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src/interface/orthnull.jl

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@@ -7,11 +7,27 @@
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Compute an orthonormal basis `V` for the image of the matrix `A`, as well as a matrix `C`
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(the corestriction) such that `A` factors as `A = V * C`.
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This is a high-level wrapper where te keyword arguments can be used to specify and control
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This is a high-level wrapper where the keyword arguments can be used to specify and control
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the specific orthogonal decomposition that should be used to factor `A`, whereas `trunc`
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can optionally be used to control the precision in determining the rank of `A`, typically
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via its singular values.
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## Truncation
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The optional truncation strategy can be controlled via the `trunc` keyword argument, and
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any non-trivial strategy typically requires an SVD-based decompositions. This keyword can
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be either a `NamedTuple` or a [`TruncationStrategy`](@ref).
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### `trunc::NamedTuple`
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The supported truncation keyword arguments are:
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$(docs_truncation_kwargs)
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### `trunc::TruncationStrategy`
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For more control, a truncation strategy can be supplied directly.
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By default, MatrixAlgebraKit supplies the following:
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$(docs_truncation_strategies)
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## Keyword arguments
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There are 3 major modes of operation, based on the `alg` keyword, with slightly different
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application purposes.
@@ -51,22 +67,6 @@ In this expert mode the algorithm is supplied directly, and the kind of decompos
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deduced from that. This hinges on the implementation of the algorithm trait
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[`MatrixAlgebraKit.left_orth_kind(alg)`](@ref).
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## Truncation
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The optional truncation strategy can be controlled via the `trunc` keyword argument, and
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any non-trivial strategy typically requires an SVD-based decompositions. This keyword can
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be either a `NamedTuple` or a [`TruncationStrategy`](@ref).
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### `trunc::NamedTuple`
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The supported truncation keyword arguments are:
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$(docs_truncation_kwargs)
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### `trunc::TruncationStrategy`
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For more control, a truncation strategy can be supplied directly.
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By default, MatrixAlgebraKit supplies the following:
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$(docs_truncation_strategies)
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---
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!!! note
@@ -96,6 +96,22 @@ the specific orthogonal decomposition that should be used to factor `A`, whereas
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optionally be used to control the precision in determining the rank of `A`, typically via
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its singular values.
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## Truncation
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The optional truncation strategy can be controlled via the `trunc` keyword argument, and
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any non-trivial strategy typically requires an SVD-based decompositions. This keyword can
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be either a `NamedTuple` or a [`TruncationStrategy`](@ref).
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### `trunc::NamedTuple`
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The supported truncation keyword arguments are:
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$(docs_truncation_kwargs)
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### `trunc::TruncationStrategy`
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For more control, a truncation strategy can be supplied directly.
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By default, MatrixAlgebraKit supplies the following:
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$(docs_truncation_strategies)
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## Keyword arguments
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There are 3 major modes of operation, based on the `alg` keyword, with slightly different
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application purposes.
@@ -135,22 +151,6 @@ In this expert mode the algorithm is supplied directly, and the kind of decompos
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deduced from that. This hinges on the implementation of the algorithm trait
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[`MatrixAlgebraKit.right_orth_kind(alg)`](@ref).
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## Truncation
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The optional truncation strategy can be controlled via the `trunc` keyword argument, and
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any non-trivial strategy typically requires an SVD-based decompositions. This keyword can
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be either a `NamedTuple` or a [`TruncationStrategy`](@ref).
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### `trunc::NamedTuple`
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The supported truncation keyword arguments are:
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$(docs_truncation_kwargs)
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### `trunc::TruncationStrategy`
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For more control, a truncation strategy can be supplied directly.
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By default, MatrixAlgebraKit supplies the following:
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$(docs_truncation_strategies)
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---
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!!! note
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whereas `trunc` can optionally be used to control the precision in determining the rank of
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`A`, typically via its singular values.
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## Truncation
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The optional truncation strategy can be controlled via the `trunc` keyword argument, and any
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non-trivial strategy typically requires an SVD-based decomposition. This keyword can be
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either a `NamedTuple` or a [`TruncationStrategy`](@ref).
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### `trunc::NamedTuple`
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The supported truncation keyword arguments are:
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$(docs_null_truncation_kwargs)
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### `trunc::TruncationStrategy`
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For more control, a truncation strategy can be supplied directly. By default,
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MatrixAlgebraKit supplies the following:
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$(docs_truncation_strategies)
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!!! note
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Here [`notrunc`](@ref) has special meaning, and signifies keeping the values that
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correspond to the exact zeros determined from the additional columns of `A`.
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## Keyword arguments
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There are 3 major modes of operation, based on the `alg` keyword, with slightly different
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application purposes.
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deduced from that. This hinges on the implementation of the algorithm trait
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[`MatrixAlgebraKit.left_null_kind(alg)`](@ref).
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## Truncation
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The optional truncation strategy can be controlled via the `trunc` keyword argument, and any
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non-trivial strategy typically requires an SVD-based decomposition. This keyword can be
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either a `NamedTuple` or a [`TruncationStrategy`](@ref).
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### `trunc::NamedTuple`
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The supported truncation keyword arguments are:
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$(docs_null_truncation_kwargs)
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### `trunc::TruncationStrategy`
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For more control, a truncation strategy can be supplied directly. By default,
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MatrixAlgebraKit supplies the following:
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$(docs_truncation_strategies)
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!!! note
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Here [`notrunc`](@ref) has special meaning, and signifies keeping the values that
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correspond to the exact zeros determined from the additional columns of `A`.
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---
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!!! note
@@ -263,6 +263,26 @@ the underlying orthogonal decomposition that should be used to find the null spa
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whereas `trunc` can optionally be used to control the precision in determining the rank of
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`A`, typically via its singular values.
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## Truncation
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The optional truncation strategy can be controlled via the `trunc` keyword argument, and any
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non-trivial strategy typically requires an SVD-based decomposition. This keyword can be
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either a `NamedTuple` or a [`TruncationStrategy`](@ref).
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### `trunc::NamedTuple`
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The supported truncation keyword arguments are:
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$(docs_null_truncation_kwargs)
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### `trunc::TruncationStrategy`
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For more control, a truncation strategy can be supplied directly. By default,
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MatrixAlgebraKit supplies the following:
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$(docs_truncation_strategies)
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!!! note
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Here [`notrunc`](@ref) has special meaning, and signifies keeping the values that
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correspond to the exact zeros determined from the additional rows of `A`.
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## Keyword arguments
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There are 3 major modes of operation, based on the `alg` keyword, with slightly different
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application purposes.
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deduced from that. This hinges on the implementation of the algorithm trait
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[`MatrixAlgebraKit.right_null_kind(alg)`](@ref).
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## Truncation
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The optional truncation strategy can be controlled via the `trunc` keyword argument, and any
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non-trivial strategy typically requires an SVD-based decomposition. This keyword can be
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either a `NamedTuple` or a [`TruncationStrategy`](@ref).
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### `trunc::NamedTuple`
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The supported truncation keyword arguments are:
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$(docs_null_truncation_kwargs)
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### `trunc::TruncationStrategy`
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For more control, a truncation strategy can be supplied directly. By default,
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MatrixAlgebraKit supplies the following:
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$(docs_truncation_strategies)
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!!! note
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Here [`notrunc`](@ref) has special meaning, and signifies keeping the values that
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correspond to the exact zeros determined from the additional rows of `A`.
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---
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!!! note

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