diff options
Diffstat (limited to 'numpy/polynomial')
| -rw-r--r-- | numpy/polynomial/chebyshev.py | 38 | ||||
| -rw-r--r-- | numpy/polynomial/hermite.py | 48 | ||||
| -rw-r--r-- | numpy/polynomial/hermite_e.py | 45 | ||||
| -rw-r--r-- | numpy/polynomial/laguerre.py | 30 | ||||
| -rw-r--r-- | numpy/polynomial/legendre.py | 41 | ||||
| -rw-r--r-- | numpy/polynomial/polynomial.py | 53 | ||||
| -rw-r--r-- | numpy/polynomial/polyutils.py | 30 |
7 files changed, 144 insertions, 141 deletions
diff --git a/numpy/polynomial/chebyshev.py b/numpy/polynomial/chebyshev.py index 92cdb18d2..e0734e1b8 100644 --- a/numpy/polynomial/chebyshev.py +++ b/numpy/polynomial/chebyshev.py @@ -361,12 +361,12 @@ def poly2cheb(pol): >>> from numpy import polynomial as P >>> p = P.Polynomial(range(4)) >>> p - Polynomial([ 0., 1., 2., 3.], domain=[-1, 1], window=[-1, 1]) + Polynomial([0., 1., 2., 3.], domain=[-1, 1], window=[-1, 1]) >>> c = p.convert(kind=P.Chebyshev) >>> c - Chebyshev([ 1. , 3.25, 1. , 0.75], domain=[-1, 1], window=[-1, 1]) + Chebyshev([1. , 3.25, 1. , 0.75], domain=[-1., 1.], window=[-1., 1.]) >>> P.chebyshev.poly2cheb(range(4)) - array([ 1. , 3.25, 1. , 0.75]) + array([1. , 3.25, 1. , 0.75]) """ [pol] = pu.as_series([pol]) @@ -413,12 +413,12 @@ def cheb2poly(c): >>> from numpy import polynomial as P >>> c = P.Chebyshev(range(4)) >>> c - Chebyshev([ 0., 1., 2., 3.], [-1., 1.]) + Chebyshev([0., 1., 2., 3.], domain=[-1, 1], window=[-1, 1]) >>> p = c.convert(kind=P.Polynomial) >>> p - Polynomial([ -2., -8., 4., 12.], [-1., 1.]) + Polynomial([-2., -8., 4., 12.], domain=[-1., 1.], window=[-1., 1.]) >>> P.chebyshev.cheb2poly(range(4)) - array([ -2., -8., 4., 12.]) + array([-2., -8., 4., 12.]) """ from .polynomial import polyadd, polysub, polymulx @@ -538,7 +538,7 @@ def chebfromroots(roots): array([ 0. , -0.25, 0. , 0.25]) >>> j = complex(0,1) >>> C.chebfromroots((-j,j)) # x^2 + 1 relative to the standard basis - array([ 1.5+0.j, 0.0+0.j, 0.5+0.j]) + array([1.5+0.j, 0. +0.j, 0.5+0.j]) """ if len(roots) == 0: @@ -594,7 +594,7 @@ def chebadd(c1, c2): >>> c1 = (1,2,3) >>> c2 = (3,2,1) >>> C.chebadd(c1,c2) - array([ 4., 4., 4.]) + array([4., 4., 4.]) """ # c1, c2 are trimmed copies @@ -688,7 +688,7 @@ def chebmulx(c): -------- >>> from numpy.polynomial import chebyshev as C >>> C.chebmulx([1,2,3]) - array([ 1., 2.5, 3., 1.5, 2.]) + array([1. , 2.5, 1. , 1.5]) """ # c is a trimmed copy @@ -796,10 +796,10 @@ def chebdiv(c1, c2): >>> c1 = (1,2,3) >>> c2 = (3,2,1) >>> C.chebdiv(c1,c2) # quotient "intuitive," remainder not - (array([ 3.]), array([-8., -4.])) + (array([3.]), array([-8., -4.])) >>> c2 = (0,1,2,3) >>> C.chebdiv(c2,c1) # neither "intuitive" - (array([ 0., 2.]), array([-2., -4.])) + (array([0., 2.]), array([-2., -4.])) """ # c1, c2 are trimmed copies @@ -853,7 +853,7 @@ def chebpow(c, pow, maxpower=16): -------- >>> from numpy.polynomial import chebyshev as C >>> C.chebpow([1, 2, 3, 4], 2) - array([15.5, 22. , 16. , 14. , 12.5, 12. , 8. ]) + array([15.5, 22. , 16. , ..., 12.5, 12. , 8. ]) """ # c is a trimmed copy @@ -928,13 +928,13 @@ def chebder(c, m=1, scl=1, axis=0): >>> from numpy.polynomial import chebyshev as C >>> c = (1,2,3,4) >>> C.chebder(c) - array([ 14., 12., 24.]) + array([14., 12., 24.]) >>> C.chebder(c,3) - array([ 96.]) + array([96.]) >>> C.chebder(c,scl=-1) array([-14., -12., -24.]) >>> C.chebder(c,2,-1) - array([ 12., 96.]) + array([12., 96.]) """ c = np.array(c, ndmin=1, copy=1) @@ -1048,8 +1048,8 @@ def chebint(c, m=1, k=[], lbnd=0, scl=1, axis=0): >>> C.chebint(c) array([ 0.5, -0.5, 0.5, 0.5]) >>> C.chebint(c,3) - array([ 0.03125 , -0.1875 , 0.04166667, -0.05208333, 0.01041667, - 0.00625 ]) + array([ 0.03125 , -0.1875 , 