apply sqrt division first

Signed-off-by: Kyle Sayers <kylesayrs@gmail.com>

Author: kylesayrs

src/compressed_tensors/transform/utils/hadamard.py

@@ -23,7 +23,7 @@
 
 # adapted from:
 # https://github.com/scipy/scipy/blob/v1.15.2/scipy/linalg/_special_matrices.py
-def deterministic_hadamard_matrix(size: int) -> numpy.ndarray:
+def deterministic_hadamard_matrix(size: int) -> torch.Tensor:
     """
     Construct an Hadamard matrix.
 
@@ -47,7 +47,7 @@ def deterministic_hadamard_matrix(size: int) -> numpy.ndarray:
     for i in range(0, log2):
         H = numpy.vstack((numpy.hstack((H, H)), numpy.hstack((H, -H))))
 
-    return H
+    return torch.from_numpy(H / math.sqrt(size))
 
 
 # adapted from:
@@ -75,7 +75,7 @@ def random_hadamard_matrix(size: int) -> torch.Tensor:
     Q = torch.randint(low=0, high=2, size=(size,)).to(torch.float64)
     Q = Q * 2 - 1
     Q = torch.diag(Q)
-    return _matmul_hadU(Q)
+    return _matmul_hadU(Q) / math.sqrt(size)
 
 
 def _get_hadK(n: int, transpose: bool = False) -> Tuple[torch.Tensor, int]:

tests/test_transform/utils/test_hadamards.py renamed to tests/test_transform/utils/test_hadamard.py

@@ -33,10 +33,10 @@
 )
 def test_packed_hadamard_compliant(had_func):
     had_matrix = had_func()
-    size = had_matrix.shape[0]
+    size = had_matrix.size(0)
     # HH.T == nI
-    val_1 = had_matrix @ had_matrix.T
-    assert torch.equal(val_1 / size, torch.eye(size))
+    product = had_matrix @ had_matrix.T
+    assert torch.equal(product, size * torch.eye(size))
 
 
 @pytest.mark.parametrize(
@@ -45,8 +45,8 @@ def test_packed_hadamard_compliant(had_func):
 )
 def test_random_hadamard_matrix_compliant(size):
     had_matrix = random_hadamard_matrix(size)
-    val_1 = torch.round(had_matrix @ had_matrix.T)
-    assert torch.equal(val_1 / size, torch.eye(size))
+    product = torch.round(had_matrix @ had_matrix.T)
+    assert torch.equal(product, torch.eye(size))
 
 
 @pytest.mark.parametrize(
@@ -55,6 +55,6 @@ def test_random_hadamard_matrix_compliant(size):
 )
 def test_deterministic_hadamard_compliant(size):
     had_matrix = deterministic_hadamard_matrix(size)
-    # HH.T == nI
-    val_1 = had_matrix @ had_matrix.T
-    assert numpy.array_equal(val_1 / size, numpy.eye(size))
+    # (H / sqrt(n))(H.T / sqrt(n)) == I
+    product = had_matrix @ had_matrix.T
+    assert numpy.array_equal(product, numpy.eye(size))