diff --git a/docs/_build/doctest/output.txt b/docs/_build/doctest/output.txt index 61d6320..3a24cc5 100644 --- a/docs/_build/doctest/output.txt +++ b/docs/_build/doctest/output.txt @@ -1,12 +1,12 @@ -Results of doctest builder run on 2024-04-14 00:34:19 +Results of doctest builder run on 2024-04-14 01:59:36 ===================================================== -Document: operations +Document: embeddings -------------------- 1 items passed all tests: - 186 tests in default -186 tests in 1 items. -186 passed and 0 failed. + 35 tests in default +35 tests in 1 items. +35 passed and 0 failed. Test passed. Document: models @@ -17,68 +17,26 @@ Document: models 115 passed and 0 failed. Test passed. -Document: embeddings +Document: operations -------------------- 1 items passed all tests: - 35 tests in default -35 tests in 1 items. -35 passed and 0 failed. + 186 tests in default +186 tests in 1 items. +186 passed and 0 failed. Test passed. Document: components -------------------- ********************************************************************** File "../tensorkrowch/components.py", line ?, in default -Failed example: - node.set_tensor(init_method='randn', mean=1., std=2., device='cuda') -Exception raised: - Traceback (most recent call last): - File "/home/jose/anaconda3/envs/test_tk/lib/python3.10/doctest.py", line 1350, in __run - exec(compile(example.source, filename, "single", - File "", line 1, in - node.set_tensor(init_method='randn', mean=1., std=2., device='cuda') - File "/home/jose/VSCodeProjects/tensorkrowch/tensorkrowch/components.py", line 1448, in set_tensor - self._unrestricted_set_tensor(tensor=tensor, - File "/home/jose/VSCodeProjects/tensorkrowch/tensorkrowch/components.py", line 1364, in _unrestricted_set_tensor - tensor = self.make_tensor( - File "/home/jose/VSCodeProjects/tensorkrowch/tensorkrowch/components.py", line 1253, in make_tensor - return self._make_randn_tensor(shape, device=device, **kwargs) - File "/home/jose/VSCodeProjects/tensorkrowch/tensorkrowch/components.py", line 1205, in _make_randn_tensor - return torch.randn(shape, device=device) * std + mean - File "/home/jose/anaconda3/envs/test_tk/lib/python3.10/site-packages/torch/cuda/__init__.py", line 302, in _lazy_init - torch._C._cuda_init() - RuntimeError: Unexpected error from cudaGetDeviceCount(). Did you run some cuda functions before calling NumCudaDevices() that might have already set an error? Error 804: forward compatibility was attempted on non supported HW -********************************************************************** -File "../tensorkrowch/components.py", line ?, in default -Failed example: - torch.equal(node.tensor, torch.zeros(node.shape, device='cuda')) -Exception raised: - Traceback (most recent call last): - File "/home/jose/anaconda3/envs/test_tk/lib/python3.10/doctest.py", line 1350, in __run - exec(compile(example.source, filename, "single", - File "", line 1, in - torch.equal(node.tensor, torch.zeros(node.shape, device='cuda')) - File "/home/jose/anaconda3/envs/test_tk/lib/python3.10/site-packages/torch/cuda/__init__.py", line 302, in _lazy_init - torch._C._cuda_init() - RuntimeError: Unexpected error from cudaGetDeviceCount(). Did you run some cuda functions before calling NumCudaDevices() that might have already set an error? Error 804: forward compatibility was attempted on non supported HW -********************************************************************** -File "../tensorkrowch/components.py", line ?, in default -Failed example: - node.device -Expected: - device(type='cuda', index=0) -Got: - device(type='cpu') -********************************************************************** -File "../tensorkrowch/components.py", line ?, in default Failed example: node.tensor Expected: tensor([[-0.2799, -0.4383, -0.8387], [ 