Fix concatenate and add missing functionality to backends:

pyhf/tensor/mxnet_backend.py

@@ -127,6 +127,10 @@ def product(self, tensor_in, axis=None):
         else:
             return nd.prod(tensor_in, axis)
 
+    def abs(self, tensor):
+        tensor = self.astensor(tensor)
+        return nd.abs(tensor)
+
     def ones(self, shape):
         """
         A new array filled with all ones, with the given shape.
@@ -269,17 +273,18 @@ def where(self, mask, tensor_in_1, tensor_in_2):
         return nd.add(nd.multiply(mask, tensor_in_1),
                       nd.multiply(nd.subtract(1, mask), tensor_in_2))
 
-    def concatenate(self, sequence):
+    def concatenate(self, sequence, axis=0):
         """
         Join the elements of the sequence.
 
         Args:
             sequence (Array of Tensors): The sequence of arrays to join
+            axis: dimension along which to concatenate
 
         Returns:
             MXNet NDArray: The ndarray of the joined elements.
         """
-        return nd.concat(*sequence, dim=0)
+        return nd.concat(*sequence, dim=axis)
 
     def simple_broadcast(self, *args):
         """
@@ -319,6 +324,23 @@ def simple_broadcast(self, *args):
                      for arg in args]
         return nd.stack(*broadcast)
 
+    def einsum(self, subscripts, *operands):
+        """
+        A generalized contraction between tensors of arbitrary dimension.
+
+        Warning: not implemented in MXNet
+
+        Args:
+            subscripts: str, specifies the subscripts for summation
+            operands: list of array_like, these are the tensors for the operation
+
+        Returns:
+            tensor: the calculation based on the Einstein summation convention
+        """
+        raise NotImplementedError("mxnet::einsum is not implemented.")
+        return self.astensor([])
+
+
     def poisson(self, n, lam):
         """
         The continous approximation to the probability density function of the Poisson

pyhf/tensor/numpy_backend.py

@@ -60,9 +60,16 @@ def product(self, tensor_in, axis=None):
         tensor_in = self.astensor(tensor_in)
         return np.product(tensor_in, axis = axis)
 
+    def abs(self, tensor):
+        tensor = self.astensor(tensor)
+        return np.abs(tensor)
+
     def ones(self,shape):
         return np.ones(shape)
 
+    def zeros(self,shape):
+        return np.zeros(shape)
+
     def power(self,tensor_in_1, tensor_in_2):
         tensor_in_1 = self.astensor(tensor_in_1)
         tensor_in_2 = self.astensor(tensor_in_2)
@@ -94,8 +101,19 @@ def where(self, mask, tensor_in_1, tensor_in_2):
         tensor_in_2 = self.astensor(tensor_in_2)
         return np.where(mask, tensor_in_1, tensor_in_2)
 
-    def concatenate(self, sequence):
-        return np.concatenate(sequence)
+    def concatenate(self, sequence, axis=0):
+        """
+        Join a sequence of arrays along an existing axis.
+
+        Args:
+            sequence: sequence of tensors
+            axis: dimension along which to concatenate
+
+        Returns:
+            output: the concatenated tensor
+
+        """
+        return np.concatenate(sequence, axis=axis)
 
     def simple_broadcast(self, *args):
         """
@@ -119,6 +137,25 @@ def simple_broadcast(self, *args):
         """
         return np.broadcast_arrays(*args)
 
+    def einsum(self, subscripts, *operands):
+        """
+        Evaluates the Einstein summation convention on the operands.
+
+        Using the Einstein summation convention, many common multi-dimensional
+        array operations can be represented in a simple fashion. This function
+        provides a way to compute such summations. The best way to understand
+        this function is to try the examples below, which show how many common
+        NumPy functions can be implemented as calls to einsum.
+
+        Args:
+            subscripts: str, specifies the subscripts for summation
+            operands: list of array_like, these are the tensors for the operation
+
+        Returns:
+            tensor: the calculation based on the Einstein summation convention
+        """
+        return np.einsum(subscripts, *operands)
+
     def poisson(self, n, lam):
         n = np.asarray(n)
         if self.pois_from_norm:

pyhf/tensor/pytorch_backend.py

@@ -65,9 +65,16 @@ def product(self, tensor_in, axis=None):
         tensor_in = self.astensor(tensor_in)
         return torch.prod(tensor_in) if axis is None else torch.prod(tensor_in, axis)
 
+    def abs(self, tensor):
+        tensor = self.astensor(tensor)
+        return torch.abs(tensor)
+
     def ones(self, shape):
         return torch.Tensor(torch.ones(shape))
 
+    def zeros(self, shape):
+        return torch.Tensor(torch.zeros(shape))
+
     def power(self, tensor_in_1, tensor_in_2):
         tensor_in_1 = self.astensor(tensor_in_1)
         tensor_in_2 = self.astensor(tensor_in_2)
@@ -99,8 +106,19 @@ def where(self, mask, tensor_in_1, tensor_in_2):
         tensor_in_2 = self.astensor(tensor_in_2)
         return mask * tensor_in_1 + (1-mask) * tensor_in_2
 
