Convert core data structures and tools to use 4D arrays

[rafmudaf]

Convert core FLORIS to use 4D arrays as low-level data structures

As part of the ongoing effort to support a higher degree of wind farm controls, FLORIS is undergoing a major change from the current 5-dimensional data structures at the lowest level to 4-dimensional data structures. Currently, FLORIS relies heavily on Numpy arrays to do all computations. The shape and size of the arrays vary depending on the context, but they all always have the same first two dimensions (left most) that map to a wind direction and wind speed. Common array shapes are:

# For TurbineGrid-based calculations and data structures that require the full grid
(
    n wind directions,
    n wind speeds,
    n turbines,
    grid dimension 1,
    grid dimension 2
)

# For FlowFieldGrid, FlowFieldPlanarGrid, and PointsGrid calculations
(
    n wind directions,
    n wind speeds,
    grid dimension 1,
    grid dimension 2,
    grid dimension 3
)

# For data structures that contain a scalar value per turbine
(
    n wind directions,
    n wind speeds,
    n turbines
)

This was introduced during the v3 redesign in order to vectorize computations with Numpy broadcasting and SIMD instructions. While the new Structure of Arrays architecture was an improvement over the Array of Structures in FLORIS v2, it also introduced some unintended complexities including the default scenario of creating a product of all wind speeds and wind directions. The alternative to this has been to create a tuple of wind directions and wind speeds in the first dimension and use size 1 for the second dimension - this has been called time_series mode in FLORIS v3. Noting that this is the most explicit method to define a calculation, FLORIS v4 is adoption 4D arrays to directly support this use.

This pull request changes the floris.simulation package to support the 4D arrays. Where possible, dimensional constraints are removed entirely so that any future changes to the low level data structures are made easier. This change typically involves removing a : in array indexing and changing the axis for particular Numpy operations. For example, a typical changes is including below from solver.py.

- x_i = np.mean(grid.x_sorted[:, :, i:i+1], axis=(3, 4))
- x_i = x_i[:, :, :, None, None]
- y_i = np.mean(grid.y_sorted[:, :, i:i+1], axis=(3, 4))
- y_i = y_i[:, :, :, None, None]
- z_i = np.mean(grid.z_sorted[:, :, i:i+1], axis=(3, 4))
- z_i = z_i[:, :, :, None, None]
+ x_i = np.mean(grid.x_sorted[:, i:i+1], axis=(2, 3))
+ x_i = x_i[:, :, None, None]
+ y_i = np.mean(grid.y_sorted[:, i:i+1], axis=(2, 3))
+ y_i = y_i[:, :, None, None]
+ z_i = np.mean(grid.z_sorted[:, i:i+1], axis=(2, 3))
+ z_i = z_i[:, :, None, None]

Though this pull request focuses specifically on the floris.simulation package, portions of the floris.tools package have also been updated to reflect this change to facilitate testing. The test suite has also been updated to reflect this change. Most of the set of examples have been updated, but tests including the optimization routines are not updated since the floris.tools.optimization package is outside of the scope of this pull request.

Impacted areas of the software

This impacts nearly all of the floris.simulation package as well as FlorisInterface and floris.tools.visualization.