/NumPy 1.17

# numpy.polynomial.laguerre.lagvander

`numpy.polynomial.laguerre.lagvander(x, deg)` [source]

Pseudo-Vandermonde matrix of given degree.

Returns the pseudo-Vandermonde matrix of degree `deg` and sample points `x`. The pseudo-Vandermonde matrix is defined by where `0 <= i <= deg`. The leading indices of `V` index the elements of `x` and the last index is the degree of the Laguerre polynomial.

If `c` is a 1-D array of coefficients of length `n + 1` and `V` is the array `V = lagvander(x, n)`, then `np.dot(V, c)` and `lagval(x, 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 Laguerre series of the same degree and sample points.

Parameters: `x : array_like` Array of points. The dtype is converted to float64 or complex128 depending on whether any of the elements are complex. If `x` is scalar it is converted to a 1-D array. `deg : int` Degree of the resulting matrix. `vander : ndarray` The pseudo-Vandermonde matrix. The shape of the returned matrix is `x.shape + (deg + 1,)`, where The last index is the degree of the corresponding Laguerre polynomial. The dtype will be the same as the converted `x`.

#### Examples

```>>> from numpy.polynomial.laguerre import lagvander
>>> x = np.array([0, 1, 2])
>>> lagvander(x, 3)
array([[ 1.        ,  1.        ,  1.        ,  1.        ],
[ 1.        ,  0.        , -0.5       , -0.66666667],
[ 1.        , -1.        , -1.        , -0.33333333]])
```

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https://docs.scipy.org/doc/numpy-1.17.0/reference/generated/numpy.polynomial.laguerre.lagvander.html