def quad_double_cascade_step(dim, embsys, esols, tasks=0):
r"""
Given in *embsys* an embedded polynomial system and
solutions with nonzero slace variables in *esols*, does one step
in the homotopy cascade, with quad 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_quaddobl_container_to_start_system
from phcpy.phcpy2c2 import py2c_copy_quaddobl_container_to_start_solutions
from phcpy.phcpy2c2 import py2c_quaddobl_cascade_homotopy
from phcpy.phcpy2c2 import py2c_solve_by_quaddobl_homotopy_continuation
from phcpy.phcpy2c2 import py2c_solcon_clear_quaddobl_solutions
from phcpy.phcpy2c2 import py2c_copy_quaddobl_target_solutions_to_container
from phcpy.interface import store_quaddobl_witness_set
from phcpy.interface import load_quaddobl_solutions
store_quaddobl_system(len(embsys), dim, embsys, esols)
py2c_copy_quaddobl_container_to_start_system()
py2c_copy_quaddobl_container_to_start_solutions()
py2c_quaddobl_cascade_homotopy()
py2c_solve_by_quaddobl_homotopy_continuation(tasks)
py2c_solcon_clear_quaddobl_solutions()
py2c_copy_quaddobl_target_solutions_to_container()
return load_quaddobl_solutions()
def quaddobl_laursys_solve(pols, topdim=-1, \
filter=True, factor=True, tasks=0, verbose=True):
"""
Runs the cascades of homotopies on the Laurent polynomial system in pols
in quad double precision. The default top dimension topdim
is the number of variables in pols minus one.
"""
from phcpy.phcpy2c3 import py2c_quaddobl_laursys_solve
from phcpy.phcpy2c3 import py2c_copy_quaddobl_laursys_witset
from phcpy.solver import number_of_symbols
from phcpy.interface import store_quaddobl_laurent_system
from phcpy.interface import load_quaddobl_laurent_system
from phcpy.interface import load_quaddobl_solutions
dim = number_of_symbols(pols)
if(topdim == -1):
topdim = dim - 1
fail = store_quaddobl_laurent_system(pols, nbvar=dim)
fail = py2c_quaddobl_laursys_solve(tasks,topdim, \
int(filter),int(factor),int(verbose))
witsols = []
for soldim in range(0, topdim+1):
fail = py2c_copy_quaddobl_laursys_witset(soldim)
witset = (load_quaddobl_laurent_system(), load_quaddobl_solutions())
witsols.append(witset)
return witsols
def quaddobl_solve(pols, silent=False, tasks=0):
"""
Calls the blackbox solver. On input in pols is a list of strings.
By default, the solver will print to screen the computed root counts.
To make the solver silent, set the flag silent to True.
The number of tasks for multithreading is given by tasks.
The solving happens in quad double precision arithmetic.
"""
from phcpy.phcpy2c3 import py2c_syscon_clear_quaddobl_Laurent_system
from phcpy.phcpy2c3 \
import py2c_syscon_initialize_number_of_quaddobl_Laurentials
from phcpy.phcpy2c3 import py2c_syscon_store_quaddobl_Laurential
from phcpy.phcpy2c3 import py2c_solcon_clear_quaddobl_solutions
from phcpy.phcpy2c3 import py2c_solve_quaddobl_Laurent_system
from phcpy.interface import load_quaddobl_solutions
py2c_syscon_clear_quaddobl_Laurent_system()
py2c_solcon_clear_quaddobl_solutions()
dim = len(pols)
py2c_syscon_initialize_number_of_quaddobl_Laurentials(dim)
for ind in range(0, dim):
pol = pols[ind]
nchar = len(pol)
py2c_syscon_store_quaddobl_Laurential(nchar, dim, ind+1, pol)
py2c_solve_quaddobl_Laurent_system(silent, tasks)
return load_quaddobl_solutions()
def quaddobl_start_diagonal_cascade(gamma=0, tasks=0):
r"""
Does the path tracking to start a diagonal cascade in quad double
precision. For this to work, the functions quaddobl_diagonal_homotopy
and quaddobl_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 is activated by the *tasks* parameter.
Returns the target (system and its corresponding) solutions.