0.04166667, -0.05208333, 0.01041667, # may vary + 0.00625 ]) >>> C.chebint(c, k=3) array([ 3.5, -0.5, 0.5, 0.5]) >>> C.chebint(c,lbnd=-2) @@ -1674,7 +1674,7 @@ def chebfit(x, y, deg, rcond=None, full=False, w=None): warnings can be turned off by >>> import warnings - >>> warnings.simplefilter('ignore', RankWarning) + >>> warnings.simplefilter('ignore', np.RankWarning) See Also -------- @@ -1885,7 +1885,7 @@ def chebroots(c): -------- >>> import numpy.polynomial.chebyshev as cheb >>> cheb.chebroots((-1, 1,-1, 1)) # T3 - T2 + T1 - T0 has real roots - array([ -5.00000000e-01, 2.60860684e-17, 1.00000000e+00]) + array([ -5.00000000e-01, 2.60860684e-17, 1.00000000e+00]) # may vary """ # c is a trimmed copy diff --git a/numpy/polynomial/hermite.py b/numpy/polynomial/hermite.py index 4905f366f..93c9fc564 100644 --- a/numpy/polynomial/hermite.py +++ b/numpy/polynomial/hermite.py @@ -114,7 +114,7 @@ def poly2herm(pol): -------- >>> from numpy.polynomial.hermite import poly2herm >>> poly2herm(np.arange(4)) - array([ 1. , 2.75 , 0.5 , 0.375]) + array([1. , 2.75 , 0.5 , 0.375]) """ [pol] = pu.as_series([pol]) @@ -160,7 +160,7 @@ def herm2poly(c): -------- >>> from numpy.polynomial.hermite import herm2poly >>> herm2poly([ 1. , 2.75 , 0.5 , 0.375]) - array([ 0., 1., 2., 3.]) + array([0., 1., 2., 3.]) """ from .polynomial import polyadd, polysub, polymulx @@ -280,10 +280,10 @@ def hermfromroots(roots): >>> from numpy.polynomial.hermite import hermfromroots, hermval >>> coef = hermfromroots((-1, 0, 1)) >>> hermval((-1, 0, 1), coef) - array([ 0., 0., 0.]) + array([0., 0., 0.]) >>> coef = hermfromroots((-1j, 1j)) >>> hermval((-1j, 1j), coef) - array([ 0.+0.j, 0.+0.j]) + array([0.+0.j, 0.+0.j]) """ if len(roots) == 0: @@ -337,7 +337,7 @@ def hermadd(c1, c2): -------- >>> from numpy.polynomial.hermite import hermadd >>> hermadd([1, 2, 3], [1, 2, 3, 4]) - array([ 2., 4., 6., 4.]) + array([2., 4., 6., 4.]) """ # c1, c2 are trimmed copies @@ -385,7 +385,7 @@ def hermsub(c1, c2): -------- >>> from numpy.polynomial.hermite import hermsub >>> hermsub([1, 2, 3, 4], [1, 2, 3]) - array([ 0., 0., 0., 4.]) + array([0., 0., 0., 4.]) """ # c1, c2 are trimmed copies @@ -435,7 +435,7 @@ def hermmulx(c): -------- >>> from numpy.polynomial.hermite import hermmulx >>> hermmulx([1, 2, 3]) - array([ 2. , 6.5, 1. , 1.5]) + array([2. , 6.5, 1. , 1.5]) """ # c is a trimmed copy @@ -488,7 +488,7 @@ def hermmul(c1, c2): -------- >>> from numpy.polynomial.hermite import hermmul >>> hermmul([1, 2, 3], [0, 1, 2]) - array([ 52., 29., 52., 7., 6.]) + array([52., 29., 52., 7., 6.]) """ # s1, s2 are trimmed copies @@ -557,11 +557,11 @@ def hermdiv(c1, c2): -------- >>> from numpy.polynomial.hermite import hermdiv >>> hermdiv([ 52., 29., 52., 7., 6.], [0, 1, 2]) - (array([ 1., 2., 3.]), array([ 0.])) + (array([1., 2., 3.]), array([0.])) >>> hermdiv([ 54., 31., 52., 7., 6.], [0, 1, 2]) - (array([ 1., 2., 3.]), array([ 2., 2.])) + (array([1., 2., 3.]), array([2., 2.])) >>> hermdiv([ 53., 30., 52., 7., 6.], [0, 1, 2]) - (array([ 1., 2., 3.]), array([ 1., 1.])) + (array([1., 2., 3.]), array([1., 1.])) """ # c1, c2 are trimmed copies @@ -617,7 +617,7 @@ def hermpow(c, pow, maxpower=16): -------- >>> from numpy.polynomial.hermite import hermpow >>> hermpow([1, 2, 3], 2) - array([ 81., 52., 82., 12., 9.]) + array([81., 52., 82., 12., 9.]) """ # c is a trimmed copy @@ -690,9 +690,9 @@ def hermder(c, m=1, scl=1, axis=0): -------- >>> from numpy.polynomial.hermite import hermder >>> hermder([ 1. , 0.5, 0.5, 0.5]) - array([ 1., 2., 3.]) + array([1., 2., 3.]) >>> hermder([-0.5, 1./2., 1./8., 1./12., 1./16.], m=2) - array([ 1., 2., 3.]) + array([1., 2., 3.]) """ c = np.array(c, ndmin=1, copy=1) @@ -799,15 +799,15 @@ def hermint(c, m=1, k=[], lbnd=0, scl=1, axis=0): -------- >>> from numpy.polynomial.hermite import hermint >>> hermint([1,2,3]) # integrate once, value 0 at 0. - array([ 1. , 0.5, 0.5, 0.5]) + array([1. , 0.5, 0.5, 0.5]) >>> hermint([1,2,3], m=2) # integrate twice, value & deriv 0 at 0 - array([-0.5 , 0.5 , 0.125 , 0.08333333, 0.0625 ]) + array([-0.5 , 0.5 , 0.125 , 0.08333333, 0.0625 ]) # may vary >>> hermint([1,2,3], k=1) # integrate once, value 1 at 0. - array([ 2. , 0.5, 0.5, 0.5]) + array([2. , 0.5, 0.5, 0.5]) >>> hermint([1,2,3], lbnd=-1) # integrate once, value 0 at -1 array([-2. , 0.5, 0.5, 0.5]) >>> hermint([1,2,3], m=2, k=[1,2], lbnd=-1) - array([ 1.66666667, -0.5 , 0.125 , 0.08333333, 0.0625 ]) + array([ 1.66666667, -0.5 , 0.125 , 0.08333333, 0.0625 ]) # may vary """ c = np.array(c, ndmin=1, copy=1) @@ -918,8 +918,8 @@ def hermval(x, c, tensor=True): >>> hermval(1, coef) 11.0 >>> hermval([[1,2],[3,4]], coef) - array([[ 11., 51.], - [ 115., 203.]]) + array([[ 11., 51.], + [115., 203.]]) """ c = np.array(c, ndmin=1, copy=0) @@ -1437,7 +1437,7 @@ def hermfit(x, y, deg, rcond=None, full=False, w=None): warnings can be turned off by >>> import warnings - >>> warnings.simplefilter('ignore', RankWarning) + >>> warnings.simplefilter('ignore', np.RankWarning) See Also -------- @@ -1490,7 +1490,7 @@ def hermfit(x, y, deg, rcond=None, full=False, w=None): >>> err = np.random.randn(len(x))/10 >>> y = hermval(x, [1, 2, 3]) + err >>> hermfit(x, y, 2) - array([ 0.97902637, 1.99849131, 3.00006 ]) + array([1.0218, 1.9986, 2.9999]) # may vary """ x = np.asarray(x) + 0.0 @@ -1656,9 +1656,9 @@ def hermroots(c): >>> from numpy.polynomial.hermite import hermroots, hermfromroots >>> coef = hermfromroots([-1, 0, 1]) >>> coef - array([ 0. , 0.25 , 0. , 0.125]) + array([0. , 0.25 , 0. , 0.125]) >>> hermroots(coef) - array([ -1.00000000e+00, -1.38777878e-17, 1.00000000e+00]) + array([-1.00000000e+00, -1.38777878e-17, 1.00000000e+00]) """ # c is a trimmed copy diff --git a/numpy/polynomial/hermite_e.py b/numpy/polynomial/hermite_e.py index 6cb044a55..bafb4b997 100644 --- a/numpy/polynomial/hermite_e.py +++ b/numpy/polynomial/hermite_e.py @@ -161,7 +161,7 @@ def herme2poly(c): -------- >>> from numpy.polynomial.hermite_e import herme2poly >>> herme2poly([ 2., 10., 2., 3.]) - array([ 0., 1., 2., 3.]) + array([0., 1., 2., 3.]) """ from .polynomial import polyadd, polysub, polymulx @@ -281,10 +281,10 @@ def hermefromroots(roots): >>> from numpy.polynomial.hermite_e import hermefromroots, hermeval >>> coef = hermefromroots((-1, 0, 1)) >>> hermeval((-1, 0, 1), coef) - array([ 0., 0., 0.]) + array([0., 0., 0.]) >>> coef = hermefromroots((-1j, 1j)) >>> hermeval((-1j, 1j), coef) - array([ 0.+0.j, 0.+0.j]) + array([0.+0.j, 0.+0.j]) """ if len(roots) == 0: @@ -338,7 +338,7 @@ def hermeadd(c1, c2): -------- >>> from numpy.polynomial.hermite_e import hermeadd >>> hermeadd([1, 2, 3], [1, 2, 3, 4]) - array([ 2., 4., 6., 4.]) + array([2., 4., 6., 4.]) """ # c1, c2 are trimmed copies @@ -386,7 +386,7 @@ def hermesub(c1, c2): -------- >>> from numpy.polynomial.hermite_e import hermesub >>> hermesub([1, 2, 3, 4], [1, 2, 3]) - array([ 0., 0., 0., 4.]) + array([0., 0., 0., 4.]) """ # c1, c2 are trimmed copies @@ -432,7 +432,7 @@ def hermemulx(c): -------- >>> from numpy.polynomial.hermite_e import hermemulx >>> hermemulx([1, 2, 3]) - array([ 2., 7., 2., 3.]) + array([2., 7., 2., 3.]) """ # c is a trimmed copy @@ -485,7 +485,7 @@ def hermemul(c1, c2): -------- >>> from numpy.polynomial.hermite_e import hermemul >>> hermemul([1, 2, 3], [0, 1, 2]) - array([ 14., 15., 28., 7., 6.]) + array([14., 15., 28., 7., 6.]) """ # s1, s2 are trimmed copies @@ -554,9 +554,9 @@ def