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Diffstat (limited to 'doc/source/reference/routines.polynomials.classes.rst')
| -rw-r--r-- | doc/source/reference/routines.polynomials.classes.rst | 56 |
1 files changed, 28 insertions, 28 deletions
diff --git a/doc/source/reference/routines.polynomials.classes.rst b/doc/source/reference/routines.polynomials.classes.rst index da0394305..71e635866 100644 --- a/doc/source/reference/routines.polynomials.classes.rst +++ b/doc/source/reference/routines.polynomials.classes.rst @@ -52,7 +52,7 @@ the conventional Polynomial class because of its familiarity:: >>> from numpy.polynomial import Polynomial as P >>> p = P([1,2,3]) >>> p - Polynomial([ 1., 2., 3.], domain=[-1, 1], window=[-1, 1]) + Polynomial([1., 2., 3.], domain=[-1, 1], window=[-1, 1]) Note that there are three parts to the long version of the printout. The first is the coefficients, the second is the domain, and the third is the @@ -68,8 +68,8 @@ window:: Printing a polynomial yields a shorter form without the domain and window:: - >>> print p - poly([ 1. 2. 3.]) + >>> print(p) + poly([1. 2. 3.]) We will deal with the domain and window when we get to fitting, for the moment we ignore them and run through the basic algebraic and arithmetic operations. @@ -77,19 +77,19 @@ we ignore them and run through the basic algebraic and arithmetic operations. Addition and Subtraction:: >>> p + p - Polynomial([ 2., 4., 6.], domain=[-1, 1], window=[-1, 1]) + Polynomial([2., 4., 6.], domain=[-1., 1.], window=[-1., 1.]) >>> p - p - Polynomial([ 0.], domain=[-1, 1], window=[-1, 1]) + Polynomial([0.], domain=[-1., 1.], window=[-1., 1.]) Multiplication:: >>> p * p - Polynomial([ 1., 4., 10., 12., 9.], domain=[-1, 1], window=[-1, 1]) + Polynomial([ 1., 4., 10., 12., 9.], domain=[-1., 1.], window=[-1., 1.]) Powers:: >>> p**2 - Polynomial([ 1., 4., 10., 12., 9.], domain=[-1, 1], window=[-1, 1]) + Polynomial([ 1., 4., 10., 12., 9.], domain=[-1., 1.], window=[-1., 1.]) Division: @@ -100,20 +100,20 @@ versions the '/' will only work for division by scalars. At some point it will be deprecated:: >>> p // P([-1, 1]) - Polynomial([ 5., 3.], domain=[-1, 1], window=[-1, 1]) + Polynomial([5., 3.], domain=[-1., 1.], window=[-1., 1.]) Remainder:: >>> p % P([-1, 1]) - Polynomial([ 6.], domain=[-1, 1], window=[-1, 1]) + Polynomial([6.], domain=[-1., 1.], window=[-1., 1.]) Divmod:: >>> quo, rem = divmod(p, P([-1, 1])) >>> quo - Polynomial([ 5., 3.], domain=[-1, 1], window=[-1, 1]) + Polynomial([5., 3.], domain=[-1., 1.], window=[-1., 1.]) >>> rem - Polynomial([ 6.], domain=[-1, 1], window=[-1, 1]) + Polynomial([6.], domain=[-1., 1.], window=[-1., 1.]) Evaluation:: @@ -134,7 +134,7 @@ the polynomials are regarded as functions this is composition of functions:: >>> p(p) - Polynomial([ 6., 16., 36., 36., 27.], domain=[-1, 1], window=[-1, 1]) + Polynomial([ 6., 16., 36., 36., 27.], domain=[-1., 1.], window=[-1., 1.]) Roots:: @@ -148,11 +148,11 @@ tuples, lists, arrays, and scalars are automatically cast in the arithmetic operations:: >>> p + [1, 2, 3] - Polynomial([ 2., 4., 6.], domain=[-1, 1], window=[-1, 1]) + Polynomial([2., 4., 6.], domain=[-1., 1.], window=[-1., 1.]) >>> [1, 2, 3] * p - Polynomial([ 1., 4., 10., 12., 9.], domain=[-1, 1], window=[-1, 1]) + Polynomial([ 1., 4., 10., 12., 9.], domain=[-1., 1.], window=[-1., 1.]) >>> p / 2 - Polynomial([ 0.5, 1. , 1.5], domain=[-1, 1], window=[-1, 1]) + Polynomial([0.5, 1. , 1.5], domain=[-1., 