Improve runtime and peak memory usage of PVEngine.run_full_mode

docs/sphinx/whatsnew/v1.5.3.rst

@@ -6,12 +6,17 @@ v1.5.3 (TBD)
 Enhancements
 ------------
 
-* Add python3.10 to test configuration (ghpull:`129`)
+* Add python 3.10 to test configuration (:ghpull:`129`)
+* :py:meth:`pvfactors.engine.PVEngine.run_full_mode` is faster and uses less
+  memory for simulations with large ``n_pvrows`` and many timestamps (:ghpull:`140`)
 
 
 Requirements
 ------------
 
+* ``scipy>=1.2.0`` is now a direct requirement (before now it was only
+  indirectly required through pvlib) (:ghpull:`140`)
+
 
 Bug Fixes
 ----------

pvfactors/engine.py

@@ -2,11 +2,51 @@
 timeseries simulations."""
 
 import numpy as np
+from scipy.sparse import csc_matrix
+from scipy.sparse.linalg import spsolve
 from pvfactors.viewfactors import VFCalculator
 from pvfactors.irradiance import HybridPerezOrdered
 from pvfactors.config import DEFAULT_RHO_FRONT, DEFAULT_RHO_BACK
 
 
+def _sparse_solve_3D(A, b):
+    """
+    Solve the linear system A*x=b for x, where A is sparse (contains mostly
+    zeros).
+
+    For large matrices with many zeros, this is faster and uses less memory
+    than the dense analog `np.linalg.solve`.
+
+    Parameters
+    ----------
+    A : np.ndarray of shape (M, N, N)
+        First dimension is timestamps, second and third are surface dimensions
+    b : np.ndarray of shape (M, N)
+        First dimension is timestamps, second is surfaces
+
+    Returns
+    -------
+    x : np.ndarray of shape (M, N)
+        First dimension is timestamps, second is surfaces
+    """
+    # implementation notes:
+    # - csc_matrix seemed to be the fastest option of the various
+    #   sparse matrix formats in scipy.sparse
+    # - unfortunately the sparse matrix formats are 2-D only, so
+    #   iteration across the time dimension is required
+    # - scipy 1.8.0 added new sparse arrays (as opposed to sparse matrices);
+    #   they are 2-D only at time of writing, but in the future if they
+    #   become N-D then it may make sense to use them here.
+    xs = []
+    for A_slice, b_slice in zip(A, b):
+        A_sparse = csc_matrix(A_slice)
+        b_sparse = csc_matrix(b_slice).T
+        x = spsolve(A_sparse, b_sparse)
+        xs.append(x)
+    x = np.stack(xs)
+    return x
+
+
 class PVEngine(object):
     """Class putting all of the calculations together into simple
     workflows.
@@ -215,33 +255,36 @@ def run_full_mode(self, fn_build_report=None):
         invrho_ts_diag = np.zeros(shape_system)
         for idx_surf in range(shape_system[1]):
             invrho_ts_diag[:, idx_surf, idx_surf] = invrho_mat[idx_surf, :]
+        del invrho_mat
         # Subtract matrices: will rely on broadcasting
         # shape = n_timesteps, n_surfaces + 1, n_surfaces + 1
         a_mat = invrho_ts_diag - ts_vf_matrix_reshaped
-        # Calculate inverse, requires specific shape
-        # shape = n_timesteps, n_surfaces + 1, n_surfaces + 1
-        inv_a_mat = np.linalg.inv(a_mat)
-        # Use einstein sum to get final timeseries radiosities
-        # shape = n_surfaces + 1, n_timesteps
-        q0 = np.einsum('ijk,ki->ji', inv_a_mat, irradiance_mat)
+        del ts_vf_matrix_reshaped
+        # solve the linear system a_mat * q0 = irradiance_mat for q0
+        q0 = _sparse_solve_3D(a_mat, irradiance_mat.T).T
+        del a_mat
         # Calculate incident irradiance: will rely on broadcasting
         # shape = n_surfaces + 1, n_timesteps
         qinc = np.einsum('ijk,ki->ji', invrho_ts_diag, q0)
+        del invrho_ts_diag
 
         # --- Derive other irradiance terms
         # shape = n_surfaces, n_timesteps
         isotropic_mat = ts_vf_matrix[:-1, -1, :] * irradiance_mat[-1, :]
+        del ts_vf_matrix
         reflection_mat = qinc[:-1, :] - irradiance_mat[:-1, :] - isotropic_mat
-
+        del irradiance_mat
         # --- Calculate AOI losses and absorbed irradiance
         # Create tiled reflection matrix of
         # shape = n_surfaces + 1, n_surfaces + 1, n_timestamps
         rho_ts_tiled = np.moveaxis(np.tile(rho_mat.T, (shape_system[1], 1, 1)),
                                    -1, 0)
+        del rho_mat
         # Get vf AOI matrix
         # shape [n_surfaces + 1, n_surfaces + 1, n_timestamps]
         vf_aoi_matrix = (self.vf_calculator
                          .build_ts_vf_aoi_matrix(pvarray, rho_ts_tiled))
+        del rho_ts_tiled
         pvarray.ts_vf_aoi_matrix = vf_aoi_matrix
         # Get absorbed irradiance matrix
         # shape [n_surfaces, n_timestamps]
@@ -250,6 +293,8 @@ def run_full_mode(self, fn_build_report=None):
         # Calculate absorbed irradiance
         qabs = (np.einsum('ijk,jk->ik', vf_aoi_matrix, q0)[:-1, :]
                 + irradiance_abs_mat)
+        del irradiance_abs_mat
+        del vf_aoi_matrix
 
         # --- Update surfaces with values: the lists are ordered by index
         for idx_surf, ts_surface in enumerate(pvarray.all_ts_surfaces):

pvfactors/tests/test_engine.py

@@ -1,4 +1,4 @@
-from pvfactors.engine import PVEngine
+from pvfactors.engine import PVEngine, _sparse_solve_3D
 from pvfactors.geometry.pvarray import OrderedPVArray
 from pvfactors.irradiance import IsotropicOrdered, HybridPerezOrdered
 from pvfactors.irradiance.utils import breakup_df_inputs
@@ -709,3 +709,13 @@ def test_engine_variable_albedo(params, df_inputs_clearsky_8760):
     expected_bfg_after_aoi = 14.670709
     np.testing.assert_allclose(bfg, expected_bfg)
     np.testing.assert_allclose(bfg_after_aoi, expected_bfg_after_aoi)
+
+
+def test__sparse_solve_3d():
+    """Verify the sparse solver returns same results as np.linalg.solve"""
+    A = np.random.rand(5, 3, 3)
+    b = np.random.rand(5, 3)
+    x_dense = np.linalg.solve(A, b)
+    x_sparse = _sparse_solve_3D(A, b)
+    assert x_sparse.shape == b.shape
+    np.testing.assert_allclose(x_dense, x_sparse)

requirements.txt

@@ -1,5 +1,6 @@
 pvlib>=0.9.0,<0.10.0
 shapely>=1.6.4.post2,<2
+scipy>=1.2.0
 matplotlib
 future
 six