numpy.poly1d — NumPy v2.4.dev0 Manual (original) (raw)
class numpy.poly1d(c_or_r, r=False, variable=None)[source]#
A one-dimensional polynomial class.
Note
This forms part of the old polynomial API. Since version 1.4, the new polynomial API defined in numpy.polynomial is preferred. A summary of the differences can be found in thetransition guide.
A convenience class, used to encapsulate “natural” operations on polynomials so that said operations may take on their customary form in code (see Examples).
Parameters:
c_or_rarray_like
The polynomial’s coefficients, in decreasing powers, or if the value of the second parameter is True, the polynomial’s roots (values where the polynomial evaluates to 0). For example,poly1d([1, 2, 3]) returns an object that represents\(x^2 + 2x + 3\), whereas poly1d([1, 2, 3], True) returns one that represents \((x-1)(x-2)(x-3) = x^3 - 6x^2 + 11x -6\).
rbool, optional
If True, c_or_r specifies the polynomial’s roots; the default is False.
variablestr, optional
Changes the variable used when printing p from x to variable(see Examples).
Examples
Construct the polynomial \(x^2 + 2x + 3\):
p = np.poly1d([1, 2, 3]) print(np.poly1d(p)) 2 1 x + 2 x + 3
Evaluate the polynomial at \(x = 0.5\):
Find the roots:
p.r array([-1.+1.41421356j, -1.-1.41421356j]) p(p.r) 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
Show the coefficients:
Display the order (the leading zero-coefficients are removed):
Show the coefficient of the k-th power in the polynomial (which is equivalent to p.c[-(i+1)]):
Polynomials can be added, subtracted, multiplied, and divided (returns quotient and remainder):
p * p poly1d([ 1, 4, 10, 12, 9])
(p**3 + 4) / p (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:
p**2 # square of polynomial poly1d([ 1, 4, 10, 12, 9])
np.square(p) # square of individual coefficients array([1, 4, 9])
The variable used in the string representation of p can be modified, using the variable parameter:
p = np.poly1d([1,2,3], variable='z') print(p) 2 1 z + 2 z + 3
Construct a polynomial from its roots:
np.poly1d([1, 2], True) poly1d([ 1., -3., 2.])
This is the same polynomial as obtained by:
np.poly1d([1, -1]) * np.poly1d([1, -2]) poly1d([ 1, -3, 2])
Attributes:
The polynomial coefficients
The polynomial coefficients
The polynomial coefficients
The polynomial coefficients
The order or degree of the polynomial
The order or degree of the polynomial
The roots of the polynomial, where self(x) == 0
The roots of the polynomial, where self(x) == 0
The name of the polynomial variable
Methods