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Diffstat (limited to 'numpy/polynomial/laguerre.py')
| -rw-r--r-- | numpy/polynomial/laguerre.py | 100 |
1 files changed, 97 insertions, 3 deletions
diff --git a/numpy/polynomial/laguerre.py b/numpy/polynomial/laguerre.py index dbbb2c401..39463b0cb 100644 --- a/numpy/polynomial/laguerre.py +++ b/numpy/polynomial/laguerre.py @@ -37,6 +37,8 @@ Misc Functions - `lagfromroots` -- create a Laguerre series with specified roots. - `lagroots` -- find the roots of a Laguerre series. - `lagvander` -- Vandermonde-like matrix for Laguerre polynomials. +- `lagvander2d` -- Vandermonde-like matrix for 2D power series. +- `lagvander3d` -- Vandermonde-like matrix for 3D power series. - `lagfit` -- least-squares fit returning a Laguerre series. - `lagtrim` -- trim leading coefficients from a Laguerre series. - `lagline` -- Laguerre series of given straight line. @@ -62,9 +64,9 @@ from polytemplate import polytemplate __all__ = ['lagzero', 'lagone', 'lagx', 'lagdomain', 'lagline', 'lagadd', 'lagsub', 'lagmulx', 'lagmul', 'lagdiv', 'lagpow', - 'lagval', 'lagval2d', 'lagval3d', 'laggrid2d', 'laggrid3d', - 'lagder', 'lagint', 'lag2poly', 'poly2lag', 'lagfromroots', - 'lagvander', 'lagfit', 'lagtrim', 'lagroots', 'Laguerre'] + 'lagval', 'lagder', 'lagint', 'lag2poly', 'poly2lag', 'lagfromroots', + 'lagvander', 'lagfit', 'lagtrim', 'lagroots', 'Laguerre', 'lagval2d', + 'lagval3d', 'laggrid2d', 'laggrid3d', 'lagvander2d', 'lagvander3d'] lagtrim = pu.trimcoef @@ -1100,6 +1102,98 @@ def lagvander(x, deg) : return np.rollaxis(v, 0, v.ndim) +def lagvander2d(x, y, deg) : + """Pseudo Vandermonde matrix of given degree. + + Returns the pseudo Vandermonde matrix for 2D Laguerre 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 Laguerre 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 + -------- + lagvander, lagvander3d. lagval2d, lagval3d + + """ + 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 = lagvander(x, degx) + vy = lagvander(y, degy) + v = np.einsum("...i,...j->...ij", vx, vy) + return v.reshape(v.shape[:-2] + (-1,)) + + +def lagvander3d(x, y, z, deg) : + """Psuedo Vandermonde matrix of given degree. + + Returns the pseudo Vandermonde matrix for 3D Laguerre 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 Laguerre 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 + -------- + lagvander, lagvander3d. lagval2d, lagval3d + + """ + 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 = lagvander(x, deg_x) + vy = lagvander(y, deg_y) + vz = lagvander(z, deg_z) + v = np.einsum("...i,...j,...k->...ijk", vx, vy, vz) + return v.reshape(v.shape[:-3] + (-1,)) + + def lagfit(x, y, deg, rcond=None, full=False, w=None): """ Least squares fit of Laguerre series to data. |