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optimize.py
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optimize.py
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""" Optimization (minimization) functions """
#***************************************************************************************************
# Copyright 2015, 2019 National Technology & Engineering Solutions of Sandia, LLC (NTESS).
# Under the terms of Contract DE-NA0003525 with NTESS, the U.S. Government retains certain rights
# in this software.
# Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except
# in compliance with the License. You may obtain a copy of the License at
# http://www.apache.org/licenses/LICENSE-2.0 or in the LICENSE file in the root pyGSTi directory.
#***************************************************************************************************
import numpy as _np
import time as _time
import sys as _sys
import os as _os
import scipy.optimize as _spo
try:
from scipy.optimize import Result as _optResult # for earlier scipy versions
except:
from scipy.optimize import OptimizeResult as _optResult # for later scipy versions
from .customcg import fmax_cg
def minimize(fn, x0, method='cg', callback=None,
tol=1e-10, maxiter=1000000, maxfev=None,
stopval=None, jac=None):
"""
Minimizes the function fn starting at x0.
This is a gateway function to all other minimization routines within this
module, providing a common interface to many different minimization methods
(including and extending beyond those available from scipy.optimize).
Parameters
----------
fn : function
The function to minimize.
x0 : numpy array
The starting point (argument to fn).
method : string, optional
Which minimization method to use. Allowed values are:
"simplex" : uses fmin_simplex
"supersimplex" : uses fmin_supersimplex
"customcg" : uses fmax_cg (custom CG method)
"brute" : uses scipy.optimize.brute
"basinhopping" : uses scipy.optimize.basinhopping with L-BFGS-B
"swarm" : uses fmin_particle_swarm
"evolve" : uses fmin_evolutionary (which uses DEAP)
< methods available from scipy.optimize.minimize >
callback : function, optional
A callback function to be called in order to track optimizer progress.
Should have signature: myCallback(x, f=None, accepted=None). Note that
create_obj_func_printer(...) function can be used to create a callback.
tol : float, optional
Tolerance value used for all types of tolerances available in a given method.
maxiter : int, optional
Maximum iterations.
maxfev : int, optional
Maximum function evaluations; used only when available, and defaults to maxiter.
stopval : float, optional
For basinhopping method only. When f <= stopval then basinhopping outer loop
will terminate. Useful when a bound on the minimum is known.
jac : function
Jacobian function.
Returns
-------
scipy.optimize.Result object
Includes members 'x', 'fun', 'success', and 'message'.
"""
if maxfev is None: maxfev = maxiter
#Run Minimization Algorithm
if method == 'simplex':
solution = fmin_simplex(fn, x0, slide=1.0, tol=tol, maxiter=maxiter)
elif method == 'supersimplex':
solution = fmin_supersimplex(fn, x0, outer_tol=1.0, inner_tol=tol,
max_outer_iter=100, min_inner_maxiter=100, max_inner_maxiter=maxiter)
elif method == 'customcg':
def fn_to_max(x):
""" Function to maximize """
f = fn(x); return -f if f is not None else None
if jac is not None:
def dfdx_and_bdflag(x):
""" Returns derivative and boundary flag """
j = -jac(x)
bd = _np.zeros(len(j)) # never say fn is on boundary, since this is an analytic derivative
return j, bd
else:
dfdx_and_bdflag = None
# Note: even though we maximize, return value is negated to conform to min routines
solution = fmax_cg(fn_to_max, x0, maxiter, tol, dfdx_and_bdflag, None)
elif method == 'brute':
ranges = [(0.0, 1.0)] * len(x0); Ns = 4 # params for 'brute' algorithm
xmin, _ = _spo.brute(fn, ranges, (), Ns) # jac=jac
#print "DEBUG: Brute fmin = ",fmin
solution = _spo.minimize(fn, xmin, method="Nelder-Mead", options={}, tol=tol, callback=callback, jac=jac)
elif method == 'basinhopping':
def _basin_callback(x, f, accept):
if callback is not None: callback(x, f=f, accepted=accept)
if stopval is not None and f <= stopval:
return True # signals basinhopping to stop
return False
solution = _spo.basinhopping(fn, x0, niter=maxiter, T=2.0, stepsize=1.0,
callback=_basin_callback, minimizer_kwargs={'method': "L-BFGS-B", 'jac': jac})
#DEBUG -- follow with Nelder Mead to make sure basinhopping found a minimum. (It seems to)
#print "DEBUG: running Nelder-Mead:"
#opts = { 'maxfev': maxiter, 'maxiter': maxiter }
#solution = _spo.minimize(fn, solution.x, options=opts, method="Nelder-Mead", tol=1e-8, callback=callback)
#print "DEBUG: done: best f = ",solution.fun
solution.success = True # basinhopping doesn't seem to set this...
