Least squares fit of Hermite series to data. Return the coefficients of a HermiteE 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, on
(x, y, deg, rcond=None, full=False, w=None)
| 1264 | |
| 1265 | |
| 1266 | def hermefit(x, y, deg, rcond=None, full=False, w=None): |
| 1267 | """ |
| 1268 | Least squares fit of Hermite series to data. |
| 1269 | |
| 1270 | Return the coefficients of a HermiteE series of degree `deg` that is |
| 1271 | the least squares fit to the data values `y` given at points `x`. If |
| 1272 | `y` is 1-D the returned coefficients will also be 1-D. If `y` is 2-D |
| 1273 | multiple fits are done, one for each column of `y`, and the resulting |
| 1274 | coefficients are stored in the corresponding columns of a 2-D return. |
| 1275 | The fitted polynomial(s) are in the form |
| 1276 | |
| 1277 | .. math:: p(x) = c_0 + c_1 * He_1(x) + ... + c_n * He_n(x), |
| 1278 | |
| 1279 | where `n` is `deg`. |
| 1280 | |
| 1281 | Parameters |
| 1282 | ---------- |
| 1283 | x : array_like, shape (M,) |
| 1284 | x-coordinates of the M sample points ``(x[i], y[i])``. |
| 1285 | y : array_like, shape (M,) or (M, K) |
| 1286 | y-coordinates of the sample points. Several data sets of sample |
| 1287 | points sharing the same x-coordinates can be fitted at once by |
| 1288 | passing in a 2D-array that contains one dataset per column. |
| 1289 | deg : int or 1-D array_like |
| 1290 | Degree(s) of the fitting polynomials. If `deg` is a single integer |
| 1291 | all terms up to and including the `deg`'th term are included in the |
| 1292 | fit. For NumPy versions >= 1.11.0 a list of integers specifying the |
| 1293 | degrees of the terms to include may be used instead. |
| 1294 | rcond : float, optional |
| 1295 | Relative condition number of the fit. Singular values smaller than |
| 1296 | this relative to the largest singular value will be ignored. The |
| 1297 | default value is len(x)*eps, where eps is the relative precision of |
| 1298 | the float type, about 2e-16 in most cases. |
| 1299 | full : bool, optional |
| 1300 | Switch determining nature of return value. When it is False (the |
| 1301 | default) just the coefficients are returned, when True diagnostic |
| 1302 | information from the singular value decomposition is also returned. |
| 1303 | w : array_like, shape (`M`,), optional |
| 1304 | Weights. If not None, the weight ``w[i]`` applies to the unsquared |
| 1305 | residual ``y[i] - y_hat[i]`` at ``x[i]``. Ideally the weights are |
| 1306 | chosen so that the errors of the products ``w[i]*y[i]`` all have the |
| 1307 | same variance. When using inverse-variance weighting, use |
| 1308 | ``w[i] = 1/sigma(y[i])``. The default value is None. |
| 1309 | |
| 1310 | Returns |
| 1311 | ------- |
| 1312 | coef : ndarray, shape (M,) or (M, K) |
| 1313 | Hermite coefficients ordered from low to high. If `y` was 2-D, |
| 1314 | the coefficients for the data in column k of `y` are in column |
| 1315 | `k`. |
| 1316 | |
| 1317 | [residuals, rank, singular_values, rcond] : list |
| 1318 | These values are only returned if ``full == True`` |
| 1319 | |
| 1320 | - residuals -- sum of squared residuals of the least squares fit |
| 1321 | - rank -- the numerical rank of the scaled Vandermonde matrix |
| 1322 | - singular_values -- singular values of the scaled Vandermonde matrix |
| 1323 | - rcond -- value of `rcond`. |