275 lines
7.1 KiB
Python
Executable file
275 lines
7.1 KiB
Python
Executable file
#!/usr/bin/python3
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'''=pod
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=head1 NAME
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find-optimal - Find optimal values
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=head1 SYNOPSIS
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B<find-optimal> I<command> [[options] I<value>] [options]
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=head1 DESCRIPTION
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B<find-optimal> will search for the optimal values for options.
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It does this by calling I<command> with different values.
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I<command> must as the last line output a value that says how bad it
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was. B<find-optimal> will search for the smallest value.
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=head1 EXAMPLE
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Find the best value of pi - use 10 as a starting guess:
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pi() { perl -e 'print(abs(shift()-3.14159265))' -- "$@"; }
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export -f pi
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find-optimal pi 10
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Find the best values of pi and e - use 10 as starting guess for pi,
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and 100 for e:
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pie() { perl -e 'print(abs(shift()-3.14159265)+abs(shift()-2.718281828))' -- "$@"; }
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export -f pie
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find-optimal pie 10 100
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=cut
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#Find the fastest block size for dd
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#
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# mydd() { ( \time -f%e dd bs=$@ if=/dev/zero | head -c1G >/dev/null) 2>&1;}
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# export -f mydd
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# find-optimal mydd 10
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# find-optimal -i --min 1 mydd 10
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=pod
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=head1 BUGS
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B<find-optimal> used Nelder-Mead. Unfortunately, this only works well
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for continous functions and not integers.
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So currently B<find-optimal> will not work well for integers.
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=head1 AUTHOR
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Copyright (C) 2022 Ole Tange,
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http://ole.tange.dk and Free Software Foundation, Inc.
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=head1 LICENSE
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Copyright (C) 2012 Free Software Foundation, Inc.
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This program is free software; you can redistribute it and/or modify
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it under the terms of the GNU General Public License as published by
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the Free Software Foundation; either version 3 of the License, or
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at your option any later version.
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This program is distributed in the hope that it will be useful,
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but WITHOUT ANY WARRANTY; without even the implied warranty of
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MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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GNU General Public License for more details.
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You should have received a copy of the GNU General Public License
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along with this program. If not, see <http://www.gnu.org/licenses/>.
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=head1 DEPENDENCIES
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B<vid> uses B<G>, and B<vlc>.
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=head1 SEE ALSO
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B<G>
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=cut
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'''
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def add(x,y):
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z = list(0 for i in x)
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for i in range(0,len(x)):
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z[i] = x[i] + y[i]
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return (z)
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def sub(x,y):
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z = list(0 for i in x)
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for i in range(0,len(x)):
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z[i] = x[i] - y[i]
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return (z)
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def mul(x,y):
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z = list(0 for i in y)
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for i in range(0,len(y)):
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z[i] = x * y[i]
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return (z)
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def nelder_mead(f, x_start,
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step=0.001, no_improve_thr=10e-6,
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no_improv_break=10, max_iter=0,
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alpha=1., gamma=2., rho=-0.5, sigma=0.5):
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'''
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Pure Python implementation of the Nelder-Mead algorithm.
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Reference: https://en.wikipedia.org/wiki/Nelder%E2%80%93Mead_method
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MIT Licence. Copyright (c) 2017 Matteo Maggioni
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@param f (function): function to optimize, must return a scalar score
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and operate over a numpy array of the same dimensions as x_start
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@param x_start (numpy array): initial position
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@param step (float): look-around radius in initial step
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@no_improv_thr, no_improv_break (float, int): break after no_improv_break iterations with
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an improvement lower than no_improv_thr
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@max_iter (int): always break after this number of iterations.
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Set it to 0 to loop indefinitely.
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@alpha, gamma, rho, sigma (floats): parameters of the algorithm
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(see Wikipedia page for reference)
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return: tuple (best parameter array, best score)
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'''
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# init
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dim = len(x_start)
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prev_best = f(x_start)
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no_improv = 0
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res = [[x_start, prev_best]]
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for i in range(dim):
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x = mul(1,x_start)
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x[i] = x[i] + step
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score = f(x)
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res.append([x, score])
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# simplex iter
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iters = 0
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while 1:
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# order
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res.sort(key=lambda x: x[1])
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best = res[0][1]
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# break after max_iter
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if max_iter and iters >= max_iter:
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return res[0]
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iters += 1
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if best < prev_best - no_improve_thr:
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no_improv = 0
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prev_best = best
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else:
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no_improv += 1
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if no_improv >= no_improv_break:
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return res[0]
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# centroid
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x0 = [0.] * dim
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for tup in res[:-1]:
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for i, c in enumerate(tup[0]):
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x0[i] += c / (len(res)-1)
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# reflection
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xr = add(x0, mul(alpha,(sub(x0, res[-1][0]))))
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rscore = f(xr)
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if res[0][1] <= rscore < res[-2][1]:
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del res[-1]
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res.append([xr, rscore])
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continue
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# expansion
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if rscore < res[0][1]:
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xe = add(x0, mul(gamma,(sub(x0, res[-1][0]))))
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escore = f(xe)
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if escore < rscore:
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del res[-1]
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res.append([xe, escore])
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continue
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else:
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del res[-1]
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res.append([xr, rscore])
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continue
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# contraction
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xc = add(x0, mul(rho,(sub(x0, res[-1][0]))))
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cscore = f(xc)
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if cscore < res[-1][1]:
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del res[-1]
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res.append([xc, cscore])
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continue
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# reduction
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x1 = res[0][0]
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nres = []
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for tup in res:
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redx = add(x1, mul(sigma,(sub(tup[0],x1))))
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score = f(redx)
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nres.append([redx, score])
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res = nres
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def test():
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import math
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def f(x):
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return math.sin(x[0]) * math.cos(x[1]) * (1. / (abs(x[2]) + 1))
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print(nelder_mead(f, list([0., 20., 0.])))
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if __name__ == "__main__":
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import sys
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import subprocess
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import re
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opt_verbose=True
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def f(x):
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# Run the shell command with the numeric values
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# return the value of last line of output
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run_arr=[]
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i=0
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for s in cmdtemplate:
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if s == "0":
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v = x[i];
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try:
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if opt_integer:
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v = int(v)
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if v < opt_min:
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v = opt_min
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except NameError:
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True
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run_arr.append(str(v))
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i += 1
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else:
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run_arr.append(s)
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run = ' '.join(run_arr)
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try:
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if opt_verbose:
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print(run)
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except NameError:
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True
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# Last line of stdout
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try:
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return float(subprocess.check_output(args=run,
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shell=True,
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executable='/bin/bash')
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.splitlines()[-1])
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except IndexError:
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print("Command returns nothing.")
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exit(1);
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except subprocess.CalledProcessError:
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exit(1);
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cmdtemplate = []
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values = []
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# Convert:
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# cmd -s 6 -f 7 -o foo
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# =>
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# [cmd -s 0 -f 0 -o foo],[6,7]
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for s in sys.argv[1:]:
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if re.match(r'^[-0-9.]+$',s):
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values.append(s)
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cmdtemplate.append("0")
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else:
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cmdtemplate.append(s)
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print(nelder_mead(f, list([float(i) for i in values])))
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