hermediv(c1, c2): -------- >>> from numpy.polynomial.hermite_e import hermediv >>> hermediv([ 14., 15., 28., 7., 6.], [0, 1, 2]) - (array([ 1., 2., 3.]), array([ 0.])) + (array([1., 2., 3.]), array([0.])) >>> hermediv([ 15., 17., 28., 7., 6.], [0, 1, 2]) - (array([ 1., 2., 3.]), array([ 1., 2.])) + (array([1., 2., 3.]), array([1., 2.])) """ # c1, c2 are trimmed copies @@ -612,7 +612,7 @@ def hermepow(c, pow, maxpower=16): -------- >>> from numpy.polynomial.hermite_e import hermepow >>> hermepow([1, 2, 3], 2) - array([ 23., 28., 46., 12., 9.]) + array([23., 28., 46., 12., 9.]) """ # c is a trimmed copy @@ -685,9 +685,9 @@ def hermeder(c, m=1, scl=1, axis=0): -------- >>> from numpy.polynomial.hermite_e import hermeder >>> hermeder([ 1., 1., 1., 1.]) - array([ 1., 2., 3.]) + array([1., 2., 3.]) >>> hermeder([-0.25, 1., 1./2., 1./3., 1./4 ], m=2) - array([ 1., 2., 3.]) + array([1., 2., 3.]) """ c = np.array(c, ndmin=1, copy=1) @@ -794,15 +794,15 @@ def hermeint(c, m=1, k=[], lbnd=0, scl=1, axis=0): -------- >>> from numpy.polynomial.hermite_e import hermeint >>> hermeint([1, 2, 3]) # integrate once, value 0 at 0. - array([ 1., 1., 1., 1.]) + array([1., 1., 1., 1.]) >>> hermeint([1, 2, 3], m=2) # integrate twice, value & deriv 0 at 0 - array([-0.25 , 1. , 0.5 , 0.33333333, 0.25 ]) + array([-0.25 , 1. , 0.5 , 0.33333333, 0.25 ]) # may vary >>> hermeint([1, 2, 3], k=1) # integrate once, value 1 at 0. - array([ 2., 1., 1., 1.]) + array([2., 1., 1., 1.]) >>> hermeint([1, 2, 3], lbnd=-1) # integrate once, value 0 at -1 array([-1., 1., 1., 1.]) >>> hermeint([1, 2, 3], m=2, k=[1, 2], lbnd=-1) - array([ 1.83333333, 0. , 0.5 , 0.33333333, 0.25 ]) + array([ 1.83333333, 0. , 0.5 , 0.33333333, 0.25 ]) # may vary """ c = np.array(c, ndmin=1, copy=1) @@ -913,8 +913,8 @@ def hermeval(x, c, tensor=True): >>> hermeval(1, coef) 3.0 >>> hermeval([[1,2],[3,4]], coef) - array([[ 3., 14.], - [ 31., 54.]]) + array([[ 3., 14.], + [31., 54.]]) """ c = np.array(c, ndmin=1, copy=0) @@ -1430,7 +1430,7 @@ def hermefit(x, y, deg, rcond=None, full=False, w=None): warnings can be turned off by >>> import warnings - >>> warnings.simplefilter('ignore', RankWarning) + >>> warnings.simplefilter('ignore', np.RankWarning) See Also -------- @@ -1480,10 +1480,11 @@ def hermefit(x, y, deg, rcond=None, full=False, w=None): -------- >>> from numpy.polynomial.hermite_e import hermefit, hermeval >>> x = np.linspace(-10, 10) + >>> np.random.seed(123) >>> err = np.random.randn(len(x))/10 >>> y = hermeval(x, [1, 2, 3]) + err >>> hermefit(x, y, 2) - array([ 1.01690445, 1.99951418, 2.99948696]) + array([ 1.01690445, 1.99951418, 2.99948696]) # may vary """ x = np.asarray(x) + 0.0 @@ -1650,9 +1651,9 @@ def hermeroots(c): >>> from numpy.polynomial.hermite_e import hermeroots, hermefromroots >>> coef = hermefromroots([-1, 0, 1]) >>> coef - array([ 0., 2., 0., 1.]) + array([0., 2., 0., 1.]) >>> hermeroots(coef) - array([-1., 0., 1.]) + array([-1., 0., 1.]) # may vary """ # c is a trimmed copy diff --git a/numpy/polynomial/laguerre.py b/numpy/polynomial/laguerre.py index a116d20a7..9207c9afe 100644 --- a/numpy/polynomial/laguerre.py +++ b/numpy/polynomial/laguerre.py @@ -160,7 +160,7 @@ def lag2poly(c): -------- >>> from numpy.polynomial.laguerre import lag2poly >>> lag2poly([ 23., -63., 58., -18.]) - array([ 0., 1., 2., 3.]) + array([0., 1., 2., 3.]) """ from .polynomial import polyadd, polysub, polymulx @@ -277,10 +277,10 @@ def lagfromroots(roots): >>> from numpy.polynomial.laguerre import lagfromroots, lagval >>> coef = lagfromroots((-1, 0, 1)) >>> lagval((-1, 0, 1), coef) - array([ 0., 0., 0.]) + array([0., 0., 0.]) >>> coef = lagfromroots((-1j, 1j)) >>> lagval((-1j, 1j), coef) - array([ 0.