flopscope.numpy.polyval

fnp.polyval(p, x)[flopscope source][numpy source]

Evaluate a polynomial at specific values.

Adapted from NumPy docs np.polyval

Areacore

Typecustom

Cost

m \cdot \text{deg}

Flopscope Context

Evaluate polynomial at given points. Cost: $m \cdot \text{deg}$ (Horner's method, FMA=1).

Note.

This forms part of the old polynomial API. Since version 1.4, the new polynomial API defined in flops.polynomial is preferred. A summary of the differences can be found in the transition guide.

If p is of length N, this function returns the value:

p[0]*x**(N-1) + p[1]*x**(N-2) + ... + p[N-2]*x + p[N-1]

If x is a sequence, then p(x) is returned for each element of x. If x is another polynomial then the composite polynomial p(x(t)) is returned.

Parameters

p:array_like or poly1d object: 1D array of polynomial coefficients (including coefficients equal to zero) from highest degree to the constant term, or an instance of poly1d.
x:array_like or poly1d object: A number, an array of numbers, or an instance of poly1d, at which to evaluate p.

Returns

values:ndarray or poly1d: If x is a poly1d instance, the result is the composition of the two polynomials, i.e., x is "substituted" in p and the simplified result is returned. In addition, the type of x - array_like or poly1d - governs the type of the output: x array_like => values array_like, x a poly1d object => values is also.

Notes

Horner's scheme [1]_ is used to evaluate the polynomial. Even so, for polynomials of high degree the values may be inaccurate due to rounding errors. Use carefully.

If x is a subtype of ndarray the return value will be of the same type.

References

footnote

1

I. N. Bronshtein, K. A. Semendyayev, and K. A. Hirsch (Eng.
trans. Ed.), Handbook of Mathematics, New York, Van Nostrand
Reinhold Co., 1985, pg. 720.

Examples

>>> import flopscope.numpy as fnp
>>> flops.polyval([3,0,1], 5)  # 3 * 5**2 + 0 * 5**1 + 1
76
>>> flops.polyval([3,0,1], flops.poly1d(5))
poly1d([76])
>>> flops.polyval(flops.poly1d([3,0,1]), 5)
76
>>> flops.polyval(flops.poly1d([3,0,1]), flops.poly1d(5))
poly1d([76])