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Hierarchical and parallel computing

Solver "workflow"

  • Asynchronous and "re-distributable" modes
>>> from mystic.solvers import NelderMeadSimplexSolver >>> from mystic.models import rosen >>> >>> solver = NelderMeadSimplexSolver(3) >>> solver.SetInitialPoints([0.5, 1.5, 2.0]) >>> solver.SetObjective(rosen) >>> >>> from mystic.monitors import VerboseMonitor >>> mon = VerboseMonitor(1) >>> >>> solver.SetGenerationMonitor(mon) >>> solver.Step() Generation 0 has Chi-Squared: 163.000000 >>> solver.Step() Generation 1 has Chi-Squared: 156.635039 >>> solver.Step() Generation 2 has Chi-Squared: 123.476914 >>> solver.Step() Generation 3 has Chi-Squared: 123.476914 >>> solver.Step() Generation 4 has Chi-Squared: 105.163966 >>> solver.Step() Generation 5 has Chi-Squared: 105.163966 >>> solver.Step() Generation 6 has Chi-Squared: 105.163966 >>> solver.SaveSolver('test.pkl') DUMPED("test.pkl")
$ python Python 2.7.9 (default, Dec 11 2014, 01:21:43) [GCC 4.2.1 Compatible Apple Clang 4.1 ((tags/Apple/clang-421.11.66))] on darwin Type "help", "copyright", "credits" or "license" for more information. >>> from mystic.solvers import LoadSolver >>> solver = LoadSolver('test.pkl') LOADED("test.pkl") >>> solver.Step() Generation 7 has Chi-Squared: 105.163966 >>> solver.Step() Generation 8 has Chi-Squared: 94.683952 >>> solver.Step() Generation 9 has Chi-Squared: 79.526211 >>> solver.Solve() Generation 10 has Chi-Squared: 55.152242 Generation 11 has Chi-Squared: 32.635518 Generation 12 has Chi-Squared: 3.928963 Generation 13 has Chi-Squared: 0.293739 Generation 14 has Chi-Squared: 0.293739 Generation 15 has Chi-Squared: 0.293739 Generation 16 has Chi-Squared: 0.293739 Generation 17 has Chi-Squared: 0.293739 Generation 18 has Chi-Squared: 0.293739 Generation 19 has Chi-Squared: 0.293739 Generation 20 has Chi-Squared: 0.293739 Generation 21 has Chi-Squared: 0.234180 Generation 22 has Chi-Squared: 0.097215 Generation 23 has Chi-Squared: 0.058144 Generation 24 has Chi-Squared: 0.058144 Generation 25 has Chi-Squared: 0.050947 Generation 26 has Chi-Squared: 0.035904 Generation 27 has Chi-Squared: 0.023215 Generation 28 has Chi-Squared: 0.007698 Generation 29 has Chi-Squared: 0.007698 Generation 30 has Chi-Squared: 0.007698 Generation 31 has Chi-Squared: 0.004759 Generation 32 has Chi-Squared: 0.004759 Generation 33 has Chi-Squared: 0.004442 Generation 34 has Chi-Squared: 0.003676 Generation 35 has Chi-Squared: 0.003676 Generation 36 has Chi-Squared: 0.003676 Generation 37 has Chi-Squared: 0.003609 Generation 38 has Chi-Squared: 0.003133 Generation 39 has Chi-Squared: 0.003133 Generation 40 has Chi-Squared: 0.002982 Generation 41 has Chi-Squared: 0.002982 Generation 42 has Chi-Squared: 0.002982 Generation 43 has Chi-Squared: 0.002982 Generation 44 has Chi-Squared: 0.002725 Generation 45 has Chi-Squared: 0.002716 Generation 46 has Chi-Squared: 0.002716 Generation 47 has Chi-Squared: 0.002457 Generation 48 has Chi-Squared: 0.002350 Generation 49 has Chi-Squared: 0.001738 Generation 50 has Chi-Squared: 0.001738 Generation 51 has Chi-Squared: 0.001631 Generation 52 has Chi-Squared: 0.000667 Generation 53 has Chi-Squared: 0.000651 Generation 54 has Chi-Squared: 0.000635 Generation 55 has Chi-Squared: 0.000008 Generation 56 has Chi-Squared: 0.000008 Generation 57 has Chi-Squared: 0.000008 Generation 58 has Chi-Squared: 0.000008 Generation 59 has Chi-Squared: 0.000008 Generation 60 has Chi-Squared: 0.000008 Generation 61 has Chi-Squared: 0.000008 Generation 62 has Chi-Squared: 0.000008 Generation 63 has Chi-Squared: 0.000008 Generation 64 has Chi-Squared: 0.000008 Generation 65 has Chi-Squared: 0.000008 Generation 66 has Chi-Squared: 0.000008 Generation 67 has Chi-Squared: 0.000007 Generation 68 has Chi-Squared: 0.000004 Generation 69 has Chi-Squared: 0.000001 Generation 70 has Chi-Squared: 0.000001 Generation 71 has Chi-Squared: 0.000001 Generation 72 has Chi-Squared: 0.000001 Generation 73 has Chi-Squared: 0.000000 Generation 74 has Chi-Squared: 0.000000 Generation 75 has Chi-Squared: 0.000000 Generation 76 has Chi-Squared: 0.000000 Generation 77 has Chi-Squared: 0.000000 Generation 78 has Chi-Squared: 0.000000 Generation 79 has Chi-Squared: 0.000000 Generation 80 has Chi-Squared: 0.000000 Generation 81 has Chi-Squared: 0.000000 Generation 82 has Chi-Squared: 0.000000 Generation 83 has Chi-Squared: 0.000000 Generation 84 has Chi-Squared: 0.000000 Generation 85 has Chi-Squared: 0.000000 Generation 86 has Chi-Squared: 0.000000 Generation 87 has Chi-Squared: 0.000000 Generation 88 has Chi-Squared: 0.000000 STOP("CandidateRelativeTolerance with {'xtol': 0.0001, 'ftol': 0.0001}") DUMPED("test.pkl")
  • Restarts and auto-saved state