+0.j, 0.+0.j]) + array([0.+0.j, 0.+0.j]) """ if len(roots) == 0: @@ -334,7 +334,7 @@ def lagadd(c1, c2): -------- >>> from numpy.polynomial.laguerre import lagadd >>> lagadd([1, 2, 3], [1, 2, 3, 4]) - array([ 2., 4., 6., 4.]) + array([2., 4., 6., 4.]) """ @@ -383,7 +383,7 @@ def lagsub(c1, c2): -------- >>> from numpy.polynomial.laguerre import lagsub >>> lagsub([1, 2, 3, 4], [1, 2, 3]) - array([ 0., 0., 0., 4.]) + array([0., 0., 0., 4.]) """ # c1, c2 are trimmed copies @@ -433,7 +433,7 @@ def lagmulx(c): -------- >>> from numpy.polynomial.laguerre import lagmulx >>> lagmulx([1, 2, 3]) - array([ -1., -1., 11., -9.]) + array([-1., -1., 11., -9.]) """ # c is a trimmed copy @@ -556,9 +556,9 @@ def lagdiv(c1, c2): -------- >>> from numpy.polynomial.laguerre import lagdiv >>> lagdiv([ 8., -13., 38., -51., 36.], [0, 1, 2]) - (array([ 1., 2., 3.]), array([ 0.])) + (array([1., 2., 3.]), array([0.])) >>> lagdiv([ 9., -12., 38., -51., 36.], [0, 1, 2]) - (array([ 1., 2., 3.]), array([ 1., 1.])) + (array([1., 2., 3.]), array([1., 1.])) """ # c1, c2 are trimmed copies @@ -687,9 +687,9 @@ def lagder(c, m=1, scl=1, axis=0): -------- >>> from numpy.polynomial.laguerre import lagder >>> lagder([ 1., 1., 1., -3.]) - array([ 1., 2., 3.]) + array([1., 2., 3.]) >>> lagder([ 1., 0., 0., -4., 3.], m=2) - array([ 1., 2., 3.]) + array([1., 2., 3.]) """ c = np.array(c, ndmin=1, copy=1) @@ -805,9 +805,9 @@ def lagint(c, m=1, k=[], lbnd=0, scl=1, axis=0): >>> lagint([1,2,3], k=1) array([ 2., 1., 1., -3.]) >>> lagint([1,2,3], lbnd=-1) - array([ 11.5, 1. , 1. , -3. ]) + array([11.5, 1. , 1. , -3. ]) >>> lagint([1,2], m=2, k=[1,2], lbnd=-1) - array([ 11.16666667, -5. , -3. , 2. ]) + array([ 11.16666667, -5. , -3. , 2. ]) # may vary """ c = np.array(c, ndmin=1, copy=1) @@ -1436,7 +1436,7 @@ def lagfit(x, y, deg, rcond=None, full=False, w=None): warnings can be turned off by >>> import warnings - >>> warnings.simplefilter('ignore', RankWarning) + >>> warnings.simplefilter('ignore', np.RankWarning) See Also -------- @@ -1489,7 +1489,7 @@ def lagfit(x, y, deg, rcond=None, full=False, w=None): >>> err = np.random.randn(len(x))/10 >>> y = lagval(x, [1, 2, 3]) + err >>> lagfit(x, y, 2) - array([ 0.96971004, 2.00193749, 3.00288744]) + array([ 0.96971004, 2.00193749, 3.00288744]) # may vary """ x = np.asarray(x) + 0.0 @@ -1656,7 +1656,7 @@ def lagroots(c): >>> coef array([ 2., -8., 12., -6.]) >>> lagroots(coef) - array([ -4.44089210e-16, 1.00000000e+00, 2.00000000e+00]) + array([-4.4408921e-16, 1.0000000e+00, 2.0000000e+00]) """ # c is a trimmed copy diff --git a/numpy/polynomial/legendre.py b/numpy/polynomial/legendre.py index e9c24594b..f81bc002c 100644 --- a/numpy/polynomial/legendre.py +++ b/numpy/polynomial/legendre.py @@ -136,10 +136,10 @@ def poly2leg(pol): >>> from numpy import polynomial as P >>> p = P.Polynomial(np.arange(4)) >>> p - Polynomial([ 0., 1., 2., 3.], domain=[-1, 1], window=[-1, 1]) + Polynomial([0., 1., 2., 3.], domain=[-1, 1], window=[-1, 1]) >>> c = P.Legendre(P.legendre.poly2leg(p.coef)) >>> c - Legendre([ 1. , 3.25, 1. , 0.75], domain=[-1, 1], window=[-1, 1]) + Legendre([ 1. , 3.25, 1. , 0.75], domain=[-1, 1], window=[-1, 1]) # may vary """ [pol] = pu.as_series([pol]) @@ -183,12 +183,13 @@ def leg2poly(c): Examples -------- + >>> from numpy import polynomial as P >>> c = P.Legendre(range(4)) >>> c - Legendre([ 0., 1., 2., 3.], [-1., 1.]) + Legendre([0., 1., 2., 3.], domain=[-1, 1], window=[-1, 1]) >>> p = c.convert(kind=P.Polynomial) >>> p - Polynomial([-1. , -3.5, 3. , 7.5], [-1., 1.]) + Polynomial([-1. , -3.5, 3. , 7.5], domain=[-1., 1.], window=[-1., 1.]) >>> P.leg2poly(range(4)) array([-1. , -3.5, 3. , 7.5]) @@ -310,7 +311,7 @@ def