1.], window=[-1., 1.]) Polynomials that differ in domain, window, or class can't be mixed in arithmetic:: @@ -180,7 +180,7 @@ conversion of Polynomial classes among themselves is done for type, domain, and window casting:: >>> p(T([0, 1])) - Chebyshev([ 2.5, 2. , 1.5], domain=[-1, 1], window=[-1, 1]) + Chebyshev([2.5, 2. , 1.5], domain=[-1., 1.], window=[-1., 1.]) Which gives the polynomial `p` in Chebyshev form. This works because :math:`T_1(x) = x` and substituting :math:`x` for :math:`x` doesn't change @@ -200,18 +200,18 @@ Polynomial instances can be integrated and differentiated.:: >>> from numpy.polynomial import Polynomial as P >>> p = P([2, 6]) >>> p.integ() - Polynomial([ 0., 2., 3.], domain=[-1, 1], window=[-1, 1]) + Polynomial([0., 2., 3.], domain=[-1., 1.], window=[-1., 1.]) >>> p.integ(2) - Polynomial([ 0., 0., 1., 1.], domain=[-1, 1], window=[-1, 1]) + Polynomial([0., 0., 1., 1.], domain=[-1., 1.], window=[-1., 1.]) The first example integrates `p` once, the second example integrates it twice. By default, the lower bound of the integration and the integration constant are 0, but both can be specified.:: >>> p.integ(lbnd=-1) - Polynomial([-1., 2., 3.], domain=[-1, 1], window=[-1, 1]) + Polynomial([-1., 2., 3.], domain=[-1., 1.], window=[-1., 1.]) >>> p.integ(lbnd=-1, k=1) - Polynomial([ 0., 2., 3.], domain=[-1, 1], window=[-1, 1]) + Polynomial([0., 2., 3.], domain=[-1., 1.], window=[-1., 1.]) In the first case the lower bound of the integration is set to -1 and the integration constant is 0. In the second the constant of integration is set @@ -220,9 +220,9 @@ number of times the polynomial is differentiated:: >>> p = P([1, 2, 3]) >>> p.deriv(1) - Polynomial([ 2., 6.], domain=[-1, 1], window=[-1, 1]) + Polynomial([2., 6.], domain=[-1., 1.], window=[-1., 1.]) >>> p.deriv(2) - Polynomial([ 6.], domain=[-1, 1], window=[-1, 1]) + Polynomial([6.], domain=[-1., 1.], window=[-1., 1.]) Other Polynomial Constructors @@ -238,25 +238,25 @@ are demonstrated below:: >>> from numpy.polynomial import Chebyshev as T >>> p = P.fromroots([1, 2, 3]) >>> p - Polynomial([ -6., 11., -6., 1.], domain=[-1, 1], window=[-1, 1]) + Polynomial([-6., 11., -6., 1.], domain=[-1., 1.], window=[-1., 1.]) >>> p.convert(kind=T) - Chebyshev([ -9. , 11.75, -3. , 0.25], domain=[-1, 1], window=[-1, 1]) + Chebyshev([-9. , 11.75, -3. , 0.25], domain=[-1., 1.], window=[-1., 1.]) The convert method can also convert domain and window:: >>> p.convert(kind=T, domain=[0, 1]) - Chebyshev([-2.4375 , 2.96875, -0.5625 , 0.03125], [ 0., 1.], [-1., 1.]) + Chebyshev([-2.4375 , 2.96875, -0.5625 , 0.03125], domain=[0., 1.], window=[-1., 1.]) >>> p.convert(kind=P, domain=[0, 1]) - Polynomial([-1.875, 2.875, -1.125, 0.125], [ 0., 1.], [-1., 1.]) + Polynomial([-1.875, 2.875, -1.125, 0.125], domain=[0., 1.], window=[-1., 1.]) In numpy versions >= 1.7.0 the `basis` and `cast` class methods are also available. The cast method works like the convert method while the basis method returns the basis polynomial of given degree:: >>> P.basis(3) - Polynomial([ 0., 0., 0., 1.], domain=[-1, 1], window=[-1, 1]) + Polynomial([0., 0., 0., 1.], domain=[-1., 1.], window=[-1., 1.]) >>> T.cast(p) - Chebyshev([ -9. , 11.75, -3. , 0.25], domain=[-1, 1], window=[-1, 1]) + Chebyshev([-9. , 11.75, -3. , 0.25], domain=[-1., 1.], window=[-1., 1.]) Conversions between types can be useful, but it is *not* recommended for routine use. The loss of numerical precision in passing from a |