"""
from phcpy.phcpy2c2 import py2c_create_quaddobl_homotopy
from phcpy.phcpy2c2 import py2c_create_quaddobl_homotopy_with_gamma
from phcpy.phcpy2c2 import py2c_solve_by_quaddobl_homotopy_continuation
from phcpy.phcpy2c2 import py2c_solcon_clear_quaddobl_solutions
from phcpy.phcpy2c2 import py2c_syscon_clear_quaddobl_system
from phcpy.phcpy2c2 import py2c_copy_quaddobl_target_solutions_to_container
from phcpy.phcpy2c2 import py2c_copy_quaddobl_target_system_to_container
from phcpy.interface import load_quaddobl_solutions
from phcpy.interface import load_quaddobl_system
if(gamma == 0):
py2c_create_quaddobl_homotopy()
else:
py2c_create_quaddobl_homotopy_with_gamma(gamma.real, gamma.imag)
py2c_solve_by_quaddobl_homotopy_continuation(tasks)
py2c_solcon_clear_quaddobl_solutions()
py2c_syscon_clear_quaddobl_system()
py2c_copy_quaddobl_target_solutions_to_container()
# from phcpy.phcpy2c2 import py2c_write_quaddobl_target_system
# print 'the quaddobl target system :'
# py2c_write_quaddobl_target_system()
py2c_copy_quaddobl_target_system_to_container()
tsys = load_quaddobl_system()
sols = load_quaddobl_solutions()
return (tsys, sols)
def quaddobl_littlewood_richardson_homotopies(
ndim, kdim, brackets, verbose=True, vrfcnd=False, minrep=True, tosqr=False, outputfilename=""
):
r"""
In n-dimensional space we consider k-dimensional planes,
subject to intersection conditions represented by brackets.
The parameters *ndim* and *kdim* give values for n and k respectively.
The parameter brackets is a list of brackets. A bracket is a list
of as many natural numbers (in the range 1..*ndim*) as *kdim*.
The Littlewood-Richardson homotopies compute k-planes that
meet the flags at spaces of dimensions prescribed by the brackets,
in quad double precision. Four options are passed as Booleans:
*verbose*: for adding extra output during computations,
*vrfcnd*: for extra diagnostic verification of Schubert conditions,
*minrep*: for a minimial representation of the problem formulation,
*tosqr*: to square the overdetermined systems.
On return is a 4-tuple. The first item of the tuple is the
formal root count, sharp for general flags, then as second
item the coordinates of the flags. The coordinates of the
flags are stored row wise in a list of real and imaginary parts.
The third and fourth item of the tuple on return are respectively
the polynomial system that has been solved and its solutions.
The length of the list of solution should match the root count.
"""
from phcpy.phcpy2c2 import py2c_solcon_clear_quaddobl_solutions
from phcpy.phcpy2c2 import py2c_schubert_quaddobl_littlewood_richardson_homotopies as qdlrhom
from phcpy.interface import load_quaddobl_solutions, load_quaddobl_system
py2c_solcon_clear_quaddobl_solutions()
nbc = len(brackets)
cds = ""
for bracket in brackets:
for num in bracket:
cds = cds + " " + str(num)
# print 'the condition string :', cds
(roco, sflags) = qdlrhom(
ndim,
kdim,
nbc,
len(cds),
cds,
int(verbose),
int(vrfcnd),
int(minrep),
int(tosqr),
len(outputfilename),
outputfilename,
)
rflags = eval(sflags)
flgs = []
for k in range(len(rflags) / 8):
flgs.append(complex(rflags[2 * k], rflags[2 * k + 4]))
fsys = load_quaddobl_system()
sols = load_quaddobl_solutions()
return (roco, flgs, fsys, sols)
def quad_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 quad 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_quaddobl_container_to_start_system
from phcpy.phcpy2c3 import py2c_copy_quaddobl_container_to_start_solutions
from phcpy.phcpy2c3 import py2c_quaddobl_cascade_homotopy
from phcpy.phcpy2c3 import py2c_solve_by_quaddobl_homotopy_continuation
from phcpy.phcpy2c3 import py2c_solcon_clear_quaddobl_solutions
from phcpy.phcpy2c3 import py2c_copy_quaddobl_target_solutions_to_container
from phcpy.interface import store_quaddobl_witness_set
from phcpy.interface import load_quaddobl_solutions
store_quaddobl_witness_set(len(embsys), dim, embsys, esols)
py2c_copy_quaddobl_container_to_start_system()
py2c_copy_quaddobl_container_to_start_solutions()
py2c_quaddobl_cascade_homotopy()
py2c_solve_by_quaddobl_homotopy_continuation(tasks)
py2c_solcon_clear_quaddobl_solutions()
py2c_copy_quaddobl_target_solutions_to_container()
return load_quaddobl_solutions()
