Evaluate an Hermite series at points x. If `c` is of length `n + 1`, this function returns the value: .. math:: p(x) = c_0 * H_0(x) + c_1 * H_1(x) + ... + c_n * H_n(x) The parameter `x` is converted to an array only if it is a tuple or a list, otherwise it is treated as a sca
(x, c, tensor=True)
| 800 | |
| 801 | |
| 802 | def hermval(x, c, tensor=True): |
| 803 | """ |
| 804 | Evaluate an Hermite series at points x. |
| 805 | |
| 806 | If `c` is of length `n + 1`, this function returns the value: |
| 807 | |
| 808 | .. math:: p(x) = c_0 * H_0(x) + c_1 * H_1(x) + ... + c_n * H_n(x) |
| 809 | |
| 810 | The parameter `x` is converted to an array only if it is a tuple or a |
| 811 | list, otherwise it is treated as a scalar. In either case, either `x` |
| 812 | or its elements must support multiplication and addition both with |
| 813 | themselves and with the elements of `c`. |
| 814 | |
| 815 | If `c` is a 1-D array, then `p(x)` will have the same shape as `x`. If |
| 816 | `c` is multidimensional, then the shape of the result depends on the |
| 817 | value of `tensor`. If `tensor` is true the shape will be c.shape[1:] + |
| 818 | x.shape. If `tensor` is false the shape will be c.shape[1:]. Note that |
| 819 | scalars have shape (,). |
| 820 | |
| 821 | Trailing zeros in the coefficients will be used in the evaluation, so |
| 822 | they should be avoided if efficiency is a concern. |
| 823 | |
| 824 | Parameters |
| 825 | ---------- |
| 826 | x : array_like, compatible object |
| 827 | If `x` is a list or tuple, it is converted to an ndarray, otherwise |
| 828 | it is left unchanged and treated as a scalar. In either case, `x` |
| 829 | or its elements must support addition and multiplication with |
| 830 | themselves and with the elements of `c`. |
| 831 | c : array_like |
| 832 | Array of coefficients ordered so that the coefficients for terms of |
| 833 | degree n are contained in c[n]. If `c` is multidimensional the |
| 834 | remaining indices enumerate multiple polynomials. In the two |
| 835 | dimensional case the coefficients may be thought of as stored in |
| 836 | the columns of `c`. |
| 837 | tensor : boolean, optional |
| 838 | If True, the shape of the coefficient array is extended with ones |
| 839 | on the right, one for each dimension of `x`. Scalars have dimension 0 |
| 840 | for this action. The result is that every column of coefficients in |
| 841 | `c` is evaluated for every element of `x`. If False, `x` is broadcast |
| 842 | over the columns of `c` for the evaluation. This keyword is useful |
| 843 | when `c` is multidimensional. The default value is True. |
| 844 | |
| 845 | .. versionadded:: 1.7.0 |
| 846 | |
| 847 | Returns |
| 848 | ------- |
| 849 | values : ndarray, algebra_like |
| 850 | The shape of the return value is described above. |
| 851 | |
| 852 | See Also |
| 853 | -------- |
| 854 | hermval2d, hermgrid2d, hermval3d, hermgrid3d |
| 855 | |
| 856 | Notes |
| 857 | ----- |
| 858 | The evaluation uses Clenshaw recursion, aka synthetic division. |
| 859 |