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BlockDiagonals.jl\n\n[![Stable](https://img.shields.io/badge/docs-stable-blue.svg)](https://invenia.github.io/BlockDiagonals.jl/stable)\n[![Dev](https://img.shields.io/badge/docs-dev-blue.svg)](https://invenia.github.io/BlockDiagonals.jl/dev)\n[![CI](https://github.com/invenia/BlockDiagonals.jl/workflows/CI/badge.svg)](https://github.com/Invenia/BlockDiagonals.jl/actions?query=workflow%3ACI)\n[![Codecov](https://codecov.io/gh/invenia/BlockDiagonals.jl/branch/master/graph/badge.svg)](https://codecov.io/gh/invenia/BlockDiagonals.jl)\n[![code style blue](https://img.shields.io/badge/code%20style-blue-4495d1.svg)](https://github.com/invenia/BlueStyle)\n\nFunctionality for working efficiently with [block diagonal matrices](https://en.wikipedia.org/wiki/Block_matrix#Block_diagonal_matrices).\n_Note that non-square blocks are allowed_, similarly to [`scipy.block_diag`](https://docs.scipy.org/doc/scipy/reference/generated/scipy.linalg.block_diag.html), but in contrast to the mathematical definition above.\n\nConstruct a `BlockDiagonal` matrix by passing in only the non-zero blocks on the diagonal, and use it as a regular matrix\n```julia\njulia\u003e using BlockDiagonals\n\njulia\u003e bm = BlockDiagonal([rand(2, 3), ones(3, 2)])\n5×5 BlockDiagonal{Float64, Matrix{Float64}}:\n 0.289276  0.994487  0.287658  0.0  0.0\n 0.659821  0.334724  0.780973  0.0  0.0\n 0.0       0.0       0.0       1.0  1.0\n 0.0       0.0       0.0       1.0  1.0\n 0.0       0.0       0.0       1.0  1.0\n\njulia\u003e v = ones(5);\n\njulia\u003e bm * v\n5-element Vector{Float64}:\n 1.5714204086879524\n 1.7755185907265039\n 2.0\n 2.0\n 2.0\n\njulia\u003e svd(bm)\nSVD{Float64, Float64, Matrix{Float64}}\nU factor:\n5×4 Matrix{Float64}:\n  0.0      -0.70666   -0.707553   0.0\n  0.0      -0.707553   0.70666    0.0\n -0.57735   0.0        0.0       -0.57735\n -0.57735   0.0        0.0        0.788675\n -0.57735   0.0        0.0       -0.211325\nsingular values:\n4-element Vector{Float64}:\n 2.4494897427831783\n 1.3801377610748038\n 0.6387290946600256\n 0.0\nVt factor:\n4×5 Matrix{Float64}:\n  0.0        0.0        0.0       -0.707107  -0.707107\n -0.486385  -0.680801  -0.547667   0.0        0.0\n  0.409549  -0.731322   0.545379   0.0        0.0\n  0.0        0.0        0.0       -0.707107   0.707107\n```\n\nAdditional functionality includes\n```julia\njulia\u003e nblocks(bm)\n2\n\njulia\u003e blocks(bm)\n2-element Vector{Matrix{Float64}}:\n [0.2892758623451861 0.9944869494674535 0.2876575968753128; 0.6598212430288488 0.33472423873340906 0.780973108964246]\n [1.0 1.0; 1.0 1.0; 1.0 1.0]\n\njulia\u003e blocksizes(bm)\n2-element Vector{Tuple{Int64, Int64}}:\n (2, 3)\n (3, 2)\n\njulia\u003e blocksize(bm, 1)\n(2, 3)\n```\n","project_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Fjuliaarrays%2Fblockdiagonals.jl","html_url":"https://awesome.ecosyste.ms/projects/github.com%2Fjuliaarrays%2Fblockdiagonals.jl","lists_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Fjuliaarrays%2Fblockdiagonals.jl/lists"}