numpy.poly1d
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class numpy.poly1d(c_or_r, r=False, variable=None)
[source] -
A one-dimensional polynomial class.
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_r : array_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, whereas
poly1d([1, 2, 3], True)
returns one that represents.
-
r : bool, optional
-
If True,
c_or_r
specifies the polynomial’s roots; the default is False. -
variable : str, optional
-
Changes the variable used when printing
p
fromx
tovariable
(see Examples).
Examples
Construct the polynomial
:
>>> p = np.poly1d([1, 2, 3]) >>> print(np.poly1d(p)) 2 1 x + 2 x + 3
Evaluate the polynomial at
:
>>> p(0.5) 4.25
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:
>>> p.c array([1, 2, 3])
Display the order (the leading zero-coefficients are removed):
>>> p.order 2
Show the coefficient of the k-th power in the polynomial (which is equivalent to
p.c[-(i+1)]
):>>> p[1] 2
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 thevariable
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: -
c
-
The polynomial coefficients
-
coef
-
The polynomial coefficients
-
coefficients
-
The polynomial coefficients
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coeffs
-
The polynomial coefficients
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o
-
The order or degree of the polynomial
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order
-
The order or degree of the polynomial
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r
-
The roots of the polynomial, where self(x) == 0
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roots
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The roots of the polynomial, where self(x) == 0
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variable
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The name of the polynomial variable
Methods
__call__
(self, val)Call self as a function. deriv
(self[, m])Return a derivative of this polynomial. integ
(self[, m, k])Return an antiderivative (indefinite integral) of this polynomial. -
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Licensed under the 3-clause BSD License.
https://docs.scipy.org/doc/numpy-1.17.0/reference/generated/numpy.poly1d.html