def newton_laurent_step(system, solutions, precision='d', decimals=100):
"""
Applies one Newton step to the solutions of the Laurent 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_laurent_system
from phcpy.interface import store_standard_solutions
from phcpy.interface import load_standard_solutions
store_standard_laurent_system(system, nbvar=dim)
store_standard_solutions(dim, solutions)
from phcpy.phcpy2c3 import py2c_standard_Newton_Laurent_step
py2c_standard_Newton_Laurent_step()
result = load_standard_solutions()
elif (precision == 'dd'):
from phcpy.interface import store_dobldobl_laurent_system
from phcpy.interface import store_dobldobl_solutions
from phcpy.interface import load_dobldobl_solutions
store_dobldobl_laurent_system(system, nbvar=dim)
store_dobldobl_solutions(dim, solutions)
from phcpy.phcpy2c3 import py2c_dobldobl_Newton_Laurent_step
py2c_dobldobl_Newton_Laurent_step()
result = load_dobldobl_solutions()
elif (precision == 'qd'):
from phcpy.interface import store_quaddobl_laurent_system
from phcpy.interface import store_quaddobl_solutions
from phcpy.interface import load_quaddobl_solutions
store_quaddobl_laurent_system(system, nbvar=dim)
store_quaddobl_solutions(dim, solutions)
from phcpy.phcpy2c3 import py2c_quaddobl_Newton_Laurent_step
py2c_quaddobl_Newton_Laurent_step()
result = load_quaddobl_solutions()
elif (precision == 'mp'):
from phcpy.interface import store_multprec_laurent_system
from phcpy.interface import store_multprec_solutions
from phcpy.interface import load_multprec_solutions
store_multprec_laurent_system(system, decimals, nbvar=dim)
store_multprec_solutions(dim, solutions)
from phcpy.phcpy2c3 import py2c_multprec_Newton_Laurent_step
py2c_multprec_Newton_Laurent_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_laurent_step(system, solutions, precision='d', decimals=100):
"""
Applies one Newton step to the solutions of the Laurent 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_laurent_system
from phcpy.interface import store_standard_solutions
from phcpy.interface import load_standard_solutions
store_standard_laurent_system(system)
store_standard_solutions(len(system), solutions)
from phcpy.phcpy2c3 import py2c_standard_Newton_Laurent_step
py2c_standard_Newton_Laurent_step()
result = load_standard_solutions()
elif(precision == 'dd'):
from phcpy.interface import store_dobldobl_laurent_system
from phcpy.interface import store_dobldobl_solutions
from phcpy.interface import load_dobldobl_solutions
store_dobldobl_laurent_system(system)
store_dobldobl_solutions(len(system), solutions)
from phcpy.phcpy2c3 import py2c_dobldobl_Newton_Laurent_step
py2c_dobldobl_Newton_Laurent_step()
result = load_dobldobl_solutions()
elif(precision == 'qd'):
from phcpy.interface import store_quaddobl_laurent_system
from phcpy.interface import store_quaddobl_solutions
from phcpy.interface import load_quaddobl_solutions
store_quaddobl_laurent_system(system)
store_quaddobl_solutions(len(system), solutions)
from phcpy.phcpy2c3 import py2c_quaddobl_Newton_Laurent_step
py2c_quaddobl_Newton_Laurent_step()
result = load_quaddobl_solutions()
elif(precision == 'mp'):
from phcpy.interface import store_multprec_laurent_system
from phcpy.interface import store_multprec_solutions
from phcpy.interface import load_multprec_solutions
store_multprec_laurent_system(system, decimals)
store_multprec_solutions(len(system), solutions)
from phcpy.phcpy2c3 import py2c_multprec_Newton_Laurent_step
py2c_multprec_Newton_Laurent_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 quaddobl_usolve(pol, mxi, eps):
"""
Applies the method of Durand-Kerner (aka Weierstrass)
to the polynomial in the string pol, in quad double precision
The maximum number of iterations is in mxi,
the requirement on the accuracy in eps.
"""
from phcpy.phcpy2c3 import py2c_usolve_quaddobl
from phcpy.interface import store_quaddobl_system, load_quaddobl_solutions
store_quaddobl_system([pol])
nit = py2c_usolve_quaddobl(mxi, eps)
rts = load_quaddobl_solutions()
return (nit, rts)
def quaddobl_usolve(pol, mxi, eps):
"""
Applies the method of Durand-Kerner (aka Weierstrass)
to the polynomial in the string pol, in quad double precision
The maximum number of iterations is in mxi,
the requirement on the accuracy in eps.
