy_multprec_container_to_start_system
    from phcpy.phcpy2c3 import py2c_copy_multprec_container_to_start_solutions
    from phcpy.phcpy2c3 import py2c_create_multprec_homotopy
    from phcpy.phcpy2c3 import py2c_create_multprec_homotopy_with_gamma
    from phcpy.phcpy2c3 import py2c_solve_by_multprec_homotopy_continuation
    from phcpy.phcpy2c3 import py2c_solcon_clear_multprec_solutions
    from phcpy.phcpy2c3 import py2c_copy_multprec_target_solutions_to_container
    from phcpy.interface import store_multprec_system
    from phcpy.interface import store_multprec_solutions
    from phcpy.interface import load_multprec_solutions
    store_multprec_system(target, decimals)
    py2c_copy_multprec_container_to_target_system()
    store_multprec_system(start, decimals)
    py2c_copy_multprec_container_to_start_system()
    # py2c_clear_multprec_homotopy()
    if (gamma == 0):
        py2c_create_multprec_homotopy()
    else:
        py2c_create_multprec_homotopy_with_gamma(gamma.real, gamma.imag)
    dim = len(start)
    store_multprec_solutions(dim, sols)
    py2c_copy_multprec_container_to_start_solutions()
    py2c_solve_by_multprec_homotopy_continuation(decimals)
    py2c_solcon_clear_multprec_solutions()
    py2c_copy_multprec_target_solutions_to_container()
    return load_multprec_solutions()
Example #2
0
def multiprecision_track(target, start, sols, gamma=0, decimals=80):
    r"""
    Does path tracking with multiprecision.
    On input are a target system, a start system with solutions,
    and optionally a (random) *gamma* constant.
    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 decimal places in the working precision is
    given by the value of *decimals*.
    On return are the string representations of the solutions
    computed at the end of the paths.
    """
    from phcpy.phcpy2c3 import py2c_copy_multprec_container_to_target_system
    from phcpy.phcpy2c3 import py2c_copy_multprec_container_to_start_system
    from phcpy.phcpy2c3 import py2c_copy_multprec_container_to_start_solutions
    from phcpy.phcpy2c3 import py2c_create_multprec_homotopy
    from phcpy.phcpy2c3 import py2c_create_multprec_homotopy_with_gamma
    from phcpy.phcpy2c3 import py2c_solve_by_multprec_homotopy_continuation
    from phcpy.phcpy2c3 import py2c_solcon_clear_multprec_solutions
    from phcpy.phcpy2c3 import py2c_copy_multprec_target_solutions_to_container
    from phcpy.interface import store_multprec_system
    from phcpy.interface import store_multprec_solutions
    from phcpy.interface import load_multprec_solutions
    store_multprec_system(target, decimals)
    py2c_copy_multprec_container_to_target_system()
    store_multprec_system(start, decimals)
    py2c_copy_multprec_container_to_start_system()
    # py2c_clear_multprec_homotopy()
    if(gamma == 0):
        py2c_create_multprec_homotopy()
    else:
        py2c_create_multprec_homotopy_with_gamma(gamma.real, gamma.imag)
    dim = len(start)
    store_multprec_solutions(dim, sols)
    py2c_copy_multprec_container_to_start_solutions()
    py2c_solve_by_multprec_homotopy_continuation(decimals)
    py2c_solcon_clear_multprec_solutions()
    py2c_copy_multprec_target_solutions_to_container()
    return load_multprec_solutions()
Example #3
0
def initialize_multprec_tracker(target, start, fixedgamma=True, decimals=100):
    """
    Initializes a path tracker with a generator for a target
    and start system given in arbitrary multiprecision, with
    the number of decimal places in the working precision
    given by the value of decimals.
    If fixedgamma, then gamma will be a fixed default value,
    otherwise, a random complex constant for gamma is generated.
    """
    from phcpy.phcpy2c3 import py2c_copy_multprec_container_to_target_system
    from phcpy.phcpy2c3 import py2c_copy_multprec_container_to_start_system
    from phcpy.phcpy2c3 import py2c_initialize_multprec_homotopy
    from phcpy.interface import store_multprec_system
    store_multprec_system(target, decimals)
    py2c_copy_multprec_container_to_target_system()
    store_multprec_system(start, decimals)
    py2c_copy_multprec_container_to_start_system()
    if fixedgamma:
        return py2c_initialize_multprec_homotopy(1, decimals)
    else:
        return py2c_initialize_multprec_homotopy(0, decimals)
Example #4
0
def initialize_multprec_tracker(target, start, fixedgamma=True, decimals=100):
    r"""
    Initializes a path tracker with a generator for a *target*
    and *start* system given in arbitrary multiprecision,
    with the number of decimal places in the working precision
    given by the value of *decimals*.
    If *fixedgamma*, then gamma will be a fixed default value,
    otherwise, a random complex constant for gamma is generated.
    """
    from phcpy.phcpy2c3 import py2c_copy_multprec_container_to_target_system
    from phcpy.phcpy2c3 import py2c_copy_multprec_container_to_start_system
    from phcpy.phcpy2c3 import py2c_initialize_multprec_homotopy
    from phcpy.interface import store_multprec_system
    store_multprec_system(target, decimals)
    py2c_copy_multprec_container_to_target_system()
    store_multprec_system(start, decimals)
    py2c_copy_multprec_container_to_start_system()
    if fixedgamma:
        return py2c_initialize_multprec_homotopy(1, decimals)
    else:
        return py2c_initialize_multprec_homotopy(0, decimals)