diff options
Diffstat (limited to 'numpy/lib/polynomial.py')
| -rw-r--r-- | numpy/lib/polynomial.py | 43 |
1 files changed, 22 insertions, 21 deletions
diff --git a/numpy/lib/polynomial.py b/numpy/lib/polynomial.py index e3defdca2..7904092ed 100644 --- a/numpy/lib/polynomial.py +++ b/numpy/lib/polynomial.py @@ -110,7 +110,7 @@ def poly(seq_of_zeros): Given a sequence of a polynomial's zeros: >>> np.poly((0, 0, 0)) # Multiple root example - array([1, 0, 0, 0]) + array([1., 0., 0., 0.]) The line above represents z**3 + 0*z**2 + 0*z + 0. @@ -119,14 +119,14 @@ def poly(seq_of_zeros): The line above represents z**3 - z/4 - >>> np.poly((np.random.random(1.)[0], 0, np.random.random(1.)[0])) - array([ 1. , -0.77086955, 0.08618131, 0. ]) #random + >>> np.poly((np.random.random(1)[0], 0, np.random.random(1)[0])) + array([ 1. , -0.77086955, 0.08618131, 0. ]) # random Given a square array object: >>> P = np.array([[0, 1./3], [-1./2, 0]]) >>> np.poly(P) - array([ 1. , 0. , 0.16666667]) + array([1. , 0. , 0.16666667]) Note how in all cases the leading coefficient is always 1. @@ -295,7 +295,7 @@ def polyint(p, m=1, k=None): >>> p = np.poly1d([1,1,1]) >>> P = np.polyint(p) >>> P - poly1d([ 0.33333333, 0.5 , 1. , 0. ]) + poly1d([ 0.33333333, 0.5 , 1. , 0. ]) # may vary >>> np.polyder(P) == p True @@ -310,7 +310,7 @@ def polyint(p, m=1, k=None): 0.0 >>> P = np.polyint(p, 3, k=[6,5,3]) >>> P - poly1d([ 0.01666667, 0.04166667, 0.16666667, 3. , 5. , 3. ]) + poly1d([ 0.01666667, 0.04166667, 0.16666667, 3. , 5. , 3. ]) # may vary Note that 3 = 6 / 2!, and that the constants are given in the order of integrations. Constant of the highest-order polynomial term comes first: @@ -404,7 +404,7 @@ def polyder(p, m=1): >>> np.polyder(p, 3) poly1d([6]) >>> np.polyder(p, 4) - poly1d([ 0.]) + poly1d([0.]) """ m = int(m) @@ -552,28 +552,29 @@ def polyfit(x, y, deg, rcond=None, full=False, w=None, cov=False): >>> y = np.array([0.0, 0.8, 0.9, 0.1, -0.8, -1.0]) >>> z = np.polyfit(x, y, 3) >>> z - array([ 0.08703704, -0.81349206, 1.69312169, -0.03968254]) + array([ 0.08703704, -0.81349206, 1.69312169, -0.03968254]) # may vary It is convenient to use `poly1d` objects for dealing with polynomials: >>> p = np.poly1d(z) >>> p(0.5) - 0.6143849206349179 + 0.6143849206349179 # may vary >>> p(3.5) - -0.34732142857143039 + -0.34732142857143039 # may vary >>> p(10) - 22.579365079365115 + 22.579365079365115 # may vary High-order polynomials may oscillate wildly: >>> p30 = np.poly1d(np.polyfit(x, y, 30)) - /... RankWarning: Polyfit may be poorly conditioned... + ... + >>> # RankWarning: Polyfit may be poorly conditioned... >>> p30(4) - -0.80000000000000204 + -0.80000000000000204 # may vary >>> p30(5) - -0.99999999999999445 + -0.99999999999999445 # may vary >>> p30(4.5) - -0.10547061179440398 + -0.10547061179440398 # may vary Illustration: @@ -714,11 +715,11 @@ def polyval(p, x): >>> np.polyval([3,0,1], 5) # 3 * 5**2 + 0 * 5**1 + 1 76 >>> np.polyval([3,0,1], np.poly1d(5)) - poly1d([ 76.]) + poly1d([76.]) >>> np.polyval(np.poly1d([3,0,1]), 5) 76 >>> np.polyval(np.poly1d([3,0,1]), np.poly1d(5)) - poly1d([ 76.]) + poly1d([76.]) """ p = NX.asarray(p) @@ -951,7 +952,7 @@ def polydiv(u, v): >>> x = np.array([3.0, 5.0, 2.0]) >>> y = np.array([2.0, 1.0]) >>> np.polydiv(x, y) - (array([ 1.5 , 1.75]), array([ 0.25])) + (array([1.5 , 1.75]), array([0.25])) """ truepoly = (isinstance(u, poly1d) or isinstance(u, poly1d)) @@ -1046,7 +1047,7 @@ class poly1d(object): >>> p.r array([-1.+1.41421356j, -1.-1.41421356j]) >>> p(p.r) - array([ -4.44089210e-16+0.j, -4.44089210e-16+0.j]) + array([ -4.44089210e-16+0.j, -4.44089210e-16+0.j]) # may vary These numbers in the previous line represent (0, 0) to machine precision @@ -1073,7 +1074,7 @@ class poly1d(object): poly1d([ 1, 4, 10, 12, 9]) >>> (p**3 + 4) / p - (poly1d([ 1., 4., 10., 12., 9.]), poly1d([ 4.])) + (poly1d([ 1., 4., 10., 12., 9.]), poly1d([4.])) ``asarray(p)`` gives the coefficient array, so polynomials can be used in all functions that accept arrays: @@ -1095,7 +1096,7 @@ class poly1d(object): Construct a polynomial from its roots: >>> np.poly1d([1, 2], True) - poly1d([ 1, -3, 2]) + poly1d([ 1., -3., 2.]) This is the same polynomial as obtained by: |