implement truncation_error keyword arg for truncate!

src/abstractmps.jl

@@ -1672,13 +1672,18 @@ provided as keyword arguments.
 
 Keyword arguments:
 * `site_range`=1:N - only truncate the MPS bonds between these sites
+* `truncation_error` - if provided, will store the truncation error from all SVDs performed in a single call to `truncate!`. This should be a `Ref` type, for example `truncation_error = Ref{Float64}()`. It should be initialized to some value (likely 0.0, e.g., `truncation_error[] = 0.0`).
 """
 function truncate!(M::AbstractMPS; alg="frobenius", kwargs...)
   return truncate!(Algorithm(alg), M; kwargs...)
 end
 
 function truncate!(
-  ::Algorithm"frobenius", M::AbstractMPS; site_range=1:length(M), kwargs...
+  ::Algorithm"frobenius",
+  M::AbstractMPS;
+  site_range=1:length(M),
+  truncation_error=nothing,
+  kwargs...,
 )
   N = length(M)
 
@@ -1690,7 +1695,10 @@ function truncate!(
   for j in reverse((first(site_range) + 1):last(site_range))
     rinds = uniqueinds(M[j], M[j - 1])
     ltags = tags(commonind(M[j], M[j - 1]))
-    U, S, V = svd(M[j], rinds; lefttags=ltags, kwargs...)
+    U, S, V, spec = svd(M[j], rinds; lefttags=ltags, kwargs...)
+    if !isnothing(truncation_error)
+      truncation_error[] += spec.truncerr
+    end
     M[j] = U
     M[j - 1] *= (S * V)
     setrightlim!(M, j)

test/base/test_mps.jl

@@ -755,6 +755,16 @@ end
     truncate!(M; site_range=3:7, maxdim=2)
     @test linkdims(M) == [2, 4, 2, 2, 2, 2, 8, 4, 2]
   end
+
+  @testset "truncate! with truncation_error" begin
+    M = basicRandomMPS(10; dim=10)
+    truncation_error = Ref{Float64}()
+    truncation_error[] = 0.0
+    truncate!(M, maxdim=3, cutoff=1E-3, truncation_error=truncation_error)
+    @test truncation_error[] > 0.0
+  end
+
+
 end
 
 @testset "Other MPS methods" begin