1.6225, -0.3370, -1.2316]]) Got: - tensor([[-0.2140, 0.8589, 1.3626], - [ 2.0270, -0.3952, -0.2620]]) + tensor([[ 0.2628, -0.6672, -0.9051], + [-0.6796, -0.4245, -0.5780]]) ********************************************************************** File "../tensorkrowch/components.py", line ?, in default Failed example: @@ -86,7 +44,7 @@ Failed example: Expected: tensor(-1.5029) Got: - tensor(3.3773) + tensor(-2.9916) ********************************************************************** File "../tensorkrowch/components.py", line ?, in default Failed example: @@ -94,7 +52,7 @@ Failed example: Expected: tensor([ 1.3427, -0.7752, -2.0704]) Got: - tensor([1.8130, 0.4637, 1.1006]) + tensor([-0.4168, -1.0916, -1.4831]) ********************************************************************** File "../tensorkrowch/components.py", line ?, in default Failed example: @@ -103,8 +61,8 @@ Expected: tensor([[ 1.4005, -0.0521, -1.2091], [ 1.9844, 0.3513, -0.5920]]) Got: - tensor([[ 0.7954, -0.5302, 0.4238], - [-0.9560, 1.1048, -0.6040]]) + tensor([[-0.5314, -0.7805, -0.6475], + [-0.1279, 0.7409, 0.5816]]) ********************************************************************** File "../tensorkrowch/components.py", line ?, in default Failed example: @@ -112,7 +70,7 @@ Failed example: Expected: tensor(0.3139) Got: - tensor(0.0390) + tensor(-0.1275) ********************************************************************** File "../tensorkrowch/components.py", line ?, in default Failed example: @@ -120,7 +78,7 @@ Failed example: Expected: tensor([ 1.6925, 0.1496, -0.9006]) Got: - tensor([-0.0803, 0.2873, -0.0901]) + tensor([-0.3296, -0.0198, -0.0330]) ********************************************************************** File "../tensorkrowch/components.py", line ?, in default Failed example: @@ -129,8 +87,8 @@ Expected: tensor([[ 0.2111, -0.9551, -0.7812], [ 0.2254, 0.3381, -0.2461]]) Got: - tensor([[-0.8081, 0.7974, 0.5201], - [-0.8739, -1.2455, -1.2520]]) + tensor([[-1.8500, -0.4944, 0.5940], + [-0.9353, -0.6008, -0.4320]]) ********************************************************************** File "../tensorkrowch/components.py", line ?, in default Failed example: @@ -138,7 +96,7 @@ Failed example: Expected: tensor(0.5567) Got: - tensor(0.9029) + tensor(0.7922) ********************************************************************** File "../tensorkrowch/components.py", line ?, in default Failed example: @@ -146,7 +104,7 @@ Failed example: Expected: tensor([0.0101, 0.9145, 0.3784]) Got: - tensor([0.0465, 1.4445, 1.2530]) + tensor([0.6468, 0.0752, 0.7255]) ********************************************************************** File "../tensorkrowch/components.py", line ?, in default Failed example: @@ -155,8 +113,8 @@ Expected: tensor([[ 1.5570, 1.8441, -0.0743], [ 0.4572, 0.7592, 0.6356]]) Got: - tensor([[-1.1420, -0.4181, -0.9147], - [-1.0355, 0.3765, -1.0369]]) + tensor([[ 1.5611, -0.1317, -1.2049], + [-0.8746, 0.7130, -1.7564]]) ********************************************************************** File "../tensorkrowch/components.py", line ?, in default Failed example: @@ -164,7 +122,7 @@ Failed example: Expected: tensor(2.6495) Got: - tensor(2.1458) + tensor(2.8748) ********************************************************************** File "../tensorkrowch/components.py", line ?, in default Failed example: @@ -172,7 +130,7 @@ Failed example: Expected: tensor([1.6227, 1.9942, 0.6399]) Got: - tensor([1.5416, 0.5626, 1.3826]) + tensor([1.7894, 0.7251, 2.1299]) ********************************************************************** File "../tensorkrowch/components.py", line ?, in default Failed example: @@ -203,17 +161,17 @@ Got: Node( name: my_node tensor: - tensor([[[-0.3790, -0.2875], - [-0.2694, -2.6073], - [ 0.9747, 