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49 lines
1.6 KiB
ReStructuredText
49 lines
1.6 KiB
ReStructuredText
.. meta::
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:description: hipSPARSELt storage formats
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:keywords: hipSPARSELt, ROCm, API library, API reference, storage formats
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.. _storage-format:
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********************************
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hipSPARSELt storage format
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********************************
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hipSPARSELt uses a structured sparsity storage format, which is represented by an
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:math:`m \times n` matrix, where:
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* **m** = number of rows (integer)
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* **n** = number of columns (integer)
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* **sparsity** = 50%, the ratio of ``nnz`` elements in every 2:1 (int) or 4:2 (others) element along the row
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(4:2 means every 4 continuous elements only has 2 ``nnz`` elements)
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* **compressed matrix** = matrix of ``nnz`` elements containing data
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* **metadata** = matrix of ``nnz`` elements containing the element indices in every 4:2 or 2:1 array
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along the row (the contents or structure of the metadata is dependent on the chosen solution by the backend
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implementation)
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Consider the following :math:`4 \times 4` matrix and the structured sparsity structures using
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:math:`m = 4, n = 4`:
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.. math::
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A = \begin{pmatrix}
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1.0 & 2.0 & 0.0 & 0.0 \\
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0.0 & 0.0 & 3.0 & 4.0 \\
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0.0 & 6.0 & 7.0 & 0.0 \\
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0.0 & 6.0 & 0.0 & 8.0 \\
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\end{pmatrix}
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where
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.. math::
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Compressed A = \begin{pmatrix}
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1.0 & 2.0 \\
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3.0 & 4.0 \\
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6.0 & 7.0 \\
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6.0 & 8.0 \\
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\end{pmatrix}
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metadata = \begin{pmatrix}
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0 & 1 \\
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2 & 3 \\
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1 & 2 \\
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1 & 3 \\
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\end{pmatrix}
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