Initialization of orthogonal tensors with respect to a pivot #931

pragyasrivastava0805 · 2021-08-25T21:16:57Z

created a new method in tensornetwork/linalg/initialization.py for initializing a random tensor with entries distributed according to normal distribution and performing QR Decomposition on it and returning the tensor Q so that when a tensor is contracted about a given pivot index,the result is orthogonal

google-cla · 2021-08-25T21:17:02Z

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pragyasrivastava0805 · 2021-08-26T09:28:23Z

@googlebot I have signed

tensornetwork/backends/abstract_backend.py

mganahl

thanks for the PR! Sorry for the delay, I left some comments for you to fix!

mganahl · 2021-09-07T07:51:25Z

tensornetwork/backends/numpy/numpy_backend.py

+    if ((np.dtype(dtype) is np.dtype(np.complex128)) or
+        (np.dtype(dtype) is np.dtype(np.complex64))):
+      q,r= decompositions.qr(np,np.random.randn(
+          *shape).astype(dtype) + 1j * np.random.randn(*shape).astype(dtype),pivot_axis,non_negative_diagonal)


there is an else clause missing, otherwise line 804 gets overwritten

mganahl · 2021-09-07T07:56:09Z

tensornetwork/linalg/tests/initialization_test.py

+  for dtype in dtypes[backend]["rand"]:
+    tnI = tensornetwork.initialize_orthogonal_tensor_wrt_pivot(
+        shape,
+        dtype=dtype,pivot_axis,


that line should throw a syntax error because your passing an argument between named arguments

mganahl · 2021-09-07T07:56:26Z

tensornetwork/linalg/tests/initialization_test.py

+        shape,
+        dtype=dtype,pivot_axis,
+        seed=seed,
+        backend=backend,non_negative_diagonal)


mganahl · 2021-09-07T08:16:44Z

tensornetwork/linalg/tests/initialization_test.py

+        dtype=dtype,pivot_axis,
+        seed=seed,
+        backend=backend,non_negative_diagonal)
+    npI = backend_obj.initialize_orthogonal_tensor_wrt_pivot(shape, dtype=dtype, pivot_axis, seed=seed,non_negative_diagonal)


remove the function from the backend

mganahl · 2021-09-07T07:58:27Z

tensornetwork/linalg/tests/initialization_test.py

+def test_initialize_orthogonal_tensor_wrt_pivot(backend):
+  shape=(5, 10, 3, 2)
+  pivot_axis=1
+  seed = int(time.time())


pls use deterministic seed initialization

mganahl · 2021-09-07T08:10:45Z

tensornetwork/linalg/initialization.py

@@ -200,3 +201,7 @@ def random_uniform(shape: Sequence[int],
  the_tensor = initialize_tensor("random_uniform", shape, backend=backend,
                                 seed=seed, boundaries=boundaries, dtype=dtype)
  return the_tensor
+def initialize_orthogonal_tensor_wrt_pivot(shape=Sequence[int],dtype:Optional[Type[np.number]]=None,pivot_axis:int=-1,seed=Optional[int]=None,backend: Optional[Union[Text, AbstractBackend]] = None,non_negative_diagonal:bool=False) ->Tensor:
+    the_tensor=initialize_tensor("randn",shape,backend=backend,seed=seed,dtype=dtype)
+    q,r=linalg.qr(the_tensor,pivot_axis,non_negative_diagonal)


us _ instead of r (unused variable)

mganahl · 2021-09-07T08:12:51Z

tensornetwork/linalg/initialization.py

@@ -200,3 +201,7 @@ def random_uniform(shape: Sequence[int],
  the_tensor = initialize_tensor("random_uniform", shape, backend=backend,
                                 seed=seed, boundaries=boundaries, dtype=dtype)
  return the_tensor
+def initialize_orthogonal_tensor_wrt_pivot(shape=Sequence[int],dtype:Optional[Type[np.number]]=None,pivot_axis:int=-1,seed=Optional[int]=None,backend: Optional[Union[Text, AbstractBackend]] = None,non_negative_diagonal:bool=False) ->Tensor:


I'm wondering if we could find a less clunky name. Some possibilities that come to my mind are random_orthogonal or random_isometry @alewis?

Pls add a docstring that explains what the function is doing, what the arguments are, and what the returned values are.

mganahl · 2021-09-07T08:13:58Z

tensornetwork/backends/abstract_backend.py

@@ -1044,3 +1044,6 @@ def eps(self, dtype: Type[np.number]) -> float:



Why did you add this function to the backend? I don't think we need it here

mganahl · 2021-09-07T08:14:44Z

tensornetwork/backends/numpy/numpy_backend.py

@@ -795,3 +795,13 @@ def eps(self, dtype: Type[np.number]) -> float:
      float: Machine epsilon.
    """
    return np.finfo(dtype).eps
+  def initialize_orthogonal_tensor_wrt_pivot(self,shape=Sequence[int],dtype:Optional[Type[np.number]]=None,pivot_axis:int=-1,seed=Optional[int]=None,backend: Optional[Union[Text, AbstractBackend]] = None,non_negative_diagonal: bool = False):->Tensor


I don't think we need this function

mganahl · 2021-09-07T08:17:25Z

tensornetwork/linalg/tests/initialization_test.py

+        seed=seed,
+        backend=backend,non_negative_diagonal)
+    npI = backend_obj.initialize_orthogonal_tensor_wrt_pivot(shape, dtype=dtype, pivot_axis, seed=seed,non_negative_diagonal)
+    np.testing.assert_allclose(tnI.array, npI)


pls replace with a test that checks if the initialized tensor has the desired properties

heading:changed

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google-cla bot added the cla: no label Aug 25, 2021

pragyasrivastava0805 mentioned this pull request Aug 25, 2021

orthogonalization for tensors #800

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google-cla bot added cla: yes and removed cla: no labels Aug 26, 2021

pragyasrivastava0805 added 4 commits September 1, 2021 18:03

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mganahl reviewed Sep 6, 2021

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Initialization of orthogonal tensors with respect to a pivot #931

Initialization of orthogonal tensors with respect to a pivot #931

pragyasrivastava0805 commented Aug 25, 2021

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pragyasrivastava0805 commented Aug 26, 2021

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mganahl Sep 7, 2021

		@@ -1044,3 +1044,6 @@ def eps(self, dtype: Type[np.number]) -> float:

Initialization of orthogonal tensors with respect to a pivot #931

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Initialization of orthogonal tensors with respect to a pivot #931

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