Change defaults for checking vectors/linearity/symmetry in check_ fun…

…ctions (#247)

* Set the vector check default to false – at least until we have a nicer control about tolerances.
* Change the format a bit, such that the kwargs are passed down to `is_vector` and tolerances can be set.
* bump version.

Project.toml

@@ -1,7 +1,7 @@
 name = "Manopt"
 uuid = "0fc0a36d-df90-57f3-8f93-d78a9fc72bb5"
 authors = ["Ronny Bergmann <[email protected]>"]
-version = "0.4.19"
+version = "0.4.20"
 
 [deps]
 ColorSchemes = "35d6a980-a343-548e-a6ea-1d62b119f2f4"

src/helpers/checks.jl

@@ -67,8 +67,9 @@ function prepare_check_result(
     throw_error && throw(ErrorException(msg))
     return false
 end
+
 @doc raw"""
-    check_differential(M, F, dF, p=rand(M), X=rand(M; vector_at=p))
+    check_differential(M, F, dF, p=rand(M), X=rand(M; vector_at=p); kwargs...)
 
 Check numerivcally whether the differential `dF(M,p,X)` of `F(M,p)` is correct.
 
@@ -167,10 +168,13 @@ no plot will be generated.
 * `plot`              - (`false`) whether to plot the resulting check (if `Plots.jl` is loaded). The plot is in log-log-scale. This is returned and can then also be saved.
 * `retraction_method` - (`default_retraction_method(M, typeof(p))`) retraction method to use for the check
 * `slope_tol`         – (`0.1`) tolerance for the slope (global) of the approximation
+* `atol`, `rtol`      – (same defaults as `isapprox`) tolerances that are passed down to `is_vector` if `check_vector` is set to `true`
 * `throw_error`       - (`false`) throw an error message if the gradient is wrong
 * `window` – (`nothing`) specify window sizes within the `log_range` that are used for the slope estimation.
   the default is, to use all window sizes `2:N`.
 
+The `kwargs...` are also passed down to the `check_vector` call, such that tolerances can
+easily be set.
 
 """
 function check_gradient(
@@ -180,11 +184,14 @@ function check_gradient(
     p=rand(M),
     X=rand(M; vector_at=p);
     gradient=grad_f(M, p),
-    check_vector=true,
+    check_vector=false,
     throw_error=false,
+    atol::Real=0,
+    rtol::Real=atol > 0 ? 0 : sqrt(eps(eltype(p))),
     kwargs...,
 )
-    check_vector && (!is_vector(M, p, gradient, throw_error;) && return false)
+    check_vector &&
+        (!is_vector(M, p, gradient, throw_error; atol=atol, rtol=rtol) && return false)
     # function for the directional derivative - real so it also works on complex manifolds
     df(M, p, Y) = real(inner(M, p, gradient, Y))
     return check_differential(
@@ -214,15 +221,16 @@ no plot will be generated.
 
 # Keyword arguments
 
-* `check_grad`   – (`true`) check whether ``\operatorname{grad} f(p) \in T_p\mathcal M``.
+* `check_grad`       – (`true`) check whether ``\operatorname{grad} f(p) \in T_p\mathcal M``.
 * `check_linearity`  – (`true`) check whether the Hessian is linear, see [`is_Hessian_linear`](@ref) using `a`, `b`, `X`, and `Y`
 * `check_symmetry`   – (`true`) check whether the Hessian is symmetric, see [`is_Hessian_symmetric`](@ref)
-* `check_vector`     – (`true`) check whether ``\operatorname{Hess} f(p)[X] \in T_p\mathcal M`` using `is_vector`.
+* `check_vector`     – (`false`) check whether ``\operatorname{Hess} f(p)[X] \in T_p\mathcal M`` using `is_vector`.
 * `mode`             - (`:Default`) specify the mode, by default we assume to have a second order retraction given by `retraction_method=`
   you can also this method if you already _have_ a cirtical point `p`.
   Set to `:CritalPoint` to use [`gradient_descent`](@ref) to find a critical point.
   Note: This requires (and evaluates) new tangent vectors `X` and `Y`
 
+* `atol`, `rtol`      – (same defaults as `isapprox`) tolerances that are passed down to all checks
 * `a`, `b`            – two real values to check linearity of the Hessian (if `check_linearity=true`)
 * `N`                 - (`101`) number of points to check within the `log_range` default range ``[10^{-8},10^{0}]``
 * `exactness_tol`     - (`1e-12`) if all errors are below this tolerance, the check is considered to be exact
@@ -239,6 +247,9 @@ no plot will be generated.
 * `throw_error`       - (`false`) throw an error message if the Hessian is wrong
 * `window` – (`nothing`) specify window sizes within the `log_range` that are used for the slope estimation.
   the default is, to use all window sizes `2:N`.
+
+The `kwargs...` are also passed down to the `check_vector` call, such that tolerances can
+easily be set.
 """
 function check_Hessian(
     M::AbstractManifold,
@@ -249,9 +260,10 @@ function check_Hessian(
     X=rand(M; vector_at=p),
     Y=rand(M; vector_at=p);
     a=randn(),
+    atol::Real=0,
     b=randn(),
     check_grad=true,
-    check_vector=true,
+    check_vector=false,
     check_symmetry=true,
     check_linearity=true,
     exactness_tol=1e-12,
@@ -264,29 +276,41 @@ function check_Hessian(
     log_range=range(limits[1], limits[2]; length=N),
     plot=false,
     retraction_method=default_retraction_method(M, typeof(p)),
+    rtol::Real=atol > 0 ? 0 : sqrt(eps(eltype(p))),
     slope_tol=0.1,
     throw_error=false,
     window=nothing,
     kwargs...,
 )
     if check_grad
         if !check_gradient(
-            M, f, grad_f, p, X; gradient=gradient, throw_error=throw_error, io=io, kwargs...
+            M,
+            f,
+            grad_f,
+            p,
+            X;
+            gradient=gradient,
+            throw_error=throw_error,
+            io=io,
+            atol=atol,
+            rtol=rtol,
+            kwargs...,
         )
             return false
         end
     end
-    check_vector && (!is_vector(M, p, Hessian, throw_error) && return false)
+    check_vector &&
+        (!is_vector(M, p, Hessian, throw_error; atol=atol, rtol=rtol) && return false)
     if check_linearity
         if !is_Hessian_linear(
-            M, Hess_f, p, X, Y, a, b; throw_error=throw_error, io=io, kwargs...
+            M, Hess_f, p, X, Y, a, b; throw_error=throw_error, io=io, atol=atol, rtol=rtol
         )
             return false
         end
     end
     if check_symmetry
         if !is_Hessian_symmetric(
-            M, Hess_f, p, X, Y; throw_error=throw_error, io=io, kwargs...
+            M, Hess_f, p, X, Y; throw_error=throw_error, io=io, atol=atol, rtol=rtol
         )
             return false
         end