Default tolerances for SVD-based nullspaces (#172)

* change default null truncation strategy

* update changelog

* Use relative instead of absolute tolerance

Author: lkdvos

docs/src/changelog.md

@@ -24,6 +24,7 @@ When releasing a new version, move the "Unreleased" changes to a new version sec
 
 ### Changed
 
+- The default behavior of SVD-based nullspaces now includes some small tolerance ([#172](https://github.com/QuantumKitHub/MatrixAlgebraKit.jl/pull/170)).
 - The Mooncake rules for truncated decompositions with `TruncatedAlgorithm` now use the pullbacks that make use of the full decomposition. ([#171](https://github.com/QuantumKitHub/MatrixAlgebraKit.jl/pull/171))
 
 ### Deprecated

src/algorithms.jl

@@ -243,14 +243,17 @@ function select_truncation(trunc)
 end
 
 @doc """
-    MatrixAlgebraKit.select_null_truncation(trunc)
+    MatrixAlgebraKit.select_null_truncation(A, trunc)
 
-Construct a [`TruncationStrategy`](@ref) from the given `NamedTuple` of keywords or input strategy, to implement a nullspace selection.
+Construct a [`TruncationStrategy`](@ref) for `A` from the given `NamedTuple` of keywords or input strategy, to implement a nullspace selection.
 """ select_null_truncation
 
+select_null_truncation(A, trunc) = select_null_truncation(typeof(A), trunc)
+select_null_truncation(A::Type, trunc) =
+    isnothing(trunc) ? select_null_truncation((; rtol = defaulttol(eltype(A)))) : select_null_truncation(trunc)
 function select_null_truncation(trunc)
     if isnothing(trunc)
-        return NoTruncation()
+        return null_truncation_strategy()
     elseif trunc isa NamedTuple
         return null_truncation_strategy(; trunc...)
     elseif trunc isa TruncationStrategy

src/interface/orthnull.jl

@@ -378,7 +378,7 @@ end
 end
 @inline function select_algorithm(::typeof(left_null!), A, ::Val{:svd}; trunc = nothing, kwargs...)
     alg_svd = select_algorithm(svd_full!, A, get(kwargs, :svd, nothing))
-    alg = TruncatedAlgorithm(alg_svd, select_null_truncation(trunc))
+    alg = TruncatedAlgorithm(alg_svd, select_null_truncation(A, trunc))
     return LeftNullViaSVD(alg)
 end
 
@@ -390,7 +390,7 @@ end
 end
 @inline function select_algorithm(::typeof(right_null!), A, ::Val{:svd}; trunc = nothing, kwargs...)
     alg_svd = select_algorithm(svd_full!, A; kwargs...)
-    alg = TruncatedAlgorithm(alg_svd, select_null_truncation(trunc))
+    alg = TruncatedAlgorithm(alg_svd, select_null_truncation(A, trunc))
     return RightNullViaSVD(alg)
 end