elif method == 'swarm':
solution = fmin_particle_swarm(fn, x0, tol, maxiter, popsize=1000) # , callback = callback)
elif method == 'evolve':
solution = fmin_evolutionary(fn, x0, num_generations=maxiter, num_individuals=500)
# elif method == 'homebrew':
# solution = fmin_homebrew(fn, x0, maxiter)
else:
#Set options for different algorithms
opts = {'maxiter': maxiter, 'disp': False}
if method == "BFGS": opts['gtol'] = tol # gradient norm tolerance
elif method == "L-BFGS-B": opts['gtol'] = opts['ftol'] = tol # gradient norm and fractional y-tolerance
elif method == "Nelder-Mead": opts['maxfev'] = maxfev # max fn evals (note: ftol and xtol can also be set)
if method in ("BFGS", "CG", "Newton-CG", "L-BFGS-B", "TNC", "SLSQP", "dogleg", "trust-ncg"): # use jacobian
solution = _spo.minimize(fn, x0, options=opts, method=method, tol=tol, callback=callback, jac=jac)
else:
solution = _spo.minimize(fn, x0, options=opts, method=method, tol=tol, callback=callback)
return solution
def fmin_supersimplex(fn, x0, outer_tol, inner_tol, max_outer_iter, min_inner_maxiter, max_inner_maxiter):
"""
Minimize a function using repeated applications of the simplex algorithm.
By varying the maximum number of iterations and repeatedly calling scipy's
Nelder-Mead simplex optimization, this function performs as a robust (but
slow) minimization.
Parameters
----------
fn : function
The function to minimize.
x0 : numpy array
The starting point (argument to fn).
outer_tol : float
Tolerance of outer loop
inner_tol : float
Tolerance fo inner loop
max_outer_iter : int
Maximum number of outer-loop iterations
min_inner_maxiter : int
Minimum number of inner-loop iterations
max_inner_maxiter : int
Maxium number of outer-loop iterations
Returns
-------
scipy.optimize.Result object
Includes members 'x', 'fun', 'success', and 'message'.
"""
f_init = fn(x0)
f_final = f_init - 10 * outer_tol # prime the loop
x_start = x0
i = 1
cnt_at_same_maxiter = 1
inner_maxiter = min_inner_maxiter
while (f_init - f_final > outer_tol or inner_maxiter < max_inner_maxiter) and i < max_outer_iter:
if f_init - f_final <= outer_tol and inner_maxiter < max_inner_maxiter:
inner_maxiter *= 10; cnt_at_same_maxiter = 1
if cnt_at_same_maxiter > 10 and inner_maxiter > min_inner_maxiter:
inner_maxiter /= 10; cnt_at_same_maxiter = 1
f_init = f_final
print(">>> fmin_supersimplex: outer iteration %d (inner_maxiter = %d)" % (i, inner_maxiter))
i += 1; cnt_at_same_maxiter += 1
opts = {'maxiter': inner_maxiter, 'maxfev': inner_maxiter, 'disp': False}
inner_solution = _spo.minimize(fn, x_start, options=opts, method='Nelder-Mead', callback=None, tol=inner_tol)
if not inner_solution.success:
print("WARNING: fmin_supersimplex inner loop failed (tol=%g, maxiter=%d): %s"
% (inner_tol, inner_maxiter, inner_solution.message))
f_final = inner_solution.fun
x_start = inner_solution.x
print(">>> fmin_supersimplex: outer iteration %d gives min = %f" % (i, f_final))
solution = _optResult()
solution.x = inner_solution.x
solution.fun = inner_solution.fun
if i < max_outer_iter:
solution.success = True
else:
solution.success = False
solution.message = "Maximum iterations exceeded"
return solution
def fmin_simplex(fn, x0, slide=1.0, tol=1e-8, maxiter=1000):
"""
Minimizes a function using a custom simplex implmentation.
