test: add discriminating noise-application checks to sparse noise tests

Author: singhharsh1708

lib/StochasticDiffEq/test/sparse_noise_tests.jl

@@ -1,11 +1,5 @@
 using StochasticDiffEq, SparseArrays, Test, Random
 
-Random.seed!(42)
-
-# 4-state system driven by 2 independent Wiener processes.
-# Only states 1 and 3 are coupled to noise; states 2 and 4 are purely deterministic.
-# The noise matrix is 4×2 sparse: g[1,1] = 0.1*u[1], g[3,2] = 0.1*u[3], rest zero.
-
 function f_sparse!(du, u, p, t)
     return du .= -u
 end
@@ -25,23 +19,29 @@ noise_prototype[3, 2] = 1.0
 prob = SDEProblem(f_sparse!, g_sparse!, u0, tspan, noise_rate_prototype = noise_prototype)
 
 @testset "Sparse noise_rate_prototype — EM IIP" begin
+    Random.seed!(42)
     sol = solve(prob, EM(), dt = 0.01)
     @test sol.retcode == ReturnCode.Success
     @test length(sol) > 1
-    # States 2 and 4 have zero noise rows → evolve purely as du/dt = -u → u(1) = exp(-1)
+    # Dimensions 2 and 4 have no noise: pure drift exp(-t)
     @test sol.u[end][2] ≈ exp(-1.0) rtol = 0.02
     @test sol.u[end][4] ≈ exp(-1.0) rtol = 0.02
+    # Dimensions 1 and 3 receive noise: path must deviate from pure drift
+    @test !isapprox(sol.u[end][1], exp(-1.0), rtol = 0.005)
+    @test !isapprox(sol.u[end][3], exp(-1.0), rtol = 0.005)
 end
 
 @testset "Sparse noise_rate_prototype — EulerHeun IIP" begin
+    Random.seed!(42)
     sol = solve(prob, EulerHeun(), dt = 0.01)
     @test sol.retcode == ReturnCode.Success
     @test length(sol) > 1
     @test sol.u[end][2] ≈ exp(-1.0) rtol = 0.02
     @test sol.u[end][4] ≈ exp(-1.0) rtol = 0.02
+    @test !isapprox(sol.u[end][1], exp(-1.0), rtol = 0.005)
+    @test !isapprox(sol.u[end][3], exp(-1.0), rtol = 0.005)
 end
 
-# OOP variant
 function f_sparse_oop(u, p, t)
     return -u
 end
@@ -56,8 +56,11 @@ end
 prob_oop = SDEProblem(f_sparse_oop, g_sparse_oop, u0, tspan, noise_rate_prototype = noise_prototype)
 
 @testset "Sparse noise_rate_prototype — EM OOP" begin
+    Random.seed!(42)
     sol = solve(prob_oop, EM(), dt = 0.01)
     @test sol.retcode == ReturnCode.Success
     @test sol.u[end][2] ≈ exp(-1.0) rtol = 0.02
     @test sol.u[end][4] ≈ exp(-1.0) rtol = 0.02
+    @test !isapprox(sol.u[end][1], exp(-1.0), rtol = 0.005)
+    @test !isapprox(sol.u[end][3], exp(-1.0), rtol = 0.005)
 end

lib/StochasticDiffEqCore/src/solve.jl

@@ -405,8 +405,6 @@ function _sde_init(
                     SciMLBase.parameterless_type(u), zeros(randElType, size(noise_rate_prototype, 2))
                 )
             elseif issparse(noise_rate_prototype)
-                # Wiener increments must always be a dense vector regardless of whether
-                # the noise matrix g is sparse; sparse dW has no defined mul! with sparse g.
                 rand_prototype = zeros(randElType, size(noise_rate_prototype, 2))
             else
                 rand_prototype = false .* noise_rate_prototype[1, :]