PartialDerivative¶

class odl.discr.diff_ops.PartialDerivative(*args, **kwargs)[source]¶

Bases: PointwiseTensorFieldOperator

Calculate the discrete partial derivative along a given axis.

Calls helper function finite_diff to calculate finite difference. Preserves the shape of the underlying grid.

Attributes:

adjoint: Return the adjoint operator.
base_space: Base space X of this operator's domain and range.
domain: Set of objects on which this operator can be evaluated.
inverse: Return the operator inverse.
is_functional: True if this operator's range is a Field.
is_linear: True if this operator is linear.
range: Set in which the result of an evaluation of this operator lies.

Methods

`__call__`(x[, out])	Return `self(x[, out, **kwargs])`.
`derivative`([point])	Return the derivative operator.
`norm`([estimate])	Return the operator norm of this operator.

__init__(domain, axis, range=None, method='forward', pad_mode='constant', pad_const=0)[source]¶

Initialize a new instance.

Parameters:

domainDiscretizedSpace

Space of elements on which the operator can act.

axisint

Axis along which the partial derivative is evaluated.

rangeDiscretizedSpace, optional

Space of elements to which the operator maps, must have the same shape as domain. For the default None, the range is the same as domain.

method{'forward', 'backward', 'central'}, optional

Finite difference method which is used in the interior of the domain of f.

pad_modestring, optional

The padding mode to use outside the domain.

'constant': Fill with pad_const.

'symmetric': Reflect at the boundaries, not doubling the outmost values.

'periodic': Fill in values from the other side, keeping the order.

'order0': Extend constantly with the outmost values (ensures continuity).

'order1': Extend with constant slope (ensures continuity of the first derivative). This requires at least 2 values along each axis where padding is applied.

'order2': Extend with second order accuracy (ensures continuity of the second derivative). This requires at least 3 values along the axis where padding is applied.

pad_constfloat, optional

For pad_mode == 'constant', f assumes pad_const for indices outside the domain of f

Examples

>>> f = np.array([[ 0.,  1.,  2.,  3.,  4.],
...               [ 0.,  2.,  4.,  6.,  8.]])
>>> discr = odl.uniform_discr([0, 0], [2, 1], f.shape)
>>> par_deriv = PartialDerivative(discr, axis=0, pad_mode='order1')
>>> par_deriv(f)
uniform_discr([ 0.,  0.], [ 2.,  1.], (2, 5)).element(
    [[ 0.,  1.,  2.,  3.,  4.],
     [ 0.,  1.,  2.,  3.,  4.]]
)