"""
from phcpy.phcpy2c3 import py2c_usolve_quaddobl
from phcpy.interface import store_quaddobl_system, load_quaddobl_solutions
store_quaddobl_system([pol])
nit = py2c_usolve_quaddobl(mxi, eps)
rts = load_quaddobl_solutions()
return (nit, rts)
def quaddobl_littlewood_richardson_homotopies(ndim, kdim, brackets, \
verbose=True, vrfcnd=False, minrep=True, tosqr=False, outputfilename=''):
r"""
In n-dimensional space we consider k-dimensional planes,
subject to intersection conditions represented by brackets.
The parameters *ndim* and *kdim* give values for n and k respectively.
The parameter *brackets* is a list of brackets. A bracket is a list
of as many natural numbers (in the range 1..ndim) as kdim.
The Littlewood-Richardson homotopies compute k-planes that
meet the flags at spaces of dimensions prescribed by the brackets,
in quad double precision. Four options are passed as Booleans:
*verbose*: for adding extra output during computations,
*vrfcnd*: for extra diagnostic verification of Schubert conditions,
*minrep*: for a minimial representation of the problem formulation,
*tosqr*: to square the overdetermined systems.
On return is a 4-tuple. The first item of the tuple is the
formal root count, sharp for general flags, then as second
item the coordinates of the flags. The coordinates of the
flags are stored row wise in a list of real and imaginary parts.
The third and fourth item of the tuple on return are respectively
the polynomial system that has been solved and its solutions.
The length of the list of solution should match the root count.
"""
from phcpy.phcpy2c3 import py2c_solcon_clear_quaddobl_solutions
from phcpy.phcpy2c3 \
import py2c_schubert_quaddobl_littlewood_richardson_homotopies \
as qdlrhom
from phcpy.interface import load_quaddobl_solutions, load_quaddobl_system
py2c_solcon_clear_quaddobl_solutions()
nbc = len(brackets)
cds = ''
for bracket in brackets:
for num in bracket:
cds = cds + ' ' + str(num)
# print 'the condition string :', cds
(roco, sflags) = qdlrhom(ndim, kdim, nbc, len(cds), cds, \
int(verbose), int(vrfcnd), int(minrep), int(tosqr), \
len(outputfilename), outputfilename)
rflags = eval(sflags)
flgs = []
for k in range(len(rflags)//8):
flgs.append(complex(rflags[2*k], rflags[2*k+4]))
fsys = load_quaddobl_system()
sols = load_quaddobl_solutions()
return (roco, flgs, fsys, sols)
def quaddobl_scale_solutions(nvar, sols, cffs):
"""
Scales the solutions in the list sols using the coefficients in cffs,
using quad double precision arithmetic.
The number of variables is given in the parameter nvar.
If the sols are the solution of the polynomials in the output of
quaddobl_scale_system(pols), then the solutions on return will be
solutions of the original polynomials in the list pols.
"""
from phcpy.interface import store_quaddobl_solutions
from phcpy.interface import load_quaddobl_solutions
from phcpy.phcpy2c3 import py2c_scale_quaddobl_solutions
store_quaddobl_solutions(nvar, sols)
py2c_scale_quaddobl_solutions(len(cffs), str(cffs))
return load_quaddobl_solutions()
def quaddobl_scale_solutions(nvar, sols, cffs):
"""
Scales the solutions in the list sols using the coefficients in cffs,
using quad double precision arithmetic.
The number of variables is given in the parameter nvar.
If the sols are the solution of the polynomials in the output of
quaddobl_scale_system(pols), then the solutions on return will be
solutions of the original polynomials in the list pols.
"""
from phcpy.interface import store_quaddobl_solutions
from phcpy.interface import load_quaddobl_solutions
from phcpy.phcpy2c3 import py2c_scale_quaddobl_solutions
store_quaddobl_solutions(nvar, sols)
py2c_scale_quaddobl_solutions(len(cffs), str(cffs))
return load_quaddobl_solutions()
def ade_tuned_quad_double_track(target, start, sols, pars, gamma=0, verbose=1):
r"""
Does path tracking with algorithm differentiation,
in quad double precision, with tuned path parameters.
On input are a target system, a start system with solutions.
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.
