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sdh_documentation/docs/benchmarking.md

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@@ -48,12 +48,12 @@ letting us measure only the performance of the computation itself.
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TACO's computational performance, since timing those functions will
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include the time it takes to generate code for performing the computation.
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**The time it takes to construct the initial input tensors should also not be
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**The time it takes to construct the initial operand tensors should also not be
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measured**, since again this overhead can often be amortized in practice. By
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default, `pytaco.read` and functions for converting NumPy arrays and SciPy
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matrices to TACO tensors return fully constructed tensors. If you add nonzero
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elements to an input tensor by calling `insert` though, then `pack` must also
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be explicitly invoked before any benchmarking is done:
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elements to an operand tensor by invoking its `insert` method though, then
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`pack` must also be explicitly invoked before any benchmarking is done:
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```python
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import pytaco as pt

sdh_documentation/docs/data_analytics.md

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@@ -9,7 +9,7 @@ $$A = B_{(1)} (D \odot C),$$
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where \(A\), \(C\), and \(D\) are typically dense matrices, \(B\) is a
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three-dimensional tensor (matricizied along the first mode), and \(\odot\)
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denotes the Khatri-Rao product. This operation can also be expressed in [index
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notation](computations.md#specifying-tensor-algebra-computations) as
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notation](pycomputations.md#specifying-tensor-algebra-computations) as
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$$A_{ij} = B_{ikl} \cdot D_{lj} \cdot C_{kj}.$$
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sdh_documentation/docs/machine_learning.md

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where \(A\) and \(B\) are sparse matrices, \(C\) and \(D\) are dense matrices,
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and \(\circ\) denotes component-wise multiplication. This operation can also be
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expressed in [index
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notation](computations.md#specifying-tensor-algebra-computations) as
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notation](pycomputations.md#specifying-tensor-algebra-computations) as
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$$A_{ij} = B_{ij} \cdot C_{ik} \cdot C_{kj}.$$
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sdh_documentation/docs/scientific_computing.md

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where \(A\) is a sparse matrix and \(x\), \(y\), and \(z\)
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are dense vectors. The computation can also be expressed in [index
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notation](computations.md#specifying-tensor-algebra-computations) as
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notation](pycomputations.md#specifying-tensor-algebra-computations) as
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$$y_i = A_{ij} \cdot x_j + z_i.$$
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