Python numpy.logspace() Examples

def test_dist_sma(self):
        """
        Test that smas outside of the range have zero probability

        """

        for mod in self.allmods:
            if 'dist_sma' in mod.__dict__:
                with RedirectStreams(stdout=self.dev_null):
                    pp = mod(**self.spec)

                a = np.logspace(np.log10(pp.arange[0].to('AU').value/10.),np.log10(pp.arange[1].to('AU').value*10.),100)

                fa = pp.dist_sma(a)
                self.assertTrue(np.all(fa[a < pp.arange[0].to('AU').value] == 0),'dist_sma high bound failed for %s'%mod.__name__)
                self.assertTrue(np.all(fa[a > pp.arange[1].to('AU').value] == 0),'dist_sma low bound failed for %s'%mod.__name__)
                self.assertTrue(np.all(fa[(a >= pp.arange[0].to('AU').value) & (a <= pp.arange[1].to('AU').value)] >= 0.),'dist_sma generates negative densities within range for %s'%mod.__name__) 

def test_dist_radius(self):
        """
        Test that radii outside of the range have zero probability

        """
        for mod in self.allmods:
            if 'dist_radius' in mod.__dict__:
                with RedirectStreams(stdout=self.dev_null):
                    pp = mod(**self.spec)

                Rp = np.logspace(np.log10(pp.Rprange[0].to('earthRad').value/10.),np.log10(pp.Rprange[1].to('earthRad').value*100.),100) 

                fr = pp.dist_radius(Rp)
                self.assertTrue(np.all(fr[Rp < pp.Rprange[0].to('earthRad').value] == 0),'dist_radius high bound failed for %s'%mod.__name__)
                self.assertTrue(np.all(fr[Rp > pp.Rprange[1].to('earthRad').value] == 0),'dist_radius high bound failed for %s'%mod.__name__)
                self.assertTrue(np.all(fr[(Rp >= pp.Rprange[0].to('earthRad').value) & (Rp <= pp.Rprange[1].to('earthRad').value)] > 0),'dist_radius generates zero probabilities within range for %s'%mod.__name__) 

def test_dist_mass(self):
        """
        Test that masses outside of the range have zero probability

        """

        for mod in self.allmods:
            if 'dist_mass' in mod.__dict__:
                with RedirectStreams(stdout=self.dev_null):
                    pp = mod(**self.spec)

                Mp = np.logspace(np.log10(pp.Mprange[0].value/10.),np.log10(pp.Mprange[1].value*100.),100) 

                fr = pp.dist_mass(Mp)
                self.assertTrue(np.all(fr[Mp < pp.Mprange[0].value] == 0),'dist_mass high bound failed for %s'%mod.__name__)
                self.assertTrue(np.all(fr[Mp > pp.Mprange[1].value] == 0),'dist_mass high bound failed for %s'%mod.__name__)
                self.assertTrue(np.all(fr[(Mp >= pp.Mprange[0].value) & (Mp <= pp.Mprange[1].value)] > 0)) 

def test_dist_sma_radius(self):
        """
        Test that sma and radius values outside of the range have zero probability
        """
        
        for mod in self.allmods:
            if 'dist_sma_radius' in mod.__dict__:
                with RedirectStreams(stdout=self.dev_null):
                    pp = mod(**self.spec)
                
                a = np.logspace(np.log10(pp.arange[0].value/10.),np.log10(pp.arange[1].value*100),100)
                Rp = np.logspace(np.log10(pp.Rprange[0].value/10.),np.log10(pp.Rprange[1].value*100),100)
                
                aa, RR = np.meshgrid(a,Rp)
                
