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"""
Unit tests for optimization routines from minpack.py.
"""
from numpy.testing import assert_, assert_almost_equal, assert_array_equal, \
assert_array_almost_equal, TestCase, run_module_suite, assert_raises
import numpy as np
from numpy import array, float64
from scipy import optimize
from scipy.optimize.minpack import leastsq, curve_fit, fixed_point
class ReturnShape(object):
"""This class exists to create a callable that does not have a 'func_name' attribute.
__init__ takes the argument 'shape', which should be a tuple of ints. When an instance
it called with a single argument 'x', it returns numpy.ones(shape).
"""
def __init__(self, shape):
self.shape = shape
def __call__(self, x):
return np.ones(self.shape)
def dummy_func(x, shape):
"""A function that returns an array of ones of the given shape.
`x` is ignored.
"""
return np.ones(shape)
class TestFSolve(object):
def pressure_network(self, flow_rates, Qtot, k):
"""Evaluate non-linear equation system representing
the pressures and flows in a system of n parallel pipes::
f_i = P_i - P_0, for i = 1..n
f_0 = sum(Q_i) - Qtot
Where Q_i is the flow rate in pipe i and P_i the pressure in that pipe.
Pressure is modeled as a P=kQ**2 where k is a valve coefficient and
Q is the flow rate.
Parameters
----------
flow_rates : float
A 1D array of n flow rates [kg/s].
k : float
A 1D array of n valve coefficients [1/kg m].
Qtot : float
A scalar, the total input flow rate [kg/s].
Returns
-------
F : float
A 1D array, F[i] == f_i.
"""
P = k * flow_rates**2
F = np.hstack((P[1:] - P[0], flow_rates.sum() - Qtot))
return F
def pressure_network_jacobian(self, flow_rates, Qtot, k):
"""Return the jacobian of the equation system F(flow_rates)
computed by `pressure_network` with respect to
*flow_rates*. See `pressure_network` for the detailed
description of parrameters.
Returns
-------
jac : float
*n* by *n* matrix ``df_i/dQ_i`` where ``n = len(flow_rates)``
and *f_i* and *Q_i* are described in the doc for `pressure_network`
"""
n = len(flow_rates)
pdiff = np.diag(flow_rates[1:] * 2 * k[1:] - 2 * flow_rates[0] * k[0])
jac = np.empty((n, n))
jac[:n-1, :n-1] = pdiff
jac[:n-1, n-1] = 0
jac[n-1, :] = np.ones(n)
return jac
def test_pressure_network_no_gradient(self):
"""fsolve without gradient, equal pipes -> equal flows"""
k = np.ones(4) * 0.5
Qtot = 4
initial_guess = array([2., 0., 2., 0.])
final_flows = optimize.fsolve(
self.pressure_network, initial_guess, args=(Qtot, k))
assert_array_almost_equal(final_flows, np.ones(4))
def test_pressure_network_with_gradient(self):
"""fsolve with gradient, equal pipes -> equal flows"""
k = np.ones(4) * 0.5
Qtot = 4
initial_guess = array([2., 0., 2., 0.])
final_flows = optimize.fsolve(
self.pressure_network, initial_guess, args=(Qtot, k),
fprime=self.pressure_network_jacobian)
assert_array_almost_equal(final_flows, np.ones(4))
def test_wrong_shape_func_callable(self):
"""The callable 'func' has no 'func_name' attribute."""
func = ReturnShape(1)
# x0 is a list of two elements, but func will return an array with
# length 1, so this should result in a TypeError.
x0 = [1.5, 2.0]
assert_raises(TypeError, optimize.fsolve, func, x0)
def test_wrong_shape_func_function(self):
# x0 is a list of two elements, but func will return an array with
# length 1, so this should result in a TypeError.
x0 = [1.5, 2.0]
assert_raises(TypeError, optimize.fsolve, dummy_func, x0, args=((1,),))
def test_wrong_shape_fprime_callable(self):
"""The callables 'func' and 'deriv_func' have no 'func_name' attribute."""
func = ReturnShape(1)
deriv_func = ReturnShape((2,2))
assert_raises(TypeError, optimize.fsolve, func, x0=[0,1], fprime=deriv_func)
def test_wrong_shape_fprime_function(self):
func = lambda x: dummy_func(x, (2,))
deriv_func = lambda x: dummy_func(x, (3,3))
assert_raises(TypeError, optimize.fsolve, func, x0=[0,1], fprime=deriv_func)
class TestLeastSq(TestCase):
def setUp(self):
x = np.linspace(0, 10, 40)
a,b,c = 3.1, 42, -304.2
self.x = x
self.abc = a,b,c
y_true = a*x**2 + b*x + c
np.random.seed(0)
self.y_meas = y_true + 0.01*np.random.standard_normal(y_true.shape)
def residuals(self, p, y, x):
a,b,c = p
err = y-(a*x**2 + b*x + c)
return err
def test_basic(self):
p0 = array([0,0,0])
params_fit, ier = leastsq(self.residuals, p0,
args=(self.y_meas, self.x))
assert_(ier in (1,2,3,4), 'solution not found (ier=%d)'%ier)
# low precision due to random
assert_array_almost_equal(params_fit, self.abc, decimal=2)
def test_full_output(self):
p0 = array([0,0,0])
full_output = leastsq(self.residuals, p0,
args=(self.y_meas, self.x),
full_output=True)
params_fit, cov_x, infodict, mesg, ier = full_output
assert_(ier in (1,2,3,4), 'solution not found: %s'%mesg)
def test_input_untouched(self):
p0 = array([0,0,0],dtype=float64)
p0_copy = array(p0, copy=True)
full_output = leastsq(self.residuals, p0,
args=(self.y_meas, self.x),
full_output=True)
params_fit, cov_x, infodict, mesg, ier = full_output
assert_(ier in (1,2,3,4), 'solution not found: %s'%mesg)
assert_array_equal(p0, p0_copy)
def test_wrong_shape_func_callable(self):
"""The callable 'func' has no 'func_name' attribute."""