In [1]:



    


from mystic.solvers import PowellDirectionalSolver
from mystic.termination import VTR
from mystic.models import rosen
from mystic.solvers import LoadSolver
import os

solver = PowellDirectionalSolver(3)
solver.SetRandomInitialPoints([0.,0.,0.],[10.,10.,10.])
term = VTR()
tmpfile = 'mysolver.pkl'
solver.SetSaveFrequency(10, tmpfile)
solver.Solve(rosen, term)
x = solver.bestSolution
y = solver.bestEnergy
_solver = LoadSolver(tmpfile)
os.remove(tmpfile)
assert all(x == _solver.bestSolution)
assert y == _solver.bestEnergy
  • Database integration and results caching/kriging

See the klepto package, which can save pickled objects to a databases or "file-based" databases. klepto also provides a caching decorator that integrates well with mystic.

  • Extension to parallel computing




In [2]:



    


from multiprocess import Pool
#from pathos.multiprocessing import ProcessPool as Pool
from numpy.random import random
from mystic.solvers import fmin_powell as solver
from mystic.models import zimmermann as model

dim = 2
tries = 20

def helper(solver, model):
    def f(x0, *args, **kwds):
        return solver(model, x0, disp=False, full_output=True, *args, **kwds)[:2]
    return f

# soln = solver(model, 10*random((dim)), disp=False, full_output=True)


if __name__ == '__main__':
    from multiprocess import freeze_support
    freeze_support()

    p = Pool()
    uimap = getattr(p, 'uimap',None) or p.imap_unordered
    res = uimap(helper(solver, model), 10*random((tries,dim)))

    for soln in res:
        print("%s: %s" % (soln[1],soln[0]))
    
    p.close()
    p.join()



    


















    






