Prevent svdlibc from seeing a zero-entry sparse matrix.

The fact that svdlibc's state can be permanently corrupted by a matrix with no
entries indicates to me that its memory handling is unsafe. We should see if
it's feasible to switch to SciPy sometime.

divisi2/algorithms/svd.py

@@ -3,6 +3,7 @@
 from divisi2.reconstructed import ReconstructedMatrix
 from divisi2._svdlib import svd_llmat, svd_ndarray
 from divisi2 import operators
+import numpy as np
 
 def svd(matrix, k=50):
     """
@@ -22,6 +23,13 @@ def svd(matrix, k=50):
     if isinstance(matrix, DenseMatrix):
         Ut, S, Vt = svd_ndarray(matrix, k)
     elif isinstance(matrix, SparseMatrix):
+        if matrix.nnz == 0:
+            # don't let svdlib touch a matrix of all zeros. It explodes and
+            # corrupts its state. Just return a zero result instead.
+            U = DenseMatrix((matrix.shape[0], k))
+            S = np.zeros((k,))
+            V = DenseMatrix((matrix.shape[1], k))
+            return U, S, V
         if matrix.shape[1] >= matrix.shape[0] * 1.2:
             # transpose the matrix for speed
             V, S, U = matrix.T.svd(k)