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Diffstat (limited to 'numpy/polynomial/polynomial.py')
| -rw-r--r-- | numpy/polynomial/polynomial.py | 104 |
1 files changed, 101 insertions, 3 deletions
diff --git a/numpy/polynomial/polynomial.py b/numpy/polynomial/polynomial.py index a0c9f903a..bf9c1a216 100644 --- a/numpy/polynomial/polynomial.py +++ b/numpy/polynomial/polynomial.py @@ -37,6 +37,8 @@ Misc Functions - `polyfromroots` -- create a polynomial with specified roots. - `polyroots` -- find the roots of a polynomial. - `polyvander` -- Vandermonde-like matrix for powers. +- `polyvander2d` -- Vandermonde-like matrix for 2D power series. +- `polyvander3d` -- Vandermonde-like matrix for 3D power series. - `polyfit` -- least-squares fit returning a polynomial. - `polytrim` -- trim leading coefficients from a polynomial. - `polyline` -- polynomial representing given straight line. @@ -54,9 +56,9 @@ from __future__ import division __all__ = ['polyzero', 'polyone', 'polyx', 'polydomain', 'polyline', 'polyadd', 'polysub', 'polymulx', 'polymul', 'polydiv', 'polypow', - 'polyval', 'polyval2d', 'polyval3d', 'polygrid2d', 'polygrid3d', - 'polyder', 'polyint', 'polyfromroots', 'polyvander', 'polyfit', - 'polytrim', 'polyroots', 'Polynomial'] + 'polyval', 'polyder', 'polyint', 'polyfromroots', 'polyvander', + 'polyfit', 'polytrim', 'polyroots', 'Polynomial','polyval2d', + 'polyval3d', 'polygrid2d', 'polygrid3d', 'polyvander2d','polyvander3d'] import numpy as np import numpy.linalg as la @@ -891,6 +893,10 @@ def polyvander(x, deg) : The shape of the returned matrix is ``x.shape + (deg+1,)``. The last index is the degree. + See Also + -------- + polyvander2d, polyvander3d + """ ideg = int(deg) if ideg != deg: @@ -908,6 +914,98 @@ def polyvander(x, deg) : return np.rollaxis(v, 0, v.ndim) +def polyvander2d(x, y, deg) : + """Pseudo Vandermonde matrix of given degree. + + Returns the pseudo Vandermonde matrix for 2D polynomials 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 polynomials 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 + -------- + polyvander, polyvander3d. polyval2d, polyval3d + + """ + 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 = polyvander(x, degx) + vy = polyvander(y, degy) + v = np.einsum("...i,...j->...ij", vx, vy) + return v.reshape(v.shape[:-2] + (-1,)) + + +def polyvander3d(x, y, z, deg) : + """Psuedo Vandermonde matrix of given degree. + + Returns the pseudo Vandermonde matrix for 3D polynomials 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 polynomials 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 + -------- + polyvander, polyvander3d. polyval2d, polyval3d + + """ + 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 = polyvander(x, deg_x) + vy = polyvander(y, deg_y) + vz = polyvander(z, deg_z) + v = np.einsum("...i,...j,...k->...ijk", vx, vy, vz) + return v.reshape(v.shape[:-3] + (-1,)) + + def polyfit(x, y, deg, rcond=None, full=False, w=None): """ Least-squares fit of a polynomial to data. |