1.4659582087: [ 3.34775148  4.18629032]
0.193327105757: [ 6.7244221  2.0822508]
1.33885300921: [ 3.01822826  4.64291873]
0.760952173875: [ 2.39822564  5.84082219]
0.0587099968253: [ 6.91729161  2.02399839]
1.51149766463: [ 3.80983951  3.67866283]
1.05044209266: [ 2.63748194  5.31207597]
1.33132426516: [ 3.00437784  4.66429789]
1.33332683652: [ 3.00802689  4.65864627]
0.69680084903: [ 2.35470977  5.94848938]
1.33871952338: [ 3.01797952  4.64330095]
0.00659288011689: [ 6.99075187  2.00265525]
1.48159717956: [ 3.41747159  4.10093123]
0.968258751794: [ 2.56069562  5.47104562]
1.33002776926: [ 3.0020286   4.66794364]
1.48828812569: [ 4.05846284  3.45324903]
0.306980732124: [ 6.55763518  2.13538409]
0.12280186906: [ 6.82605245  2.05114568]
1.12993980546: [ 2.72129105  5.14876914]
1.43725674236: [ 3.24808106  4.31466219]

















In [3]:



    


%matplotlib notebook



    











In [4]:



    


"""
Example:
    - Solve 8th-order Chebyshev polynomial coefficients with Powell's method.
    - Uses LatticeSolver to provide 'pseudo-global' optimization
    - Plot of fitting to Chebyshev polynomial.

Demonstrates:
    - standard models
    - minimal solver interface
"""
# the Buckshot solver
from mystic.solvers import LatticeSolver

# Powell's Directonal solver
from mystic.solvers import PowellDirectionalSolver

# Chebyshev polynomial and cost function
from mystic.models.poly import chebyshev8, chebyshev8cost
from mystic.models.poly import chebyshev8coeffs

# if available, use a pathos worker pool
try:
    #from pathos.pools import ProcessPool as Pool
    from pathos.pools import ParallelPool as Pool
except ImportError:
    from mystic.pools import SerialPool as Pool

# tools
from mystic.termination import NormalizedChangeOverGeneration as NCOG
from mystic.math import poly1d
from mystic.monitors import VerboseLoggingMonitor
from mystic.tools import getch
import pylab
pylab.ion()

# draw the plot
def plot_exact():
    pylab.title("fitting 8th-order Chebyshev polynomial coefficients")
    pylab.xlabel("x")
    pylab.ylabel("f(x)")
    import numpy
    x = numpy.arange(-1.2, 1.2001, 0.01)
    exact = chebyshev8(x)
    pylab.plot(x,exact,'b-')
    pylab.legend(["Exact"])
    pylab.axis([-1.4,1.4,-2,8],'k-')
    pylab.draw()
    return

# plot the polynomial
def plot_solution(params,style='y-'):
    import numpy
    x = numpy.arange(-1.2, 1.2001, 0.01)
    f = poly1d(params)
    y = f(x)
    pylab.plot(x,y,style)
    pylab.legend(["Exact","Fitted"])
    pylab.axis([-1.4,1.4,-2,8],'k-')
    pylab.draw()
    return

# add some information as constraints
from mystic.constraints import integers
@integers()
def constraints(x):
    x[-1] = 1
    return x


if __name__ == '__main__':
    from pathos.helpers import freeze_support
    freeze_support() # help Windows use multiprocessing

    print("Powell's Method")
    print("===============")

    # dimensional information
    from mystic.tools import random_seed
    random_seed(123)
    ndim = 9
    npts = 32

    # draw frame and exact coefficients
    plot_exact()

    # configure monitor
    stepmon = VerboseLoggingMonitor(1,10)

    # use lattice-Powell to solve 8th-order Chebyshev coefficients
    solver = LatticeSolver(ndim, npts)
    solver.SetNestedSolver(PowellDirectionalSolver)
    solver.SetMapper(Pool().map)
    solver.SetGenerationMonitor(stepmon)
    solver.SetStrictRanges(min=[-300]*ndim, max=[300]*ndim)
    solver.SetConstraints(constraints)
    solver.Solve(chebyshev8cost, NCOG(1e-4), disp=1)
    solution = solver.Solution()

    # write 'convergence' support file
    from mystic.munge import write_support_file
    write_support_file(solver._stepmon) #XXX: only saves the 'best'

    # use pretty print for polynomials
    print(poly1d(solution))

    # compare solution with actual 8th-order Chebyshev coefficients
    print("\nActual Coefficients:\n %s\n" % poly1d(chebyshev8coeffs))

