Evaluate a polynomial at specific values. .. 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 the :doc:`transition guide </referen
(p, x)
| 704 | |
| 705 | @array_function_dispatch(_polyval_dispatcher) |
| 706 | def polyval(p, x): |
| 707 | """ |
| 708 | Evaluate a polynomial at specific values. |
| 709 | |
| 710 | .. note:: |
| 711 | This forms part of the old polynomial API. Since version 1.4, the |
| 712 | new polynomial API defined in `numpy.polynomial` is preferred. |
| 713 | A summary of the differences can be found in the |
| 714 | :doc:`transition guide </reference/routines.polynomials>`. |
| 715 | |
| 716 | If `p` is of length N, this function returns the value: |
| 717 | |
| 718 | ``p[0]*x**(N-1) + p[1]*x**(N-2) + ... + p[N-2]*x + p[N-1]`` |
| 719 | |
| 720 | If `x` is a sequence, then ``p(x)`` is returned for each element of ``x``. |
| 721 | If `x` is another polynomial then the composite polynomial ``p(x(t))`` |
| 722 | is returned. |
| 723 | |
| 724 | Parameters |
| 725 | ---------- |
| 726 | p : array_like or poly1d object |
| 727 | 1D array of polynomial coefficients (including coefficients equal |
| 728 | to zero) from highest degree to the constant term, or an |
| 729 | instance of poly1d. |
| 730 | x : array_like or poly1d object |
| 731 | A number, an array of numbers, or an instance of poly1d, at |
| 732 | which to evaluate `p`. |
| 733 | |
| 734 | Returns |
| 735 | ------- |
| 736 | values : ndarray or poly1d |
| 737 | If `x` is a poly1d instance, the result is the composition of the two |
| 738 | polynomials, i.e., `x` is "substituted" in `p` and the simplified |
| 739 | result is returned. In addition, the type of `x` - array_like or |
| 740 | poly1d - governs the type of the output: `x` array_like => `values` |
| 741 | array_like, `x` a poly1d object => `values` is also. |
| 742 | |
| 743 | See Also |
| 744 | -------- |
| 745 | poly1d: A polynomial class. |
| 746 | |
| 747 | Notes |
| 748 | ----- |
| 749 | Horner's scheme [1]_ is used to evaluate the polynomial. Even so, |
| 750 | for polynomials of high degree the values may be inaccurate due to |
| 751 | rounding errors. Use carefully. |
| 752 | |
| 753 | If `x` is a subtype of `ndarray` the return value will be of the same type. |
| 754 | |
| 755 | References |
| 756 | ---------- |
| 757 | .. [1] I. N. Bronshtein, K. A. Semendyayev, and K. A. Hirsch (Eng. |
| 758 | trans. Ed.), *Handbook of Mathematics*, New York, Van Nostrand |
| 759 | Reinhold Co., 1985, pg. 720. |
| 760 | |
| 761 | Examples |
| 762 | -------- |
| 763 | >>> np.polyval([3,0,1], 5) # 3 * 5**2 + 0 * 5**1 + 1 |
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