0.2449], - [-0.2402, -0.0971], - [-0.6163, -0.0845]], + tensor([[[-0.2232, -0.0576], + [-2.0650, -1.6126], + [ 0.3369, -0.6012], + [-1.5875, -0.0953], + [-0.3129, 0.5625]], - [[ 1.3292, -0.5639], - [ 0.6551, -0.5135], - [ 1.4094, -0.5872], - [ 1.3754, -1.3123], - [ 0.6744, -1.2268]]]) + [[ 2.0660, -0.9154], + [ 0.0753, 0.9608], + [ 0.7278, -0.2497], + [ 0.9090, -0.5242], + [ 1.4432, 2.6149]]]) axes: [left input @@ -252,17 +210,17 @@ Got: Node( name: node tensor: - tensor([[[ 0.5618, -0.7985], - [-1.9137, -1.0750], - [ 0.2035, 0.2413], - [ 1.2439, -0.0756], - [ 0.9225, -0.0071]], + tensor([[[-0.0399, 0.5602], + [-1.3402, 1.1127], + [ 0.0795, -1.6100], + [ 2.3359, 1.8294], + [-0.2258, -0.2929]], - [[ 0.1849, -0.2401], - [-0.0954, -0.2486], - [-0.3592, -1.3031], - [ 0.0455, 0.5307], - [-1.3908, -0.9176]]]) + [[ 0.2125, -1.1086], + [-0.6906, -0.8028], + [-1.4547, 0.0981], + [-1.5869, 0.2020], + [-0.5355, -0.1357]]]) axes: [axis_0 axis_1 @@ -314,17 +272,17 @@ Got: name: my_paramnode tensor: Parameter containing: - tensor([[[-0.8812, 0.5985], - [-1.0907, 0.4343], - [ 2.1201, 0.7496], - [ 0.1640, -0.2248], - [-1.3572, 0.7016]], + tensor([[[ 1.0837, 1.7036], + [-0.8799, -0.1600], + [-0.5867, -1.7778], + [ 0.1615, 1.0249], + [ 0.1880, 1.1234]], - [[ 1.0295, 0.0301], - [ 1.1299, 1.0379], - [-0.2408, 1.4896], - [ 0.1914, -0.7828], - [ 0.5660, 1.7213]]], requires_grad=True) + [[ 0.7499, -0.7739], + [-0.5278, 1.1947], + [-0.7586, -1.4460], + [-0.1016, -0.1954], + [ 0.1579, 0.0572]]], requires_grad=True) axes: [left input @@ -365,17 +323,17 @@ Got: name: paramnode tensor: Parameter containing: - tensor([[[ 0.0967, 0.1681], - [-0.2095, -0.0135], - [ 0.4699, -0.3885], - [-1.2067, -0.5064], - [-0.7848, 0.2031]], + tensor([[[-0.7419, 0.3802], + [ 0.4183, 0.2084], + [-0.4384, -0.6852], + [-0.2616, -0.4692], + [ 0.4573, 2.0465]], - [[-0.4146, -0.5403], - [-0.1077, -0.4261], - [ 1.2183, 0.4285], - [-0.1007, -0.8319], - [-0.1851, 0.1278]]], requires_grad=True) + [[ 0.5333, 0.6722], + [-0.9125, 0.1184], + [ 0.1689, -0.0498], + [-1.2576, 0.5516], + [-0.0805, -0.2896]]], requires_grad=True) axes: [axis_0 axis_1 @@ -394,8 +352,8 @@ Expected: [ 1.3371, 1.4761, 0.6551]], requires_grad=True) Got: Parameter containing: - tensor([[-1.4677, -0.2316, 0.4469], - [-0.9964, -0.5450, -0.8290]], requires_grad=True) + tensor([[-1.4491, 0.7555, -1.2827], + [ 1.3534, -1.0071, 0.1320]], requires_grad=True) ********************************************************************** File "../tensorkrowch/components.py", line ?, in default Failed example: @@ -446,14 +404,14 @@ Got: data_0[feature] <-> nodeA[input]]) ********************************************************************** 1 items had failures: - 24 of 395 in default + 21 of 395 in default 395 tests in 1 items. -371 passed and 24 failed. -***Test Failed*** 24 failures. +374 passed and 21 failed. +***Test Failed*** 21 failures. Doctest summary =============== 731 tests - 24 failures in tests + 21 failures in tests 0 failures in setup code 0 failures in cleanup code diff --git a/docs/_build/doctrees/environment.pickle b/docs/_build/doctrees/environment.pickle index bacb9cc..505278e 100644 Binary files a/docs/_build/doctrees/environment.pickle and b/docs/_build/doctrees/environment.pickle differ diff --git a/docs/_build/doctrees/models.doctree b/docs/_build/doctrees/models.doctree index f864f92..507e800 100644 Binary files a/docs/_build/doctrees/models.doctree and b/docs/_build/doctrees/models.doctree differ diff --git a/docs/_build/html/_modules/tensorkrowch/models/mps.html b/docs/_build/html/_modules/tensorkrowch/models/mps.html index 1239e35..4488acf 100644 --- a/docs/_build/html/_modules/tensorkrowch/models/mps.html +++ b/docs/_build/html/_modules/tensorkrowch/models/mps.html @@ -1491,6 +1491,10 @@