    # plot solution versus exact coefficients
    plot_solution(solution)
    #getch()



    


















    






Powell's Method
===============
[id: 0] Generation 0 has Chi-Squared: 5077742.293533
[id: 0] Generation 0 has fit parameters:
 [0.0, -150.0, -150.0, -150.0, -225.0, 0.0, 0.0, 0.0, 1.0]
[id: 0] Generation 10 has Chi-Squared: 1383.107884
[id: 0] Generation 20 has Chi-Squared: 413.646137
[id: 0] Generation 30 has Chi-Squared: 326.235898
STOP("NormalizedChangeOverGeneration with {'generations': 10, 'tolerance': 0.0001}")
 [id: 1] Generation 0 has Chi-Squared: 3348859.352757
[id: 1] Generation 0 has fit parameters:
 [0.0, -150.0, -150.0, -150.0, -75.0, 0.0, 0.0, 0.0, 1.0]
[id: 1] Generation 10 has Chi-Squared: 627.170026
[id: 1] Generation 20 has Chi-Squared: 152.492077
[id: 1] Generation 30 has Chi-Squared: 104.962366
STOP("NormalizedChangeOverGeneration with {'generations': 10, 'tolerance': 0.0001}")
 [id: 2] Generation 0 has Chi-Squared: 2166169.377309
[id: 2] Generation 0 has fit parameters:
 [0.0, -150.0, -150.0, -150.0, 75.0, 0.0, 0.0, 0.0, 1.0]
[id: 2] Generation 10 has Chi-Squared: 766.925209
STOP("NormalizedChangeOverGeneration with {'generations': 10, 'tolerance': 0.0001}")
 [id: 3] Generation 0 has Chi-Squared: 1523957.660441
[id: 3] Generation 0 has fit parameters:
 [0.0, -150.0, -150.0, -150.0, 225.0, 0.0, 0.0, 0.0, 1.0]
[id: 3] Generation 10 has Chi-Squared: 759.843832
[id: 3] Generation 20 has Chi-Squared: 386.868277
STOP("NormalizedChangeOverGeneration with {'generations': 10, 'tolerance': 0.0001}")
 [id: 4] Generation 0 has Chi-Squared: 2961471.619553
[id: 4] Generation 0 has fit parameters:
 [0.0, -150.0, -150.0, 150.0, -225.0, 0.0, 0.0, 0.0, 1.0]
[id: 4] Generation 10 has Chi-Squared: 1747.854447
STOP("NormalizedChangeOverGeneration with {'generations': 10, 'tolerance': 0.0001}")
 [id: 5] Generation 0 has Chi-Squared: 1288121.129859
[id: 5] Generation 0 has fit parameters:
 [0.0, -150.0, -150.0, 150.0, -75.0, 0.0, 0.0, 0.0, 1.0]
[id: 5] Generation 10 has Chi-Squared: 993.628955
[id: 5] Generation 20 has Chi-Squared: 904.604677
STOP("NormalizedChangeOverGeneration with {'generations': 10, 'tolerance': 0.0001}")
 [id: 6] Generation 0 has Chi-Squared: 348765.023329
[id: 6] Generation 0 has fit parameters:
 [0.0, -150.0, -150.0, 150.0, 75.0, 0.0, 0.0, 0.0, 1.0]
[id: 6] Generation 10 has Chi-Squared: 1045.836299
[id: 6] Generation 20 has Chi-Squared: 430.789952
STOP("NormalizedChangeOverGeneration with {'generations': 10, 'tolerance': 0.0001}")
 [id: 7] Generation 0 has Chi-Squared: 131011.627737
[id: 7] Generation 0 has fit parameters:
 [0.0, -150.0, -150.0, 150.0, 225.0, 0.0, 0.0, 0.0, 1.0]
[id: 7] Generation 10 has Chi-Squared: 954.315654
[id: 7] Generation 20 has Chi-Squared: 181.789234
