Selection Technique: QR with Column Pivoting

docs/make.jl

@@ -33,7 +33,8 @@ makedocs(
             "Approximators" => [
                 "Approximators Overview" => "api/approximators.md",
                 "Approximator Sub-routines" => [
-                    "ApproximatorErrors" => "api/approximator_errors.md"
+                    "ApproximatorErrors" => "api/approximator_errors.md",
+                    "Selectors" => "api/selectors.md"
                                            ],
             ],
         ],

docs/src/api/compressors.md

@@ -34,6 +34,10 @@ Gaussian
 
 GaussianRecipe
 
+Identity
+
+IdentityRecipe
+
 Sampling
 
 SamplingRecipe

docs/src/api/selectors.md

@@ -0,0 +1,36 @@
+# Selectors 
+```@contents
+Pages = ["selectors.md"]
+```
+
+## Abstract Types
+```@docs
+Selector
+
+SelectorRecipe
+```
+
+## Selector Structures
+```@docs
+RLinearAlgebra.LUPP
+
+LUPPRecipe
+
+QRCP
+
+QRCPRecipe
+```
+
+## Exported Functions
+```@docs
+complete_selector
+
+update_selector!
+
+select_indices!
+```
+
+## Internal Functions
+```@docs
+
+```

src/Approximators.jl

@@ -56,6 +56,7 @@ randomized rangefinder.
 """
 abstract type RangeApproximatorRecipe <: ApproximatorRecipe end
 
+
 ###################################
 # Docstring Components  
 ###################################
@@ -72,6 +73,7 @@ approx_arg_list = Dict{Symbol,String}(
     :A => "`A::AbstractMatrix`, a target matrix for approximation.",
     :compressor_recipe => "`S::CompressorRecipe`, a fully initialized realization for a 
     compression method for a specific matrix or collection of matrices and vectors.",
+
 )
 
 approx_output_list = Dict{Symbol,String}(
@@ -82,8 +84,10 @@ approx_output_list = Dict{Symbol,String}(
 approx_method_description = Dict{Symbol,String}(
     :complete_approximator => "A function that generates an `ApproximatorRecipe` given 
     arguments.",
+
     :update_approximator => "A function that updates the `ApproximatorRecipe` in place
     given the arguments.",
+
     :rapproximate => "A function that computes a low-rank approximation of the matrix `A`
     using the information in the provided `Approximator` data structure.",
     :complete_approximator_error => "A function that generates an `ApproximatorErrorRecipe`
@@ -161,6 +165,7 @@ function complete_approximator(approximator::Approximator, A::AbstractMatrix)
     )
 end
 
+
 ###################################
 # rapproximate Interface 
 ###################################
@@ -430,3 +435,8 @@ end
 include("Approximators/RangeApproximators/rangefinder.jl")
 include("Approximators/RangeApproximators/randsvd.jl")
 include("Approximators/RangeApproximators/helpers/power_its.jl")
+
+############################################
+# Include the selector files
+############################################
+include("Approximators/Selectors.jl")

