Least squares fit of Legendre series to data. Return the coefficients of a Legendre series of degree `deg` that is the least squares fit to the data values `y` given at points `x`. If `y` is 1-D the returned coefficients will also be 1-D. If `y` is 2-D multiple fits are done, o
(x, y, deg, rcond=None, full=False, w=None)
| 1284 | |
| 1285 | |
| 1286 | def legfit(x, y, deg, rcond=None, full=False, w=None): |
| 1287 | """ |
| 1288 | Least squares fit of Legendre series to data. |
| 1289 | |
| 1290 | Return the coefficients of a Legendre series of degree `deg` that is the |
| 1291 | least squares fit to the data values `y` given at points `x`. If `y` is |
| 1292 | 1-D the returned coefficients will also be 1-D. If `y` is 2-D multiple |
| 1293 | fits are done, one for each column of `y`, and the resulting |
| 1294 | coefficients are stored in the corresponding columns of a 2-D return. |
| 1295 | The fitted polynomial(s) are in the form |
| 1296 | |
| 1297 | .. math:: p(x) = c_0 + c_1 * L_1(x) + ... + c_n * L_n(x), |
| 1298 | |
| 1299 | where `n` is `deg`. |
| 1300 | |
| 1301 | Parameters |
| 1302 | ---------- |
| 1303 | x : array_like, shape (M,) |
| 1304 | x-coordinates of the M sample points ``(x[i], y[i])``. |
| 1305 | y : array_like, shape (M,) or (M, K) |
| 1306 | y-coordinates of the sample points. Several data sets of sample |
| 1307 | points sharing the same x-coordinates can be fitted at once by |
| 1308 | passing in a 2D-array that contains one dataset per column. |
| 1309 | deg : int or 1-D array_like |
| 1310 | Degree(s) of the fitting polynomials. If `deg` is a single integer |
| 1311 | all terms up to and including the `deg`'th term are included in the |
| 1312 | fit. For NumPy versions >= 1.11.0 a list of integers specifying the |
| 1313 | degrees of the terms to include may be used instead. |
| 1314 | rcond : float, optional |
| 1315 | Relative condition number of the fit. Singular values smaller than |
| 1316 | this relative to the largest singular value will be ignored. The |
| 1317 | default value is len(x)*eps, where eps is the relative precision of |
| 1318 | the float type, about 2e-16 in most cases. |
| 1319 | full : bool, optional |
| 1320 | Switch determining nature of return value. When it is False (the |
| 1321 | default) just the coefficients are returned, when True diagnostic |
| 1322 | information from the singular value decomposition is also returned. |
| 1323 | w : array_like, shape (`M`,), optional |
| 1324 | Weights. If not None, the weight ``w[i]`` applies to the unsquared |
| 1325 | residual ``y[i] - y_hat[i]`` at ``x[i]``. Ideally the weights are |
| 1326 | chosen so that the errors of the products ``w[i]*y[i]`` all have the |
| 1327 | same variance. When using inverse-variance weighting, use |
| 1328 | ``w[i] = 1/sigma(y[i])``. The default value is None. |
| 1329 | |
| 1330 | .. versionadded:: 1.5.0 |
| 1331 | |
| 1332 | Returns |
| 1333 | ------- |
| 1334 | coef : ndarray, shape (M,) or (M, K) |
| 1335 | Legendre coefficients ordered from low to high. If `y` was |
| 1336 | 2-D, the coefficients for the data in column k of `y` are in |
| 1337 | column `k`. If `deg` is specified as a list, coefficients for |
| 1338 | terms not included in the fit are set equal to zero in the |
| 1339 | returned `coef`. |
| 1340 | |
| 1341 | [residuals, rank, singular_values, rcond] : list |
| 1342 | These values are only returned if ``full == True`` |
| 1343 |