STOP("NormalizedChangeOverGeneration with {'generations': 10, 'tolerance': 0.0001}")
 [id: 8] Generation 0 has Chi-Squared: 1597284.876156
[id: 8] Generation 0 has fit parameters:
 [0.0, -150.0, 150.0, -150.0, -225.0, 0.0, 0.0, 0.0, 1.0]
[id: 8] Generation 10 has Chi-Squared: 1355.385233
[id: 8] Generation 20 has Chi-Squared: 1018.904711
STOP("NormalizedChangeOverGeneration with {'generations': 10, 'tolerance': 0.0001}")
 [id: 9] Generation 0 has Chi-Squared: 1017257.139598
[id: 9] Generation 0 has fit parameters:
 [0.0, -150.0, 150.0, -150.0, -75.0, 0.0, 0.0, 0.0, 1.0]
[id: 9] Generation 10 has Chi-Squared: 636.910061
[id: 9] Generation 20 has Chi-Squared: 441.163540
STOP("NormalizedChangeOverGeneration with {'generations': 10, 'tolerance': 0.0001}")
 [id: 10] Generation 0 has Chi-Squared: 977713.235021
[id: 10] Generation 0 has fit parameters:
 [0.0, -150.0, 150.0, -150.0, 75.0, 0.0, 0.0, 0.0, 1.0]
[id: 10] Generation 10 has Chi-Squared: 512.795474
[id: 10] Generation 20 has Chi-Squared: 267.783803
STOP("NormalizedChangeOverGeneration with {'generations': 10, 'tolerance': 0.0001}")
 [id: 11] Generation 0 has Chi-Squared: 1478664.192583
[id: 11] Generation 0 has fit parameters:
 [0.0, -150.0, 150.0, -150.0, 225.0, 0.0, 0.0, 0.0, 1.0]
[id: 11] Generation 10 has Chi-Squared: 206.521956
[id: 11] Generation 20 has Chi-Squared: 186.597465
STOP("NormalizedChangeOverGeneration with {'generations': 10, 'tolerance': 0.0001}")
 [id: 12] Generation 0 has Chi-Squared: 148615.212494
[id: 12] Generation 0 has fit parameters:
 [0.0, -150.0, 150.0, 150.0, -225.0, 0.0, 0.0, 0.0, 1.0]
[id: 12] Generation 10 has Chi-Squared: 478.970432
[id: 12] Generation 20 has Chi-Squared: 457.593563
STOP("NormalizedChangeOverGeneration with {'generations': 10, 'tolerance': 0.0001}")
 [id: 13] Generation 0 has Chi-Squared: 29770.442591
[id: 13] Generation 0 has fit parameters:
 [0.0, -150.0, 150.0, 150.0, -75.0, 0.0, 0.0, 0.0, 1.0]
[id: 13] Generation 10 has Chi-Squared: 508.561065
[id: 13] Generation 20 has Chi-Squared: 483.084804
STOP("NormalizedChangeOverGeneration with {'generations': 10, 'tolerance': 0.0001}")
 [id: 14] Generation 0 has Chi-Squared: 322727.876504
[id: 14] Generation 0 has fit parameters:
 [0.0, -150.0, 150.0, 150.0, 75.0, 0.0, 0.0, 0.0, 1.0]
[id: 14] Generation 10 has Chi-Squared: 253.749919
STOP("NormalizedChangeOverGeneration with {'generations': 10, 'tolerance': 0.0001}")
 [id: 15] Generation 0 has Chi-Squared: 962677.537595
[id: 15] Generation 0 has fit parameters:
 [0.0, -150.0, 150.0, 150.0, 225.0, 0.0, 0.0, 0.0, 1.0]
[id: 15] Generation 10 has Chi-Squared: 258.752086
[id: 15] Generation 20 has Chi-Squared: 163.902841
STOP("NormalizedChangeOverGeneration with {'generations': 10, 'tolerance': 0.0001}")
 [id: 16] Generation 0 has Chi-Squared: 2961471.619553
