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from __future__ import division, absolute_import, print_function
'''
>>> p = np.poly1d([1.,2,3])
>>> p
poly1d([ 1., 2., 3.])
>>> print(p)
2
1 x + 2 x + 3
>>> q = np.poly1d([3.,2,1])
>>> q
poly1d([ 3., 2., 1.])
>>> print(q)
2
3 x + 2 x + 1
>>> print(np.poly1d([1.89999+2j, -3j, -5.12345678, 2+1j]))
3 2
(1.9 + 2j) x - 3j x - 5.123 x + (2 + 1j)
>>> print(np.poly1d([-3, -2, -1]))
2
-3 x - 2 x - 1
>>> p(0)
3.0
>>> p(5)
38.0
>>> q(0)
1.0
>>> q(5)
86.0
>>> p * q
poly1d([ 3., 8., 14., 8., 3.])
>>> p / q
(poly1d([ 0.33333333]), poly1d([ 1.33333333, 2.66666667]))
>>> p + q
poly1d([ 4., 4., 4.])
>>> p - q
poly1d([-2., 0., 2.])
>>> p ** 4
poly1d([ 1., 8., 36., 104., 214., 312., 324., 216., 81.])
>>> p(q)
poly1d([ 9., 12., 16., 8., 6.])
>>> q(p)
poly1d([ 3., 12., 32., 40., 34.])
>>> np.asarray(p)
array([ 1., 2., 3.])
>>> len(p)
2
>>> p[0], p[1], p[2], p[3]
(3.0, 2.0, 1.0, 0)
>>> p.integ()
poly1d([ 0.33333333, 1. , 3. , 0. ])
>>> p.integ(1)
poly1d([ 0.33333333, 1. , 3. , 0. ])
>>> p.integ(5)
poly1d([ 0.00039683, 0.00277778, 0.025 , 0. , 0. ,
0. , 0. , 0. ])
>>> p.deriv()
poly1d([ 2., 2.])
>>> p.deriv(2)
poly1d([ 2.])
>>> q = np.poly1d([1.,2,3], variable='y')
>>> print(q)
2
1 y + 2 y + 3
>>> q = np.poly1d([1.,2,3], variable='lambda')
>>> print(q)
2
1 lambda + 2 lambda + 3
>>> np.polydiv(np.poly1d([1,0,-1]), np.poly1d([1,1]))
(poly1d([ 1., -1.]), poly1d([ 0.]))
'''
import numpy as np
from numpy.testing import (
run_module_suite, TestCase, assert_, assert_equal, assert_array_equal,
assert_almost_equal, assert_array_almost_equal, assert_raises, rundocs
)
class TestDocs(TestCase):
def test_doctests(self):
return rundocs()
def test_poly(self):
assert_array_almost_equal(np.poly([3, -np.sqrt(2), np.sqrt(2)]),
[1, -3, -2, 6])
# From matlab docs
A = [[1, 2, 3], [4, 5, 6], [7, 8, 0]]
assert_array_almost_equal(np.poly(A), [1, -6, -72, -27])
# Should produce real output for perfect conjugates
assert_(np.isrealobj(np.poly([+1.082j, +2.613j, -2.613j, -1.082j])))
assert_(np.isrealobj(np.poly([0+1j, -0+-1j, 1+2j,
1-2j, 1.+3.5j, 1-3.5j])))
assert_(np.isrealobj(np.poly([1j, -1j, 1+2j, 1-2j, 1+3j, 1-3.j])))
assert_(np.isrealobj(np.poly([1j, -1j, 1+2j, 1-2j])))
assert_(np.isrealobj(np.poly([1j, -1j, 2j, -2j])))
assert_(np.isrealobj(np.poly([1j, -1j])))
assert_(np.isrealobj(np.poly([1, -1])))
assert_(np.iscomplexobj(np.poly([1j, -1.0000001j])))
np.random.seed(42)
a = np.random.randn(100) + 1j*np.random.randn(100)
assert_(np.isrealobj(np.poly(np.concatenate((a, np.conjugate(a))))))
def test_roots(self):
assert_array_equal(np.roots([1, 0, 0]), [0, 0])
def test_str_leading_zeros(self):
p = np.poly1d([4, 3, 2, 1])
p[3] = 0
assert_equal(str(p),
" 2\n"
"3 x + 2 x + 1")
p = np.poly1d([1, 2])
p[0] = 0
p[1] = 0
assert_equal(str(p), " \n0")
def test_polyfit(self):
c = np.array([3., 2., 1.])
