Renamed decomposition algorithms (#162)

matfree/decomp.py

@@ -20,7 +20,7 @@ class _Alg(containers.NamedTuple):
     """Range of the for-loop used to decompose a matrix."""
 
 
-def tridiagonal_full_reortho(depth, /):
+def lanczos_tridiag_full_reortho(depth, /):
     """Construct an implementation of **tridiagonalisation**.
 
     Uses pre-allocation. Fully reorthogonalise vectors at every step.
@@ -83,7 +83,7 @@ def extract(state: State, /):
     return _Alg(init=init, step=apply, extract=extract, lower_upper=(0, depth + 1))
 
 
-def bidiagonal_full_reortho(depth, /, matrix_shape):
+def lanczos_bidiag_full_reortho(depth, /, matrix_shape):
     """Construct an implementation of **bidiagonalisation**.
 
     Uses pre-allocation. Fully reorthogonalise vectors at every step.
@@ -161,7 +161,7 @@ def _gram_schmidt_orthogonalise(vec1, vec2):
     return vec_ortho, coeff
 
 
-def svd(
+def svd_approx(
     v0: Array, depth: int, Av: Callable, vA: Callable, matrix_shape: Tuple[int, ...]
 ):
     """Approximate singular value decomposition.
@@ -185,7 +185,7 @@ def svd(
         Shape of the matrix involved in matrix-vector and vector-matrix products.
     """
     # Factorise the matrix
-    algorithm = bidiagonal_full_reortho(depth, matrix_shape=matrix_shape)
+    algorithm = lanczos_bidiag_full_reortho(depth, matrix_shape=matrix_shape)
     u, (d, e), vt, _ = decompose_fori_loop(v0, Av, vA, algorithm=algorithm)
 
     # Compute SVD of factorisation
@@ -222,7 +222,7 @@ class _DecompAlg(containers.NamedTuple):
 """Decomposition algorithm type.
 
 For example, the output of
-[matfree.decomp.tridiagonal_full_reortho(...)][matfree.decomp.tridiagonal_full_reortho].
+[matfree.decomp.lanczos_tridiag_full_reortho(...)][matfree.decomp.lanczos_tridiag_full_reortho].
 """
 
 

matfree/slq.py

@@ -22,7 +22,7 @@ def _quadratic_form_slq_spd(matfun, order, Av, /):
     """
 
     def quadform(v0, /):
-        algorithm = decomp.tridiagonal_full_reortho(order)
+        algorithm = decomp.lanczos_tridiag_full_reortho(order)
         _, tridiag = decomp.decompose_fori_loop(v0, Av, algorithm=algorithm)
         (diag, off_diag) = tridiag
 
@@ -85,7 +85,7 @@ def _quadratic_form_slq_product(matfun, depth, *matvec_funs, matrix_shape):
 
     def quadform(v0, /):
         # Decompose into orthogonal-bidiag-orthogonal
-        algorithm = decomp.bidiagonal_full_reortho(depth, matrix_shape=matrix_shape)
+        algorithm = decomp.lanczos_bidiag_full_reortho(depth, matrix_shape=matrix_shape)
         output = decomp.decompose_fori_loop(v0, *matvec_funs, algorithm=algorithm)
         u, (d, e), vt, _ = output
 

tests/test_decomp/test_bidiagonal_full_reortho.py

@@ -18,12 +18,12 @@ def A(nrows, ncols, num_significant_singular_vals):
 @testing.parametrize("ncols", [49])
 @testing.parametrize("num_significant_singular_vals", [4])
 @testing.parametrize("order", [6])  # ~1.5 * num_significant_eigvals
-def test_bidiagonal_full_reortho(A, order):
+def test_lanczos_bidiag_full_reortho(A, order):
     """Test that Lanczos tridiagonalisation yields an orthogonal-tridiagonal decomp."""
     nrows, ncols = np.shape(A)
     key = prng.prng_key(1)
     v0 = prng.normal(key, shape=(ncols,))
-    alg = decomp.bidiagonal_full_reortho(order, matrix_shape=np.shape(A))
+    alg = decomp.lanczos_bidiag_full_reortho(order, matrix_shape=np.shape(A))
 
     def Av(v):
         return A @ v
@@ -74,7 +74,7 @@ def test_error_too_high_depth(A):
     max_depth = min(nrows, ncols) - 1
 
     with testing.raises(ValueError):
-        _ = decomp.bidiagonal_full_reortho(max_depth + 1, matrix_shape=np.shape(A))
+        _ = decomp.lanczos_bidiag_full_reortho(max_depth + 1, matrix_shape=np.shape(A))
 
 
 @testing.parametrize("nrows", [5])
@@ -84,7 +84,7 @@ def test_error_too_low_depth(A):
     """Assert that a ValueError is raised when the depth is negative."""
     min_depth = 0
     with testing.raises(ValueError):
-        _ = decomp.bidiagonal_full_reortho(min_depth - 1, matrix_shape=np.shape(A))
+        _ = decomp.lanczos_bidiag_full_reortho(min_depth - 1, matrix_shape=np.shape(A))
 
 
 @testing.parametrize("nrows", [15])
@@ -93,7 +93,7 @@ def test_error_too_low_depth(A):
 def test_no_error_zero_depth(A):
     """Assert the corner case of zero-depth does not raise an error."""
     nrows, ncols = np.shape(A)
-    algorithm = decomp.bidiagonal_full_reortho(0, matrix_shape=np.shape(A))
+    algorithm = decomp.lanczos_bidiag_full_reortho(0, matrix_shape=np.shape(A))
     key = prng.prng_key(1)
     v0 = prng.normal(key, shape=(ncols,))
 

tests/test_decomp/test_svd.py

@@ -34,7 +34,7 @@ def vA(v):
         return v @ A
 
     v0 = np.ones((ncols,))
-    U, S, Vt = decomp.svd(v0, depth, Av, vA, matrix_shape=np.shape(A))
+    U, S, Vt = decomp.svd_approx(v0, depth, Av, vA, matrix_shape=np.shape(A))
     U_, S_, Vt_ = linalg.svd(A, full_matrices=False)
 
     tols_decomp = {"atol": 1e-5, "rtol": 1e-5}

tests/test_decomp/test_tridiagonal_full_reortho.py

@@ -22,7 +22,7 @@ def test_max_order(A):
     order = n - 1
     key = prng.prng_key(1)
     v0 = prng.normal(key, shape=(n,))
-    alg = decomp.tridiagonal_full_reortho(order)
+    alg = decomp.lanczos_tridiag_full_reortho(order)
     Q, (d_m, e_m) = decomp.decompose_fori_loop(v0, lambda v: A @ v, algorithm=alg)
 
     # Lanczos is not stable.
@@ -63,7 +63,7 @@ def test_identity(A, order):
     n, _ = np.shape(A)
     key = prng.prng_key(1)
     v0 = prng.normal(key, shape=(n,))
-    alg = decomp.tridiagonal_full_reortho(order)
+    alg = decomp.lanczos_tridiag_full_reortho(order)
     Q, tridiag = decomp.decompose_fori_loop(v0, lambda v: A @ v, algorithm=alg)
     (d_m, e_m) = tridiag