6.5.1.1.3. statsmodels.sandbox.nonparametric.densityorthopoly.is_orthonormal_cont

statsmodels.sandbox.nonparametric.densityorthopoly.is_orthonormal_cont(polys, lower, upper, rtol=0, atol=1e-08)

check whether functions are orthonormal

Parameters:

polys : list of polynomials or function

Returns:

is_orthonormal : bool

is False if the innerproducts are not close to 0 or 1

Notes

this stops as soon as the first deviation from orthonormality is found.

Examples

>>> from scipy.special import chebyt
>>> polys = [chebyt(i) for i in range(4)]
>>> r, e = inner_cont(polys, -1, 1)
>>> r
array([[ 2.        ,  0.        , -0.66666667,  0.        ],
       [ 0.        ,  0.66666667,  0.        , -0.4       ],
       [-0.66666667,  0.        ,  0.93333333,  0.        ],
       [ 0.        , -0.4       ,  0.        ,  0.97142857]])
>>> is_orthonormal_cont(polys, -1, 1, atol=1e-6)
False

>>> polys = [ChebyTPoly(i) for i in range(4)]
>>> r, e = inner_cont(polys, -1, 1)
>>> r
array([[  1.00000000e+00,   0.00000000e+00,  -9.31270888e-14,
          0.00000000e+00],
       [  0.00000000e+00,   1.00000000e+00,   0.00000000e+00,
         -9.47850712e-15],
       [ -9.31270888e-14,   0.00000000e+00,   1.00000000e+00,
          0.00000000e+00],
       [  0.00000000e+00,  -9.47850712e-15,   0.00000000e+00,
          1.00000000e+00]])
>>> is_orthonormal_cont(polys, -1, 1, atol=1e-6)
True