                fr = pp.dist_sma_radius(aa,RR)
                self.assertTrue(np.all(fr[aa < pp.arange[0].value] == 0),'dist_sma_radius low bound failed on sma for %s'%mod.__name__)
                self.assertTrue(np.all(fr[aa > pp.arange[1].value] == 0),'dist_sma_radius high bound failed on sma for %s'%mod.__name__)
                self.assertTrue(np.all(fr[RR < pp.Rprange[0].value] == 0),'dist_sma_radius low bound failed on radius for %s'%mod.__name__)
                self.assertTrue(np.all(fr[RR > pp.Rprange[1].value] == 0),'dist_sma_radius high bound failed on radius for %s'%mod.__name__)
                self.assertTrue(np.all(fr[(aa > pp.arange[0].value) & (aa < pp.arange[1].value) & (RR > pp.Rprange[0].value) & (RR < pp.Rprange[1].value)] > 0),'dist_sma_radius is improper pdf for %s'%mod.__name__) 

def test_nocross(self):
        # what happens when no gain/phase crossover?
        s = TransferFunction([1, 0], [1])
        h1 = 1/(1+s)
        h2 = 3*(10+s)/(2+s)
        h3 = 0.01*(10-s)/(2+s)/(1+s)
        gm, pm, wm, wg, wp, ws = stability_margins(h1)
        assert_array_almost_equal(
            [gm, pm, wg, wp],
            [float('Inf'), float('Inf'), float('NaN'), float('NaN')]) 
        gm, pm, wm, wg, wp, ws = stability_margins(h2)
        self.assertEqual(pm, float('Inf'))
        gm, pm, wm, wg, wp, ws = stability_margins(h3)
        self.assertTrue(np.isnan(wp))
        omega = np.logspace(-2,2, 100)
        out1b = stability_margins(FRD(h1, omega))
        out2b = stability_margins(FRD(h2, omega))
        out3b = stability_margins(FRD(h3, omega)) 

def test_feedback_args(self):
        # Added 25 May 2019 to cover missing exception handling in feedback()
        # If first argument is not LTI or convertable, generate an exception
        args = ([1], self.sys2)
        self.assertRaises(TypeError, ctrl.feedback, *args)

        # If second argument is not LTI or convertable, generate an exception
        args = (self.sys1, np.array([1]))
        self.assertRaises(TypeError, ctrl.feedback, *args)

        # Convert first argument to FRD, if needed
        h = TransferFunction([1], [1, 2, 2])
        omega = np.logspace(-1, 2, 10)
        frd = ctrl.FRD(h, omega)
        sys = ctrl.feedback(1, frd)
        self.assertTrue(isinstance(sys, ctrl.FRD)) 

def testMIMOSmooth(self):
        sys = StateSpace([[-0.5, 0.0], [0.0, -1.0]],
                         [[1.0, 0.0], [0.0, 1.0]],
                         [[1.0, 0.0], [0.0, 1.0], [1.0, 1.0]],
                         [[0.0, 0.0], [0.0, 0.0], [0.0, 0.0]])
        sys2 = np.matrix([[1, 0, 0], [0, 1, 0]]) * sys
        omega = np.logspace(-1, 2, 10)
        f1 = FRD(sys, omega, smooth=True)
        f2 = FRD(sys2, omega, smooth=True)
        np.testing.assert_array_almost_equal(
            (f1*f2).freqresp([0.1, 1.0, 10])[0],
            (sys*sys2).freqresp([0.1, 1.0, 10])[0])
        np.testing.assert_array_almost_equal(
            (f1*f2).freqresp([0.1, 1.0, 10])[1],
            (sys*sys2).freqresp([0.1, 1.0, 10])[1])
        np.testing.assert_array_almost_equal(
            (f1*f2).freqresp([0.1, 1.0, 10])[2],
            (sys*sys2).freqresp([0.1, 1.0, 10])[2]) 

def test_size_mismatch(self):
        sys1 = FRD(ct.rss(2, 2, 2), np.logspace(-1, 1, 10))

        # Different number of inputs
        sys2 = FRD(ct.rss(3, 1, 2), np.logspace(-1, 1, 10))
        self.assertRaises(ValueError, FRD.__add__, sys1, sys2)

