Return the derivative of the specified order of a polynomial. .. note:: This forms part of the old polynomial API. Since version 1.4, the new polynomial API defined in `numpy.polynomial` is preferred. A summary of the differences can be found in the :doc:`transi
(p, m=1)
| 376 | |
| 377 | @array_function_dispatch(_polyder_dispatcher) |
| 378 | def polyder(p, m=1): |
| 379 | """ |
| 380 | Return the derivative of the specified order of a polynomial. |
| 381 | |
| 382 | .. note:: |
| 383 | This forms part of the old polynomial API. Since version 1.4, the |
| 384 | new polynomial API defined in `numpy.polynomial` is preferred. |
| 385 | A summary of the differences can be found in the |
| 386 | :doc:`transition guide </reference/routines.polynomials>`. |
| 387 | |
| 388 | Parameters |
| 389 | ---------- |
| 390 | p : poly1d or sequence |
| 391 | Polynomial to differentiate. |
| 392 | A sequence is interpreted as polynomial coefficients, see `poly1d`. |
| 393 | m : int, optional |
| 394 | Order of differentiation (default: 1) |
| 395 | |
| 396 | Returns |
| 397 | ------- |
| 398 | der : poly1d |
| 399 | A new polynomial representing the derivative. |
| 400 | |
| 401 | See Also |
| 402 | -------- |
| 403 | polyint : Anti-derivative of a polynomial. |
| 404 | poly1d : Class for one-dimensional polynomials. |
| 405 | |
| 406 | Examples |
| 407 | -------- |
| 408 | |
| 409 | The derivative of the polynomial :math:`x^3 + x^2 + x^1 + 1` is: |
| 410 | |
| 411 | >>> import numpy as np |
| 412 | |
| 413 | >>> p = np.poly1d([1,1,1,1]) |
| 414 | >>> p2 = np.polyder(p) |
| 415 | >>> p2 |
| 416 | poly1d([3, 2, 1]) |
| 417 | |
| 418 | which evaluates to: |
| 419 | |
| 420 | >>> p2(2.) |
| 421 | 17.0 |
| 422 | |
| 423 | We can verify this, approximating the derivative with |
| 424 | ``(f(x + h) - f(x))/h``: |
| 425 | |
| 426 | >>> (p(2. + 0.001) - p(2.)) / 0.001 |
| 427 | 17.007000999997857 |
| 428 | |
| 429 | The fourth-order derivative of a 3rd-order polynomial is zero: |
| 430 | |
| 431 | >>> np.polyder(p, 2) |
| 432 | poly1d([6, 2]) |
| 433 | >>> np.polyder(p, 3) |
| 434 | poly1d([6]) |
| 435 | >>> np.polyder(p, 4) |