@@ -373,7 +373,7 @@ function test_ctflows()
373373 t0 = 0
374374 tf = 1
375375 x0 = 1.0
376-
376+
377377 ocp = @def begin
378378 λ ∈ R, variable
379379 t ∈ [t0, tf], time
@@ -382,10 +382,10 @@ function test_ctflows()
382382 ẋ (t) == λ * x (t)
383383 ∫ (x (t)^ 2 ) → min
384384 end
385-
385+
386386 # Test: Flow(ocp) works for control-free problems
387387 f = Flow (ocp)
388-
388+
389389 # Test: basic call returns 2 values (state, costate)
390390 λ_val = 0.5
391391 p0 = 1.0
@@ -400,7 +400,7 @@ function test_ctflows()
400400 t0 = 0
401401 tf = 1
402402 x0 = 1.0
403-
403+
404404 ocp = @def begin
405405 λ ∈ R, variable
406406 t ∈ [t0, tf], time
@@ -409,11 +409,11 @@ function test_ctflows()
409409 ẋ (t) == λ * x (t)
410410 ∫ (x (t)^ 2 ) → min
411411 end
412-
412+
413413 f = Flow (ocp)
414414 λ_val = 0.5
415415 p0 = 1.0
416-
416+
417417 # Test: augment=true returns 3 values (state, costate, variable costate)
418418 xf, pf, pλ = f (t0, x0, p0, tf, λ_val; augment= true )
419419 Test. @test xf isa Real
@@ -428,7 +428,7 @@ function test_ctflows()
428428 x0 = 1.0
429429 λ_val = 0.5
430430 p0 = 1.0
431-
431+
432432 ocp = @def begin
433433 λ ∈ R, variable
434434 t ∈ [t0, tf], time
@@ -437,7 +437,7 @@ function test_ctflows()
437437 ẋ (t) == λ * x (t)
438438 ∫ (x (t)^ 2 ) → min
439439 end
440-
440+
441441 # Manual Hamiltonian construction
442442 H (x, p, λ) = p * λ * x - x^ 2
443443 function H_aug (x_, p_)
@@ -446,14 +446,14 @@ function test_ctflows()
446446 return H (x, p, λ)
447447 end
448448 f_manual = Flow (OptimalControl. Hamiltonian (H_aug))
449-
449+
450450 # Automatic Flow from OCP
451451 f_auto = Flow (ocp)
452-
452+
453453 # Test: both give similar results
454454 xf_manual, pf_manual = f_manual (t0, [x0, λ_val], [p0, 0.0 ], tf)
455455 xf_auto, pf_auto = f_auto (t0, x0, p0, tf, λ_val)
456-
456+
457457 Test. @test xf_manual[1 ] ≈ xf_auto rtol= 1e-6
458458 Test. @test pf_manual[1 ] ≈ pf_auto rtol= 1e-6
459459 end
@@ -463,7 +463,7 @@ function test_ctflows()
463463 t0 = 0
464464 tf = 1
465465 x0 = 1.0
466-
466+
467467 ocp = @def begin
468468 λ ∈ R, variable
469469 t ∈ [t0, tf], time
@@ -472,11 +472,11 @@ function test_ctflows()
472472 ẋ (t) == λ * x (t)
473473 ∫ (x (t)^ 2 ) → min
474474 end
475-
475+
476476 f = Flow (ocp)
477477 λ_zero = 0.0
478478 p0 = 1.0
479-
479+
480480 xf, pf = f (t0, x0, p0, tf, λ_zero)
481481 Test. @test xf ≈ x0 rtol= 1e-10 # x remains constant
482482 end
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