        # Different number of outputs
        sys2 = FRD(ct.rss(3, 2, 1), np.logspace(-1, 1, 10))
        self.assertRaises(ValueError, FRD.__add__, sys1, sys2)

        # Inputs and outputs don't match
        self.assertRaises(ValueError, FRD.__mul__, sys2, sys1)

        # Feedback mismatch
        self.assertRaises(ValueError, FRD.feedback, sys2, sys1) 

def test_evalfr_deprecated(self):
        sys_tf = ct.tf([1], [1, 2, 1])
        frd_tf = FRD(sys_tf, np.logspace(-1, 1, 3))

        # Deprecated version of the call (should generate warning)
        import warnings
        with warnings.catch_warnings():
            # Make warnings generate an exception
            warnings.simplefilter('error')

            # Make sure that we get a pending deprecation warning
            self.assertRaises(PendingDeprecationWarning, frd_tf.evalfr, 1.)

        # FRD.evalfr() is being deprecated
        import warnings
        with warnings.catch_warnings():
            # Make warnings generate an exception
            warnings.simplefilter('error')

            # Make sure that we get a pending deprecation warning
            self.assertRaises(PendingDeprecationWarning, frd_tf.evalfr, 1.) 

def test_custom_bode_default(self):
        ct.config.defaults['bode.dB'] = True
        ct.config.defaults['bode.deg'] = True
        ct.config.defaults['bode.Hz'] = True

        # Generate a Bode plot
        plt.figure()
        omega = np.logspace(-3, 3, 100)
        ct.bode_plot(self.sys, omega, dB=True)
        mag_x, mag_y = (((plt.gcf().axes[0]).get_lines())[0]).get_data()
        np.testing.assert_almost_equal(mag_y[0], 20*log10(10), decimal=3)

        # Override defaults
        plt.figure()
        ct.bode_plot(self.sys, omega, Hz=True, deg=False, dB=True)
        mag_x, mag_y = (((plt.gcf().axes[0]).get_lines())[0]).get_data()
        phase_x, phase_y = (((plt.gcf().axes[1]).get_lines())[0]).get_data()
        np.testing.assert_almost_equal(mag_x[0], 0.001 / (2*pi), decimal=6)
        np.testing.assert_almost_equal(mag_y[0], 20*log10(10), decimal=3)
        np.testing.assert_almost_equal(phase_y[-1], -pi, decimal=2)

        ct.reset_defaults() 

def test_celer_path(sparse_X, alphas, pb):
    """Test Lasso path convergence."""
    X, y = build_dataset(n_samples=30, n_features=50, sparse_X=sparse_X)
    if pb == "logreg":
        y = np.sign(y)
    n_samples = X.shape[0]
    if alphas is not None:
        alpha_max = np.max(np.abs(X.T.dot(y))) / n_samples
        n_alphas = 10
        alphas = alpha_max * np.logspace(0, -2, n_alphas)

    tol = 1e-6
    alphas, coefs, gaps, thetas, n_iters = celer_path(
        X, y, pb, alphas=alphas, tol=tol, return_thetas=True,
        verbose=1, return_n_iter=True)
    np.testing.assert_array_less(gaps, tol)
    # hack because array_less wants strict inequality
    np.testing.assert_array_less(0.99, n_iters) 

def test_warm_start():
    """Test Lasso path convergence."""
    X, y = build_dataset(
        n_samples=100, n_features=100, sparse_X=True)
    n_samples, n_features = X.shape
    alpha_max = np.max(np.abs(X.T.dot(y))) / n_samples
    n_alphas = 10
    alphas = alpha_max * np.logspace(0, -2, n_alphas)

    reg1 = Lasso(tol=1e-6, warm_start=True, p0=10)
    reg1.coef_ = np.zeros(n_features)