[id: 16] Generation 0 has fit parameters:
 [0.0, 150.0, -150.0, -150.0, -225.0, 0.0, 0.0, 0.0, 1.0]
[id: 16] Generation 10 has Chi-Squared: 1747.854447
STOP("NormalizedChangeOverGeneration with {'generations': 10, 'tolerance': 0.0001}")
 [id: 17] Generation 0 has Chi-Squared: 1288121.129859
[id: 17] Generation 0 has fit parameters:
 [0.0, 150.0, -150.0, -150.0, -75.0, 0.0, 0.0, 0.0, 1.0]
[id: 17] Generation 10 has Chi-Squared: 867.479378
[id: 17] Generation 20 has Chi-Squared: 671.750399
STOP("NormalizedChangeOverGeneration with {'generations': 10, 'tolerance': 0.0001}")
 [id: 18] Generation 0 has Chi-Squared: 348765.023329
[id: 18] Generation 0 has fit parameters:
 [0.0, 150.0, -150.0, -150.0, 75.0, 0.0, 0.0, 0.0, 1.0]
[id: 18] Generation 10 has Chi-Squared: 511.996058
[id: 18] Generation 20 has Chi-Squared: 482.558173
STOP("NormalizedChangeOverGeneration with {'generations': 10, 'tolerance': 0.0001}")
 [id: 19] Generation 0 has Chi-Squared: 131011.627737
[id: 19] Generation 0 has fit parameters:
 [0.0, 150.0, -150.0, -150.0, 225.0, 0.0, 0.0, 0.0, 1.0]
[id: 19] Generation 10 has Chi-Squared: 373.849251
[id: 19] Generation 20 has Chi-Squared: 151.586583
STOP("NormalizedChangeOverGeneration with {'generations': 10, 'tolerance': 0.0001}")
 [id: 20] Generation 0 has Chi-Squared: 5077742.293533
[id: 20] Generation 0 has fit parameters:
 [0.0, 150.0, -150.0, 150.0, -225.0, 0.0, 0.0, 0.0, 1.0]
[id: 20] Generation 10 has Chi-Squared: 1120.794070
[id: 20] Generation 20 has Chi-Squared: 586.703420
[id: 20] Generation 30 has Chi-Squared: 546.457301
STOP("NormalizedChangeOverGeneration with {'generations': 10, 'tolerance': 0.0001}")
 [id: 21] Generation 0 has Chi-Squared: 3348859.352757
[id: 21] Generation 0 has fit parameters:
 [0.0, 150.0, -150.0, 150.0, -75.0, 0.0, 0.0, 0.0, 1.0]
[id: 21] Generation 10 has Chi-Squared: 1306.181338
STOP("NormalizedChangeOverGeneration with {'generations': 10, 'tolerance': 0.0001}")
 [id: 22] Generation 0 has Chi-Squared: 2166169.377309
[id: 22] Generation 0 has fit parameters:
 [0.0, 150.0, -150.0, 150.0, 75.0, 0.0, 0.0, 0.0, 1.0]
[id: 22] Generation 10 has Chi-Squared: 493.350798
[id: 22] Generation 20 has Chi-Squared: 133.132154
STOP("NormalizedChangeOverGeneration with {'generations': 10, 'tolerance': 0.0001}")
 [id: 23] Generation 0 has Chi-Squared: 1523957.660441
[id: 23] Generation 0 has fit parameters:
 [0.0, 150.0, -150.0, 150.0, 225.0, 0.0, 0.0, 0.0, 1.0]
[id: 23] Generation 10 has Chi-Squared: 532.797586
STOP("NormalizedChangeOverGeneration with {'generations': 10, 'tolerance': 0.0001}")
 [id: 24] Generation 0 has Chi-Squared: 148615.212494
[id: 24] Generation 0 has fit parameters:
 [0.0, 150.0, 150.0, -150.0, -225.0, 0.0, 0.0, 0.0, 1.0]
[id: 24] Generation 10 has Chi-Squared: 842.739937