Source code for tensorkrowch.models.mps

         it should be ``reset`` before calling ``partial_density`` to avoid
         undesired behaviour.
         
+        Since the density matrix is computed by contracting the MPS, it means
+        one can take gradients of it with respect to the MPS tensors, if it
+        is needed.
+        
         This method may also alter the attribute :attr:`n_batches` of the
         :class:`MPS`.
         
@@ -1558,6 +1562,131 @@ 
Source code for tensorkrowch.models.mps
             result = self.forward(marginalize_output=True)
         
         return result

+    
+
[docs]    @torch.no_grad()
+    def mi(self,
+           middle_site: int,
+           renormalize: bool = False) -> Union[float, Tuple[float]]:
+        r"""
+        Computes the Mutual Information between subsystems :math:`A` and
+        :math:`B`, :math:`\textrm{MI}(A:B)`, where :math:`A` goes from site
+        0 to ``middle_site``, and :math:`B` goes from ``middle_site + 1`` to
+        ``n_features - 1``.
+        
+        To compute the mutual information, the MPS is put into canonical form
+        with orthogonality center at ``middle_site``. Bond dimensions are not
+        changed if possible. Only when the bond dimension is bigger than the
+        physical dimension multiplied by the other bond dimension of the node,
+        it will be cropped to that size.
+        
+        If the MPS is not normalized, it may happen that the computation of the
+        mutual information fails due to errors in the Singular Value
+        Decompositions. To avoid this, it is recommended to set
+        ``renormalize = True``. In this case, the norm of each node after the
+        SVD is extracted in logarithmic form, and accumulated. As a result,
+        the function will return the tuple ``(mi, log_norm)``, which is a sort
+        of `scaled` mutual information. The actual mutual information could be
+        obtained as ``exp(log_norm) * mi``.
+        
+        Parameters
+        ----------
+        middle_site : int
+            Position that separates regios :math:`A` and :math:`B`. It should
+            be between 0 and ``n_features - 2``.
+        renormalize : bool
+            Indicates whether nodes should be renormalized after SVD/QR
+            decompositions. If not, it may happen that the norm explodes as it
+            is being accumulated from all nodes. Renormalization aims to avoid
+            this undesired behavior by extracting the norm of each node on a
+            logarithmic scale after SVD/QR decompositions are computed. Finally,
+            the normalization factor is evenly distributed among all nodes of
+            the MPS.
+        
+        Returns
+        -------
+        float or tuple[float, float]
+        """
+        self.reset()
+
+        prev_auto_stack = self._auto_stack
+        self.auto_stack = False
+        
+        if (middle_site < 0) or (middle_site > (self._n_features - 2)):
+            raise ValueError(
+                '`middle_site` should be between 0 and `n_features` - 2')
+        
+        log_norm = 0
+        
+        nodes = self._mats_env[:]
+        if self._boundary == 'obc':
+            nodes[0].tensor[1:] = torch.zeros_like(
+                nodes[0].tensor[1:])
+            nodes[-1].tensor[..., 1:] = torch.zeros_like(
+                nodes[-1].tensor[..., 1:])
+        
+        for i in range(middle_site):
+            result1, result2 = nodes[i]['right'].svd_(
+                side='right',
+                rank=nodes[i]['right'].size())
+            
+            if renormalize:
+                aux_norm = result2.norm() / sqrt(result2.shape[0])
+                if not aux_norm.isinf() and (aux_norm > 0):
+                    result2.tensor = result2.tensor / aux_norm
+                    log_norm += aux_norm.log()
+
+            result1 = result1.parameterize()
+            nodes[i] = result1
+            nodes[i + 1] = result2
+
+        for i in range(len(nodes) - 1, middle_site, -1):
+            result1, result2 = nodes[i]['left'].svd_(
+                side='left',
+                rank=nodes[i]['left'].size())
+            
+            if renormalize:
+                aux_norm = result1.norm() / sqrt(result1.shape[0])
+                if not aux_norm.isinf() and (aux_norm > 0):
+                    result1.tensor = result1.tensor / aux_norm
+                    log_norm += aux_norm.log()
+
+            result2 = result2.parameterize()
+            nodes[i] = result2
+            nodes[i - 1] = result1
+
+        nodes[middle_site] = nodes[middle_site].parameterize()
+        
+        # Compute mutual information
+        middle_tensor = nodes[middle_site].tensor.clone()
+        _, s, _ = torch.linalg.svd(
+            middle_tensor.reshape(middle_tensor.shape[:-1].numel(), # left x input
+                                  middle_tensor.shape[-1]),         # right
+            full_matrices=False)
+        
+        s = s[s > 0]
+        mutual_info = -(s * (s.log() + log_norm)).sum()
+        
+        # Rescale
+        if log_norm != 0:
+            rescale = (log_norm / len(nodes)).exp()
+        
+        if renormalize and (log_norm != 0):
+            for node in nodes:
+                node.tensor = node.tensor * rescale
+        
+        # Update variables
+        if self._boundary == 'obc':
+            self._bond_dim = [node['right'].size() for node in nodes[:-1]]
+        else:
+            self._bond_dim = [node['right'].size() for node in nodes]
+        self._mats_env = nodes
+
+        self.auto_stack = prev_auto_stack
+        
+        if renormalize:
+            return mutual_info, log_norm
+        else:
+            return mutual_info