    for alpha in alphas:
        reg1.set_params(alpha=alpha)
        reg1.fit(X, y)
        # refitting with warm start should take less than 2 iters:
        reg1.fit(X, y)
        # hack because assert_array_less does strict comparison...
        np.testing.assert_array_less(reg1.n_iter_, 2.01) 

def _define_line_spacing(self, maximum_distance, spacing, as_log=False):
        """
        The user may wish to define the line spacing in either log or
        linear space
        """
        nvals = int(maximum_distance / spacing) + 1
        if as_log:
            spacings = np.logspace(-3., np.log10(maximum_distance), nvals)
            spacings[0] = 0.0
        else:
            spacings = np.linspace(0.0, maximum_distance, nvals)

        if spacings[-1] < (maximum_distance - 1.0E-7):
            spacings = np.hstack([spacings, maximum_distance])

        return spacings 

def PlotEStarRStarTheoretical():
    """
    This makes the theoretical E* vs R* plot. It prints to the current open figure.
    SMM Note: This would be better if it used a supploed figure. Can the default be get_clf()?

    MDH

    """
    # Calculate analytical relationship
    EStar = np.logspace(-1,3,1000)
    RStar = CalculateRStar(EStar)

    # Plot with open figure
    plt.plot(EStar,RStar,'k--')


#-------------------------------------------------------------------------------#
# PLOTTING FUNCTIONS
#-------------------------------------------------------------------------------#
# SMM: Checked and working 13/06/2018 

def __init__(self, base_estimator=LogisticRegression(penalty='l1'), lambda_name='C',
                 lambda_grid=np.logspace(-5, -2, 25), n_bootstrap_iterations=100,
                 sample_fraction=0.5, threshold=0.6, bootstrap_func=bootstrap_without_replacement,
                 bootstrap_threshold=None, verbose=0, n_jobs=1, pre_dispatch='2*n_jobs',
                 random_state=None):
        self.base_estimator = base_estimator
        self.lambda_name = lambda_name
        self.lambda_grid = lambda_grid
        self.n_bootstrap_iterations = n_bootstrap_iterations
        self.sample_fraction = sample_fraction
        self.threshold = threshold
        self.bootstrap_func = bootstrap_func
        self.bootstrap_threshold = bootstrap_threshold
        self.verbose = verbose
        self.n_jobs = n_jobs
        self.pre_dispatch = pre_dispatch
        self.random_state = random_state 

def test_stability_selection_regression():
    n, p, k = 500, 1000, 5

    X, y, important_betas = _generate_dummy_regression_data(n=n, k=k)

    base_estimator = Pipeline([
        ('scaler', StandardScaler()),
        ('model', Lasso())
    ])

    lambdas_grid = np.logspace(-1, 1, num=10)

    selector = StabilitySelection(base_estimator=base_estimator,
                                  lambda_name='model__alpha',
                                  lambda_grid=lambdas_grid)
    selector.fit(X, y)

    chosen_betas = selector.get_support(indices=True)

    assert_almost_equal(important_betas, chosen_betas) 

def test_with_complementary_pairs_bootstrap():
    n, p, k = 500, 1000, 5

    X, y, important_betas = _generate_dummy_regression_data(n=n, k=k)

    base_estimator = Pipeline([
        ('scaler', StandardScaler()),
        ('model', Lasso())
    ])

    lambdas_grid = np.logspace(-1, 1, num=10)

    selector = StabilitySelection(base_estimator=base_estimator,
                                  lambda_name='model__alpha',
                                  lambda_grid=lambdas_grid,
                                  bootstrap_func='complementary_pairs')
    selector.fit(X, y)

    chosen_betas = selector.get_support(indices=True)

    assert_almost_equal(important_betas, chosen_betas) 

def test_different_shape():
    n, p, k = 100, 200, 5

    X, y, important_betas = _generate_dummy_regression_data(n=n, k=k)

