Divide one Legendre series by another. Returns the quotient-with-remainder of two Legendre series `c1` / `c2`. The arguments are sequences of coefficients from lowest order "term" to highest, e.g., [1,2,3] represents the series ``P_0 + 2*P_1 + 3*P_2``. Parameters ----
(c1, c2)
| 530 | |
| 531 | |
| 532 | def legdiv(c1, c2): |
| 533 | """ |
| 534 | Divide one Legendre series by another. |
| 535 | |
| 536 | Returns the quotient-with-remainder of two Legendre series |
| 537 | `c1` / `c2`. The arguments are sequences of coefficients from lowest |
| 538 | order "term" to highest, e.g., [1,2,3] represents the series |
| 539 | ``P_0 + 2*P_1 + 3*P_2``. |
| 540 | |
| 541 | Parameters |
| 542 | ---------- |
| 543 | c1, c2 : array_like |
| 544 | 1-D arrays of Legendre series coefficients ordered from low to |
| 545 | high. |
| 546 | |
| 547 | Returns |
| 548 | ------- |
| 549 | quo, rem : ndarrays |
| 550 | Of Legendre series coefficients representing the quotient and |
| 551 | remainder. |
| 552 | |
| 553 | See Also |
| 554 | -------- |
| 555 | legadd, legsub, legmulx, legmul, legpow |
| 556 | |
| 557 | Notes |
| 558 | ----- |
| 559 | In general, the (polynomial) division of one Legendre series by another |
| 560 | results in quotient and remainder terms that are not in the Legendre |
| 561 | polynomial basis set. Thus, to express these results as a Legendre |
| 562 | series, it is necessary to "reproject" the results onto the Legendre |
| 563 | basis set, which may produce "unintuitive" (but correct) results; see |
| 564 | Examples section below. |
| 565 | |
| 566 | Examples |
| 567 | -------- |
| 568 | >>> from numpy.polynomial import legendre as L |
| 569 | >>> c1 = (1,2,3) |
| 570 | >>> c2 = (3,2,1) |
| 571 | >>> L.legdiv(c1,c2) # quotient "intuitive," remainder not |
| 572 | (array([3.]), array([-8., -4.])) |
| 573 | >>> c2 = (0,1,2,3) |
| 574 | >>> L.legdiv(c2,c1) # neither "intuitive" |
| 575 | (array([-0.07407407, 1.66666667]), array([-1.03703704, -2.51851852])) # may vary |
| 576 | |
| 577 | """ |
| 578 | return pu._div(legmul, c1, c2) |
| 579 | |
| 580 | |
| 581 | def legpow(c, pow, maxpower=16): |