 
 
[docs]    @torch.no_grad()
     def canonicalize(self,
@@ -1570,11 +1699,20 @@ 
Source code for tensorkrowch.models.mps
         r"""
         Turns MPS into canonical form via local SVD/QR decompositions.
         
+        To specify the new bond dimensions, the arguments ``rank``,
+        ``cum_percentage`` or ``cutoff`` can be specified. These will be used
+        equally for all SVD computations.
+        
+        If none of them are specified, the bond dimensions won't be modified
+        if possible. Only when the bond dimension is bigger than the physical
+        dimension multiplied by the other bond dimension of the node, it will
+        be cropped to that size.
+        
         Parameters
         ----------
         oc : int
             Position of the orthogonality center. It should be between 0 and 
-            ``n_features -1``.
+            ``n_features - 1``.
         mode : {"svd", "svdr", "qr"}
             Indicates which decomposition should be used to split a node after
             contracting it. See more at :func:`~tensorkrowch.svd_`,
@@ -1619,9 +1757,9 @@ 
Source code for tensorkrowch.models.mps
 
         if oc is None:
             oc = self._n_features - 1
-        elif oc >= self._n_features:
-            raise ValueError(f'Orthogonality center position `oc` should be '
-                             f'between 0 and {self._n_features - 1}')
+        elif (oc < 0) or (oc >= self._n_features):
+            raise ValueError('Orthogonality center position `oc` should be '
+                             'between 0 and `n_features` - 1')
         
         log_norm = 0
         
@@ -1632,17 +1770,23 @@ 
Source code for tensorkrowch.models.mps
             nodes[-1].tensor[..., 1:] = torch.zeros_like(
                 nodes[-1].tensor[..., 1:])
         
+        # If mode is svd or svr and none of the args is provided, the ranks are
+        # kept as they were originally
+        keep_rank = False
+        if (rank is None) and (cum_percentage is None) and (cutoff is None):
+            keep_rank = True
+        
         for i in range(oc):
             if mode == 'svd':
                 result1, result2 = nodes[i]['right'].svd_(
                     side='right',
-                    rank=rank,
+                    rank=nodes[i]['right'].size() if keep_rank else rank,
                     cum_percentage=cum_percentage,
                     cutoff=cutoff)
             elif mode == 'svdr':
                 result1, result2 = nodes[i]['right'].svdr_(
                     side='right',
-                    rank=rank,
+                    rank=nodes[i]['right'].size() if keep_rank else rank,
                     cum_percentage=cum_percentage,
                     cutoff=cutoff)
             elif mode == 'qr':
@@ -1664,13 +1808,13 @@ 
Source code for tensorkrowch.models.mps
             if mode == 'svd':
                 result1, result2 = nodes[i]['left'].svd_(
                     side='left',
-                    rank=rank,
+                    rank=nodes[i]['left'].size() if keep_rank else rank,
                     cum_percentage=cum_percentage,
                     cutoff=cutoff)
             elif mode == 'svdr':
                 result1, result2 = nodes[i]['left'].svdr_(
                     side='left',
-                    rank=rank,
+                    rank=nodes[i]['left'].size() if keep_rank else rank,
                     cum_percentage=cum_percentage,
                     cutoff=cutoff)
             elif mode == 'qr':
diff --git a/docs/_build/html/genindex.html b/docs/_build/html/genindex.html
index 0887b8d..f14cfc7 100644
--- a/docs/_build/html/genindex.html
+++ b/docs/_build/html/genindex.html
@@ -778,6 +778,8 @@ 
M