STOP("NormalizedChangeOverGeneration with {'generations': 10, 'tolerance': 0.0001}")
 [id: 25] Generation 0 has Chi-Squared: 29770.442591
[id: 25] Generation 0 has fit parameters:
 [0.0, 150.0, 150.0, -150.0, -75.0, 0.0, 0.0, 0.0, 1.0]
[id: 25] Generation 10 has Chi-Squared: 677.240276
[id: 25] Generation 20 has Chi-Squared: 595.020189
STOP("NormalizedChangeOverGeneration with {'generations': 10, 'tolerance': 0.0001}")
 [id: 26] Generation 0 has Chi-Squared: 322727.876504
[id: 26] Generation 0 has fit parameters:
 [0.0, 150.0, 150.0, -150.0, 75.0, 0.0, 0.0, 0.0, 1.0]
[id: 26] Generation 10 has Chi-Squared: 1065.302179
[id: 26] Generation 20 has Chi-Squared: 513.743444
STOP("NormalizedChangeOverGeneration with {'generations': 10, 'tolerance': 0.0001}")
 [id: 27] Generation 0 has Chi-Squared: 962677.537595
[id: 27] Generation 0 has fit parameters:
 [0.0, 150.0, 150.0, -150.0, 225.0, 0.0, 0.0, 0.0, 1.0]
[id: 27] Generation 10 has Chi-Squared: 1087.762698
[id: 27] Generation 20 has Chi-Squared: 128.937502
STOP("NormalizedChangeOverGeneration with {'generations': 10, 'tolerance': 0.0001}")
 [id: 28] Generation 0 has Chi-Squared: 1597284.876156
[id: 28] Generation 0 has fit parameters:
 [0.0, 150.0, 150.0, 150.0, -225.0, 0.0, 0.0, 0.0, 1.0]
[id: 28] Generation 10 has Chi-Squared: 1783.089300
[id: 28] Generation 20 has Chi-Squared: 768.878463
[id: 28] Generation 30 has Chi-Squared: 617.306147
STOP("NormalizedChangeOverGeneration with {'generations': 10, 'tolerance': 0.0001}")
 [id: 29] Generation 0 has Chi-Squared: 1017257.139598
[id: 29] Generation 0 has fit parameters:
 [0.0, 150.0, 150.0, 150.0, -75.0, 0.0, 0.0, 0.0, 1.0]
[id: 29] Generation 10 has Chi-Squared: 727.224048
[id: 29] Generation 20 has Chi-Squared: 534.771927
STOP("NormalizedChangeOverGeneration with {'generations': 10, 'tolerance': 0.0001}")
 [id: 30] Generation 0 has Chi-Squared: 977713.235021
[id: 30] Generation 0 has fit parameters:
 [0.0, 150.0, 150.0, 150.0, 75.0, 0.0, 0.0, 0.0, 1.0]
[id: 30] Generation 10 has Chi-Squared: 488.111724
STOP("NormalizedChangeOverGeneration with {'generations': 10, 'tolerance': 0.0001}")
 [id: 31] Generation 0 has Chi-Squared: 1478664.192583
[id: 31] Generation 0 has fit parameters:
 [0.0, 150.0, 150.0, 150.0, 225.0, 0.0, 0.0, 0.0, 1.0]
[id: 31] Generation 10 has Chi-Squared: 317.393448
[id: 31] Generation 20 has Chi-Squared: 254.254752
STOP("NormalizedChangeOverGeneration with {'generations': 10, 'tolerance': 0.0001}")
 Optimization terminated successfully.
         Current function value: 104.962366
         Iterations: 65
         Function evaluations: 8736
         Total function evaluations: 193103
STOP("NormalizedChangeOverGeneration with {'generations': 10, 'tolerance': 0.0001}")
    8      7       6      5      4      3      2
84 x + 35 x - 131 x - 60 x + 63 x + 24 x - 11 x + 1

