diff --git a/code/nnv/engine/nn/layers/FullyConnectedLayer.m b/code/nnv/engine/nn/layers/FullyConnectedLayer.m index fd960f61e9..b2d07ce997 100644 --- a/code/nnv/engine/nn/layers/FullyConnectedLayer.m +++ b/code/nnv/engine/nn/layers/FullyConnectedLayer.m @@ -284,15 +284,8 @@ n = in_image.numPred; V(1, 1, :, in_image.numPred + 1) = zeros(obj.OutputSize, 1, 'like', in_image.V); - for i=1:n+1 - I = in_image.V(:,:,:,i); - I = reshape(I,N,1); % flatten input - if i==1 - V(1, 1,:,i) = obj.Weights*I + obj.Bias; - else - V(1, 1,:,i) = obj.Weights*I; - end - end + V(1, 1, :, :) = obj.Weights*reshape(in_image.V, N, n + 1); + V(1, 1, :, 1) = reshape(V(1, 1, :, 1), obj.OutputSize, 1) + obj.Bias; % output set image = ImageStar(V, in_image.C, in_image.d, in_image.pred_lb, in_image.pred_ub); else % reach Star set diff --git a/code/nnv/engine/nn/layers/ImageInputLayer.m b/code/nnv/engine/nn/layers/ImageInputLayer.m index 8e923501b3..98f16379a7 100644 --- a/code/nnv/engine/nn/layers/ImageInputLayer.m +++ b/code/nnv/engine/nn/layers/ImageInputLayer.m @@ -116,6 +116,12 @@ image = in_image; elseif strcmp(obj.Normalization, 'zerocenter') image = in_image.affineMap([], -obj.Mean); + elseif strcmp(obj.Normalization, 'zscore') + image = in_image.affineMap([], -obj.Mean); + layer_std = obj.StandardDeviation; + for nc = 1:image.numChannel + image.V(:,:,nc,:) = image.V(:,:,nc,:)/layer_std(nc); + end else error('The normalization method is not supported yet.') end diff --git a/code/nnv/engine/set/Box.m b/code/nnv/engine/set/Box.m index 3dc872f52f..f36580ccca 100644 --- a/code/nnv/engine/set/Box.m +++ b/code/nnv/engine/set/Box.m @@ -40,7 +40,7 @@ % Speeding up implementation gens = diag(vec); % generate matrix if numel(gens) > 1 - gens(:,all(gens(gens==0))) = []; % delete colums with no info + gens(:,all(gens==0)) = []; % delete colums with no info end obj.generators = gens; catch diff --git a/code/nnv/engine/set/VolumeStar.m b/code/nnv/engine/set/VolumeStar.m index bbda1ac899..390a540695 100644 --- a/code/nnv/engine/set/VolumeStar.m +++ b/code/nnv/engine/set/VolumeStar.m @@ -554,16 +554,16 @@ S.V = gather(S.V); S.C = gather(S.C); S.d = gather(S.d); - S.predicate_lb = gather(S.predicate_lb); - S.predicate_ub = gather(S.predicate_ub); + S.pred_lb = gather(S.pred_lb); + S.pred_ub = gather(S.pred_ub); S.vol_lb = gather(S.vol_lb); S.vol_ub = gather(S.vol_ub); elseif strcmp(deviceTarget, 'gpu') S.V = gpuArray(S.V); S.C = gpuArray(S.C); S.d = gpuArray(S.d); - S.predicate_lb = gpuArray(S.predicate_lb); - S.predicate_ub = gpuArray(S.predicate_ub); + S.pred_lb = gpuArray(S.pred_lb); + S.pred_ub = gpuArray(S.pred_ub); S.vol_lb = gpuArray(S.vol_lb); S.vol_ub = gpuArray(S.vol_ub); else diff --git a/code/nnv/engine/utils/lpsolver.m b/code/nnv/engine/utils/lpsolver.m index ccde224ead..41c320658c 100644 --- a/code/nnv/engine/utils/lpsolver.m +++ b/code/nnv/engine/utils/lpsolver.m @@ -49,8 +49,8 @@ % Define solver parameters params = struct; % for now, leave default options/params params.OutputFlag = 0; % no display - params.OptimalityTol = 1e-09; - params.FeasibilityTol = 1e-09; + % params.OptimalityTol = 1e-09; + % params.FeasibilityTol = 1e-09; result = gurobi(model, params); fval = result.objval; % get fval value from results % get exitflag and match those of linprog for easier parsing diff --git a/code/nnv/engine/utils/verify_specification.m b/code/nnv/engine/utils/verify_specification.m index 0de36f7193..e6af98b1bc 100644 --- a/code/nnv/engine/utils/verify_specification.m +++ b/code/nnv/engine/utils/verify_specification.m @@ -32,6 +32,9 @@ if ~isa(Set, "Star") Set = Set.toStar; end + if isa(Set.V, 'gpuArray') + Set = Set.changeDevice('cpu'); + end S = Set.intersectHalfSpace(property.G, property.g); % compute intersection with unsafe/not robust region if isempty(S) result = 1; % no intersection with unsafe region = safe (unsat) @@ -57,6 +60,7 @@ continue; % does nothing, just need an statement, wanted to make this clear else result = 2; % unknown if approx, 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b/code/nnv/examples/Submission/WiP_3d/resultsGPU/verification_vessel_remove_1_50.mat differ diff --git a/code/nnv/examples/Submission/WiP_3d/resultsGPU/verification_vessel_remove_1_500.mat b/code/nnv/examples/Submission/WiP_3d/resultsGPU/verification_vessel_remove_1_500.mat new file mode 100644 index 0000000000..260c3e47c9 Binary files /dev/null and b/code/nnv/examples/Submission/WiP_3d/resultsGPU/verification_vessel_remove_1_500.mat differ diff --git a/code/nnv/examples/Submission/WiP_3d/run_all.m b/code/nnv/examples/Submission/WiP_3d/run_all.m index 6ff562bd3b..3ebff61697 100644 --- a/code/nnv/examples/Submission/WiP_3d/run_all.m +++ b/code/nnv/examples/Submission/WiP_3d/run_all.m @@ -1,31 +1,52 @@ -%% Shape only data (3d) +% %% Shape only data (3d) +% +% disp("... adrenal ..."); +% verify_adrenal; +% +% disp("... vessel ..."); +% verify_vessel; +% +% +% %% Volume data (general 3D) +% +% +% disp("... fracture ..."); +% verify_fracture; +% +% +% disp("... nodule ...") +% verify_nodule; +% +% +% disp("... organ ...") +% verify_organ; +% +% +% disp("... synapse ...") +% verify_synapse; + + +% disp("... Creating plots..."); +% visualize_results_gen; +% visualize_results_shape; + + +%% GPU disp("... adrenal ..."); -verify_adrenal; +verify_adrenal_gpu; disp("... vessel ..."); -verify_vessel; - - -%% Volume data (general 3D) - +verify_vessel_gpu; disp("... fracture ..."); -verify_fracture; - +verify_fracture_gpu; disp("... nodule ...") -verify_nodule; - +verify_nodule_gpu; disp("... organ ...") -verify_organ; - +verify_organ_gpu; disp("... synapse ...") -verify_synapse; - - -disp("... Creating plots..."); -visualize_results_gen; -visualize_results_shape; +verify_synapse_gpu; \ No newline at end of file diff --git a/code/nnv/examples/Submission/WiP_3d/verify_adrenal_gpu.m b/code/nnv/examples/Submission/WiP_3d/verify_adrenal_gpu.m new file mode 100644 index 0000000000..1a5af828f8 --- /dev/null +++ b/code/nnv/examples/Submission/WiP_3d/verify_adrenal_gpu.m @@ -0,0 +1,82 @@ +%% Verify adrenal dataset +% adrenalMNIST3D, input size: 28x28x28 + +% Data +dataset = "../../../../../data/medmnist/mat_files/adrenalmnist3d.mat"; % path to data +modelpath = "../../../../../data/medmnist/models/model_adrenalmnist3d.mat"; + +disp("Begin verification of adrenal3d"); + +% Load data +load(dataset); + +% data to verify (test set) +test_images = squeeze(permute(test_images, [2 3 4 5 1])); +test_labels = test_labels + 1; + +% load network +load(modelpath); +matlabNet = net; +net = matlab2nnv(net); + +% select volumes to verify +N = 50; +idxs = zeros(N,1); +count = 1; + +for i = 1:length(test_labels) + y = classify(matlabNet,test_images(:,:,:,i)); + if single(y) == test_labels(i) + idxs(count) = i; + count = count + 1; + end + if count > N + break + end +end + +inputs = single(test_images(:,:,:,idxs)); +targets = single(test_labels(idxs)); + +% Reachability parameters +reachOptions = struct; +reachOptions.reachMethod = 'relax-star-area'; +reachOptions.relaxFactor = 0.95; +reachOptions.lp_solver = "gurobi"; +reachOptions.device = 'gpu'; + + +% Study variables +advType = ["add", "remove"]; +maxpixels = [50, 100, 500, 1000]; %out of 28x28x28 pixels +% maxpixels = 1000; +epsilon = 1; % ep / 255 + + +%% Verification analysis +for a=advType + for mp=maxpixels + for ep=epsilon + + % 1) Initialize results var + results = zeros(N,2); + + % 2) Create adversarial attack + adv_attack = struct; + adv_attack.Name = a; % add or remove + adv_attack.max_pixels = mp; % Max number of pixels to modify from input image + adv_attack.noise_de = ep/255; % disturbance (noise) on pixels + + % 3) Begin verification analysis + for i=1:N + img = inputs(:,:,:,i); + target = targets(i); + results(i,:) = verify_instance_shape(net, img, target, adv_attack, reachOptions); + end + + % 4) % save results + save("resultsGPU/verification_adrenal_"+ a +"_" + ep +"_" + mp + ".mat", "results"); + + end + end +end \ No newline at end of file diff --git a/code/nnv/examples/Submission/WiP_3d/verify_fracture_gpu.m b/code/nnv/examples/Submission/WiP_3d/verify_fracture_gpu.m new file mode 100644 index 0000000000..fafc9f81fc --- /dev/null +++ b/code/nnv/examples/Submission/WiP_3d/verify_fracture_gpu.m @@ -0,0 +1,86 @@ +%% Verify fracture dataset +% VesselMNIST3D, input size: 28x28x28 + +% Data +dataset = "../../../../../data/medmnist/mat_files/fracturemnist3d.mat"; % path to data +modelpath = "../../../../../data/medmnist/models/model_fracturemnist3d.mat"; + +disp("Begin verification of fracture3d"); + +% Load data +load(dataset); + +% data to verify (test set) +test_images = permute(test_images, [2 3 4 5 1]); +test_labels = test_labels + 1; + +% load network +load(modelpath); +matlabNet = net; +net = matlab2nnv(net); + +% select volumes to verify +N = 50; +idxs = zeros(N,1); +count = 1; + +for i = 1:length(test_labels) + y = classify(matlabNet,test_images(:,:,:,i)); + if single(y) == test_labels(i) + idxs(count) = i; + count = count + 1; + end + if count > N + break + end +end + +inputs = single(test_images(:,:,:,idxs)); +targets = single(test_labels(idxs)); + +% Reachability parameters +reachOptions = struct; +reachOptions.reachMethod = 'relax-star-area'; +reachOptions.relaxFactor = 0.95; +reachOptions.lp_solver = "gurobi"; +reachOptions.device = 'gpu'; + + +% Study variables +advType = ["bright", "dark"]; +maxpixels = [50, 100, 500, 1000]; %out of 28x28x28 pixels +epsilon = [2, 5, 10, 25]; % ep / 255 +threshold = [100; 150]; % bright ; dark + +%% Verification analysis +for a=advType + for mp=maxpixels + for ep=epsilon + + % 1) Initialize results var + results = zeros(N,2); + + % 2) Create adversarial attack + adv_attack = struct; + adv_attack.Name = a; % bright or dark + if strcmp(a, "bright") + adv_attack.threshold = threshold(1); % perturb pixels below this value + else + adv_attack.threshold = threshold(2); % perturb pixels below this value + end + adv_attack.max_pixels = mp; % Max number of pixels to modify from input image + adv_attack.noise_de = ep/255; % disturbance (noise) on pixels + + % 3) Begin verification analysis + for i=1:N + img = inputs(:,:,:,i); + target = targets(i); + results(i,:) = verify_instance_3d(net, img, target, adv_attack, reachOptions); + end + + % 4) % save results + save("resultsGPU/verification_fracture_"+ a +"_" + ep +"_" + mp + ".mat", "results"); + + end + end +end \ No newline at end of file diff --git a/code/nnv/examples/Submission/WiP_3d/verify_nodule_gpu.m b/code/nnv/examples/Submission/WiP_3d/verify_nodule_gpu.m new file mode 100644 index 0000000000..c034292d5a --- /dev/null +++ b/code/nnv/examples/Submission/WiP_3d/verify_nodule_gpu.m @@ -0,0 +1,86 @@ +%% Verify nodule dataset +% NoduleMNIST3D, input size: 28x28x28 + +% Data +dataset = "../../../../../data/medmnist/mat_files/nodulemnist3d.mat"; % path to data +modelpath = "../../../../../data/medmnist/models/model_nodulemnist3d.mat"; + +disp("Begin verification of nodule3d"); + +% Load data +load(dataset); + +% data to verify (test set) +test_images = permute(test_images, [2 3 4 5 1]); +test_labels = test_labels + 1; + +% load network +load(modelpath); +matlabNet = net; +net = matlab2nnv(net); + +% select volumes to verify +N = 50; +idxs = zeros(N,1); +count = 1; + +for i = 1:length(test_labels) + y = classify(matlabNet,test_images(:,:,:,i)); + if single(y) == test_labels(i) + idxs(count) = i; + count = count + 1; + end + if count > N + break + end +end + +inputs = single(test_images(:,:,:,idxs)); +targets = single(test_labels(idxs)); + +% Reachability parameters +reachOptions = struct; +reachOptions.reachMethod = 'relax-star-area'; +reachOptions.relaxFactor = 0.95; +reachOptions.lp_solver = "gurobi"; +reachOptions.device = 'gpu'; + + +% Study variables +advType = ["bright", "dark"]; +maxpixels = [50, 100, 500, 1000]; %out of 28x28x28 pixels +epsilon = [2, 5, 10, 25]; % ep / 255 +threshold = [100; 150]; % bright ; dark + +%% Verification analysis +for a=advType + for mp=maxpixels + for ep=epsilon + + % 1) Initialize results var + results = zeros(N,2); + + % 2) Create adversarial attack + adv_attack = struct; + adv_attack.Name = a; % bright or dark + if strcmp(a, "bright") + adv_attack.threshold = threshold(1); % perturb pixels below this value + else + adv_attack.threshold = threshold(2); % perturb pixels below this value + end + adv_attack.max_pixels = mp; % Max number of pixels to modify from input image + adv_attack.noise_de = ep/255; % disturbance (noise) on pixels + + % 3) Begin verification analysis + for i=1:N + img = inputs(:,:,:,i); + target = targets(i); + results(i,:) = verify_instance_3d(net, img, target, adv_attack, reachOptions); + end + + % 4) % save results + save("resultsGPU/verification_nodule_"+ a +"_" + ep +"_" + mp + ".mat", "results"); + + end + end +end \ No newline at end of file diff --git a/code/nnv/examples/Submission/WiP_3d/verify_organ_gpu.m b/code/nnv/examples/Submission/WiP_3d/verify_organ_gpu.m new file mode 100644 index 0000000000..b9aaa60834 --- /dev/null +++ b/code/nnv/examples/Submission/WiP_3d/verify_organ_gpu.m @@ -0,0 +1,85 @@ +%% Verify organ dataset +% VesselMNIST3D, input size: 28x28x28 + +% Data +dataset = "../../../../../data/medmnist/mat_files/organmnist3d.mat"; % path to data +modelpath = "../../../../../data/medmnist/models/model_organmnist3d.mat"; + +disp("Begin verification of organ3d"); + +% Load data +load(dataset); + +% data to verify (test set) +test_images = permute(test_images, [2 3 4 5 1]); +test_labels = test_labels + 1; + +% load network +load(modelpath); +matlabNet = net; +net = matlab2nnv(net); + +% select volumes to verify +N = 50; +idxs = zeros(N,1); +count = 1; + +for i = 1:length(test_labels) + y = classify(matlabNet,test_images(:,:,:,i)); + if single(y) == test_labels(i) + idxs(count) = i; + count = count + 1; + end + if count > N + break + end +end + +inputs = single(test_images(:,:,:,idxs)); +targets = single(test_labels(idxs)); + +% Reachability parameters +reachOptions = struct; +reachOptions.reachMethod = 'relax-star-area'; +reachOptions.relaxFactor = 0.95; +reachOptions.lp_solver = "gurobi"; +reachOptions.device = 'gpu'; + +% Study variables +advType = ["bright", "dark"]; +maxpixels = [50, 100, 500, 1000]; %out of 28x28x28 pixels +epsilon = [2, 5, 10, 25]; % ep / 255 +threshold = [100; 150]; % bright ; dark + +%% Verification analysis +for a=advType + for mp=maxpixels + for ep=epsilon + + % 1) Initialize results var + results = zeros(N,2); + + % 2) Create adversarial attack + adv_attack = struct; + adv_attack.Name = a; % bright or dark + if strcmp(a, "bright") + adv_attack.threshold = threshold(1); % perturb pixels below this value + else + adv_attack.threshold = threshold(2); % perturb pixels below this value + end + adv_attack.max_pixels = mp; % Max number of pixels to modify from input image + adv_attack.noise_de = ep/255; % disturbance (noise) on pixels + + % 3) Begin verification analysis + for i=1:N + img = inputs(:,:,:,i); + target = targets(i); + results(i,:) = verify_instance_3d(net, img, target, adv_attack, reachOptions); + end + + % 4) % save results + save("resultsGPU/verification_organ_"+ a +"_" + ep +"_" + mp + ".mat", "results"); + + end + end +end \ No newline at end of file diff --git a/code/nnv/examples/Submission/WiP_3d/verify_synapse_gpu.m b/code/nnv/examples/Submission/WiP_3d/verify_synapse_gpu.m new file mode 100644 index 0000000000..eaafd76e6f --- /dev/null +++ b/code/nnv/examples/Submission/WiP_3d/verify_synapse_gpu.m @@ -0,0 +1,86 @@ +%% Verify synapse dataset +% SynapseMNIST3D, input size: 28x28x28 + +% Data +dataset = "../../../../../data/medmnist/mat_files/synapsemnist3d.mat"; % path to data +modelpath = "../../../../../data/medmnist/models/model_synapsemnist3d.mat"; + +disp("Begin verification of synapse3d"); + +% Load data +load(dataset); + +% data to verify (test set) +test_images = permute(test_images, [2 3 4 5 1]); +test_labels = test_labels + 1; + +% load network +load(modelpath); +matlabNet = net; +net = matlab2nnv(net); + +% select volumes to verify +N = 50; +idxs = zeros(N,1); +count = 1; + +for i = 1:length(test_labels) + y = classify(matlabNet,test_images(:,:,:,i)); + if single(y) == test_labels(i) + idxs(count) = i; + count = count + 1; + end + if count > N + break + end +end + +inputs = single(test_images(:,:,:,idxs)); +targets = single(test_labels(idxs)); + +% Reachability parameters +reachOptions = struct; +reachOptions.reachMethod = 'relax-star-area'; +reachOptions.relaxFactor = 0.95; +reachOptions.lp_solver = "gurobi"; +reachOptions.device = 'gpu'; + + +% Study variables +advType = ["bright", "dark"]; +maxpixels = [50, 100, 500, 1000]; %out of 28x28x28 pixels +epsilon = [2, 5, 10, 25]; % ep / 255 +threshold = [100; 150]; % bright ; dark + +%% Verification analysis +for a=advType + for mp=maxpixels + for ep=epsilon + + % 1) Initialize results var + results = zeros(N,2); + + % 2) Create adversarial attack + adv_attack = struct; + adv_attack.Name = a; % bright or dark + if strcmp(a, "bright") + adv_attack.threshold = threshold(1); % perturb pixels below this value + else + adv_attack.threshold = threshold(2); % perturb pixels below this value + end + adv_attack.max_pixels = mp; % Max number of pixels to modify from input image + adv_attack.noise_de = ep/255; % disturbance (noise) on pixels + + % 3) Begin verification analysis + for i=1:N + img = inputs(:,:,:,i); + target = targets(i); + results(i,:) = verify_instance_3d(net, img, target, adv_attack, reachOptions); + end + + % 4) % save results + save("resultsGPU/verification_synapse_"+ a +"_" + ep +"_" + mp + ".mat", "results"); + + end + end +end \ No newline at end of file diff --git a/code/nnv/examples/Submission/WiP_3d/verify_vessel_gpu.m b/code/nnv/examples/Submission/WiP_3d/verify_vessel_gpu.m new file mode 100644 index 0000000000..3025d0ad0b --- /dev/null +++ b/code/nnv/examples/Submission/WiP_3d/verify_vessel_gpu.m @@ -0,0 +1,82 @@ +%% Verify vessel dataset +% vesselMNIST3D, input size: 28x28x28 + +% Data +dataset = "../../../../../data/medmnist/mat_files/vesselmnist3d.mat"; % path to data +modelpath = "../../../../../data/medmnist/models/model_vesselmnist3d.mat"; + +disp("Begin verification of vessel3d"); + +% Load data +load(dataset); + +% data to verify (test set) +test_images = permute(test_images, [2 3 4 5 1]); +test_labels = test_labels + 1; + +% load network +load(modelpath); +matlabNet = net; +net = matlab2nnv(net); + +% select volumes to verify +N = 50; +idxs = zeros(N,1); +count = 1; + +for i = 1:length(test_labels) + y = classify(matlabNet,test_images(:,:,:,i)); + if single(y) == test_labels(i) + idxs(count) = i; + count = count + 1; + end + if count > N + break + end +end + +inputs = single(test_images(:,:,:,idxs)); +targets = single(test_labels(idxs)); + +% Reachability parameters +reachOptions = struct; +reachOptions.reachMethod = 'relax-star-area'; +reachOptions.relaxFactor = 0.95; +reachOptions.lp_solver = "gurobi"; +reachOptions.device = 'gpu'; + + +% Study variables +advType = ["add", "remove"]; +maxpixels = [50, 100, 500, 1000]; %out of 28x28x28 pixels +epsilon = 1; % ep / 255 + + +%% Verification analysis +for a=advType + for mp=maxpixels + for ep=epsilon + + % 1) Initialize results var + results = zeros(N,2); + + % 2) Create adversarial attack + adv_attack = struct; + adv_attack.Name = a; % add or remove + adv_attack.max_pixels = mp; % Max number of pixels to modify from input image + adv_attack.noise_de = ep/255; % disturbance (noise) on pixels + + % 3) Begin verification analysis + for i=1:N + img = inputs(:,:,:,i); + target = targets(i); + results(i,:) = verify_instance_shape(net, img, target, adv_attack, reachOptions); + end + + % 4) % save results + save("resultsGPU/verification_vessel_"+ a +"_" + ep +"_" + mp + ".mat", "results"); + + end + end +end + diff --git a/code/nnv/tests/set/image_star/test_ImageStar_getRange.m b/code/nnv/tests/set/image_star/test_ImageStar_getRange.m index 94c2955e85..90a88db6fb 100644 --- a/code/nnv/tests/set/image_star/test_ImageStar_getRange.m +++ b/code/nnv/tests/set/image_star/test_ImageStar_getRange.m @@ -11,9 +11,53 @@ UB(:,:,2) = [0.1 0.15 0 0; 0 0 0 0; 0 0 0 0; 0 0 0 0]; UB(:,:,3) = UB(:,:,2); +%% 1) Get Range image = ImageStar(IM, LB, UB); -tic; [xmin, xmax] = image.getRange(1,1,1); -toc; display(xmin); -display(xmax); \ No newline at end of file +display(xmax); + +%% 2) Get Ranges +image = ImageStar(IM, LB, UB); +[xmin, xmax] = image.getRanges; + +%% 3) Estimate Ranges +image = ImageStar(IM, LB, UB); +[xmin, xmax] = image.estimateRanges; + +%% 4) Compare ranges (estimate >= get) +image1 = ImageStar(IM, LB, UB); +t = tic; +[xmin1, xmax1] = image1.estimateRanges; +t1 = toc(t); + +% estimate ranges should be faster, but an overapproximation of getRanges +image2 = ImageStar(IM, LB, UB); +t = tic; +[xmin2, xmax2] = image2.getRanges; +t2 = toc(t); + +disp("Estimate took " + string(t1) +" seconds vs getRanges, that run on " +string(t2) +"seconds"); + +assert(all(xmin1 - xmin2 <= eps, 'all')); +assert(all(xmax1 - xmax2 >= -eps, 'all')); + +%% 5) Test from issues + +V(1,1,1,1) = 0; +V(1,1,1,2) = -1; +V(1,1,1,3) = 1; +C = [0 0]; +d = 0; +ub = [1; 1]; +lb = -ub; + +I1 = ImageStar(V, C, d, lb, ub); +I2 = ImageStar(V, C, d, lb, ub); + +[xmin1, xmax1] = I1.estimateRanges; +[xmin2, xmax2] = I2.getRanges; + + +assert(all(xmin1 - xmin2 <= eps, 'all')); +assert(all(xmax1 - xmax2 >= -eps, 'all')); \ No newline at end of file