 
   
   
    
+      
  • mi() (tensorkrowch.models.MPS method)
+
    • 
       
  • move_to_network() (tensorkrowch.AbstractNode method)
 
    • 
       
  • MPO (class in tensorkrowch.models)
diff --git a/docs/_build/html/models.html b/docs/_build/html/models.html
index 27c7b10..89c8ec2 100644
--- a/docs/_build/html/models.html
+++ b/docs/_build/html/models.html
@@ -1015,6 +1015,9 @@ 
    MPS#reset before calling partial_density to avoid
 undesired behaviour.
    
+
    Since the density matrix is computed by contracting the MPS, it means
+one can take gradients of it with respect to the MPS tensors, if it
+is needed.
    
 
    This method may also alter the attribute n_batches of the
 MPS.
    
 
    
@@ -1036,15 +1039,62 @@ 
    MPS#
 
    
 
+
    
+
    
+mi(middle_site, renormalize=False)[source]#
    
+
    Computes the Mutual Information between subsystems \(A\) and
+\(B\), \(\textrm{MI}(A:B)\), where \(A\) goes from site
+0 to middle_site, and \(B\) goes from middle_site + 1 to
+n_features - 1.
    
+
    To compute the mutual information, the MPS is put into canonical form
+with orthogonality center at middle_site. Bond dimensions are not
+changed if possible. Only when the bond dimension is bigger than the
+physical dimension multiplied by the other bond dimension of the node,
+it will be cropped to that size.
    
+
    If the MPS is not normalized, it may happen that the computation of the
+mutual information fails due to errors in the Singular Value
+Decompositions. To avoid this, it is recommended to set
+renormalize = True. In this case, the norm of each node after the
+SVD is extracted in logarithmic form, and accumulated. As a result,
+the function will return the tuple (mi, log_norm), which is a sort
+of scaled mutual information. The actual mutual information could be
+obtained as exp(log_norm) * mi.
    
+
    
+
    Parameters
    
+
      
+
    • middle_site (int) – Position that separates regios \(A\) and \(B\). It should
+be between 0 and n_features - 2.
      • 
+
    • renormalize (bool) – Indicates whether nodes should be renormalized after SVD/QR
+decompositions. If not, it may happen that the norm explodes as it
+is being accumulated from all nodes. Renormalization aims to avoid
+this undesired behavior by extracting the norm of each node on a
+logarithmic scale after SVD/QR decompositions are computed. Finally,
+the normalization factor is evenly distributed among all nodes of
+the MPS.
      • 
+
    
+
    
+
    Return type
    
+
    float or tuple[float, float]
    
+
    
+
    
+
    
+
 
    
 
    
 canonicalize(oc=None, mode='svd', rank=None, cum_percentage=None, cutoff=None, renormalize=False)[source]#
    
 
    Turns MPS into canonical form via local SVD/QR decompositions.
    
+
    To specify the new bond dimensions, the arguments rank,
+cum_percentage or cutoff can be specified. These will be used
+equally for all SVD computations.
    
+
    If none of them are specified, the bond dimensions won’t be modified
+if possible. Only when the bond dimension is bigger than the physical
+dimension multiplied by the other bond dimension of the node, it will
+be cropped to that size.
    
 
    
 
    Parameters
    
 
      
 
    • oc (int) – Position of the orthogonality center. It should be between 0 and
-n_features -1.
      • 
+n_features - 1.
      
 
    • mode ({"svd", "svdr", "qr"}) – Indicates which decomposition should be used to split a node after
 contracting it. See more at svd_(),
 svdr_(), qr_().
diff --git a/docs/_build/html/objects.inv b/docs/_build/html/objects.inv
index 1892eb0..c4de50f 100644
Binary files a/docs/_build/html/objects.inv and b/docs/_build/html/objects.inv differ
diff --git a/docs/_build/html/searchindex.js b/docs/_build/html/searchindex.js
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