@@ -8,13 +8,13 @@ Test whether a linear map is an isometry, where the type of isometry is controll
88
99The `isapprox_kwargs` are passed on to `isapprox` to control the tolerances.
1010
11- New specializations should overload [`is_left_isometry `](@ref) and [`is_right_isometry `](@ref).
11+ New specializations should overload [`isleftisometric `](@ref) and [`isrightisometric `](@ref).
1212
1313See also [`isunitary`](@ref).
1414"""
1515function isisometric (A; side:: Symbol = :left , isapprox_kwargs... )
16- side === :left && return is_left_isometry (A; isapprox_kwargs... )
17- side === :right && return is_right_isometry (A; isapprox_kwargs... )
16+ side === :left && return isleftisometric (A; isapprox_kwargs... )
17+ side === :right && return isrightisometric (A; isapprox_kwargs... )
1818
1919 throw (ArgumentError (lazy " Invalid isometry side: $side" ))
2020end
@@ -28,40 +28,40 @@ The `isapprox_kwargs` are passed on to `isapprox` to control the tolerances.
2828See also [`isisometric`](@ref).
2929"""
3030function isunitary (A; isapprox_kwargs... )
31- return is_left_isometry (A; isapprox_kwargs... ) &&
32- is_right_isometry (A; isapprox_kwargs... )
31+ return isleftisometric (A; isapprox_kwargs... ) &&
32+ isrightisometric (A; isapprox_kwargs... )
3333end
3434function isunitary (A:: AbstractMatrix ; isapprox_kwargs... )
3535 size (A, 1 ) == size (A, 2 ) || return false
36- return is_left_isometry (A; isapprox_kwargs... )
36+ return isleftisometric (A; isapprox_kwargs... )
3737end
3838
3939@doc """
40- is_left_isometry (A; isapprox_kwargs...) -> Bool
40+ isleftisometric (A; isapprox_kwargs...) -> Bool
4141
4242Test whether a linear map is a left isometry, i.e. `A' * A ≈ I`.
4343The `isapprox_kwargs` can be used to control the tolerances of the equality.
4444
45- See also [`isisometric`](@ref) and [`is_right_isometry `](@ref).
46- """ is_left_isometry
45+ See also [`isisometric`](@ref) and [`isrightisometric `](@ref).
46+ """ isleftisometric
4747
48- function is_left_isometry (A:: AbstractMatrix ; atol:: Real = 0 , rtol:: Real = defaulttol (A), norm = LinearAlgebra. norm)
48+ function isleftisometric (A:: AbstractMatrix ; atol:: Real = 0 , rtol:: Real = defaulttol (A), norm = LinearAlgebra. norm)
4949 P = A' * A
5050 nP = norm (P) # isapprox would use `rtol * max(norm(P), norm(I))`
5151 diagview (P) .- = 1
5252 return norm (P) <= max (atol, rtol * nP) # assume that the norm of I is `sqrt(n)`
5353end
5454
5555@doc """
56- is_right_isometry (A; isapprox_kwargs...) -> Bool
56+ isrightisometric (A; isapprox_kwargs...) -> Bool
5757
5858Test whether a linear map is a right isometry, i.e. `A * A' ≈ I`.
5959The `isapprox_kwargs` can be used to control the tolerances of the equality.
6060
61- See also [`isisometric`](@ref) and [`is_left_isometry `](@ref).
62- """ is_right_isometry
61+ See also [`isisometric`](@ref) and [`isleftisometric `](@ref).
62+ """ isrightisometric
6363
64- function is_right_isometry (A:: AbstractMatrix ; atol:: Real = 0 , rtol:: Real = defaulttol (A), norm = LinearAlgebra. norm)
64+ function isrightisometric (A:: AbstractMatrix ; atol:: Real = 0 , rtol:: Real = defaulttol (A), norm = LinearAlgebra. norm)
6565 P = A * A'
6666 nP = norm (P) # isapprox would use `rtol * max(norm(P), norm(I))`
6767 diagview (P) .- = 1
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