diff options
Diffstat (limited to 'numpy/polynomial/hermite.py')
| -rw-r--r-- | numpy/polynomial/hermite.py | 101 |
1 files changed, 98 insertions, 3 deletions
diff --git a/numpy/polynomial/hermite.py b/numpy/polynomial/hermite.py index 2fd28a3ff..801e8f8d9 100644 --- a/numpy/polynomial/hermite.py +++ b/numpy/polynomial/hermite.py @@ -37,6 +37,8 @@ Misc Functions - `hermfromroots` -- create a Hermite series with specified roots. - `hermroots` -- find the roots of a Hermite series. - `hermvander` -- Vandermonde-like matrix for Hermite polynomials. +- `hermvander2d` -- Vandermonde-like matrix for 2D power series. +- `hermvander3d` -- Vandermonde-like matrix for 3D power series. - `hermfit` -- least-squares fit returning a Hermite series. - `hermtrim` -- trim leading coefficients from a Hermite series. - `hermline` -- Hermite series of given straight line. @@ -62,9 +64,10 @@ from polytemplate import polytemplate __all__ = ['hermzero', 'hermone', 'hermx', 'hermdomain', 'hermline', 'hermadd', 'hermsub', 'hermmulx', 'hermmul', 'hermdiv', 'hermpow', - 'hermval', 'hermval2d', 'hermval3d', 'hermgrid2d', 'hermgrid3d', - 'hermder', 'hermint', 'herm2poly', 'poly2herm', 'hermfromroots', - 'hermvander', 'hermfit', 'hermtrim', 'hermroots', 'Hermite'] + 'hermval', 'hermder', 'hermint', 'herm2poly', 'poly2herm', + 'hermfromroots', 'hermvander', 'hermfit', 'hermtrim', 'hermroots', + 'Hermite', 'hermval2d', 'hermval3d', 'hermgrid2d', 'hermgrid3d', + 'hermvander2d', 'hermvander3d'] hermtrim = pu.trimcoef @@ -1102,6 +1105,98 @@ def hermvander(x, deg) : return np.rollaxis(v, 0, v.ndim) +def hermvander2d(x, y, deg) : + """Pseudo Vandermonde matrix of given degree. + + Returns the pseudo Vandermonde matrix for 2D Hermite series in `x` and + `y`. The sample point coordinates must all have the same shape after + conversion to arrays and the dtype will be converted to either float64 + or complex128 depending on whether any of `x` or 'y' are complex. The + maximum degrees of the 2D Hermite series in each variable are specified + in the list `deg` in the form ``[xdeg, ydeg]``. The return array has + the shape ``x.shape + (order,)`` if `x`, and `y` are arrays or + ``(1, order) if they are scalars. Here order is the number of elements + in a flattened coefficient array of original shape ``(xdeg + 1, ydeg + + 1)``. The flattening is done so that the resulting pseudo Vandermonde + array can be easily used in least squares fits. + + Parameters + ---------- + x,y : array_like + Arrays of point coordinates, each of the same shape. + deg : list + List of maximum degrees of the form [x_deg, y_deg]. + + Returns + ------- + vander2d : ndarray + The shape of the returned matrix is described above. + + See Also + -------- + hermvander, hermvander3d. hermval2d, hermval3d + + """ + ideg = [int(d) for d in deg] + is_valid = [id == d and id >= 0 for id, d in zip(ideg, deg)] + if is_valid != [1, 1]: + raise ValueError("degrees must be non-negative integers") + degx, degy = deg + x, y = np.array((x, y), copy=0) + 0.0 + + vx = hermvander(x, degx) + vy = hermvander(y, degy) + v = np.einsum("...i,...j->...ij", vx, vy) + return v.reshape(v.shape[:-2] + (-1,)) + + +def hermvander3d(x, y, z, deg) : + """Psuedo Vandermonde matrix of given degree. + + Returns the pseudo Vandermonde matrix for 3D Hermite series in `x`, + `y`, or `z`. The sample point coordinates must all have the same shape + after conversion to arrays and the dtype will be converted to either + float64 or complex128 depending on whether any of `x`, `y`, or 'z' are + complex. The maximum degrees of the 3D Hermite series in each variable + are specified in the list `deg` in the form ``[xdeg, ydeg, zdeg]``. The + return array has the shape ``x.shape + (order,)`` if `x`, `y`, and `z` + are arrays or ``(1, order) if they are scalars. Here order is the + number of elements in a flattened coefficient array of original shape + ``(xdeg + 1, ydeg + 1, zdeg + 1)``. The flattening is done so that the + resulting pseudo Vandermonde array can be easily used in least squares + fits. + + Parameters + ---------- + x,y,z : array_like + Arrays of point coordinates, each of the same shape. + deg : list + List of maximum degrees of the form [x_deg, y_deg, z_deg]. + + Returns + ------- + vander3d : ndarray + The shape of the returned matrix is described above. + + See Also + -------- + hermvander, hermvander3d. hermval2d, hermval3d + + """ + ideg = [int(d) for d in deg] + is_valid = [id == d and id >= 0 for id, d in zip(ideg, deg)] + if is_valid != [1, 1, 1]: + raise ValueError("degrees must be non-negative integers") + degx, degy, degz = deg + x, y, z = np.array((x, y, z), copy=0) + 0.0 + + vx = hermvander(x, deg_x) + vy = hermvander(y, deg_y) + vz = hermvander(z, deg_z) + v = np.einsum("...i,...j,...k->...ijk", vx, vy, vz) + return v.reshape(v.shape[:-3] + (-1,)) + + def hermfit(x, y, deg, rcond=None, full=False, w=None): """ Least squares fit of Hermite series to data. |