# PrecomputedSparseTimeFunction¶

class `devito.types.``PrecomputedSparseTimeFunction`(*args, **kwargs)[source]

Bases: `devito.types.sparse.AbstractSparseTimeFunction`, `devito.types.sparse.PrecomputedSparseFunction`

Tensor symbol representing a space- and time-varying sparse array in symbolic equations; unlike SparseTimeFunction, PrecomputedSparseTimeFunction uses externally-defined data for interpolation.

Parameters
• name (str) – Name of the symbol.

• npoint (int) – Number of sparse points.

• grid (Grid) – The computational domain from which the sparse points are sampled.

• r (int) – Number of gridpoints in each dimension to interpolate a single sparse point to. E.g. `r=2` for linear interpolation.

• gridpoints (np.ndarray, optional) – An array carrying the reference grid point corresponding to each sparse point. Of all the gridpoints that one sparse point would be interpolated to, this is the grid point closest to the origin, i.e. the one with the lowest value of each coordinate dimension. Must be a two-dimensional array of shape `(npoint, grid.ndim)`.

• interpolation_coeffs (np.ndarray, optional) – An array containing the coefficient for each of the r^2 (2D) or r^3 (3D) gridpoints that each sparse point will be interpolated to. The coefficient is split across the n dimensions such that the contribution of the point (i, j, k) will be multiplied by ```interpolation_coeffs[..., i]*interpolation_coeffs[..., j]*interpolation_coeffs[...,k]```. So for `r=6`, we will store 18 coefficients per sparse point (instead of potentially 216). Must be a three-dimensional array of shape `(npoint, grid.ndim, r)`.

• space_order (int, optional) – Discretisation order for space derivatives. Defaults to 0.

• time_order (int, optional) – Discretisation order for time derivatives. Default to 1.

• shape (tuple of ints, optional) – Shape of the object. Defaults to `(npoint,)`.

• dimensions (tuple of Dimension, optional) – Dimensions associated with the object. Only necessary if the SparseFunction defines a multi-dimensional tensor.

• dtype (data-type, optional) – Any object that can be interpreted as a numpy data type. Defaults to `np.float32`.

• initializer (callable or any object exposing the buffer interface, optional) – Data initializer. If a callable is provided, data is allocated lazily.

• allocator (MemoryAllocator, optional) – Controller for memory allocation. To be used, for example, when one wants to take advantage of the memory hierarchy in a NUMA architecture. Refer to default_allocator.__doc__ for more information.

Notes

The parameters must always be given as keyword arguments, since SymPy uses `*args` to (re-)create the dimension arguments of the symbolic object.

property `data`

The domain data values, as a numpy.ndarray.

Elements are stored in row-major format.

Notes

With this accessor you are claiming that you will modify the values you get back. If you only need to look at the values, use `data_ro()` instead.

property `data_domain`

The domain data values.

Elements are stored in row-major format.

Notes

Alias to `self.data`.

With this accessor you are claiming that you will modify the values you get back. If you only need to look at the values, use `data_ro_domain()` instead.

property `data_ro_domain`

Read-only view of the domain data values.

property `data_ro_with_halo`

Read-only view of the domain+outhalo data values.

property `data_with_halo`

The domain+outhalo data values.

Elements are stored in row-major format.

Notes

With this accessor you are claiming that you will modify the values you get back. If you only need to look at the values, use `data_ro_with_halo()` instead.

property `dimensions`

Tuple of Dimensions representing the object indices.

property `dtype`

The data type of the object.

property `grid`

The Grid on which the discretization occurred.

property `gridpoints`

The reference grid point corresponding to each sparse point.

Notes

When using MPI, this property refers to the physically owned sparse points.

`inject`(field, expr, offset=0)

Generate equations injecting an arbitrary expression into a field.

Parameters
• field (Function) – Input field into which the injection is performed.

• expr (expr-like) – Injected expression.

• offset (int, optional) – Additional offset from the boundary.

`interpolate`(expr, offset=0, u_t=None, p_t=None, increment=False)[source]

Generate equations interpolating an arbitrary expression into `self`.

Parameters
• expr (expr-like) – Input expression to interpolate.

• offset (int, optional) – Additional offset from the boundary.

• u_t (expr-like, optional) – Time index at which the interpolation is performed.

• p_t (expr-like, optional) – Time index at which the result of the interpolation is stored.

• increment (bool, optional) – If True, generate increments (Inc) rather than assignments (Eq).

property `name`

The name of the object.

`shape`

Shape of the domain region. The domain constitutes the area of the data written to by an Operator.

Notes

In an MPI context, this is the local domain region shape.

property `space_order`

The space order.

property `time_order`

The time order.