This was used primarily to check scipy's Nelder-Mead method
and runs much slower, so there's not much reason for using
this method.
Parameters
----------
fn : function
The function to minimize.
x0 : numpy array
The starting point (argument to fn).
slide : float, optional
Affects initial simplex point locations
tol : float, optional
Relative tolerance as a convergence criterion.
maxiter : int, optional
Maximum iterations.
Returns
-------
scipy.optimize.Result object
Includes members 'x', 'fun', 'success', and 'message'.
"""
# Setup intial values
n = len(x0)
f = _np.zeros(n + 1)
x = _np.zeros((n + 1, n))
x[0] = x0
# Setup intial X range
for i in range(1, n + 1):
x[i] = x0
x[i, i - 1] = x0[i - 1] + slide
# Setup intial functions based on x's just defined
for i in range(n + 1):
f[i] = fn(x[i])
# Main Loop operation, loops infinitly until break condition
counter = 0
while True:
low = _np.argmin(f)
high = _np.argmax(f)
counter += 1
# Compute Migration
d = (-(n + 1) * x[high] + sum(x)) / n
# Break if value is close
if _np.sqrt(_np.dot(d, d) / n) < tol or counter == maxiter:
solution = _optResult()
solution.x = x[low]; solution.fun = f[low]
if counter < maxiter:
solution.success = True
else:
solution.success = False
solution.message = "Maximum iterations exceeded"
return solution
newX = x[high] + 2.0 * d
newF = fn(newX)
if newF <= f[low]:
# Bad news, new value is lower than any other point => replace high point with new values
x[high] = newX
f[high] = newF
newX = x[high] + d
newF = fn(newX)
# Check if need to expand
if newF <= f[low]:
x[high] = newX
f[high] = newF
else:
# Good news, new value is higher than lowest point
# Check if need to contract
if newF <= f[high]:
x[high] = newX
f[high] = newF
else:
# Contraction
newX = x[high] + 0.5 * d
newF = fn(newX)
if newF <= f[high]:
x[high] = newX
f[high] = newF
else:
for i in range(len(x)):
if i != low:
x[i] = (x[i] - x[low])
f[i] = fn(x[i])
#TODO err_crit is never used?
def fmin_particle_swarm(f, x0, err_crit, iter_max, popsize=100, c1=2, c2=2):
"""
A simple implementation of the Particle Swarm Optimization Algorithm.
Pradeep Gowda 2009-03-16
Parameters
----------
f : function
The function to minimize.
x0 : numpy array
The starting point (argument to fn).
err_crit : float
Critical error (i.e. tolerance). Stops when error < err_crit.
iter_max : int
Maximum iterations.
popsize : int, optional
Population size. Larger populations are better at finding the global
optimum but make the algorithm take longer to run.
c1 : float, optional
Coefficient describing a particle's affinity for it's (local) maximum.
c2 : float, optional
Coefficient describing a particle's affinity for the best maximum any
particle has seen (the current global max).
Returns
-------
scipy.optimize.Result object
Includes members 'x', 'fun', 'success', and 'message'.