    base_estimator = Pipeline([
        ('scaler', StandardScaler()),
        ('model', Lasso())
    ])

    lambdas_grid = np.logspace(-1, 1, num=10)

    selector = StabilitySelection(base_estimator=base_estimator,
                                  lambda_name='model__alpha',
                                  lambda_grid=lambdas_grid)
    selector.fit(X, y)
    selector.transform(X[:, :-2]) 

def test_no_features():
    n, p, k = 100, 200, 0

    X, y, important_betas = _generate_dummy_regression_data(n=n, k=k)

    base_estimator = Pipeline([
        ('scaler', StandardScaler()),
        ('model', Lasso())
    ])

    lambdas_grid = np.logspace(-1, 1, num=10)

    selector = StabilitySelection(base_estimator=base_estimator,
                                  lambda_name='model__alpha',
                                  lambda_grid=lambdas_grid)
    selector.fit(X, y)

    assert_almost_equal(selector.transform(X),
                        np.empty(0).reshape((X.shape[0], 0))) 

def test_stability_plot():
    n, p, k = 500, 200, 5

    X, y, important_betas = _generate_dummy_regression_data(n=n, k=k)

    base_estimator = Pipeline([
        ('scaler', StandardScaler()),
        ('model', Lasso())
    ])

    lambdas_grid = np.logspace(-1, 1, num=10)

    selector = StabilitySelection(base_estimator=base_estimator,
                                  lambda_name='model__alpha',
                                  lambda_grid=lambdas_grid)
    selector.fit(X, y)

    plot_stability_path(selector, threshold_highlight=0.5) 

def example_gail_easy():
    sacred_ex_name = "train_adversarial"
    run_name = "example-gail-easy"
    n_seeds = 1
    search_space = {
        "named_configs": tune.grid_search([[env] for env in EASY_ENVS]),
        "config_updates": {
            "init_trainer_kwargs": {
                "init_rl_kwargs": {
                    "learning_rate": tune.grid_search(np.logspace(3e-6, 1e-1, num=3)),
                    "nminibatches": tune.grid_search([16, 32, 64]),
                },
            },
        },
    }
    base_config_updates = {
        "init_tensorboard": True,
        "init_trainer_kwargs": {"use_gail": True},
    } 

def proxy_a_distance(source_X, target_X, verbose=False):
    """
    Compute the Proxy-A-Distance of a source/target representation
    """
    nb_source = np.shape(source_X)[0]
    nb_target = np.shape(target_X)[0]

    if verbose:
        print('PAD on', (nb_source, nb_target), 'examples')

    C_list = np.logspace(-5, 4, 10)

    half_source, half_target = int(nb_source/2), int(nb_target/2)
    train_X = np.vstack((source_X[0:half_source, :], target_X[0:half_target, :]))
    train_Y = np.hstack((np.zeros(half_source, dtype=int), np.ones(half_target, dtype=int)))

    test_X = np.vstack((source_X[half_source:, :], target_X[half_target:, :]))
    test_Y = np.hstack((np.zeros(nb_source - half_source, dtype=int), np.ones(nb_target - half_target, dtype=int)))

    best_risk = 1.0
    for C in C_list:
        clf = svm.SVC(C=C, kernel='linear', verbose=False)
        clf.fit(train_X, train_Y)

        train_risk = np.mean(clf.predict(train_X) != train_Y)
        test_risk = np.mean(clf.predict(test_X) != test_Y)

        if verbose:
            print('[ PAD C = %f ] train risk: %f  test risk: %f' % (C, train_risk, test_risk))

        if test_risk > .5:
            test_risk = 1. - test_risk

        best_risk = min(best_risk, test_risk)

    return 2 * (1. - 2 * best_risk) 