legfromroots(roots): array([ 0. , -0.4, 0. , 0.4]) >>> j = complex(0,1) >>> L.legfromroots((-j,j)) # x^2 + 1 relative to the standard basis - array([ 1.33333333+0.j, 0.00000000+0.j, 0.66666667+0.j]) + array([ 1.33333333+0.j, 0.00000000+0.j, 0.66666667+0.j]) # may vary """ if len(roots) == 0: @@ -366,7 +367,7 @@ def legadd(c1, c2): >>> c1 = (1,2,3) >>> c2 = (3,2,1) >>> L.legadd(c1,c2) - array([ 4., 4., 4.]) + array([4., 4., 4.]) """ # c1, c2 are trimmed copies @@ -468,7 +469,7 @@ def legmulx(c): -------- >>> from numpy.polynomial import legendre as L >>> L.legmulx([1,2,3]) - array([ 0.66666667, 2.2, 1.33333333, 1.8]) + array([ 0.66666667, 2.2, 1.33333333, 1.8]) # may vary """ # c is a trimmed copy @@ -525,8 +526,8 @@ def legmul(c1, c2): >>> from numpy.polynomial import legendre as L >>> c1 = (1,2,3) >>> c2 = (3,2) - >>> P.legmul(c1,c2) # multiplication requires "reprojection" - array([ 4.33333333, 10.4 , 11.66666667, 3.6 ]) + >>> L.legmul(c1,c2) # multiplication requires "reprojection" + array([ 4.33333333, 10.4 , 11.66666667, 3.6 ]) # may vary """ # s1, s2 are trimmed copies @@ -597,10 +598,10 @@ def legdiv(c1, c2): >>> c1 = (1,2,3) >>> c2 = (3,2,1) >>> L.legdiv(c1,c2) # quotient "intuitive," remainder not - (array([ 3.]), array([-8., -4.])) + (array([3.]), array([-8., -4.])) >>> c2 = (0,1,2,3) >>> L.legdiv(c2,c1) # neither "intuitive" - (array([-0.07407407, 1.66666667]), array([-1.03703704, -2.51851852])) + (array([-0.07407407, 1.66666667]), array([-1.03703704, -2.51851852])) # may vary """ # c1, c2 are trimmed copies @@ -729,7 +730,7 @@ def legder(c, m=1, scl=1, axis=0): >>> L.legder(c) array([ 6., 9., 20.]) >>> L.legder(c, 3) - array([ 60.]) + array([60.]) >>> L.legder(c, scl=-1) array([ -6., -9., -20.]) >>> L.legder(c, 2,-1) @@ -845,16 +846,16 @@ def legint(c, m=1, k=[], lbnd=0, scl=1, axis=0): >>> from numpy.polynomial import legendre as L >>> c = (1,2,3) >>> L.legint(c) - array([ 0.33333333, 0.4 , 0.66666667, 0.6 ]) + array([ 0.33333333, 0.4 , 0.66666667, 0.6 ]) # may vary >>> L.legint(c, 3) - array([ 1.66666667e-02, -1.78571429e-02, 4.76190476e-02, - -1.73472348e-18, 1.90476190e-02, 9.52380952e-03]) + array([ 1.66666667e-02, -1.78571429e-02, 4.76190476e-02, # may vary + -1.73472348e-18, 1.90476190e-02, 9.52380952e-03]) >>> L.legint(c, k=3) - array([ 3.33333333, 0.4 , 0.66666667, 0.6 ]) + array([ 3.33333333, 0.4 , 0.66666667, 0.6 ]) # may vary >>> L.legint(c, lbnd=-2) - array([ 7.33333333, 0.4 , 0.66666667, 0.6 ]) + array([ 7.33333333, 0.4 , 0.66666667, 0.6 ]) # may vary >>> L.legint(c, scl=2) - array([ 0.66666667, 0.8 , 1.33333333, 1.2 ]) + array([ 0.66666667, 0.8 , 1.33333333, 1.2 ]) # may vary """ c = np.array(c, ndmin=1, copy=1) @@ -1476,7 +1477,7 @@ def legfit(x, y, deg, rcond=None, full=False, w=None): warnings can be turned off by >>> import warnings - >>> warnings.simplefilter('ignore', RankWarning) + >>> warnings.simplefilter('ignore', np.RankWarning) See Also -------- @@ -1686,7 +1687,7 @@ def legroots(c): -------- >>> import numpy.polynomial.legendre as leg >>> leg.legroots((1, 2, 3, 4)) # 4L_3 + 3L_2 + 2L_1 + 1L_0, all real roots - array([-0.85099543, -0.11407192, 0.51506735]) + array([-0.85099543, -0.11407192, 0.51506735]) # may vary """ # c is a trimmed copy diff --git a/numpy/polynomial/polynomial.py b/numpy/polynomial/polynomial.py index 259cd31f5..69599e3fd 100644 --- a/numpy/polynomial/polynomial.py +++ b/numpy/polynomial/polynomial.py @@ -185,7 +185,7 @@ def polyfromroots(roots): array([ 0., -1., 0., 1.]) >>> j = complex(0,1) >>> P.polyfromroots((-j,j)) # complex returned, though values are real - array([ 1.+0.j, 0.+0.j, 1.+0.j]) + array([1.+0.j, 0.+0.j, 1.