"""
dimensions = len(x0)
LARGE = 1e10
class Particle:
""" Particle "container" class """
pass
#initialize the particles
particles = []
for i in range(popsize):
p = Particle()
p.params = x0 + 2 * (_np.random.random(dimensions) - 0.5)
p.best = p.params[:]
p.fitness = LARGE # large == bad fitness
p.v = _np.zeros(dimensions)
particles.append(p)
# let the first particle be the global best
gbest = particles[0]; ibest = 0
# bDoLocalFitnessOpt = False
#DEBUG
#if False:
# import pickle as _pickle
# bestGaugeMx = _pickle.load(open("bestGaugeMx.debug"))
# lbfgsbGaugeMx = _pickle.load(open("lbfgsbGaugeMx.debug"))
# cgGaugeMx = _pickle.load(open("cgGaugeMx.debug"))
# initialGaugeMx = x0.reshape( (4,4) )
#
# #DEBUG: dump line cut to plot
# nPts = 100
# print "DEBUG: best offsets = \n", bestGaugeMx - initialGaugeMx
# print "DEBUG: lbfgs offsets = \n", lbfgsbGaugeMx - initialGaugeMx
# print "DEBUG: cg offsets = \n", cgGaugeMx - initialGaugeMx
#
# print "# DEBUG plot"
# #fDebug = open("x0ToBest.dat","w")
# #fDebug = open("x0ToLBFGS.dat","w")
# fDebug = open("x0ToCG.dat","w")
# #fDebug = open("LBFGSToBest.dat","w")
# #fDebug = open("CGToBest.dat","w")
# #fDebug = open("CGToLBFGS.dat","w")
#
# for i in range(nPts+1):
# alpha = float(i) / nPts
# #matM = (1.0-alpha) * initialGaugeMx + alpha*bestGaugeMx
# #matM = (1.0-alpha) * initialGaugeMx + alpha*lbfgsbGaugeMx
# matM = (1.0-alpha) * initialGaugeMx + alpha*cgGaugeMx
# #matM = (1.0-alpha) * lbfgsbGaugeMx + alpha*bestGaugeMx
# #matM = (1.0-alpha) * cgGaugeMx + alpha*bestGaugeMx
# #matM = (1.0-alpha) * cgGaugeMx + alpha*lbfgsbGaugeMx
# print >> fDebug, "%g %g" % (alpha, f(matM.flatten()))
# exit()
#
#
# fDebug = open("lineDataFromX0.dat","w")
# min_offset = -1; max_offset = 1
# for i in range(nPts+1):
# offset = min_offset + float(i)/nPts * (max_offset-min_offset)
# print >> fDebug, "%g" % offset,
#
# for k in range(len(x0)):
# x = x0.copy(); x[k] += offset
# try:
# print >> fDebug, " %g" % f(x),
# except:
# print >> fDebug, " nan",
# print >> fDebug, ""
#
# print >> fDebug, "#END DEBUG plot"
# exit()
#END DEBUG
#err = 1e10
for iter_num in range(iter_max):
w = 1.0 # - i/iter_max
#bDoLocalFitnessOpt = bool(iter_num > 20 and abs(lastBest-gbest.fitness) < 0.001 and iter_num % 10 == 0)
# lastBest = gbest.fitness
# minDistToBest = 1e10; minV = 1e10; maxV = 0 #DEBUG
for (ip, p) in enumerate(particles):
fitness = f(p.params)
#if bDoLocalFitnessOpt:
# opts = {'maxiter': 100, 'maxfev': 100, 'disp': False }
# local_soln = _spo.minimize(f,p.params,options=opts, method='L-BFGS-B',callback=None, tol=1e-2)
# p.params = local_soln.x
# fitness = local_soln.fun
if fitness < p.fitness: # low 'fitness' is good b/c we're minimizing
p.fitness = fitness
p.best = p.params
if fitness < gbest.fitness:
gbest = p; ibest = ip
v = w * p.v + c1 * _np.random.random() * (p.best - p.params) \
+ c2 * _np.random.random() * (gbest.params - p.params)
p.params = p.params + v
for (i, pv) in enumerate(p.params):
p.params[i] = ((pv + 1) % 2) - 1 # periodic b/c on box between -1 and 1
#from .. import tools as tools_
#matM = p.params.reshape( (4,4) ) #DEBUG
#minDistToBest = min(minDistToBest, _tools.frobeniusdist(
# bestGaugeMx,matM)) #DEBUG
#minV = min( _np.linalg.norm(v), minV)
#maxV = max( _np.linalg.norm(v), maxV)
#print "DB: min diff from best = ", minDistToBest #DEBUG
#print "DB: min,max v = ", (minV,maxV)
#if False: #bDoLocalFitnessOpt:
# opts = {'maxiter': 100, 'maxfev': 100, 'disp': False }
# print "initial fun = ",gbest.fitness,
# local_soln = _spo.minimize(f,gbest.params,options=opts, method='L-BFGS-B',callback=None, tol=1e-5)
# gbest.params = local_soln.x
# gbest.fitness = local_soln.fun
# print " final fun = ",gbest.fitness
print("Iter %d: global best = %g (index %d)" % (iter_num, gbest.fitness, ibest))
#if err < err_crit: break #TODO: stopping condition
## Uncomment to print particles
#for p in particles:
# print 'params: %s, fitness: %s, best: %s' % (p.params, p.fitness, p.best)
solution = _optResult()
solution.x = gbest.params; solution.fun = gbest.fitness
solution.success = True
# if iter_num < maxiter:
# solution.success = True
# else:
# solution.success = False
# solution.message = "Maximum iterations exceeded"
return solution
def fmin_evolutionary(f, x0, num_generations, num_individuals):
"""
Minimize a function using an evolutionary algorithm.
Uses python's deap package to perform an evolutionary
algorithm to find a function's global minimum.
Parameters
----------
fn : function
The function to minimize.
x0 : numpy array
The starting point (argument to fn).
num_generations : int
The number of generations to carry out. (similar to the number
of iterations)
num_individuals : int
The number of individuals in each generation. More individuals
make finding the global optimum more likely, but take longer
to run.
Returns
-------
scipy.optimize.Result object
Includes members 'x', 'fun', 'success', and 'message'.
"""
import deap.creator as _creator
import deap.base as _base
import deap.tools as _tools
numParams = len(x0)
# Create the individual class
_creator.create("FitnessMin", _base.Fitness, weights=(-1.0,))
_creator.create("Individual", list, fitness=_creator.FitnessMin)
# Create initialization functions
toolbox = _base.Toolbox()
toolbox.register("random", _np.random.random)
toolbox.register("individual", _tools.initRepeat, _creator.Individual,
toolbox.random, n=numParams) # fn to init an individual from a list of numParams random numbers
# fn to create a population (still need to specify n)
toolbox.register("population", _tools.initRepeat, list, toolbox.individual)
# Create operation functions
def _evaluate(individual):
return f(_np.array(individual)), # note: must return a tuple
toolbox.register("mate", _tools.cxTwoPoint)
toolbox.register("mutate", _tools.mutGaussian, mu=0, sigma=0.5, indpb=0.1)
toolbox.register("select", _tools.selTournament, tournsize=3)
toolbox.register("evaluate", _evaluate)
# Create the population
pop = toolbox.population(n=num_individuals)
# Evaluate the entire population
fitnesses = list(map(toolbox.evaluate, pop))
for ind, fit in zip(pop, fitnesses):
ind.fitness.values = fit
PROB_TO_CROSS = 0.5
PROB_TO_MUTATE = 0.2
# Initialize statistics
stats = _tools.Statistics(key=lambda ind: ind.fitness.values)
stats.register("avg", _np.mean)
stats.register("std", _np.std)
stats.register("min", _np.min)
stats.register("max", _np.max)
logbook = _tools.Logbook()
#Run algorithm
for g in range(num_generations):
record = stats.compile(pop)
logbook.record(gen=g, **record)
print("Gen %d: %s" % (g, record))
# Select the next generation individuals
offspring = toolbox.select(pop, len(pop))
# Clone the selected individuals
offspring = list(map(toolbox.clone, offspring))
# Apply crossover on the offspring
for child1, child2 in zip(offspring[::2], offspring[1::2]):
