Return the companion matrix of c. The companion matrix for power series cannot be made symmetric by scaling the basis, so this function differs from those for the orthogonal polynomials. Parameters ---------- c : array_like 1-D array of polynomial coefficients
(c)
| 1500 | |
| 1501 | |
| 1502 | def polycompanion(c): |
| 1503 | """ |
| 1504 | Return the companion matrix of c. |
| 1505 | |
| 1506 | The companion matrix for power series cannot be made symmetric by |
| 1507 | scaling the basis, so this function differs from those for the |
| 1508 | orthogonal polynomials. |
| 1509 | |
| 1510 | Parameters |
| 1511 | ---------- |
| 1512 | c : array_like |
| 1513 | 1-D array of polynomial coefficients ordered from low to high |
| 1514 | degree. |
| 1515 | |
| 1516 | Returns |
| 1517 | ------- |
| 1518 | mat : ndarray |
| 1519 | Companion matrix of dimensions (deg, deg). |
| 1520 | |
| 1521 | Examples |
| 1522 | -------- |
| 1523 | >>> from numpy.polynomial import polynomial as P |
| 1524 | >>> c = (1, 2, 3) |
| 1525 | >>> P.polycompanion(c) |
| 1526 | array([[ 0. , -0.33333333], |
| 1527 | [ 1. , -0.66666667]]) |
| 1528 | |
| 1529 | """ |
| 1530 | # c is a trimmed copy |
| 1531 | [c] = pu.as_series([c]) |
| 1532 | if len(c) < 2: |
| 1533 | raise ValueError('Series must have maximum degree of at least 1.') |
| 1534 | if len(c) == 2: |
| 1535 | return np.array([[-c[0] / c[1]]]) |
| 1536 | |
| 1537 | n = len(c) - 1 |
| 1538 | mat = np.zeros((n, n), dtype=c.dtype) |
| 1539 | bot = mat.reshape(-1)[n::n + 1] |
| 1540 | bot[...] = 1 |
| 1541 | mat[:, -1] -= c[:-1] / c[-1] |
| 1542 | return mat |
| 1543 | |
| 1544 | |
| 1545 | def polyroots(c): |