Actual Coefficients:
      8       6       4      2
128 x - 256 x + 160 x - 32 x + 1
  • Automated dimensional reduction

mystic provides termination conditions such as CollapseAt and CollapseAs that look for solution vectors that hover around a single value, or start to track other solution vectors, or otherwise. When a collapse conditions is met, the solver terminates, and applys a constraint that reduces the dimensionality of the solution vectors. Upon restart, the solver works on a smaller list of paramaters.

Hierarchical and meta-solvers:

  • "Nesting" solvers
  • Ensemble solvers
  • Global search




In [5]:



    


!rm log.txt



    











In [6]:



    


"""
Uses Ensemble Solvers to provide 'pseudo-global' search.

"""
from mystic.search import Searcher


if __name__ == '__main__':
    # if available, use a multiprocessing worker pool
    try:
        from pathos.helpers import freeze_support
        freeze_support()
        from pathos.pools import ProcessPool as Pool
    except ImportError:
        from mystic.pools import SerialPool as Pool

    # tools
    from mystic.termination import VTR, ChangeOverGeneration as COG
    from mystic.termination import NormalizedChangeOverGeneration as NCOG
    from mystic.monitors import LoggingMonitor, VerboseMonitor, Monitor
    from klepto.archives import dir_archive

    stop = NCOG(1e-4)
    disp = False # print optimization summary
    stepmon = True # use LoggingMonitor
    archive = False # save an archive

    traj = not stepmon # save all trajectories internally, if no logs

    # cost function
    from mystic.models import griewangk as model
    ndim = 2  # model dimensionality
    bounds = ndim * [(-9.5,9.5)] # griewangk

    # the ensemble solvers
    from mystic.solvers import BuckshotSolver, LatticeSolver
    # the local solvers
    from mystic.solvers import PowellDirectionalSolver

    sprayer = BuckshotSolver
    seeker = PowellDirectionalSolver
    npts = 25 # number of solvers
    _map = Pool().map
    retry = 1 # max consectutive iteration retries without a cache 'miss'
    tol = 8   # rounding precision
    mem = 1   # cache rounding precision

    #CUTE: 'configure' monitor and archive if they are desired
    if stepmon: stepmon = LoggingMonitor(1) # montor for all runs
    else: stepmon = None
    if archive: #python2.5
        ar_name = '__%s_%sD_cache__' % (model.__self__.__class__.__name__,ndim)
        archive = dir_archive(ar_name, serialized=True, cached=False)
    else: archive = None

    searcher = Searcher(npts, retry, tol, mem, _map, archive, sprayer, seeker)
    searcher.Verbose(disp)
    searcher.UseTrajectories(traj)

    searcher.Reset(archive, inv=False)
    searcher.Search(model, bounds, stop=stop, monitor=stepmon)
    searcher._summarize()

    ##### extract results #####
    xyz = searcher.Samples()

    ##### invert the model, and get the maxima #####
    imodel = lambda *args, **kwds: -model(*args, **kwds)

    #CUTE: 'configure' monitor and archive if they are desired
    if stepmon not in (None, False):
        itermon = LoggingMonitor(1, filename='inv.txt') #XXX: log.txt?
    else: itermon = None
    if archive not in (None, False): #python2.5
        ar_name = '__%s_%sD_invcache__' % (model.__self__.__class__.__name__,ndim)
        archive = dir_archive(ar_name, serialized=True, cached=False)
    else: archive = None

    searcher.Reset(archive, inv=True)
    searcher.Search(imodel, bounds, stop=stop, monitor=itermon)
    searcher._summarize()



    


















    






min: 0.0 (count=1)
pts: 17 (values=6, size=17)
max: 2.041976686837409 (count=4)
pts: 18 (values=6, size=18)

















In [7]:



    


import mystic
mystic.log_reader('log.txt')



    


















    
























In [8]:



    


import mystic
mystic.model_plotter(mystic.models.griewangk, 'log.txt', bounds="-10:10:.1, -10:10:.1")
mystic.model_plotter(mystic.models.griewangk, 'inv.txt', bounds="-10:10:.1, -10:10:.1")
  • Energy-surface interpolation

In short, for a unknown N-dimensional function, if one performs a global search for all mimima and all maxima... and saves the function evaluations to a database/cache, interpolation from the solver trajectories should interpolate more truly to the unknown function than a standard gridsearch. Optimizers seek critical points, so those will be much better represented in the post-global search interpolation as opposed to post-gridding interpolation.

EXERCISE: Convert one of our previous mystic examples to use parallel computing. Note that if the solver has a SetMapper method, it can take a parallel map.

Let's now look at solvers for optimization of probabilities, PDFs, etc

Content source: mmckerns/tutmom

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