The *pars* is a tuple of tuned values for the path parameters.
On return are the string representations of the solutions
computed at the end of the paths.
If *gamma* on input equals zero, then a random complex number is generated,
otherwise the real and imaginary parts of *gamma* are used.
"""
from phcpy.phcpy2c3 import py2c_copy_quaddobl_container_to_target_system
from phcpy.phcpy2c3 import py2c_copy_quaddobl_container_to_start_system
from phcpy.phcpy2c3 import py2c_ade_manypaths_qd_pars
from phcpy.interface import store_quaddobl_system
from phcpy.interface import store_quaddobl_solutions
from phcpy.interface import load_quaddobl_solutions
store_quaddobl_system(target)
py2c_copy_quaddobl_container_to_target_system()
store_quaddobl_system(start)
py2c_copy_quaddobl_container_to_start_system()
dim = len(start)
store_quaddobl_solutions(dim, sols)
if(gamma == 0):
from random import uniform
from cmath import exp, pi
angle = uniform(0, 2*pi)
gamma = exp(angle*complex(0, 1))
if(verbose > 0):
print('random gamma constant :', gamma)
if(verbose > 0):
print('the path parameters :\n', pars)
fail = py2c_ade_manypaths_qd_pars(verbose, gamma.real, gamma.imag, \
pars[0], pars[1], pars[2], pars[3], pars[4], pars[5], pars[6], \
pars[7], pars[8], pars[9], pars[10], pars[11], pars[12], pars[13])
if(fail == 0):
if(verbose > 0):
print('Path tracking with AD was a success!')
else:
print('Path tracking with AD failed!')
return load_quaddobl_solutions()
def quad_double_track(target, start, sols, gamma=0, tasks=0):
r"""
Does path tracking with quad 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_quaddobl_container_to_target_system
from phcpy.phcpy2c3 import py2c_copy_quaddobl_container_to_start_system
from phcpy.phcpy2c3 import py2c_copy_quaddobl_container_to_start_solutions
from phcpy.phcpy2c3 import py2c_create_quaddobl_homotopy
from phcpy.phcpy2c3 import py2c_create_quaddobl_homotopy_with_gamma
from phcpy.phcpy2c3 import py2c_solve_by_quaddobl_homotopy_continuation
from phcpy.phcpy2c3 import py2c_solcon_clear_quaddobl_solutions
from phcpy.phcpy2c3 import py2c_copy_quaddobl_target_solutions_to_container
from phcpy.interface import store_quaddobl_system
from phcpy.interface import store_quaddobl_solutions
from phcpy.interface import load_quaddobl_solutions
from phcpy.solver import number_of_symbols
dim = number_of_symbols(start)
store_quaddobl_system(target, nbvar=dim)
py2c_copy_quaddobl_container_to_target_system()
store_quaddobl_system(start, nbvar=dim)
py2c_copy_quaddobl_container_to_start_system()
# py2c_clear_quaddobl_homotopy()
if(gamma == 0):
py2c_create_quaddobl_homotopy()
else:
py2c_create_quaddobl_homotopy_with_gamma(gamma.real, gamma.imag)
store_quaddobl_solutions(dim, sols)
py2c_copy_quaddobl_container_to_start_solutions()
py2c_solve_by_quaddobl_homotopy_continuation(tasks)
py2c_solcon_clear_quaddobl_solutions()
py2c_copy_quaddobl_target_solutions_to_container()
return load_quaddobl_solutions()
def quaddobl_deflate(system, solutions):
"""
The deflation method augments the given system with
derivatives to restore the quadratic convergence of
Newton's method at isolated singular solutions,
in quad double precision.
After application of deflation with default settings,
the new approximate solutions are returned.
"""
from phcpy.phcpy2c3 import py2c_quaddobl_deflate
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)
py2c_quaddobl_deflate()
result = load_quaddobl_solutions()
return result
def gpu_quad_double_track(target, start, sols, gamma=0, verbose=1):
"""
GPU accelerated path tracking with algorithm differentiation,
in quad double precision.
On input are a target system, a start system with solutions.
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.
If gamma on input equals zero, then a random complex number is generated,
otherwise the real and imaginary parts of gamma are used.
