Python matplotlib.pyplot.subplots() Examples

def test_signal_filter():

    signal = np.cos(np.linspace(start=0, stop=10, num=1000))  # Low freq
    signal += np.cos(np.linspace(start=0, stop=100, num=1000))  # High freq
    filtered = nk.signal_filter(signal, highcut=10)
    assert np.std(signal) > np.std(filtered)

    # Generate 10 seconds of signal with 2 Hz oscillation and added 50Hz powerline-noise.
    sampling_rate = 250
    samples = np.arange(10 * sampling_rate)

    signal = np.sin(2 * np.pi * 2 * (samples / sampling_rate))
    powerline = np.sin(2 * np.pi * 50 * (samples / sampling_rate))

    signal_corrupted = signal + powerline
    signal_clean = nk.signal_filter(signal_corrupted, sampling_rate=sampling_rate, method="powerline")

    # import matplotlib.pyplot as plt
    # figure, (ax0, ax1, ax2) = plt.subplots(nrows=3, ncols=1, sharex=True)
    # ax0.plot(signal_corrupted)
    # ax1.plot(signal)
    # ax2.plot(signal_clean * 100)

    assert np.allclose(sum(signal_clean - signal), -2, atol=0.2) 

def plot_test_txt():  # from utils.utils import *; plot_test()
    # Plot test.txt histograms
    x = np.loadtxt('test.txt', dtype=np.float32)
    box = xyxy2xywh(x[:, :4])
    cx, cy = box[:, 0], box[:, 1]

    fig, ax = plt.subplots(1, 1, figsize=(6, 6))
    ax.hist2d(cx, cy, bins=600, cmax=10, cmin=0)
    ax.set_aspect('equal')
    fig.tight_layout()
    plt.savefig('hist2d.jpg', dpi=300)

    fig, ax = plt.subplots(1, 2, figsize=(12, 6))
    ax[0].hist(cx, bins=600)
    ax[1].hist(cy, bins=600)
    fig.tight_layout()
    plt.savefig('hist1d.jpg', dpi=200) 

def sample_images(self, epoch):
        r, c = 5, 5

        z = np.random.normal(size=(r*c, self.latent_dim))
        gen_imgs = self.decoder.predict(z)

        gen_imgs = 0.5 * gen_imgs + 0.5

        fig, axs = plt.subplots(r, c)
        cnt = 0
        for i in range(r):
            for j in range(c):
                axs[i,j].imshow(gen_imgs[cnt, :,:,0], cmap='gray')
                axs[i,j].axis('off')
                cnt += 1
        fig.savefig("images/mnist_%d.png" % epoch)
        plt.close() 

def sample_images(self, epoch):
        r, c = 5, 5
        noise = np.random.normal(0, 1, (r * c, self.latent_dim))
        gen_imgs = self.generator.predict(noise)
        # Rescale images 0 - 1
        gen_imgs = 0.5 * gen_imgs + 0.5

        fig, axs = plt.subplots(r, c)
        cnt = 0
        for i in range(r):
            for j in range(c):
                axs[i,j].imshow(gen_imgs[cnt, :,:,0], cmap='gray')
                axs[i,j].axis('off')
                cnt += 1
        fig.savefig("images/mnist_%d.png" % epoch)
        plt.close() 

def sample_images(self, epoch):
        r, c = 5, 5
        noise = np.random.normal(0, 1, (r * c, self.latent_dim))
        gen_imgs = self.generator.predict(noise)

        # Rescale images 0 - 1
        gen_imgs = 0.5 * gen_imgs + 0.5

        fig, axs = plt.subplots(r, c)
        cnt = 0
        for i in range(r):
            for j in range(c):
                axs[i,j].imshow(gen_imgs[cnt, :,:,0], cmap='gray')
                axs[i,j].axis('off')
                cnt += 1
        fig.savefig("images/%d.png" % epoch)
        plt.close() 

def sample_images(self, epoch):
        r, c = 5, 5
        noise = np.random.normal(0, 1, (r * c, self.latent_dim))
        gen_imgs = self.generator.predict(noise)

        # Rescale images 0 - 1
        gen_imgs = 0.5 * gen_imgs + 0.5

        fig, axs = plt.subplots(r, c)
        cnt = 0
        for i in range(r):
            for j in range(c):
                axs[i,j].imshow(gen_imgs[cnt, :,:,0], cmap='gray')
                axs[i,j].axis('off')
                cnt += 1
        fig.savefig("images/mnist_%d.png" % epoch)
        plt.close() 

def plot_alignment(alignment, gs, dir=hp.logdir):
    """Plots the alignment.

