Multiply one Laguerre series by another. Returns the product 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
(c1, c2)
| 440 | |
| 441 | |
| 442 | def lagmul(c1, c2): |
| 443 | """ |
| 444 | Multiply one Laguerre series by another. |
| 445 | |
| 446 | Returns the product of two Laguerre series `c1` * `c2`. The arguments |
| 447 | are sequences of coefficients, from lowest order "term" to highest, |
| 448 | e.g., [1,2,3] represents the series ``P_0 + 2*P_1 + 3*P_2``. |
| 449 | |
| 450 | Parameters |
| 451 | ---------- |
| 452 | c1, c2 : array_like |
| 453 | 1-D arrays of Laguerre series coefficients ordered from low to |
| 454 | high. |
| 455 | |
| 456 | Returns |
| 457 | ------- |
| 458 | out : ndarray |
| 459 | Of Laguerre series coefficients representing their product. |
| 460 | |
| 461 | See Also |
| 462 | -------- |
| 463 | lagadd, lagsub, lagmulx, lagdiv, lagpow |
| 464 | |
| 465 | Notes |
| 466 | ----- |
| 467 | In general, the (polynomial) product of two C-series results in terms |
| 468 | that are not in the Laguerre polynomial basis set. Thus, to express |
| 469 | the product as a Laguerre series, it is necessary to "reproject" the |
| 470 | product onto said basis set, which may produce "unintuitive" (but |
| 471 | correct) results; see Examples section below. |
| 472 | |
| 473 | Examples |
| 474 | -------- |
| 475 | >>> from numpy.polynomial.laguerre import lagmul |
| 476 | >>> lagmul([1, 2, 3], [0, 1, 2]) |
| 477 | array([ 8., -13., 38., -51., 36.]) |
| 478 | |
| 479 | """ |
| 480 | # s1, s2 are trimmed copies |
| 481 | [c1, c2] = pu.as_series([c1, c2]) |
| 482 | |
| 483 | if len(c1) > len(c2): |
| 484 | c = c2 |
| 485 | xs = c1 |
| 486 | else: |
| 487 | c = c1 |
| 488 | xs = c2 |
| 489 | |
| 490 | if len(c) == 1: |
| 491 | c0 = c[0]*xs |
| 492 | c1 = 0 |
| 493 | elif len(c) == 2: |
| 494 | c0 = c[0]*xs |
| 495 | c1 = c[1]*xs |
| 496 | else: |
| 497 | nd = len(c) |
| 498 | c0 = c[-2]*xs |
| 499 | c1 = c[-1]*xs |