"""
from phcpy.phcpy2c2 import py2c_copy_quaddobl_container_to_target_system
from phcpy.phcpy2c2 import py2c_copy_quaddobl_container_to_start_system
from phcpy.phcpy2c2 import py2c_gpu_manypaths_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(target)
py2c_copy_quaddobl_container_to_target_system()
store_quaddobl_system(start)
py2c_copy_quaddobl_container_to_start_system()
dim = len(start)
store_quaddobl_solutions(dim, sols)
if gamma == 0:
from random import uniform
from cmath import exp, pi
angle = uniform(0, 2 * pi)
gamma = exp(angle * complex(0, 1))
if verbose > 0:
print "random gamma constant :", gamma
fail = py2c_gpu_manypaths_qd(2, verbose, gamma.real, gamma.imag)
if fail == 0:
if verbose > 0:
print "Path tracking on the GPU was a success!"
else:
print "Path tracking on the GPU failed!"
return load_quaddobl_solutions()
def quaddobl_deflate(system, solutions):
"""
The deflation method augments the given system with
derivatives to restore the quadratic convergence of
Newton's method at isolated singular solutions,
in quad double precision.
After application of deflation with default settings,
the new approximate solutions are returned.
"""
from phcpy.phcpy2c3 import py2c_quaddobl_deflate
from phcpy.interface import store_quaddobl_system
from phcpy.interface import store_quaddobl_solutions
from phcpy.interface import load_quaddobl_solutions
dim = number_of_symbols(system)
store_quaddobl_system(system, nbvar=dim)
store_quaddobl_solutions(dim, solutions)
py2c_quaddobl_deflate()
result = load_quaddobl_solutions()
return result
def quad_double_track(target, start, sols, gamma=0, tasks=0):
"""
Does path tracking with quad 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_quaddobl_container_to_target_system
from phcpy.phcpy2c2 import py2c_copy_quaddobl_container_to_start_system
from phcpy.phcpy2c2 import py2c_copy_quaddobl_container_to_start_solutions
from phcpy.phcpy2c2 import py2c_create_quaddobl_homotopy
from phcpy.phcpy2c2 import py2c_create_quaddobl_homotopy_with_gamma
from phcpy.phcpy2c2 import py2c_solve_by_quaddobl_homotopy_continuation
from phcpy.phcpy2c2 import py2c_solcon_clear_quaddobl_solutions
from phcpy.phcpy2c2 import py2c_copy_quaddobl_target_solutions_to_container
from phcpy.interface import store_quaddobl_system
from phcpy.interface import store_quaddobl_solutions
from phcpy.interface import load_quaddobl_solutions
from phcpy.solver import number_of_symbols
dim = number_of_symbols(start)
store_quaddobl_system(target, nbvar=dim)
py2c_copy_quaddobl_container_to_target_system()
store_quaddobl_system(start, nbvar=dim)
py2c_copy_quaddobl_container_to_start_system()
# py2c_clear_quaddobl_homotopy()
if(gamma == 0):
py2c_create_quaddobl_homotopy()
else:
py2c_create_quaddobl_homotopy_with_gamma(gamma.real, gamma.imag)
store_quaddobl_solutions(dim, sols)
py2c_copy_quaddobl_container_to_start_solutions()
py2c_solve_by_quaddobl_homotopy_continuation(tasks)
py2c_solcon_clear_quaddobl_solutions()
py2c_copy_quaddobl_target_solutions_to_container()
return load_quaddobl_solutions()
def gpu_quad_double_track(target, start, sols, gamma=0, verbose=1):
"""
GPU accelerated path tracking with algorithm differentiation,
in quad double precision.
On input are a target system, a start system with solutions.
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.
If gamma on input equals zero, then a random complex number is generated,
otherwise the real and imaginary parts of gamma are used.
"""
from phcpy.phcpy2c2 import py2c_copy_quaddobl_container_to_target_system
from phcpy.phcpy2c2 import py2c_copy_quaddobl_container_to_start_system
from phcpy.phcpy2c2 import py2c_gpu_manypaths_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(target)
py2c_copy_quaddobl_container_to_target_system()
store_quaddobl_system(start)
py2c_copy_quaddobl_container_to_start_system()
dim = len(start)
store_quaddobl_solutions(dim, sols)
if(gamma == 0):
from random import uniform
from cmath import exp, pi
angle = uniform(0, 2*pi)
gamma = exp(angle*complex(0, 1))
if(verbose > 0):
print 'random gamma constant :', gamma
fail = py2c_gpu_manypaths_qd(2, verbose, gamma.real, gamma.imag)
if(fail == 0):
if(verbose > 0):
print 'Path tracking on the GPU was a success!'
else:
print 'Path tracking on the GPU failed!'
return load_quaddobl_solutions()
def quaddobl_littlewood_richardson_homotopies(ndim, kdim, brackets, \
verbose=True, vrfcnd=False, outputfilename='/tmp/output'):
"""
In n-dimensional space we consider k-dimensional planes,
subject to intersection conditions represented by brackets.