def log(self, params, total_epoch):
        params = params[0]
        left_range = params[0]
        right_range = params[1]
        np_lr = np.logspace(left_range, right_range, total_epoch)
        lr_factor = [1]
        lr = [np_lr[0]]
        for epoch in range(1, total_epoch):
            lr.append(np_lr[epoch])
            lr_factor.append(np_lr[epoch]/np_lr[epoch-1])
        if lr[0] != args.lr:
            args.lr = lr[0]
        return lr_factor, lr 

def test_target_completeness_def(self):
        """
        Compare calculated completenesses for multiple targets under default population
        settings.
        """
            
        with RedirectStreams(stdout=self.dev_null):
            TL = TargetList(ntargs=100,**copy.deepcopy(self.spec))

            mode = list(filter(lambda mode: mode['detectionMode'] == True, TL.OpticalSystem.observingModes))[0]
            IWA = mode['IWA']
            OWA = mode['OWA']
            rrange = TL.PlanetPopulation.rrange
            maxd = (rrange[1]/np.tan(IWA)).to(u.pc).value
            mind = (rrange[0]/np.tan(OWA)).to(u.pc).value

            #want distances to span from outer edge below IWA to inner edge above OWA
            TL.dist = np.logspace(np.log10(mind/10.),np.log10(maxd*10.),TL.nStars)*u.pc


        Brown = EXOSIMS.Completeness.BrownCompleteness.BrownCompleteness(**copy.deepcopy(self.spec))
        Garrett = EXOSIMS.Completeness.GarrettCompleteness.GarrettCompleteness(**copy.deepcopy(self.spec))

        cBrown = Brown.target_completeness(TL)
        cGarrett = Garrett.target_completeness(TL)
        
        np.testing.assert_allclose(cGarrett,cBrown,rtol=0.1,atol=1e-6)
        
        # test when scaleOrbits == True
        TL.L = np.exp(np.random.uniform(low=np.log(0.1), high=np.log(10.), size=TL.nStars))
        Brown.PlanetPopulation.scaleOrbits = True
        Garrett.PlanetPopulation.scaleOrbits = True

        cBrown = Brown.target_completeness(TL)
        cGarrett = Garrett.target_completeness(TL)

        cGarrett = cGarrett[cBrown != 0 ]
        cBrown = cBrown[cBrown != 0]
        meandiff = np.mean(np.abs(cGarrett - cBrown)/cBrown)

        self.assertLessEqual(meandiff,0.1) 

def eqLogSample(f, numTest, xMin, xMax, bins=10):
    out = np.array([])
    bounds = np.logspace(np.log10(xMin),np.log10(xMax),bins+1)
    for j in np.arange(1,bins+1):
        out = np.concatenate((out,simpSample(f,numTest/bins,bounds[j-1],bounds[j])))
    
    return out 

def __init__(self, pdftype, pdfshape, limits, order, order_max, interaction_order,
                 grid, regularization_factors=np.logspace(-5, 3, 9)):
        super().__init__(pdftype, pdfshape, limits, order, order_max, interaction_order, grid)
        self.regularization_factors = regularization_factors 

def test_stability_margins(self):
        omega = np.logspace(-2, 2, 2000)
        for sys,rgm,rwgm,rpm,rwpm in self.tsys:
            print(sys)
            out = np.array(stability_margins(sys))
            gm, pm, sm, wg, wp, ws = out
            outf = np.array(stability_margins(FRD(sys, omega)))
            print(out,'\n', outf)
            #print(out != np.array(None))
            assert_array_almost_equal(
                out, outf, 2)
        # final one with fixed values
        assert_array_almost_equal(
            [gm, pm, sm, wg, wp, ws],
            self.stability_margins4, 3) 

def test_mag_phase_omega(self):
        # test for bug reported in gh-58
        sys = TransferFunction(15, [1, 6, 11, 6])
        out = stability_margins(sys)
        omega = np.logspace(-2,2,1000)
        mag, phase, omega = sys.freqresp(omega)
        #print( mag, phase, omega)
        out2 = stability_margins((mag, phase*180/np.pi, omega))
        ind = [0,1,3,4]   # indices of gm, pm, wg, wp -- ignore sm
        marg1 = np.array(out)[ind]
        marg2 = np.array(out2)[ind]
        assert_array_almost_equal(marg1, marg2, 4) 