if _np.random.random() < PROB_TO_CROSS:
toolbox.mate(child1, child2)
del child1.fitness.values
del child2.fitness.values
# Apply mutation on the offspring
for mutant in offspring:
if _np.random.random() < PROB_TO_MUTATE:
toolbox.mutate(mutant)
del mutant.fitness.values
# Evaluate the individuals with an invalid fitness
invalid_ind = [ind for ind in offspring if not ind.fitness.valid]
fitnesses = toolbox.map(toolbox.evaluate, invalid_ind)
for ind, fit in zip(invalid_ind, fitnesses):
ind.fitness.values = fit
# The population is entirely replaced by the offspring
pop[:] = offspring
#get best individual and return params
indx_min_fitness = _np.argmin([ind.fitness.values[0] for ind in pop])
best_params = _np.array(pop[indx_min_fitness])
solution = _optResult()
solution.x = best_params; solution.fun = pop[indx_min_fitness].fitness.values[0]
solution.success = True
return solution
#def fmin_homebrew(f, x0, maxiter):
# """
# Cooked up by Erik, this algorithm is similar to basinhopping but with some tweaks.
#
# Parameters
# ----------
# fn : function
# The function to minimize.
#
# x0 : numpy array
# The starting point (argument to fn).
#
# maxiter : int
# The maximum number of iterations.
#
# Returns
# -------
# scipy.optimize.Result object
# Includes members 'x', 'fun', 'success', and 'message'.
# """
#
# STEP = 0.01
# MAX_STEPS = int(2.0 / STEP) # allow a change of at most 2.0
# MAX_DIR_TRIES = 1000
# T = 1.0
#
# global_best_params = cur_x0 = x0
# global_best = cur_f = f(x0)
# N = len(x0)
# trial_x0 = x0.copy()
#
# for it in range(maxiter):
#
# #Minimize using L-BFGS-B
# opts = {'maxiter': maxiter, 'maxfev': maxiter, 'disp': False }
# soln = _spo.minimize(f,trial_x0,options=opts, method='L-BFGS-B',callback=None, tol=1e-8)
#
# # Update global best
# if soln.fun < global_best:
# global_best_params = soln.x
# global_best = soln.fun
#
# #check if we accept the new minimum
# if soln.fun < cur_f or _np.random.random() < _np.exp( -(soln.fun - cur_f)/T ):
# cur_x0 = soln.x; cur_f = soln.fun
# print "Iter %d: f=%g accepted -- global best = %g" % (it, cur_f, global_best)
# else:
# print "Iter %d: f=%g declined" % (it, cur_f)
#
# trial_x0 = None; numTries = 0
# while trial_x0 is None and numTries < MAX_DIR_TRIES:
# #choose a random direction
# direction = _np.random.random( N )
# numTries += 1
#
# #print "DB: test dir %d" % numTries #DEBUG
#
# #kick solution along random direction until the value of f starts to get smaller again (if it ever does)
# # (this indicates we've gone over a maximum along this direction)
# last_f = cur_f
# for i in range(1,MAX_STEPS):
# test_x = cur_x0 + i*STEP * direction
# test_f = f(test_x)
# #print "DB: test step=%f: f=%f" % (i*STEP, test_f)
# if test_f < last_f:
# trial_x0 = test_x
# print "Found new direction in %d tries, new f(x0) = %g" % (numTries,test_f)
# break
# last_f = test_f
#
# if trial_x0 is None:
# raise ValueError("Maximum number of direction tries exceeded")
#
# solution = _optResult()
# solution.x = global_best_params; solution.fun = global_best
# solution.success = True
## if it < maxiter:
## solution.success = True
## else:
## solution.success = False
## solution.message = "Maximum iterations exceeded"
# return solution
def create_obj_func_printer(objFunc, startTime=None):
"""
Create a callback function that prints the value of an objective function.
