diff options
Diffstat (limited to 'numpy/polynomial/chebyshev.py')
| -rw-r--r-- | numpy/polynomial/chebyshev.py | 102 |
1 files changed, 98 insertions, 4 deletions
diff --git a/numpy/polynomial/chebyshev.py b/numpy/polynomial/chebyshev.py index 6212f2bc5..d6ccf25ca 100644 --- a/numpy/polynomial/chebyshev.py +++ b/numpy/polynomial/chebyshev.py @@ -40,6 +40,8 @@ Misc Functions - `chebfromroots` -- create a Chebyshev series with specified roots. - `chebroots` -- find the roots of a Chebyshev series. - `chebvander` -- Vandermonde-like matrix for Chebyshev polynomials. +- `chebvander2d` -- Vandermonde-like matrix for 2D power series. +- `chebvander3d` -- Vandermonde-like matrix for 3D power series. - `chebfit` -- least-squares fit returning a Chebyshev series. - `chebpts1` -- Chebyshev points of the first kind. - `chebpts2` -- Chebyshev points of the second kind. @@ -90,10 +92,10 @@ from polytemplate import polytemplate __all__ = ['chebzero', 'chebone', 'chebx', 'chebdomain', 'chebline', 'chebadd', 'chebsub', 'chebmulx', 'chebmul', 'chebdiv', 'chebpow', - 'chebval', 'chebval2d', 'chebval3d', 'chebgrid2d', 'chebgrid3d', - 'chebder', 'chebint', 'cheb2poly', 'poly2cheb', 'chebfromroots', - 'chebvander', 'chebfit', 'chebtrim', 'chebroots', 'chebpts1', - 'chebpts2', 'Chebyshev'] + 'chebval', 'chebder', 'chebint', 'cheb2poly', 'poly2cheb', + 'chebfromroots', 'chebvander', 'chebfit', 'chebtrim', 'chebroots', + 'chebpts1', 'chebpts2', 'Chebyshev', 'chebval2d', 'chebval3d', + 'chebgrid2d', 'chebgrid3d', 'chebvander2d','chebvander3d'] chebtrim = pu.trimcoef @@ -1315,6 +1317,98 @@ def chebvander(x, deg) : return np.rollaxis(v, 0, v.ndim) +def chebvander2d(x, y, deg) : + """Psuedo Vandermonde matrix of given degree. + + Returns the pseudo Vandermonde matrix for 2D Chebyshev 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 Chebyshev 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 + -------- + chebvander, chebvander3d. chebval2d, chebval3d + + """ + 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 = chebvander(x, degx) + vy = chebvander(y, degy) + v = np.einsum("...i,...j->...ij", vx, vy) + return v.reshape(v.shape[:-2] + (-1,)) + + +def chebvander3d(x, y, z, deg) : + """Psuedo Vandermonde matrix of given degree. + + Returns the pseudo Vandermonde matrix for 3D Chebyshev 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 Chebeshev 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 + -------- + chebvander, chebvander3d. chebval2d, chebval3d + + """ + 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 = chebvander(x, deg_x) + vy = chebvander(y, deg_y) + vz = chebvander(z, deg_z) + v = np.einsum("...i,...j,...k->...ijk", vx, vy, vz) + return v.reshape(v.shape[:-3] + (-1,)) + + def chebfit(x, y, deg, rcond=None, full=False, w=None): """ Least squares fit of Chebyshev series to data. |