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#!/usr/bin/env python
#
# Problem definition and original response:
# https://stackoverflow.com/q/12942153/2379433
# https://stackoverflow.com/a/43173143/2379433
#
# Author: Mike McKerns (mmckerns @caltech and @uqfoundation)
# Copyright (c) 2018-2024 The Uncertainty Quantification Foundation.
# License: 3-clause BSD. The full license text is available at:
# - https://github.com/uqfoundation/mystic/blob/master/LICENSE
'''
Attempt to solve equations with no solution, with a constrained search.
The equations are:
(x-x1)^2 + (y-y1)^2 - r1^2 = 0
(x-x2)^2 + (y-y2)^2 - r2^2 = 0
(x-x3)^2 + (y-y3)^2 - r3^2 = 0
with the given points (x,y) and a radii (r):
x1, y1, r1 = (0, 0, 0.88)
x2, y2, r2 = (2, 0, 1)
x3, y3, r3 = (0, 2, 0.75)
'''
def objective(x):
return 0.0
equations = """
(x0 - 0)**2 + (x1 - 0)**2 - .88**2 == 0
(x0 - 2)**2 + (x1 - 0)**2 - 1**2 == 0
(x0 - 0)**2 + (x1 - 2)**2 - .75**2 == 0
"""
bounds = [(None,None),(None,None)] #unnecessary
from mystic.symbolic import generate_constraint, generate_solvers, simplify
from mystic.symbolic import generate_penalty, generate_conditions
from mystic.solvers import diffev2
cf = generate_constraint(generate_solvers(simplify(equations)))
result = diffev2(objective, x0=bounds, bounds=bounds, \
constraints=cf, \
npop=40, gtol=50, disp=False, full_output=True)
print(result[0])
print(result[1])
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