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Diffstat (limited to 'numpy/lib/tests/test_polynomial.py')
| -rw-r--r-- | numpy/lib/tests/test_polynomial.py | 212 |
1 files changed, 116 insertions, 96 deletions
diff --git a/numpy/lib/tests/test_polynomial.py b/numpy/lib/tests/test_polynomial.py index 2aed5c924..89759bd83 100644 --- a/numpy/lib/tests/test_polynomial.py +++ b/numpy/lib/tests/test_polynomial.py @@ -1,93 +1,79 @@ 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 + assert_, assert_equal, assert_array_equal, assert_almost_equal, + assert_array_almost_equal, assert_raises, assert_allclose ) -class TestDocs(TestCase): - def test_doctests(self): - return rundocs() +class TestPolynomial(object): + def test_poly1d_str_and_repr(self): + p = np.poly1d([1., 2, 3]) + assert_equal(repr(p), 'poly1d([1., 2., 3.])') + assert_equal(str(p), + ' 2\n' + '1 x + 2 x + 3') + + q = np.poly1d([3., 2, 1]) + assert_equal(repr(q), 'poly1d([3., 2., 1.])') + assert_equal(str(q), + ' 2\n' + '3 x + 2 x + 1') + + r = np.poly1d([1.89999 + 2j, -3j, -5.12345678, 2 + 1j]) + assert_equal(str(r), + ' 3 2\n' + '(1.9 + 2j) x - 3j x - 5.123 x + (2 + 1j)') + + assert_equal(str(np.poly1d([-3, -2, -1])), + ' 2\n' + '-3 x - 2 x - 1') + + def test_poly1d_resolution(self): + p = np.poly1d([1., 2, 3]) + q = np.poly1d([3., 2, 1]) + assert_equal(p(0), 3.0) + assert_equal(p(5), 38.0) + assert_equal(q(0), 1.0) + assert_equal(q(5), 86.0) + + def test_poly1d_math(self): + # here we use some simple coeffs to make calculations easier + p = np.poly1d([1., 2, 4]) + q = np.poly1d([4., 2, 1]) + assert_equal(p/q, (np.poly1d([0.25]), np.poly1d([1.5, 3.75]))) + assert_equal(p.integ(), np.poly1d([1/3, 1., 4., 0.])) + assert_equal(p.integ(1), np.poly1d([1/3, 1., 4., 0.])) + + p = np.poly1d([1., 2, 3]) + q = np.poly1d([3., 2, 1]) + assert_equal(p * q, np.poly1d([3., 8., 14., 8., 3.])) + assert_equal(p + q, np.poly1d([4., 4., 4.])) + assert_equal(p - q, np.poly1d([-2., 0., 2.])) + assert_equal(p ** 4, np.poly1d([1., 8., 36., 104., 214., 312., 324., 216., 81.])) + assert_equal(p(q), np.poly1d([9., 12., 16., 8., 6.])) + assert_equal(q(p), np.poly1d([3., 12., 32., 40., 34.])) + assert_equal(p.deriv(), np.poly1d([2., 2.])) + assert_equal(p.deriv(2), np.poly1d([2.])) + assert_equal(np.polydiv(np.poly1d([1, 0, -1]), np.poly1d([1, 1])), + (np.poly1d([1., -1.]), np.poly1d([0.]))) + + def test_poly1d_misc(self): + p = np.poly1d([1., 2, 3]) + assert_equal(np.asarray(p), np.array([1., 2., 3.])) + assert_equal(len(p), 2) + assert_equal((p[0], p[1], p[2], p[3]), (3.0, 2.0, 1.0, 0)) + + def test_poly1d_variable_arg(self): + q = np.poly1d([1., 2, 3], variable='y') + assert_equal(str(q), + ' 2\n' + '1 y + 2 y + 3') + q = np.poly1d([1., 2, 3], variable='lambda') + assert_equal(str(q), + ' 2\n' + '1 lambda + 2 lambda + 3') def test_poly(self): assert_array_almost_equal(np.poly([3, -np.sqrt(2), np.sqrt(2)]), @@ -136,27 +122,34 @@ class TestDocs(TestCase): 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. + # the estimate requires the number of data points to exceed + # degree + 1 assert_raises(ValueError, np.polyfit, - [0, 1, 3], [0, 1, 3], deg=0, cov=True) + [1], [1], 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]] + val0 = [[ 1.4694, -2.9388, 0.8163], + [-2.9388, 6.3673, -2.1224], + [ 0.8163, -2.1224, 1.161 ]] 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]] + val = [[ 4.3964, -5.0052, 0.4878], + [-5.0052, 6.8067, -0.9089], + [ 0.4878, -0.9089, 0.3337]] assert_almost_equal(val, cov2, decimal=4) + m3, cov3 = np.polyfit(x, y+err, 2, w=weights, cov="unscaled") + assert_almost_equal([4.8927, -1.0177, 1.7768], m3, decimal=4) + val = [[ 0.1473, -0.1677, 0.0163], + [-0.1677, 0.228 , -0.0304], + [ 0.0163, -0.0304, 0.0112]] + assert_almost_equal(val, cov3, decimal=4) + # check 2D (n,1) case y = y[:, np.newaxis] c = c[:, np.newaxis] @@ -172,6 +165,29 @@ class TestDocs(TestCase): assert_almost_equal(val0, cov[:, :, 0], decimal=4) assert_almost_equal(val0, cov[:, :, 1], decimal=4) + # check order 1 (deg=0) case, were the analytic results are simple + np.random.seed(123) + y = np.random.normal(size=(4, 10000)) + mean, cov = np.polyfit(np.zeros(y.shape[0]), y, deg=0, cov=True) + # Should get sigma_mean = sigma/sqrt(N) = 1./sqrt(4) = 0.5. + assert_allclose(mean.std(), 0.5, atol=0.01) + assert_allclose(np.sqrt(cov.mean()), 0.5, atol=0.01) + # Without scaling, since reduced chi2 is 1, the result should be the same. + mean, cov = np.polyfit(np.zeros(y.shape[0]), y, w=np.ones(y.shape[0]), + deg=0, cov="unscaled") + assert_allclose(mean.std(), 0.5, atol=0.01) + assert_almost_equal(np.sqrt(cov.mean()), 0.5) + # If we estimate our errors wrong, no change with scaling: + w = np.full(y.shape[0], 1./0.5) + mean, cov = np.polyfit(np.zeros(y.shape[0]), y, w=w, deg=0, cov=True) + assert_allclose(mean.std(), 0.5, atol=0.01) + assert_allclose(np.sqrt(cov.mean()), 0.5, atol=0.01) + # But if we do not scale, our estimate for the error in the mean will + # differ. + mean, cov = np.polyfit(np.zeros(y.shape[0]), y, w=w, deg=0, cov="unscaled") + assert_allclose(mean.std(), 0.5, atol=0.01) + assert_almost_equal(np.sqrt(cov.mean()), 0.25) + def test_objects(self): from decimal import Decimal p = np.poly1d([Decimal('4.0'), Decimal('3.0'), Decimal('2.0')]) @@ -222,6 +238,14 @@ class TestDocs(TestCase): assert_equal(p == p2, False) assert_equal(p != p2, True) + def test_polydiv(self): + b = np.poly1d([2, 6, 6, 1]) + a = np.poly1d([-1j, (1+2j), -(2+1j), 1]) + q, r = np.polydiv(b, a) + assert_equal(q.coeffs.dtype, np.complex128) + assert_equal(r.coeffs.dtype, np.complex128) + assert_equal(q*a + r, b) + def test_poly_coeffs_mutable(self): """ Coefficients should be modifiable """ p = np.poly1d([1, 2, 3]) @@ -235,7 +259,3 @@ class TestDocs(TestCase): # 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() |