[ADD] Frobenius norm in structured matrix interface

singd/structures/base.py

@@ -9,6 +9,7 @@
 import torch
 import torch.distributed as dist
 from torch import Tensor, zeros
+from torch.linalg import matrix_norm
 
 from singd.structures.utils import diag_add_, supported_eye, supported_matmul
 
@@ -343,6 +344,15 @@ def infinity_vector_norm(self) -> Tensor:
         # NOTE `.max` can only be called on tensors with non-zero shape
         return max(t.abs().max() for _, t in self.named_tensors() if t.numel() > 0)
 
+    def frobenius_norm(self) -> Tensor:
+        """Compute the Frobenius norm of the represented matrix.
+
+        Returns:
+            The Frobenius norm of the represented matrix.
+        """
+        self._warn_naive_implementation("trace")
+        return matrix_norm(self.to_dense())
+
     ###############################################################################
     #                      Special initialization operations                      #
     ###############################################################################

test/structures/utils.py

@@ -11,7 +11,7 @@
 from matplotlib import pyplot as plt
 from pytest import mark
 from torch import Tensor, device, manual_seed, rand, zeros
-from torch.linalg import vector_norm
+from torch.linalg import matrix_norm, vector_norm
 
 from singd.structures.base import StructuredMatrix
 from singd.structures.utils import is_half_precision, supported_eye, supported_matmul
@@ -582,6 +582,22 @@ def test_infinity_vector_norm(self, dev: device, dtype: torch.dtype):
             structured = self.STRUCTURED_MATRIX_CLS.from_dense(sym_mat)
             report_nonclose(truth, structured.infinity_vector_norm())
 
+    @mark.parametrize("dtype", DTYPES, ids=DTYPE_IDS)
+    @mark.parametrize("dev", DEVICES, ids=DEVICE_IDS)
+    def test_frobenius_norm(self, dev: device, dtype: torch.dtype):
+        """Test Frobenius norm of a structured matrix.
+
+        Args:
+            dev: The device on which to run the test.
+            dtype: The data type of the matrices.
+        """
+        for dim in self.DIMS:
+            manual_seed(0)
+            sym_mat = symmetrize(rand((dim, dim), device=dev, dtype=dtype))
+            truth = matrix_norm(self.project(sym_mat))
+            structured = self.STRUCTURED_MATRIX_CLS.from_dense(sym_mat)
+            report_nonclose(truth, structured.frobenius_norm())
+
     @mark.expensive
     def test_visual(self):
         """Create pictures and animations of the structure.