Parameters
----------
objFunc : function
The objective function to print.
startTime : float (optional)
A reference starting time to use when printing elapsed times. If None,
then the system time when this function is called is used (which is
often what you want).
Returns
-------
function
A callback function which prints objFunc.
"""
if startTime is None:
startTime = _time.time() # for reference point of obj func printer
def print_obj_func(x, f=None, accepted=None):
"""Just print the objective function value (used to monitor convergence in a callback) """
if f is not None and accepted is not None:
print("%5ds %22.10f %s" % (_time.time() - startTime, f, 'accepted' if accepted else 'not accepted'))
else:
result = objFunc(x)
duration = _time.time() - startTime
try:
print("%5ds %22.10f" % (duration, result))
except TypeError: # Objfun returns vector, not scalar
print('%5ds %s' % (duration, result))
return print_obj_func
def _fwd_diff_jacobian(f, x0, eps=1e-10):
y0 = f(x0).copy()
M = len(y0)
N = len(x0)
jac = _np.empty((M, N), 'd')
for j in range(N):
#print('Adding eps to {}'.format(j))
xj = x0.copy(); xj[j] += eps
yj = f(xj).copy()
#print('y0, yj')
#print(y0[48:52])
#print(yj[48:52])
df = (yj - y0) / eps # df_dxj
jac[:, j] = df
#print(df[48:52])
return jac
def check_jac(f, x0, jacToCheck, eps=1e-10, tol=1e-6, errType='rel',
verbosity=1):
"""
Checks a jacobian function using finite differences.
Parameters
----------
f : function
The function to check.
x0 : numpy array
The point at which to check the jacobian.
jacToCheck : function
A function which should compute the jacobian of f at x0.
eps : float, optional
Epsilon to use in finite difference calculations of jacobian.
tol : float, optional
The allowd tolerance on the relative differene between the
values of the finite difference and jacToCheck jacobians
if errType == 'rel' or the absolute difference if errType == 'abs'.
verbosity : int, optional
Controls how much detail is printed to stdout.
Returns
-------
errSum : float
The total error between the jacobians.
errs : list
List of (row,col,err) tuples giving the error for each row and column.
ffd_jac : numpy array
The computed forward-finite-difference jacobian.
"""
orig_stdout = _sys.stdout
devnull = open(_os.devnull, 'w')
try:
_sys.stdout = devnull # redirect stdout to null during the many f(x) calls
fd_jac = _fwd_diff_jacobian(f, x0, eps)
finally:
_sys.stdout = orig_stdout
devnull.close()
assert(jacToCheck.shape == fd_jac.shape)
M, N = jacToCheck.shape
errSum = 0; errs = []
if errType == 'rel':
for i in range(M):
for j in range(N):
err = _np.abs(fd_jac[i, j] - jacToCheck[i, j]) / (_np.abs(fd_jac[i, j]) + 1e-10)
if err > tol: errs.append((i, j, err))
errSum += err
elif errType == 'abs':
for i in range(M):
for j in range(N):
err = _np.abs(fd_jac[i, j] - jacToCheck[i, j])
if err > tol:
errs.append((i, j, err))
if verbosity > 1:
print("JAC CHECK (%d,%d): %g vs %g (diff = %g)" %
(i, j, fd_jac[i, j], jacToCheck[i, j], fd_jac[i, j] - jacToCheck[i, j]))
errSum += err
errs.sort(key=lambda x: -x[2])
if len(errs) > 0:
maxabs = _np.max(_np.abs(jacToCheck))
max_err_ratio = _np.max([x[2] / maxabs for x in errs])
if verbosity > 0:
if max_err_ratio > 0.01:
print("Warning: jacobian_check has max err/jac_max = %g (jac_max = %g)" % (max_err_ratio, maxabs))
if verbosity > 0:
print("check_jac %s [err = %g]" % (("ERROR" if len(errs) else "OK"), errSum))
return errSum, errs, fd_jac