Integrate a Legendre series. Returns the Legendre 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 chang
(c, m=1, k=[], lbnd=0, scl=1, axis=0)
| 702 | |
| 703 | |
| 704 | def legint(c, m=1, k=[], lbnd=0, scl=1, axis=0): |
| 705 | """ |
| 706 | Integrate a Legendre series. |
| 707 | |
| 708 | Returns the Legendre series coefficients `c` integrated `m` times from |
| 709 | `lbnd` along `axis`. At each iteration the resulting series is |
| 710 | **multiplied** by `scl` and an integration constant, `k`, is added. |
| 711 | The scaling factor is for use in a linear change of variable. ("Buyer |
| 712 | beware": note that, depending on what one is doing, one may want `scl` |
| 713 | to be the reciprocal of what one might expect; for more information, |
| 714 | see the Notes section below.) The argument `c` is an array of |
| 715 | coefficients from low to high degree along each axis, e.g., [1,2,3] |
| 716 | represents the series ``L_0 + 2*L_1 + 3*L_2`` while [[1,2],[1,2]] |
| 717 | represents ``1*L_0(x)*L_0(y) + 1*L_1(x)*L_0(y) + 2*L_0(x)*L_1(y) + |
| 718 | 2*L_1(x)*L_1(y)`` if axis=0 is ``x`` and axis=1 is ``y``. |
| 719 | |
| 720 | Parameters |
| 721 | ---------- |
| 722 | c : array_like |
| 723 | Array of Legendre series coefficients. If c is multidimensional the |
| 724 | different axis correspond to different variables with the degree in |
| 725 | each axis given by the corresponding index. |
| 726 | m : int, optional |
| 727 | Order of integration, must be positive. (Default: 1) |
| 728 | k : {[], list, scalar}, optional |
| 729 | Integration constant(s). The value of the first integral at |
| 730 | ``lbnd`` is the first value in the list, the value of the second |
| 731 | integral at ``lbnd`` is the second value, etc. If ``k == []`` (the |
| 732 | default), all constants are set to zero. If ``m == 1``, a single |
| 733 | scalar can be given instead of a list. |
| 734 | lbnd : scalar, optional |
| 735 | The lower bound of the integral. (Default: 0) |
| 736 | scl : scalar, optional |
| 737 | Following each integration the result is *multiplied* by `scl` |
| 738 | before the integration constant is added. (Default: 1) |
| 739 | axis : int, optional |
| 740 | Axis over which the integral is taken. (Default: 0). |
| 741 | |
| 742 | .. versionadded:: 1.7.0 |
| 743 | |
| 744 | Returns |
| 745 | ------- |
| 746 | S : ndarray |
| 747 | Legendre series coefficient array of the integral. |
| 748 | |
| 749 | Raises |
| 750 | ------ |
| 751 | ValueError |
| 752 | If ``m < 0``, ``len(k) > m``, ``np.ndim(lbnd) != 0``, or |
| 753 | ``np.ndim(scl) != 0``. |
| 754 | |
| 755 | See Also |
| 756 | -------- |
| 757 | legder |
| 758 | |
| 759 | Notes |
| 760 | ----- |
| 761 | Note that the result of each integration is *multiplied* by `scl`. |
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