The parameters ndim and kdim give values for n and k respectively.
The parameter brackets is a list of brackets. A bracket is a list
of as many natural numbers (in the range 1..ndim) as kdim.
The Littlewood-Richardson homotopies compute k-planes that
meet the flags at spaces of dimensions prescribed by the brackets,
in quad double precision.
On return is a 4-tuple. The first item of the tuple is the
formal root count, sharp for general flags, then as second
item the coordinates of the flags. The coordinates of the
flags are stored row wise in a list of real and imaginary parts.
The third and fourth item of the tuple on return are respectively
the polynomial system that has been solved and its solutions.
The length of the list of solution should match the root count.
"""
from phcpy.phcpy2c3 import py2c_solcon_clear_quaddobl_solutions
from phcpy.phcpy2c3 \
import py2c_schubert_quaddobl_littlewood_richardson_homotopies \
as qdlrhom
from phcpy.interface import load_quaddobl_solutions, load_quaddobl_system
py2c_solcon_clear_quaddobl_solutions()
nbc = len(brackets)
cds = ''
for bracket in brackets:
for num in bracket:
cds = cds + ' ' + str(num)
# print 'the condition string :', cds
(roco, sflags) = qdlrhom(ndim, kdim, nbc, len(cds), cds, int(verbose), \
int(vrfcnd), len(outputfilename), outputfilename)
rflags = eval(sflags)
flgs = []
for k in range(len(rflags)/8):
flgs.append(complex(rflags[2*k], rflags[2*k+4]))
fsys = load_quaddobl_system()
sols = load_quaddobl_solutions()
return (roco, flgs, fsys, sols)
def quaddobl_track(target, start, sols, filename="", verbose=False):
"""
Wraps the tracker for Pade continuation in quad 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.phcpy2c2 import py2c_copy_quaddobl_container_to_target_system
from phcpy.phcpy2c2 import py2c_copy_quaddobl_container_to_start_system
from phcpy.phcpy2c2 import py2c_copy_quaddobl_container_to_start_solutions
from phcpy.phcpy2c2 import py2c_create_quaddobl_homotopy_with_gamma
from phcpy.phcpy2c2 import py2c_clear_quaddobl_homotopy
from phcpy.phcpy2c2 import py2c_clear_quaddobl_operations_data
from phcpy.interface import store_quaddobl_system
from phcpy.interface import store_quaddobl_solutions
from phcpy.interface import load_quaddobl_solutions
from phcpy.solver import number_of_symbols
from phcpy.phcpy2c2 import py2c_padcon_quaddobl_track
dim = number_of_symbols(start)
store_quaddobl_system(target, nbvar=dim)
py2c_copy_quaddobl_container_to_target_system()
store_quaddobl_system(start, nbvar=dim)
py2c_copy_quaddobl_container_to_start_system()
(regamma, imgamma) = get_homotopy_continuation_parameter(1)
store_quaddobl_solutions(dim, sols)
py2c_copy_quaddobl_container_to_start_solutions()
(regamma, imgamma) = get_homotopy_continuation_parameter(1)
py2c_create_quaddobl_homotopy_with_gamma(regamma, imgamma)
nbc = len(filename)
fail = py2c_padcon_quaddobl_track(nbc, filename, int(verbose))
# py2c_clear_quaddobl_homotopy()
# py2c_clear_quaddobl_operations_data()
return load_quaddobl_solutions()
def quaddobl_random_coefficient_system(silent=False):
"""
Runs the polyhedral homotopies and returns a random coefficient
system based on the contents of the cell container,
in quad double precision arithmetic.
For this to work, the mixed_volume function must be called first.