func = ReturnShape(1)
# x0 is a list of two elements, but func will return an array with
# length 1, so this should result in a TypeError.
x0 = [1.5, 2.0]
assert_raises(TypeError, optimize.leastsq, func, x0)
def test_wrong_shape_func_function(self):
# x0 is a list of two elements, but func will return an array with
# length 1, so this should result in a TypeError.
x0 = [1.5, 2.0]
assert_raises(TypeError, optimize.leastsq, dummy_func, x0, args=((1,),))
def test_wrong_shape_Dfun_callable(self):
"""The callables 'func' and 'deriv_func' have no 'func_name' attribute."""
func = ReturnShape(1)
deriv_func = ReturnShape((2,2))
assert_raises(TypeError, optimize.leastsq, func, x0=[0,1], Dfun=deriv_func)
def test_wrong_shape_Dfun_function(self):
func = lambda x: dummy_func(x, (2,))
deriv_func = lambda x: dummy_func(x, (3,3))
assert_raises(TypeError, optimize.leastsq, func, x0=[0,1], Dfun=deriv_func)
class TestCurveFit(TestCase):
def setUp(self):
self.y = array([1.0, 3.2, 9.5, 13.7])
self.x = array([1.0, 2.0, 3.0, 4.0])
def test_one_argument(self):
def func(x,a):
return x**a
popt, pcov = curve_fit(func, self.x, self.y)
assert_(len(popt) == 1)
assert_(pcov.shape == (1,1))
assert_almost_equal(popt[0], 1.9149, decimal=4)
assert_almost_equal(pcov[0,0], 0.0016, decimal=4)
# Test if we get the same with full_output. Regression test for #1415.
res = curve_fit(func, self.x, self.y, full_output=1)
(popt2, pcov2, infodict, errmsg, ier) = res
assert_array_almost_equal(popt, popt2)
def test_two_argument(self):
def func(x, a, b):
return b*x**a
popt, pcov = curve_fit(func, self.x, self.y)
assert_(len(popt) == 2)
assert_(pcov.shape == (2,2))
assert_array_almost_equal(popt, [1.7989, 1.1642], decimal=4)
assert_array_almost_equal(pcov, [[0.0852, -0.1260],[-0.1260, 0.1912]],
decimal=4)
def test_func_is_classmethod(self):
class test_self(object):
"""This class tests if curve_fit passes the correct number of
arguments when the model function is a class instance method.
"""
def func(self, x, a, b):
return b * x**a
test_self_inst = test_self()
popt, pcov = curve_fit(test_self_inst.func, self.x, self.y)
assert_(pcov.shape == (2,2))
assert_array_almost_equal(popt, [1.7989, 1.1642], decimal=4)
assert_array_almost_equal(pcov, [[0.0852, -0.1260], [-0.1260, 0.1912]],
decimal=4)
class TestFixedPoint(TestCase):
def test_scalar_trivial(self):
"""f(x) = 2x; fixed point should be x=0"""
def func(x):
return 2.0*x
x0 = 1.0
x = fixed_point(func, x0)
assert_almost_equal(x, 0.0)
def test_scalar_basic1(self):
"""f(x) = x**2; x0=1.05; fixed point should be x=1"""
def func(x):
return x**2
x0 = 1.05
x = fixed_point(func, x0)
assert_almost_equal(x, 1.0)
def test_scalar_basic2(self):
"""f(x) = x**0.5; x0=1.05; fixed point should be x=1"""
def func(x):
return x**0.5
x0 = 1.05
x = fixed_point(func, x0)
assert_almost_equal(x, 1.0)
def test_array_trivial(self):
def func(x):
return 2.0*x
x0 = [0.3, 0.15]
olderr = np.seterr(all='ignore')
try:
x = fixed_point(func, x0)
finally:
np.seterr(**olderr)
assert_almost_equal(x, [0.0, 0.0])
def test_array_basic1(self):
"""f(x) = c * x**2; fixed point should be x=1/c"""
def func(x, c):
return c * x**2
c = array([0.75, 1.0, 1.25])
x0 = [1.1, 1.15, 0.9]
olderr = np.seterr(all='ignore')
try:
x = fixed_point(func, x0, args=(c,))
finally:
np.seterr(**olderr)
assert_almost_equal(x, 1.0/c)
def test_array_basic2(self):
"""f(x) = c * x**0.5; fixed point should be x=c**2"""
def func(x, c):
return c * x**0.5
c = array([0.75, 1.0, 1.25])
x0 = [0.8, 1.1, 1.1]
x = fixed_point(func, x0, args=(c,))
assert_almost_equal(x, c**2)
if __name__ == "__main__":
run_module_suite()
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