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docs/src/user_interface/algorithms.md

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# [Algorithm Selection](@id sec_algorithmselection)
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All factorization functions in MatrixAlgebraKit accept an optional `alg` keyword argument that controls which algorithm is used and how it is configured.
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By default, an appropriate algorithm is selected automatically based on the function and the array type.
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By default, an appropriate algorithm is selected automatically based on the function and the input types.
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This page explains how to override that default, what algorithm types are available, and how to configure them.
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## The `alg` Keyword
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For example, for `qr_compact` these forms look like:
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```julia
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# Form 1: No alg — algorithm selected automatically based on function and array type.
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# Form 1: No alg — algorithm selected automatically based on function and input type.
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Q, R = qr_compact(A);
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# Form 2: Symbol — creates Algorithm{:Householder}(; positive=false).
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## Discovering the Default Algorithm
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To check which algorithm is used by default for a given function and array type, call [`MatrixAlgebraKit.default_algorithm`](@ref).
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To check which algorithm is used by default for a given function and input type, call [`MatrixAlgebraKit.default_algorithm`](@ref).
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The available keyword arguments depend on the algorithm type; refer to the docstrings listed in [Available Algorithm Types](@ref) below.
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```@docs; canonical=false

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