x = np.linspace(0, 2, 7)
y = np.polyval(c, x)
err = [1, -1, 1, -1, 1, -1, 1]
weights = np.arange(8, 1, -1)**2/7.0
# Check exception when too few points for variance estimate. Note that
# the Bayesian estimate requires the number of data points to exceed
# degree + 3.
assert_raises(ValueError, np.polyfit,
[0, 1, 3], [0, 1, 3], deg=0, cov=True)
# check 1D case
m, cov = np.polyfit(x, y+err, 2, cov=True)
est = [3.8571, 0.2857, 1.619]
assert_almost_equal(est, m, decimal=4)
val0 = [[2.9388, -5.8776, 1.6327],
[-5.8776, 12.7347, -4.2449],
[1.6327, -4.2449, 2.3220]]
assert_almost_equal(val0, cov, decimal=4)
m2, cov2 = np.polyfit(x, y+err, 2, w=weights, cov=True)
assert_almost_equal([4.8927, -1.0177, 1.7768], m2, decimal=4)
val = [[8.7929, -10.0103, 0.9756],
[-10.0103, 13.6134, -1.8178],
[0.9756, -1.8178, 0.6674]]
assert_almost_equal(val, cov2, decimal=4)
# check 2D (n,1) case
y = y[:, np.newaxis]
c = c[:, np.newaxis]
assert_almost_equal(c, np.polyfit(x, y, 2))
# check 2D (n,2) case
yy = np.concatenate((y, y), axis=1)
cc = np.concatenate((c, c), axis=1)
assert_almost_equal(cc, np.polyfit(x, yy, 2))
m, cov = np.polyfit(x, yy + np.array(err)[:, np.newaxis], 2, cov=True)
assert_almost_equal(est, m[:, 0], decimal=4)
assert_almost_equal(est, m[:, 1], decimal=4)
assert_almost_equal(val0, cov[:, :, 0], decimal=4)
assert_almost_equal(val0, cov[:, :, 1], decimal=4)
def test_objects(self):
from decimal import Decimal
p = np.poly1d([Decimal('4.0'), Decimal('3.0'), Decimal('2.0')])
p2 = p * Decimal('1.333333333333333')
assert_(p2[1] == Decimal("3.9999999999999990"))
p2 = p.deriv()
assert_(p2[1] == Decimal('8.0'))
p2 = p.integ()
assert_(p2[3] == Decimal("1.333333333333333333333333333"))
assert_(p2[2] == Decimal('1.5'))
assert_(np.issubdtype(p2.coeffs.dtype, np.object_))
p = np.poly([Decimal(1), Decimal(2)])
assert_equal(np.poly([Decimal(1), Decimal(2)]),
[1, Decimal(-3), Decimal(2)])
def test_complex(self):
p = np.poly1d([3j, 2j, 1j])
p2 = p.integ()
assert_((p2.coeffs == [1j, 1j, 1j, 0]).all())
p2 = p.deriv()
assert_((p2.coeffs == [6j, 2j]).all())
def test_integ_coeffs(self):
p = np.poly1d([3, 2, 1])
p2 = p.integ(3, k=[9, 7, 6])
assert_(
(p2.coeffs == [1/4./5., 1/3./4., 1/2./3., 9/1./2., 7, 6]).all())
def test_zero_dims(self):
try:
np.poly(np.zeros((0, 0)))
except ValueError:
pass
def test_poly_int_overflow(self):
"""
Regression test for gh-5096.
"""
v = np.arange(1, 21)
assert_almost_equal(np.poly(v), np.poly(np.diag(v)))
def test_poly_eq(self):
p = np.poly1d([1, 2, 3])
p2 = np.poly1d([1, 2, 4])
assert_equal(p == None, False)
assert_equal(p != None, True)
assert_equal(p == p, True)
assert_equal(p == p2, False)
assert_equal(p != p2, True)
def test_poly_coeffs_mutable(self):
""" Coefficients should be modifiable """
p = np.poly1d([1, 2, 3])
p.coeffs += 1
assert_equal(p.coeffs, [2, 3, 4])
p.coeffs[2] += 10
assert_equal(p.coeffs, [2, 3, 14])
# this never used to be allowed - let's not add features to deprecated
# APIs
assert_raises(AttributeError, setattr, p, 'coeffs', np.array(1))
if __name__ == "__main__":
run_module_suite()
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