[routines] Optimized QR Decomposition with SIMD and Column-Major Layout #233
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durnwalder
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durnwalder
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durnwalder
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shivasankarka
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Apr 18, 2025
shivasankarka
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Mojo-Numerics-and-Algorithms-group:pre-0.7
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This PR optimizes the QR decomposition utilizing configurable memory layouts and SIMD. When the input matrix is detected to be in row-major (C) layout, it is reordered to column-major (F) layout before performing Householder transformations. After factorization, the final Q and R are reordered to the original layout of the input Matrix, preserving consistency for downstream operations. For an input matrix with column-major (F) layout, no reordering is needed.
Changes
Vectorized Householder Transformations
Updated algorithm leverages SIMD with calls to
vectorizefor computing and applying Householder reflections.Reduced and Complete Modes
Adds support for both “reduced” and “complete” modes, similar to NumPy’s QR. For an input Matrix A with shape (m,n):
shape(m, min(m,n))and R hasshape(min(m,n), n).shape(m, m)and R hasshape(m, n).Additional tests
Beyond the existing test with
shape(20,20)and default parameters, new tests now verify the QR decomposition for non-square matrices (shape(12,5)andshape(5,12)) in both reduced and complete modes.