diff options
Diffstat (limited to 'numpy/polynomial/legendre.py')
| -rw-r--r-- | numpy/polynomial/legendre.py | 32 |
1 files changed, 20 insertions, 12 deletions
diff --git a/numpy/polynomial/legendre.py b/numpy/polynomial/legendre.py index c010c71a2..8fd64985b 100644 --- a/numpy/polynomial/legendre.py +++ b/numpy/polynomial/legendre.py @@ -1271,12 +1271,16 @@ def legvander2d(x, y, deg) : `V` index the points `(x, y)` and the last index encodes the degrees of the Legendre polynomials. - If `c` is a 2-D array of coefficients of shape `(m + 1, n + 1)` and `V` - is the matrix ``V = legvander2d(x, y, [m, n])``, then - ``np.dot(V, c.flat)`` and ``legval2d(x, y, c)`` are the same up to - roundoff. This equivalence is useful both for least squares fitting and - for the evaluation of a large number of 2-D Legendre series of the same - degrees and sample points. + If ``V = legvander2d(x, y, [xdeg, ydeg])``, then the columns of `V` + correspond to the elements of a 2-D coefficient array `c` of shape + (xdeg + 1, ydeg + 1) in the order + + .. math:: c_{00}, c_{01}, c_{02} ... , c_{10}, c_{11}, c_{12} ... + + and ``np.dot(V, c.flat)`` and ``legval2d(x, y, c)`` will be the same + up to roundoff. This equivalence is useful both for least squares + fitting and for the evaluation of a large number of 2-D Legendre + series of the same degrees and sample points. Parameters ---------- @@ -1331,12 +1335,16 @@ def legvander3d(x, y, z, deg) : indices of `V` index the points `(x, y, z)` and the last index encodes the degrees of the Legendre polynomials. - If `c` is a 3-D array of coefficients of shape `(l + 1, m + 1, n + 1)` - and `V` is the matrix ``V = legvander3d(x, y, z, [l, m, n])``, then - ``np.dot(V, c.flat)`` and ``legval3d(x, y, z, c)`` are the same up to - roundoff. This equivalence is useful both for least squares fitting and - for the evaluation of a large number of 3-D Legendre series of the same - degrees and sample points. + If ``V = legvander3d(x, y, z, [xdeg, ydeg, zdeg])``, then the columns + of `V` correspond to the elements of a 3-D coefficient array `c` of + shape (xdeg + 1, ydeg + 1, zdeg + 1) in the order + + .. math:: c_{000}, c_{001}, c_{002},... , c_{010}, c_{011}, c_{012},... + + and ``np.dot(V, c.flat)`` and ``legval3d(x, y, z, c)`` will be the + same up to roundoff. This equivalence is useful both for least squares + fitting and for the evaluation of a large number of 3-D Legendre + series of the same degrees and sample points. Parameters ---------- |