| Current File : //usr/lib64/python2.7/site-packages/numpy/lib/tests/test_polynomial.py |
"""
>>> 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.]))
"""
from numpy.testing import *
import numpy as np
class TestDocs(TestCase):
def test_doctests(self):
return rundocs()
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 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_))
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
if __name__ == "__main__":
run_module_suite()