+0.j]) """ if len(roots) == 0: @@ -233,7 +233,7 @@ def polyadd(c1, c2): >>> c1 = (1,2,3) >>> c2 = (3,2,1) >>> sum = P.polyadd(c1,c2); sum - array([ 4., 4., 4.]) + array([4., 4., 4.]) >>> P.polyval(2, sum) # 4 + 4(2) + 4(2**2) 28.0 @@ -401,9 +401,9 @@ def polydiv(c1, c2): >>> c1 = (1,2,3) >>> c2 = (3,2,1) >>> P.polydiv(c1,c2) - (array([ 3.]), array([-8., -4.])) + (array([3.]), array([-8., -4.])) >>> P.polydiv(c2,c1) - (array([ 0.33333333]), array([ 2.66666667, 1.33333333])) + (array([ 0.33333333]), array([ 2.66666667, 1.33333333])) # may vary """ # c1, c2 are trimmed copies @@ -529,7 +529,7 @@ def polyder(c, m=1, scl=1, axis=0): >>> P.polyder(c) # (d/dx)(c) = 2 + 6x + 12x**2 array([ 2., 6., 12.]) >>> P.polyder(c,3) # (d**3/dx**3)(c) = 24 - array([ 24.]) + array([24.]) >>> P.polyder(c,scl=-1) # (d/d(-x))(c) = -2 - 6x - 12x**2 array([ -2., -6., -12.]) >>> P.polyder(c,2,-1) # (d**2/d(-x)**2)(c) = 6 + 24x @@ -636,14 +636,14 @@ def polyint(c, m=1, k=[], lbnd=0, scl=1, axis=0): >>> from numpy.polynomial import polynomial as P >>> c = (1,2,3) >>> P.polyint(c) # should return array([0, 1, 1, 1]) - array([ 0., 1., 1., 1.]) + array([0., 1., 1., 1.]) >>> P.polyint(c,3) # should return array([0, 0, 0, 1/6, 1/12, 1/20]) - array([ 0. , 0. , 0. , 0.16666667, 0.08333333, - 0.05 ]) + array([ 0. , 0. , 0. , 0.16666667, 0.08333333, # may vary + 0.05 ]) >>> P.polyint(c,k=3) # should return array([3, 1, 1, 1]) - array([ 3., 1., 1., 1.]) + array([3., 1., 1., 1.]) >>> P.polyint(c,lbnd=-2) # should return array([6, 1, 1, 1]) - array([ 6., 1., 1., 1.]) + array([6., 1., 1., 1.]) >>> P.polyint(c,scl=-2) # should return array([0, -2, -2, -2]) array([ 0., -2., -2., -2.]) @@ -761,17 +761,17 @@ def polyval(x, c, tensor=True): array([[0, 1], [2, 3]]) >>> polyval(a, [1,2,3]) - array([[ 1., 6.], - [ 17., 34.]]) + array([[ 1., 6.], + [17., 34.]]) >>> coef = np.arange(4).reshape(2,2) # multidimensional coefficients >>> coef array([[0, 1], [2, 3]]) >>> polyval([1,2], coef, tensor=True) - array([[ 2., 4.], - [ 4., 7.]]) + array([[2., 4.], + [4., 7.]]) >>> polyval([1,2], coef, tensor=False) - array([ 2., 7.]) + array([2., 7.]) """ c = np.array(c, ndmin=1, copy=0) @@ -851,8 +851,8 @@ def polyvalfromroots(x, r, tensor=True): array([[0, 1], [2, 3]]) >>> polyvalfromroots(a, [-1, 0, 1]) - array([[ -0., 0.], - [ 6., 24.]]) + array([[-0., 0.], + [ 6., 24.]]) >>> r = np.arange(-2, 2).reshape(2,2) # multidimensional coefficients >>> r # each column of r defines one polynomial array([[-2, -1], @@ -1363,7 +1363,7 @@ def polyfit(x, y, deg, rcond=None, full=False, w=None): be turned off by: >>> import warnings - >>> warnings.simplefilter('ignore', RankWarning) + >>> warnings.simplefilter('ignore', np.RankWarning) See Also -------- @@ -1410,26 +1410,27 @@ def polyfit(x, y, deg, rcond=None, full=False, w=None): Examples -------- + >>> np.random.seed(123) >>> from numpy.polynomial import polynomial as P >>> x = np.linspace(-1,1,51) # x "data": [-1, -0.96, ..., 0.96, 1] >>> y = x**3 - x + np.random.randn(len(x)) # x^3 - x + N(0,1) "noise" >>> c, stats = P.polyfit(x,y,3,full=True) + >>> np.random.seed(123) >>> c # c[0], c[2] should be approx. 0, c[1] approx. -1, c[3] approx. 1 - array([ 0.01909725, -1.30598256, -0.00577963, 1.02644286]) + array([ 0.01909725, -1.30598256, -0.00577963, 1.02644286]) # may vary >>> stats # note the large SSR, explaining the rather poor results - [array([ 38.06116253]), 4, array([ 1.38446749, 1.32119158, 0.50443316, - 0.28853036]), 1.1324274851176597e-014] + [array([ 38.06116253]), 4, array([ 1.38446749, 1.32119158, 0.50443316, # may vary + 0.28853036]), 1.1324274851176597e-014] Same thing without the added noise >>> y = x**3 - x >>> c, stats = P.polyfit(x,y,3,full=True) >>> c # c[0], c[2] should be "very close to 0", c[1] ~= -1, c[3] ~= 