Wolfram Language Paclet Repository
Community-contributed installable additions to the Wolfram Language
Wolfram`TensorNetworks`
IndexedMultiply  |
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takes a list of per-tensor index lists whose lengths match the ranks of the corresponding tensors.
{,,…}
i
1
i
2
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Indices may be any expression (typically strings or symbols). Each index appearing in more than one tensor identifies an axis along which the inputs are aligned and broadcast.
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The output indices are the union of the input indices in canonical (first-occurrence) order. The output tensor has one axis per output index, with dimension equal to the maximum size of that index across the inputs.
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Tensors that do not carry every output index are extended by repetition: each missing axis is padded with the mode when the tensor has dimension 1 along that axis, and otherwise filled with 1. Tensors that share an index but have different sizes along it are aligned by padding the smaller dimension with 1.
"Fixed"
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Unlike , does not contract repeated indices; it only broadcasts and multiplies. Repeated indices within a single tensor are preserved as separate axes in the output.
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Symbolic tensors ( inputs and any expressions for which returns ) are handled by wrapping the transposed tensor in an of the broadcast shape; the final product is then a symbolic of these arrays.
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If the length of any per-tensor index list does not equal the rank of the corresponding tensor, returns a object.
Examples
(23)
Basic Examples
(3)
Join two matrices over a shared index:
In[1]:=
Amat={{1,1},{3,2}};Bmat={{1,0,1},{0,2,2}};
In[2]:=
 | IndexedMultiply |
Out[2]=
{{i,j,k},{{{1,0,1},{0,2,2}},{{3,0,3},{0,4,4}}}}
Scale the columns of a matrix by a vector :
A
i,j
v
j
In[1]:=
| IndexedMultiply |
Out[1]=
{{i,j},{{10,200,3000},{40,500,6000}}}
Disjoint indices give a pure outer product =:
C
i,j
u
i
v
j
In[1]:=
| IndexedMultiply |
Out[1]=
{{i,j},{{10,20,30},{20,40,60}}}
Scope
(16)
Applications
(2)
Properties & Relations
(2)
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