    Args:
      alignment: A numpy array with shape of (encoder_steps, decoder_steps)
      gs: (int) global step.
      dir: Output path.
    """
    if not os.path.exists(dir): os.mkdir(dir)

    fig, ax = plt.subplots()
    im = ax.imshow(alignment)

    fig.colorbar(im)
    plt.title('{} Steps'.format(gs))
    plt.savefig('{}/alignment_{}.png'.format(dir, gs), format='png')
    plt.close(fig) 

def sample_images(self, epoch, batch_i):
        os.makedirs('images/%s' % self.dataset_name, exist_ok=True)
        r, c = 3, 3

        imgs_A, imgs_B = self.data_loader.load_data(batch_size=3, is_testing=True)
        fake_A = self.generator.predict(imgs_B)

        gen_imgs = np.concatenate([imgs_B, fake_A, imgs_A])

        # Rescale images 0 - 1
        gen_imgs = 0.5 * gen_imgs + 0.5

        titles = ['Condition', 'Generated', 'Original']
        fig, axs = plt.subplots(r, c)
        cnt = 0
        for i in range(r):
            for j in range(c):
                axs[i,j].imshow(gen_imgs[cnt])
                axs[i, j].set_title(titles[i])
                axs[i,j].axis('off')
                cnt += 1
        fig.savefig("images/%s/%d_%d.png" % (self.dataset_name, epoch, batch_i))
        plt.close() 

def sample_images(self, epoch):
        r, c = 5, 5
        noise = np.random.normal(0, 1, (r * c, self.latent_dim))
        gen_imgs = self.generator.predict(noise)

        # Rescale images 0 - 1
        gen_imgs = 0.5 * gen_imgs + 0.5

        fig, axs = plt.subplots(r, c)
        cnt = 0
        for i in range(r):
            for j in range(c):
                axs[i,j].imshow(gen_imgs[cnt, :,:,0], cmap='gray')
                axs[i,j].axis('off')
                cnt += 1
        fig.savefig("images/mnist_%d.png" % epoch)
        plt.close() 

def sample_images(self, epoch):
        r, c = 5, 5
        noise = np.random.normal(0, 1, (r * c, self.latent_dim))
        gen_imgs = self.generator.predict(noise)

        # Rescale images 0 - 1
        gen_imgs = 0.5 * gen_imgs + 0.5

        fig, axs = plt.subplots(r, c)
        cnt = 0
        for i in range(r):
            for j in range(c):
                axs[i,j].imshow(gen_imgs[cnt, :,:,0], cmap='gray')
                axs[i,j].axis('off')
                cnt += 1
        fig.savefig("images/mnist_%d.png" % epoch)
        plt.close() 

def sample_images(self, epoch):
        r, c = 10, 10
        noise = np.random.normal(0, 1, (r * c, self.latent_dim))
        sampled_labels = np.array([num for _ in range(r) for num in range(c)])
        gen_imgs = self.generator.predict([noise, sampled_labels])
        # Rescale images 0 - 1
        gen_imgs = 0.5 * gen_imgs + 0.5

        fig, axs = plt.subplots(r, c)
        cnt = 0
        for i in range(r):
            for j in range(c):
                axs[i,j].imshow(gen_imgs[cnt,:,:,0], cmap='gray')
                axs[i,j].axis('off')
                cnt += 1
        fig.savefig("images/%d.png" % epoch)
        plt.close() 

def plot_results(start=0, stop=0):  # from utils.utils import *; plot_results()
    # Plot training results files 'results*.txt'
    fig, ax = plt.subplots(2, 5, figsize=(14, 7))
    ax = ax.ravel()
    s = ['GIoU', 'Objectness', 'Classification', 'Precision', 'Recall',
         'val GIoU', 'val Objectness', 'val Classification', 'mAP', 'F1']
    for f in sorted(glob.glob('results*.txt') + glob.glob('../../Downloads/results*.txt')):
        results = np.loadtxt(f, usecols=[2, 3, 4, 8, 9, 12, 13, 14, 10, 11], ndmin=2).T
        n = results.shape[1]  # number of rows
        x = range(start, min(stop, n) if stop else n)
        for i in range(10):
            y = results[i, x]
            if i in [0, 1, 2, 5, 6, 7]:
                y[y == 0] = np.nan  # dont show zero loss values
            ax[i].plot(x, y, marker='.', label=f.replace('.txt', ''))
            ax[i].set_title(s[i])
            if i in [5, 6, 7]:  # share train and val loss y axes
                ax[i].get_shared_y_axes().join(ax[i], ax[i - 5])

    fig.tight_layout()
    ax[1].legend()
    fig.savefig('results.png', dpi=200) 

def sample_images(self, epoch, imgs):
        r, c = 3, 6

        masked_imgs = self.mask_randomly(imgs)
        gen_imgs = self.generator.predict(masked_imgs)

        imgs = (imgs + 1.0) * 0.5
        masked_imgs = (masked_imgs + 1.0) * 0.5
        gen_imgs = (gen_imgs + 1.0) * 0.5