1 - array([ -1.73362882e-17, -1.00000000e+00, -2.67471909e-16, - 1.00000000e+00]) + array([-6.36925336e-18, -1.00000000e+00, -4.08053781e-16, 1.00000000e+00]) >>> stats # note the minuscule SSR - [array([ 7.46346754e-31]), 4, array([ 1.38446749, 1.32119158, - 0.50443316, 0.28853036]), 1.1324274851176597e-014] + [array([ 7.46346754e-31]), 4, array([ 1.38446749, 1.32119158, # may vary + 0.50443316, 0.28853036]), 1.1324274851176597e-014] """ x = np.asarray(x) + 0.0 @@ -1591,7 +1592,7 @@ def polyroots(c): dtype('float64') >>> j = complex(0,1) >>> poly.polyroots(poly.polyfromroots((-j,0,j))) - array([ 0.00000000e+00+0.j, 0.00000000e+00+1.j, 2.77555756e-17-1.j]) + array([ 0.00000000e+00+0.j, 0.00000000e+00+1.j, 2.77555756e-17-1.j]) # may vary """ # c is a trimmed copy diff --git a/numpy/polynomial/polyutils.py b/numpy/polynomial/polyutils.py index c1ed0c9b3..eff4a8ee1 100644 --- a/numpy/polynomial/polyutils.py +++ b/numpy/polynomial/polyutils.py @@ -156,19 +156,19 @@ def as_series(alist, trim=True): >>> from numpy.polynomial import polyutils as pu >>> a = np.arange(4) >>> pu.as_series(a) - [array([ 0.]), array([ 1.]), array([ 2.]), array([ 3.])] + [array([0.]), array([1.]), array([2.]), array([3.])] >>> b = np.arange(6).reshape((2,3)) >>> pu.as_series(b) - [array([ 0., 1., 2.]), array([ 3., 4., 5.])] + [array([0., 1., 2.]), array([3., 4., 5.])] >>> pu.as_series((1, np.arange(3), np.arange(2, dtype=np.float16))) - [array([ 1.]), array([ 0., 1., 2.]), array([ 0., 1.])] + [array([1.]), array([0., 1., 2.]), array([0., 1.])] >>> pu.as_series([2, [1.1, 0.]]) - [array([ 2.]), array([ 1.1])] + [array([2.]), array([1.1])] >>> pu.as_series([2, [1.1, 0.]], trim=False) - [array([ 2.]), array([ 1.1, 0. ])] + [array([2.]), array([1.1, 0. ])] """ arrays = [np.array(a, ndmin=1, copy=0) for a in alist] @@ -233,12 +233,12 @@ def trimcoef(c, tol=0): -------- >>> from numpy.polynomial import polyutils as pu >>> pu.trimcoef((0,0,3,0,5,0,0)) - array([ 0., 0., 3., 0., 5.]) + array([0., 0., 3., 0., 5.]) >>> pu.trimcoef((0,0,1e-3,0,1e-5,0,0),1e-3) # item == tol is trimmed - array([ 0.]) + array([0.]) >>> i = complex(0,1) # works for complex >>> pu.trimcoef((3e-4,1e-3*(1-i),5e-4,2e-5*(1+i)), 1e-3) - array([ 0.0003+0.j , 0.0010-0.001j]) + array([0.0003+0.j , 0.001 -0.001j]) """ if tol < 0: @@ -332,10 +332,10 @@ def mapparms(old, new): >>> pu.mapparms((-1,1),(-1,1)) (0.0, 1.0) >>> pu.mapparms((1,-1),(-1,1)) - (0.0, -1.0) + (-0.0, -1.0) >>> i = complex(0,1) >>> pu.mapparms((-i,-1),(1,i)) - ((1+1j), (1+0j)) + ((1+1j), (1-0j)) """ oldlen = old[1] - old[0] @@ -390,10 +390,10 @@ def mapdomain(x, old, new): >>> x = np.linspace(-1,1,6); x array([-1. , -0.6, -0.2, 0.2, 0.6, 1. ]) >>> x_out = pu.mapdomain(x, old_domain, new_domain); x_out - array([ 0. , 1.25663706, 2.51327412, 3.76991118, 5.02654825, + array([ 0. , 1.25663706, 2.51327412, 3.76991118, 5.02654825, # may vary 6.28318531]) >>> x - pu.mapdomain(x_out, new_domain, old_domain) - array([ 0., 0., 0., 0., 0., 0.]) + array([0., 0., 0., 0., 0., 0.]) Also works for complex numbers (and thus can be used to map any line in the complex plane to any other line therein). @@ -402,9 +402,9 @@ def mapdomain(x, old, new): >>> old = (-1 - i, 1 + i) >>> new = (-1 + i, 1 - i) >>> z = np.linspace(old[0], old[1], 6); z - array([-1.0-1.j , -0.6-0.6j, -0.2-0.2j, 0.2+0.2j, 0.6+0.6j, 1.0+1.j ]) - >>> new_z = P.mapdomain(z, old, new); new_z - array([-1.0+1.j , -0.6+0.6j, -0.2+0.2j, 0.2-0.2j, 0.6-0.6j, 1.0-1.j ]) + array([-1. -1.j , -0.6-0.6j, -0.2-0.2j, 0.2+0.2j, 0.6+0.6j, 1. +1.j ]) + >>> new_z = pu.mapdomain(z, old, new); new_z + array([-1.0+1.j , -0.6+0.6j, -0.2+0.2j, 0.2-0.2j, 0.6-0.6j, 1.0-1.j ]) # may vary """ x = np.asanyarray(x) |