diff options
Diffstat (limited to 'doc/source/reference/routines.polynomials.classes.rst')
| -rw-r--r-- | doc/source/reference/routines.polynomials.classes.rst | 58 |
1 files changed, 29 insertions, 29 deletions
diff --git a/doc/source/reference/routines.polynomials.classes.rst b/doc/source/reference/routines.polynomials.classes.rst index 2ce29d9d0..896e5fe83 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], symbol='x') 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 @@ -69,7 +69,7 @@ Printing a polynomial yields the polynomial expression in a more familiar format:: >>> print(p) - 1.0 + 2.0·x¹ + 3.0·x² + 1.0 + 2.0·x + 3.0·x² Note that the string representation of polynomials uses Unicode characters by default (except on Windows) to express powers and subscripts. An ASCII-based @@ -79,12 +79,12 @@ format can be toggled at the package-level with the >>> np.polynomial.set_default_printstyle('ascii') >>> print(p) - 1.0 + 2.0 x**1 + 3.0 x**2 + 1.0 + 2.0 x + 3.0 x**2 or controlled for individual polynomial instances with string formatting:: >>> print(f"{p:unicode}") - 1.0 + 2.0·x¹ + 3.0·x² + 1.0 + 2.0·x + 3.0·x² 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. @@ -92,19 +92,19 @@ 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.], symbol='x') >>> p - p - Polynomial([0.], domain=[-1., 1.], window=[-1., 1.]) + Polynomial([0.], domain=[-1., 1.], window=[-1., 1.], symbol='x') 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.], symbol='x') 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.], symbol='x') Division: @@ -115,20 +115,20 @@ 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.], symbol='x') Remainder:: >>> p % P([-1, 1]) - Polynomial([6.], domain=[-1., 1.], window=[-1., 1.]) + Polynomial([6.], domain=[-1., 1.], window=[-1., 1.], symbol='x') 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.], symbol='x') >>> rem - Polynomial([6.], domain=[-1., 1.], window=[-1., 1.]) + Polynomial([6.], domain=[-1., 1.], window=[-1., 1.], symbol='x') Evaluation:: @@ -149,7 +149,7 @@ 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.], symbol='x') Roots:: @@ -163,11 +163,11 @@ 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.], symbol='x') >>> [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.], symbol='x') >>> 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.], symbol='x') Polynomials that differ in domain, window, or class can't be mixed in arithmetic:: @@ -195,7 +195,7 @@ 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.], symbol='x') 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 @@ -215,18 +215,18 @@ 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.], symbol='x') >>> 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.], symbol='x') 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.], symbol='x') >>> 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.], symbol='x') 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 @@ -235,9 +235,9 @@ 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.], symbol='x') >>> p.deriv(2) - Polynomial([6.], domain=[-1., 1.], window=[-1., 1.]) + Polynomial([6.], domain=[-1., 1.], window=[-1., 1.], symbol='x') Other Polynomial Constructors @@ -253,25 +253,25 @@ 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.], symbol='x') >>> 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.], symbol='x') 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], domain=[0., 1.], window=[-1., 1.]) + Chebyshev([-2.4375 , 2.96875, -0.5625 , 0.03125], domain=[0., 1.], window=[-1., 1.], symbol='x') >>> p.convert(kind=P, domain=[0, 1]) - Polynomial([-1.875, 2.875, -1.125, 0.125], domain=[0., 1.], window=[-1., 1.]) + Polynomial([-1.875, 2.875, -1.125, 0.125], domain=[0., 1.], window=[-1., 1.], symbol='x') 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.], symbol='x') >>> 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.], symbol='x') Conversions between types can be useful, but it is *not* recommended for routine use. The loss of numerical precision in passing from a |