def testOperatorsTf(self):
        # get two SISO transfer functions
        h1 = TransferFunction([1], [1, 2, 2])
        h2 = TransferFunction([1], [0.1, 1])
        omega = np.logspace(-1, 2, 10)
        f1 = FRD(h1, omega)
        f2 = FRD(h2, omega)
        f2  # reference to avoid pyflakes error

        np.testing.assert_array_almost_equal(
            (f1 + h2).freqresp([0.1, 1.0, 10])[0],
            (h1 + h2).freqresp([0.1, 1.0, 10])[0])
        np.testing.assert_array_almost_equal(
            (f1 + h2).freqresp([0.1, 1.0, 10])[1],
            (h1 + h2).freqresp([0.1, 1.0, 10])[1])
        np.testing.assert_array_almost_equal(
            (f1 - h2).freqresp([0.1, 1.0, 10])[0],
            (h1 - h2).freqresp([0.1, 1.0, 10])[0])
        np.testing.assert_array_almost_equal(
            (f1 - h2).freqresp([0.1, 1.0, 10])[1],
            (h1 - h2).freqresp([0.1, 1.0, 10])[1])
        # multiplication and division
        np.testing.assert_array_almost_equal(
            (f1 * h2).freqresp([0.1, 1.0, 10])[1],
            (h1 * h2).freqresp([0.1, 1.0, 10])[1])
        np.testing.assert_array_almost_equal(
            (f1 / h2).freqresp([0.1, 1.0, 10])[1],
            (h1 / h2).freqresp([0.1, 1.0, 10])[1])
        # the reverse does not work 

def testbdalg(self):
        # get two SISO transfer functions
        h1 = TransferFunction([1], [1, 2, 2])
        h2 = TransferFunction([1], [0.1, 1])
        omega = np.logspace(-1, 2, 10)
        f1 = FRD(h1, omega)
        f2 = FRD(h2, omega)

        np.testing.assert_array_almost_equal(
            (bdalg.series(f1, f2)).freqresp([0.1, 1.0, 10])[0],
            (bdalg.series(h1, h2)).freqresp([0.1, 1.0, 10])[0])

        np.testing.assert_array_almost_equal(
            (bdalg.parallel(f1, f2)).freqresp([0.1, 1.0, 10])[0],
            (bdalg.parallel(h1, h2)).freqresp([0.1, 1.0, 10])[0])

        np.testing.assert_array_almost_equal(
            (bdalg.feedback(f1, f2)).freqresp([0.1, 1.0, 10])[0],
            (bdalg.feedback(h1, h2)).freqresp([0.1, 1.0, 10])[0])

        np.testing.assert_array_almost_equal(
            (bdalg.negate(f1)).freqresp([0.1, 1.0, 10])[0],
            (bdalg.negate(h1)).freqresp([0.1, 1.0, 10])[0])

#       append() and connect() not implemented for FRD objects
#        np.testing.assert_array_almost_equal(
#            (bdalg.append(f1, f2)).freqresp([0.1, 1.0, 10])[0],
#            (bdalg.append(h1, h2)).freqresp([0.1, 1.0, 10])[0])
#
#        f3 = bdalg.append(f1, f2, f2)
#        h3 = bdalg.append(h1, h2, h2)
#        Q = np.mat([ [1, 2], [2, -1] ])
#        np.testing.assert_array_almost_equal(
#           (bdalg.connect(f3, Q, [2], [1])).freqresp([0.1, 1.0, 10])[0],
#            (bdalg.connect(h3, Q, [2], [1])).freqresp([0.1, 1.0, 10])[0])