Integrate a Hermite series. Returns the Hermite series coefficients `c` integrated `m` times from `lbnd` along `axis`. At each iteration the resulting series is **multiplied** by `scl` and an integration constant, `k`, is added. The scaling factor is for use in a linear change
(c, m=1, k=[], lbnd=0, scl=1, axis=0)
| 678 | |
| 679 | |
| 680 | def hermint(c, m=1, k=[], lbnd=0, scl=1, axis=0): |
| 681 | """ |
| 682 | Integrate a Hermite series. |
| 683 | |
| 684 | Returns the Hermite series coefficients `c` integrated `m` times from |
| 685 | `lbnd` along `axis`. At each iteration the resulting series is |
| 686 | **multiplied** by `scl` and an integration constant, `k`, is added. |
| 687 | The scaling factor is for use in a linear change of variable. ("Buyer |
| 688 | beware": note that, depending on what one is doing, one may want `scl` |
| 689 | to be the reciprocal of what one might expect; for more information, |
| 690 | see the Notes section below.) The argument `c` is an array of |
| 691 | coefficients from low to high degree along each axis, e.g., [1,2,3] |
| 692 | represents the series ``H_0 + 2*H_1 + 3*H_2`` while [[1,2],[1,2]] |
| 693 | represents ``1*H_0(x)*H_0(y) + 1*H_1(x)*H_0(y) + 2*H_0(x)*H_1(y) + |
| 694 | 2*H_1(x)*H_1(y)`` if axis=0 is ``x`` and axis=1 is ``y``. |
| 695 | |
| 696 | Parameters |
| 697 | ---------- |
| 698 | c : array_like |
| 699 | Array of Hermite series coefficients. If c is multidimensional the |
| 700 | different axis correspond to different variables with the degree in |
| 701 | each axis given by the corresponding index. |
| 702 | m : int, optional |
| 703 | Order of integration, must be positive. (Default: 1) |
| 704 | k : {[], list, scalar}, optional |
| 705 | Integration constant(s). The value of the first integral at |
| 706 | ``lbnd`` is the first value in the list, the value of the second |
| 707 | integral at ``lbnd`` is the second value, etc. If ``k == []`` (the |
| 708 | default), all constants are set to zero. If ``m == 1``, a single |
| 709 | scalar can be given instead of a list. |
| 710 | lbnd : scalar, optional |
| 711 | The lower bound of the integral. (Default: 0) |
| 712 | scl : scalar, optional |
| 713 | Following each integration the result is *multiplied* by `scl` |
| 714 | before the integration constant is added. (Default: 1) |
| 715 | axis : int, optional |
| 716 | Axis over which the integral is taken. (Default: 0). |
| 717 | |
| 718 | .. versionadded:: 1.7.0 |
| 719 | |
| 720 | Returns |
| 721 | ------- |
| 722 | S : ndarray |
| 723 | Hermite series coefficients of the integral. |
| 724 | |
| 725 | Raises |
| 726 | ------ |
| 727 | ValueError |
| 728 | If ``m < 0``, ``len(k) > m``, ``np.ndim(lbnd) != 0``, or |
| 729 | ``np.ndim(scl) != 0``. |
| 730 | |
| 731 | See Also |
| 732 | -------- |
| 733 | hermder |
| 734 | |
| 735 | Notes |
| 736 | ----- |
| 737 | Note that the result of each integration is *multiplied* by `scl`. |
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