Divide one Laguerre series by another. Returns the quotient-with-remainder of two Laguerre 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)
| 506 | |
| 507 | |
| 508 | def lagdiv(c1, c2): |
| 509 | """ |
| 510 | Divide one Laguerre series by another. |
| 511 | |
| 512 | Returns the quotient-with-remainder of two Laguerre series |
| 513 | `c1` / `c2`. The arguments are sequences of coefficients from lowest |
| 514 | order "term" to highest, e.g., [1,2,3] represents the series |
| 515 | ``P_0 + 2*P_1 + 3*P_2``. |
| 516 | |
| 517 | Parameters |
| 518 | ---------- |
| 519 | c1, c2 : array_like |
| 520 | 1-D arrays of Laguerre series coefficients ordered from low to |
| 521 | high. |
| 522 | |
| 523 | Returns |
| 524 | ------- |
| 525 | [quo, rem] : ndarrays |
| 526 | Of Laguerre series coefficients representing the quotient and |
| 527 | remainder. |
| 528 | |
| 529 | See Also |
| 530 | -------- |
| 531 | lagadd, lagsub, lagmulx, lagmul, lagpow |
| 532 | |
| 533 | Notes |
| 534 | ----- |
| 535 | In general, the (polynomial) division of one Laguerre series by another |
| 536 | results in quotient and remainder terms that are not in the Laguerre |
| 537 | polynomial basis set. Thus, to express these results as a Laguerre |
| 538 | series, it is necessary to "reproject" the results onto the Laguerre |
| 539 | basis set, which may produce "unintuitive" (but correct) results; see |
| 540 | Examples section below. |
| 541 | |
| 542 | Examples |
| 543 | -------- |
| 544 | >>> from numpy.polynomial.laguerre import lagdiv |
| 545 | >>> lagdiv([ 8., -13., 38., -51., 36.], [0, 1, 2]) |
| 546 | (array([1., 2., 3.]), array([0.])) |
| 547 | >>> lagdiv([ 9., -12., 38., -51., 36.], [0, 1, 2]) |
| 548 | (array([1., 2., 3.]), array([1., 1.])) |
| 549 | |
| 550 | """ |
| 551 | return pu._div(lagmul, c1, c2) |
| 552 | |
| 553 | |
| 554 | def lagpow(c, pow, maxpower=16): |