Differentiate a Laguerre series. Returns the Laguerre series coefficients `c` differentiated `m` times along `axis`. At each iteration the result is multiplied by `scl` (the scaling factor is for use in a linear change of variable). The argument `c` is an array of coefficients
(c, m=1, scl=1, axis=0)
| 589 | |
| 590 | |
| 591 | def lagder(c, m=1, scl=1, axis=0): |
| 592 | """ |
| 593 | Differentiate a Laguerre series. |
| 594 | |
| 595 | Returns the Laguerre series coefficients `c` differentiated `m` times |
| 596 | along `axis`. At each iteration the result is multiplied by `scl` (the |
| 597 | scaling factor is for use in a linear change of variable). The argument |
| 598 | `c` is an array of coefficients from low to high degree along each |
| 599 | axis, e.g., [1,2,3] represents the series ``1*L_0 + 2*L_1 + 3*L_2`` |
| 600 | while [[1,2],[1,2]] represents ``1*L_0(x)*L_0(y) + 1*L_1(x)*L_0(y) + |
| 601 | 2*L_0(x)*L_1(y) + 2*L_1(x)*L_1(y)`` if axis=0 is ``x`` and axis=1 is |
| 602 | ``y``. |
| 603 | |
| 604 | Parameters |
| 605 | ---------- |
| 606 | c : array_like |
| 607 | Array of Laguerre series coefficients. If `c` is multidimensional |
| 608 | the different axis correspond to different variables with the |
| 609 | degree in each axis given by the corresponding index. |
| 610 | m : int, optional |
| 611 | Number of derivatives taken, must be non-negative. (Default: 1) |
| 612 | scl : scalar, optional |
| 613 | Each differentiation is multiplied by `scl`. The end result is |
| 614 | multiplication by ``scl**m``. This is for use in a linear change of |
| 615 | variable. (Default: 1) |
| 616 | axis : int, optional |
| 617 | Axis over which the derivative is taken. (Default: 0). |
| 618 | |
| 619 | .. versionadded:: 1.7.0 |
| 620 | |
| 621 | Returns |
| 622 | ------- |
| 623 | der : ndarray |
| 624 | Laguerre series of the derivative. |
| 625 | |
| 626 | See Also |
| 627 | -------- |
| 628 | lagint |
| 629 | |
| 630 | Notes |
| 631 | ----- |
| 632 | In general, the result of differentiating a Laguerre series does not |
| 633 | resemble the same operation on a power series. Thus the result of this |
| 634 | function may be "unintuitive," albeit correct; see Examples section |
| 635 | below. |
| 636 | |
| 637 | Examples |
| 638 | -------- |
| 639 | >>> from numpy.polynomial.laguerre import lagder |
| 640 | >>> lagder([ 1., 1., 1., -3.]) |
| 641 | array([1., 2., 3.]) |
| 642 | >>> lagder([ 1., 0., 0., -4., 3.], m=2) |
| 643 | array([1., 2., 3.]) |
| 644 | |
| 645 | """ |
| 646 | c = np.array(c, ndmin=1, copy=True) |
| 647 | if c.dtype.char in '?bBhHiIlLqQpP': |
| 648 | c = c.astype(np.double) |
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