-    def concatenate(self, sequence):
-        return torch.cat(sequence)
+    def concatenate(self, sequence, axis=0):
+        """
+        Join a sequence of arrays along an existing axis.
+
+        Args:
+            sequence: sequence of tensors
+            axis: dimension along which to concatenate
+
+        Returns:
+            output: the concatenated tensor
+
+        """
+        return torch.cat(sequence, dim=axis)
 
     def simple_broadcast(self, *args):
         """
@@ -134,6 +152,22 @@ def simple_broadcast(self, *args):
                      for arg in args]
         return broadcast
 
+    def einsum(self, subscripts, *operands):
+        """
+        This function provides a way of computing multilinear expressions (i.e.
+        sums of products) using the Einstein summation convention.
+
+        Args:
+            subscripts: str, specifies the subscripts for summation
+            operands: list of array_like, these are the tensors for the operation
+
+        Returns:
+            tensor: the calculation based on the Einstein summation convention
+        """
+        ops = tuple(self.astensor(op) for op in operands)
+        return torch.einsum(subscripts, ops)
+
+
     def poisson(self, n, lam):
         return self.normal(n,lam, self.sqrt(lam))
 

pyhf/tensor/tensorflow_backend.py

@@ -79,9 +79,16 @@ def product(self, tensor_in, axis=None):
         tensor_in = self.astensor(tensor_in)
         return tf.reduce_prod(tensor_in) if axis is None else tf.reduce_prod(tensor_in, axis)
 
+    def abs(self, tensor):
+        tensor = self.astensor(tensor)
+        return tf.abs(tensor)
+
     def ones(self, shape):
         return tf.ones(shape)
 
+    def zeros(self, shape):
+        return tf.zeros(shape)
+
     def power(self, tensor_in_1, tensor_in_2):
         tensor_in_1 = self.astensor(tensor_in_1)
         tensor_in_2 = self.astensor(tensor_in_2)
@@ -113,8 +120,19 @@ def where(self, mask, tensor_in_1, tensor_in_2):
         tensor_in_2 = self.astensor(tensor_in_2)
         return mask * tensor_in_1 + (1-mask) * tensor_in_2
 
-    def concatenate(self, sequence):
-        return tf.concat(sequence, axis=0)
+    def concatenate(self, sequence, axis=0):
+        """
+        Join a sequence of arrays along an existing axis.
+
+        Args:
+            sequence: sequence of tensors
+            axis: dimension along which to concatenate
+
+        Returns:
+            output: the concatenated tensor
+
+        """
+        return tf.concat(sequence, axis=axis)
 
     def simple_broadcast(self, *args):
         """
@@ -160,6 +178,23 @@ def generic_len(a):
                      tf.tile(tf.slice(arg, [0], [1]), tf.stack([max_dim])) for arg in args]
         return broadcast
 
+    def einsum(self, subscripts, *operands):
+        """
+        A generalized contraction between tensors of arbitrary dimension.
+
+        This function returns a tensor whose elements are defined by equation,
+        which is written in a shorthand form inspired by the Einstein summation
+        convention.
+
+        Args:
+            subscripts: str, specifies the subscripts for summation
+            operands: list of array_like, these are the tensors for the operation
+
+        Returns:
+            tensor: the calculation based on the Einstein summation convention
+        """
+        return tf.einsum(subscripts, *operands)
+
     def poisson(self, n, lam):
         # could be changed to actual Poisson easily
         return self.normal(n, lam, self.sqrt(lam))

tests/test_tensor.py

@@ -52,10 +52,36 @@ def test_common_tensor_backends():
             == [[1, 1, 1], [2, 3, 4], [5, 6, 7]]
         assert list(map(tb.tolist, tb.simple_broadcast([1], [2, 3, 4], [5, 6, 7]))) \
             == [[1, 1, 1], [2, 3, 4], [5, 6, 7]]
+        assert tb.tolist(tb.ones((4,5)))  == [[1.]*5]*4
+        assert tb.tolist(tb.zeros((4,5))) == [[0.]*5]*4
+        assert tb.tolist(tb.abs(tb.astensor([-1,-2]))) == [1,2]
         with pytest.raises(Exception):
             tb.simple_broadcast([1], [2, 3], [5, 6, 7])
 
 
+def test_einsum():
+    tf_sess = tf.Session()
+    backends = [numpy_backend(poisson_from_normal=True),
+                pytorch_backend(),
+                tensorflow_backend(session=tf_sess),
+                mxnet_backend() #no einsum in mxnet
+                ]
+
+
+
+    for b in backends[:-1]:
+        pyhf.set_backend(b)
+
+        x = np.arange(20).reshape(5,4).tolist()
+        assert np.all(b.tolist(b.einsum('ij->ji',x)) == np.asarray(x).T.tolist())
+        assert b.tolist(b.einsum('i,j->ij',b.astensor([1,1,1]),b.astensor([1,2,3]))) == [[1,2,3]]*3
+
+    for b in backends[-1:]:
+        pyhf.set_backend(b)
+        x = np.arange(20).reshape(5,4).tolist()
+        with pytest.raises(NotImplementedError):
+            assert b.einsum('ij->ji',[1,2,3])
+
 def test_pdf_eval():
     tf_sess = tf.Session()
     backends = [numpy_backend(poisson_from_normal=True),