Add derivative check for Jacobian of residual

Author: amontoison

test/runtests.jl

@@ -6,3 +6,46 @@ end
 
 include("testBundleAdjustmentModels.jl")
 include("testBundleAdjustmentAllocations.jl")
+
+# https://github.com/JuliaSmoothOptimizers/NLPModelsTest.jl/blob/src/dercheck.jl#L43
+function jacobian_residual_check(
+  nlp::AbstractNLSModel;
+  x::AbstractVector = nlp.meta.x0,
+  atol::Float64 = 1.0e-6,
+  rtol::Float64 = 1.0e-4,
+)
+
+  # Fast exit if there are no constraints.
+  J_errs = Dict{Tuple{Int, Int}, Float64}()
+  nlp.nls_meta.nequ > 0 || return J_errs
+
+  # Optimal-ish step for second-order centered finite differences.
+  step = (eps(Float64) / 3)^(1 / 3)
+
+  # Check constraints Jacobian.
+  J = jac_residual(nlp, x)
+  h = zeros(nlp.meta.nvar)
+  cxph = zeros(nlp.nls_meta.nequ)
+  cxmh = zeros(nlp.nls_meta.nequ)
+  # Differentiate all constraints with respect to each variable in turn.
+  for i = 1:(nlp.meta.nvar)
+    h[i] = step
+    residual!(nlp, x + h, cxph)
+    residual!(nlp, x - h, cxmh)
+    dcdxi = (cxph - cxmh) / 2 / step
+    for j = 1:(nlp.nls_meta.nequ)
+      err = abs(dcdxi[j] - J[j, i])
+      if err > atol + rtol * abs(dcdxi[j])
+        J_errs[(j, i)] = err
+      end
+    end
+    h[i] = 0
+  end
+  return J_errs
+end
+
+@testset "Test derivative Jacobian of residual" begin
+  nls = BundleAdjustmentModel("problem-49-7776-pre")
+  x = 10 * [-(-1.0)^i for i = 1:nls.meta.nvar]
+  @test length(jacobian_residual_check(nls, x = x)) == 0
+end