def newton_step(system, solutions, precision='d', decimals=100): """ Applies one Newton step to the solutions of the system. For each solution, prints its last line of diagnostics. Four levels of precision are supported: d : standard double precision (1.1e-15 or 2^(-53)), dd : double double precision (4.9e-32 or 2^(-104)), qd : quad double precision (1.2e-63 or 2^(-209)). mp : arbitrary precision, where the number of decimal places in the working precision is determined by decimals. """ dim = number_of_symbols(system) if (precision == 'd'): from phcpy.interface import store_standard_system from phcpy.interface import store_standard_solutions from phcpy.interface import load_standard_solutions store_standard_system(system, nbvar=dim) store_standard_solutions(dim, solutions) from phcpy.phcpy2c3 import py2c_standard_Newton_step py2c_standard_Newton_step() result = load_standard_solutions() elif (precision == 'dd'): from phcpy.interface import store_dobldobl_system from phcpy.interface import store_dobldobl_solutions from phcpy.interface import load_dobldobl_solutions store_dobldobl_system(system, nbvar=dim) store_dobldobl_solutions(dim, solutions) from phcpy.phcpy2c3 import py2c_dobldobl_Newton_step py2c_dobldobl_Newton_step() result = load_dobldobl_solutions() elif (precision == 'qd'): from phcpy.interface import store_quaddobl_system from phcpy.interface import store_quaddobl_solutions from phcpy.interface import load_quaddobl_solutions store_quaddobl_system(system, nbvar=dim) store_quaddobl_solutions(dim, solutions) from phcpy.phcpy2c3 import py2c_quaddobl_Newton_step py2c_quaddobl_Newton_step() result = load_quaddobl_solutions() elif (precision == 'mp'): from phcpy.interface import store_multprec_system from phcpy.interface import store_multprec_solutions from phcpy.interface import load_multprec_solutions store_multprec_system(system, decimals, nbvar=dim) store_multprec_solutions(dim, solutions) from phcpy.phcpy2c3 import py2c_multprec_Newton_step py2c_multprec_Newton_step(decimals) result = load_multprec_solutions() else: print('wrong argument for precision') return None for sol in result: strsol = sol.split('\n') print(strsol[-1]) return result
def newton_step(system, solutions, precision='d', decimals=100): """ Applies one Newton step to the solutions of the system. For each solution, prints its last line of diagnostics. Four levels of precision are supported: d : standard double precision (1.1e-15 or 2^(-53)), dd : double double precision (4.9e-32 or 2^(-104)), qd : quad double precision (1.2e-63 or 2^(-209)). mp : arbitrary precision, where the number of decimal places in the working precision is determined by decimals. """ if(precision == 'd'): from phcpy.interface import store_standard_system from phcpy.interface import store_standard_solutions from phcpy.interface import load_standard_solutions store_standard_system(system) store_standard_solutions(len(system), solutions) from phcpy.phcpy2c3 import py2c_standard_Newton_step py2c_standard_Newton_step() result = load_standard_solutions() elif(precision == 'dd'): from phcpy.interface import store_dobldobl_system from phcpy.interface import store_dobldobl_solutions from phcpy.interface import load_dobldobl_solutions store_dobldobl_system(system) store_dobldobl_solutions(len(system), solutions) from phcpy.phcpy2c3 import py2c_dobldobl_Newton_step py2c_dobldobl_Newton_step() result = load_dobldobl_solutions() elif(precision == 'qd'): from phcpy.interface import store_quaddobl_system from phcpy.interface import store_quaddobl_solutions from phcpy.interface import load_quaddobl_solutions store_quaddobl_system(system) store_quaddobl_solutions(len(system), solutions) from phcpy.phcpy2c3 import py2c_quaddobl_Newton_step py2c_quaddobl_Newton_step() result = load_quaddobl_solutions() elif(precision == 'mp'): from phcpy.interface import store_multprec_system from phcpy.interface import store_multprec_solutions from phcpy.interface import load_multprec_solutions store_multprec_system(system, decimals) store_multprec_solutions(len(system), solutions) from phcpy.phcpy2c3 import py2c_multprec_Newton_step py2c_multprec_Newton_step(decimals) result = load_multprec_solutions() else: print('wrong argument for precision') return None for sol in result: strsol = sol.split('\n') print(strsol[-1]) return result
def multprec_usolve(pol, mxi, eps, decimals): """ Applies the method of Durand-Kerner (aka Weierstrass) to the polynomial in the string pol, in arbitrary multiprecision, the number of decimal places in the precision is in decimals. The maximum number of iterations is in mxi, the requirement on the accuracy in eps. """ from phcpy.phcpy2c3 import py2c_usolve_multprec from phcpy.interface import store_multprec_system, load_multprec_solutions store_multprec_system([pol], decimals) nit = py2c_usolve_multprec(decimals, mxi, eps) rts = load_multprec_solutions() return (nit, rts)
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.phcpy2c2 import py2c_copy_multprec_container_to_target_system from phcpy.phcpy2c2 import py2c_copy_multprec_container_to_start_system from phcpy.phcpy2c2 import py2c_copy_multprec_container_to_start_solutions from phcpy.phcpy2c2 import py2c_create_multprec_homotopy from phcpy.phcpy2c2 import py2c_create_multprec_homotopy_with_gamma from phcpy.phcpy2c2 import py2c_solve_by_multprec_homotopy_continuation from phcpy.phcpy2c2 import py2c_solcon_clear_multprec_solutions from phcpy.phcpy2c2 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()
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.phcpy2c2 import py2c_copy_multprec_container_to_target_system from phcpy.phcpy2c2 import py2c_copy_multprec_container_to_start_system from phcpy.phcpy2c2 import py2c_copy_multprec_container_to_start_solutions from phcpy.phcpy2c2 import py2c_create_multprec_homotopy from phcpy.phcpy2c2 import py2c_create_multprec_homotopy_with_gamma from phcpy.phcpy2c2 import py2c_solve_by_multprec_homotopy_continuation from phcpy.phcpy2c2 import py2c_solcon_clear_multprec_solutions from phcpy.phcpy2c2 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()
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.phcpy2c2 import py2c_copy_multprec_container_to_target_system from phcpy.phcpy2c2 import py2c_copy_multprec_container_to_start_system from phcpy.phcpy2c2 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)
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)