feat: add ArrowheadMatrix #21
Conversation
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Can you recheck the PR? For example, this adds |
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@bvdmitri Yeah the structure is implemented but there is a nuance. Performance tests do not pass if you can help me or suggest me smt there it would be nice. |
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Right now it passed but I think it's a fluke... The only tests that fails are |
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Yes those tests fail because of the |
This PR is not ready for merging. It's many things missed here (docs for example) but I want to solve the main issue first: |
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@Nimrais can you double check coverage? I cannot see branch coverage and PR coverage. Maybe this is a problem with the bayesbase repo? |
This PR introduces an efficient implementation of ArrowheadMatrix, a specialized matrix.
ArrowheadMatrix: Implements a memory-efficient representation of arrowhead matrices https://en.wikipedia.org/wiki/Arrowhead_matrix.Basic Operations: Supports essential matrix operations like size, conversion to dense matrix, and multiplication with vectors.
Linear System Solving: Implements an efficient algorithm for solving linear systems involving arrowhead matrices.
Inverse Representation: Introduces InvArrowheadMatrix for representing the inverse of an ArrowheadMatrix without explicitly computing it.
Performance Optimizations: Utilizes the special structure of arrowhead matrices to achieve better time and space complexity compared to dense matrix operations.
Implementation Details
ArrowheadMatrix: Stores only the diagonal elements and the "arrow" parts of the matrix.mul!: Optimized matrix-vector multiplication.linsolve!: Efficient linear system solver tailored for arrowhead structure.InvArrowheadMatrix: Lazy representation of the inverse, computing elements only when needed.