"""
from phcpy.phcpy2c3 import py2c_celcon_quaddobl_random_coefficient_system
from phcpy.phcpy2c3 import py2c_celcon_copy_into_quaddobl_systems_container
from phcpy.phcpy2c3 import py2c_celcon_quaddobl_polyhedral_homotopy
from phcpy.phcpy2c3 import py2c_celcon_number_of_cells
from phcpy.phcpy2c3 import py2c_solcon_clear_quaddobl_solutions
from phcpy.phcpy2c3 import py2c_celcon_solve_quaddobl_start_system
from phcpy.phcpy2c3 import py2c_celcon_track_quaddobl_solution_path
from phcpy.phcpy2c3 \
import py2c_celcon_copy_target_quaddobl_solution_to_container
from phcpy.interface import load_quaddobl_system, load_quaddobl_solutions
py2c_celcon_quaddobl_random_coefficient_system()
py2c_celcon_copy_into_quaddobl_systems_container()
# py2c_syscon_write_dobldobl_system()
result = load_quaddobl_system()
# print result
py2c_celcon_quaddobl_polyhedral_homotopy()
nbcells = py2c_celcon_number_of_cells()
py2c_solcon_clear_quaddobl_solutions()
for cell in range(1, nbcells + 1):
mixvol = py2c_celcon_solve_quaddobl_start_system(cell)
if not silent:
print('system %d has %d solutions' % (cell, mixvol))
for j in range(1, mixvol + 1):
if not silent:
print('-> tracking path %d out of %d' % (j, mixvol))
py2c_celcon_track_quaddobl_solution_path(cell, j, 0)
py2c_celcon_copy_target_quaddobl_solution_to_container(cell, j)
sols = load_quaddobl_solutions()
# print sols
# newton_step(result, sols)
return (result, sols)
def quaddobl_random_coefficient_system(silent=False):
"""
Runs the polyhedral homotopies and returns a random coefficient
system based on the contents of the cell container,
in quad double precision arithmetic.
For this to work, the mixed_volume function must be called first.
"""
from phcpy.phcpy2c3 import py2c_celcon_quaddobl_random_coefficient_system
from phcpy.phcpy2c3 import py2c_celcon_copy_into_quaddobl_systems_container
from phcpy.phcpy2c3 import py2c_celcon_quaddobl_polyhedral_homotopy
from phcpy.phcpy2c3 import py2c_celcon_number_of_cells
from phcpy.phcpy2c3 import py2c_solcon_clear_quaddobl_solutions
from phcpy.phcpy2c3 import py2c_celcon_solve_quaddobl_start_system
from phcpy.phcpy2c3 import py2c_celcon_track_quaddobl_solution_path
from phcpy.phcpy2c3 \
import py2c_celcon_copy_target_quaddobl_solution_to_container
from phcpy.interface import load_quaddobl_system, load_quaddobl_solutions
py2c_celcon_quaddobl_random_coefficient_system()
py2c_celcon_copy_into_quaddobl_systems_container()
# py2c_syscon_write_dobldobl_system()
result = load_quaddobl_system()
# print result
py2c_celcon_quaddobl_polyhedral_homotopy()
nbcells = py2c_celcon_number_of_cells()
py2c_solcon_clear_quaddobl_solutions()
for cell in range(1, nbcells+1):
mixvol = py2c_celcon_solve_quaddobl_start_system(cell)
if not silent:
print('system %d has %d solutions' % (cell, mixvol))
for j in range(1, mixvol+1):
if not silent:
print('-> tracking path %d out of %d' % (j, mixvol))
py2c_celcon_track_quaddobl_solution_path(cell, j, 0)
py2c_celcon_copy_target_quaddobl_solution_to_container(cell, j)
sols = load_quaddobl_solutions()
# print sols
# newton_step(result, sols)
return (result, sols)
def quaddobl_polysys_solve(pols, topdim=-1, \
filter=True, factor=True, tasks=0, verbose=True):
"""
Runs the cascades of homotopies on the polynomial system in pols
in quad double precision. The default top dimension topdim
is the number of variables in pols minus one.
"""
from phcpy.phcpy2c3 import py2c_quaddobl_polysys_solve
from phcpy.phcpy2c3 import py2c_copy_quaddobl_polysys_witset
from phcpy.solver import number_of_symbols
from phcpy.interface import store_quaddobl_system
from phcpy.interface import load_quaddobl_system, load_quaddobl_solutions
dim = number_of_symbols(pols)
if (topdim == -1):
topdim = dim - 1
fail = store_quaddobl_system(pols, nbvar=dim)
fail = py2c_quaddobl_polysys_solve(tasks,topdim, \
int(filter),int(factor),int(verbose))
witsols = []
for soldim in range(0, topdim + 1):
fail = py2c_copy_quaddobl_polysys_witset(soldim)
witset = (load_quaddobl_system(), load_quaddobl_solutions())
witsols.append(witset)
return witsols