src/Approximators/Selectors.jl

@@ -0,0 +1,148 @@
+###################################
+# Abstract Types
+###################################
+"""
+    Selector
+
+An abstract type containing user controlled parameters for a technique that select indices
+from a matrix.
+"""
+abstract type Selector end
+
+"""
+    SelectorRecipe
+
+An abstract type containing user controlled parameters and preallocated memory for a
+technique that selects indices from matrix.
+"""
+abstract type SelectorRecipe end
+
+select_arg_list = Dict{Symbol,String}(
+    :selector => "`selector::Selector`, a data structure containing the user-defined
+    parameters associated with a particular selection method.",
+    :selector_recipe => "`selector_recipe::SelectorRecipe`, a fully initialized realization
+    for a selector method for a particular matrix.",
+    :idx => "`idx::vector`, a vector where selected indices will be placed.",
+    :n_idx => "`n_idx::Int64`, the number of indices to be selected.",
+    :start_idx => "`start_idx::Int64`. the starting location in `idx` where the indices 
+    will be placed.",
+    :A => "`A::AbstractMatrix`, a target matrix for approximation.",
+)
+select_output_list = Dict{Symbol,String}(
+    :selector_recipe => "A `SelectorRecipe` object.",
+)
+select_method_description = Dict{Symbol,String}(
+    :update_selector => "A function that updates the `SelectorRecipe` in place given the
+    arguments.",
+    :complete_selector => "A function that generates a `SelectorRecipe` given
+    arguments.",
+    :select_indices => "A function that selects indices from a matrix `A` using a specific
+    `SelectorRecipe`. It updates the vector `idx` in place with `n_idx` new indices starting
+    at index `start_idx`."
+)
+##################################
+# Complete Selector Interface
+##################################
+"""
+    complete_selector(selector::Selector, A::AbstractMatrix)
+
+$(select_method_description[:complete_selector])
+
+# Arguments
+- $(select_arg_list[:selector])
+- $(select_arg_list[:A]) 
+
+# Outputs
+- $(select_output_list[:selector_recipe])
+"""
+function complete_selector(selector::Selector, A::AbstractMatrix)
+    return throw(
+        ArgumentError(
+            "No method `complete_selector` exists for selector of type\
+            $(typeof(selector)) and matrix of type $(typeof(A))."
+        )
+    )
+end
+
+##################################
+# update_selector!
+##################################
+"""
+    update_selector!(selector::SelectorRecipe)
+
+$(select_method_description[:update_selector])
+
+# Arguments
+- $(select_arg_list[:selector_recipe])
+
+# Outputs
+- $(select_output_list[:selector_recipe])
+"""
+function update_selector!(selector::SelectorRecipe)
+    return throw(
+        ArgumentError(
+            "No method `update_selector!` exists for selector of type\
+            $(typeof(selector))."
+        )
+    )
+end
+
+"""
+    update_selector!(selector::SelectorRecipe, A::AbstractMatrix)
+
+$(select_method_description[:update_selector])
+
+# Arguments
+- $(select_arg_list[:selector_recipe])
+- $(select_arg_list[:A]) 
+
+# Outputs
+- $(select_output_list[:selector_recipe])
+"""
+function update_selector!(selector::SelectorRecipe, A::AbstractMatrix)
+    return update_selector!(selector) 
+end
+
+####################################
+# select_indices!
+####################################
+"""
+    select_indices!(
+        selector::SelectorRecipe, 
+        A::AbstractMatrix,
+        idx::AbstractVector,
+        n_idx::Int64, 
+        start_idx::Int64
+    )
+
+$(select_method_description[:select_indices])
+
+# Arguments
+- $(select_arg_list[:selector_recipe])
+- $(select_arg_list[:A]) 
+- $(select_arg_list[:idx])
+- $(select_arg_list[:n_idx])
+- $(select_arg_list[:start_idx])
+
+# Outputs
+-  Returns `nothing`
+"""
+function select_indices!(
+    idx::AbstractVector,
+    selector::SelectorRecipe, 
+    A::AbstractMatrix,
+    n_idx::Int64, 
+    start_idx::Int64
+)
+    return throw(
+        ArgumentError(
+            "No method `select_indices` exists for selector of type $(typeof(selector)),\
+            matrix of type $(typeof(A)), idx of type $(typeof(idx)), n_idx of type \
+            $(typeof(n_idx)), and start_idx of type $(typeof(start_idx))."
+        )
+    )
+end
+
+# Include the selector files
+include("Selectors/qrcp.jl")
+include("Selectors/lupp.jl")

src/Approximators/Selectors/lupp.jl

@@ -0,0 +1,94 @@
+"""
+    LUPP <: Selector
+
+A `Selector` that implements LU with partial pivoting for selecting column indices from a 
+matrix.
+
+# Fields
+- `compressor::Compressor`, the compression technique that will applied to the matrix, 
+    before selecting indices.
+
+# Constructor
+    LUPP(;compressor = Identity())
+
+## Keywords
+- `compressor::Compressor`, the compression technique that will applied to the matrix, 
+    before selecting indices. Defaults the `Identity` compressor.
+
+## Returns
+- Will return a `Selector` object.
+"""
+mutable struct LUPP <: Selector
+    compressor::Compressor
+end
+
+function LUPP(;compressor = Identity()) 
+    LUPP(compressor)
+end
+
+"""
+    LUPPRecipe <: SelectorRecipe
+
+A `SelectorRecipe` that contains all the necessary preallocations for selecting column 
+indices from a matrix using LU with partial pivoting.
+
+# Fields
+- `compressor::Compressor`, the compression technique that will applied to the matrix, 
+    before selecting indices.
+- `SA::AbstractMatrix`, a buffer matrix for storing the sketched matrix.
+"""
+mutable struct LUPPRecipe <: SelectorRecipe
+    compressor::CompressorRecipe
+    SA::AbstractMatrix
+end
+
+function complete_selector(ingredients::LUPP, A::AbstractMatrix)
+    compressor = complete_compressor(ingredients.compressor, A)
+    n_rows, n_cols = size(compressor)
+    SA = Matrix{eltype(A)}(undef, n_rows, n_cols)
+    return LUPPRecipe(compressor, SA)
+end
+
+function update_selector!(selector::LUPPRecipe)
+    update_compressor!(selector.compressor)
+    return nothing
+end
+
+function select_indices!(
+    idx::AbstractVector,
+    selector::LUPPRecipe, 
+    A::AbstractMatrix,
+    n_idx::Int64, 
+    start_idx::Int64
+)
+    if n_idx > size(A, 2)
+        throw(
+            DimensionMismatch( 
+                "`n_idx` cannot be larger than the number of columns in `A`."
+            )
+        )
+    end
+
+    if start_idx + n_idx - 1 > size(idx, 1)
+        throw(
+            DimensionMismatch( 
+                "`start_idx` + `n_idx` - 1 cannot be larger than the lenght of `idx`."
+            )   
+        )
+    end
+
+    if n_idx > selector.compressor.n_rows
+        throw(
+            DimensionMismatch( 
+                "Must select fewer indices then the `compression_dim`."
+            )   
+        )
+
+    end
+
+    mul!(selector.SA, selector.compressor, A)
+    # because LUPP selects rows and selectors select columns we need to pivot on A'
+    p = lu!(selector.SA').p
+    idx[start_idx:start_idx + n_idx - 1] = p[1:n_idx]
+    return nothing
+end