        gen_imgs = np.where(gen_imgs < 0, 0, gen_imgs)

        fig, axs = plt.subplots(r, c)
        for i in range(c):
            axs[0,i].imshow(imgs[i, :, :, 0], cmap='gray')
            axs[0,i].axis('off')
            axs[1,i].imshow(masked_imgs[i, :, :, 0], cmap='gray')
            axs[1,i].axis('off')
            axs[2,i].imshow(gen_imgs[i, :, :, 0], cmap='gray')
            axs[2,i].axis('off')
        fig.savefig("images/%d.png" % epoch)
        plt.close() 

def sample_images(self, epoch, imgs):
        r, c = 3, 6

        masked_imgs, missing_parts, (y1, y2, x1, x2) = self.mask_randomly(imgs)
        gen_missing = self.generator.predict(masked_imgs)

        imgs = 0.5 * imgs + 0.5
        masked_imgs = 0.5 * masked_imgs + 0.5
        gen_missing = 0.5 * gen_missing + 0.5

        fig, axs = plt.subplots(r, c)
        for i in range(c):
            axs[0,i].imshow(imgs[i, :,:])
            axs[0,i].axis('off')
            axs[1,i].imshow(masked_imgs[i, :,:])
            axs[1,i].axis('off')
            filled_in = imgs[i].copy()
            filled_in[y1[i]:y2[i], x1[i]:x2[i], :] = gen_missing[i]
            axs[2,i].imshow(filled_in)
            axs[2,i].axis('off')
        fig.savefig("images/%d.png" % epoch)
        plt.close() 

def sample_images(self, epoch):
        r, c = 5, 5
        noise = np.random.normal(0, 1, (r * c, self.latent_dim))
        gen_imgs = self.generator.predict(noise)

        # Rescale images 0 - 1
        gen_imgs = 0.5 * gen_imgs + 0.5

        fig, axs = plt.subplots(r, c)
        cnt = 0
        for i in range(r):
            for j in range(c):
                axs[i,j].imshow(gen_imgs[cnt, :,:,0], cmap='gray')
                axs[i,j].axis('off')
                cnt += 1
        fig.savefig("images/mnist_%d.png" % epoch)
        plt.close() 

def plot_results_overlay(start=0, stop=0):  # from utils.utils import *; plot_results_overlay()
    # Plot training results files 'results*.txt', overlaying train and val losses
    s = ['train', 'train', 'train', 'Precision', 'mAP', 'val', 'val', 'val', 'Recall', 'F1']  # legends
    t = ['GIoU', 'Objectness', 'Classification', 'P-R', 'mAP-F1']  # titles
    for f in sorted(glob.glob('results*.txt') + glob.glob('../../Downloads/results*.txt')):
        results = np.loadtxt(f, usecols=[2, 3, 4, 8, 9, 12, 13, 14, 10, 11], ndmin=2).T
        n = results.shape[1]  # number of rows
        x = range(start, min(stop, n) if stop else n)
        fig, ax = plt.subplots(1, 5, figsize=(14, 3.5))
        ax = ax.ravel()
        for i in range(5):
            for j in [i, i + 5]:
                y = results[j, x]
                if i in [0, 1, 2]:
                    y[y == 0] = np.nan  # dont show zero loss values
                ax[i].plot(x, y, marker='.', label=s[j])
            ax[i].set_title(t[i])
            ax[i].legend()
            ax[i].set_ylabel(f) if i == 0 else None  # add filename
        fig.tight_layout()
        fig.savefig(f.replace('.txt', '.png'), dpi=200) 

def figures(ext, show):

    for name, df in TablesRecorder.generate_dataframes('thames_output.h5'):
        df.columns = ['Very low', 'Low', 'Central', 'High', 'Very high']

        fig, (ax1, ax2) = plt.subplots(figsize=(12, 4), ncols=2, sharey='row',
                                       gridspec_kw={'width_ratios': [3, 1]})
        df['2100':'2125'].plot(ax=ax1)
        df.quantile(np.linspace(0, 1)).plot(ax=ax2)

        if name.startswith('reservoir'):
            ax1.set_ylabel('Volume [$Mm^3$]')
        else:
            ax1.set_ylabel('Flow [$Mm^3/day$]')

        for ax in (ax1, ax2):
            ax.set_title(name)
            ax.grid(True)
        plt.tight_layout()

        if ext is not None:
            fig.savefig(f'{name}.{ext}', dpi=300)

    if show:
        plt.show() 

def _embedding_dimension_plot(
    method, dimension_seq, min_dimension, E1=None, E2=None, f1=None, f2=None, f3=None, ax=None
):

    if ax is None:
        fig, ax = plt.subplots()
    else:
        fig = None
    ax.set_title("Optimization of Dimension (d)")
    ax.set_xlabel("Embedding dimension $d$")
    ax.set_ylabel("$E_1(d)$ and $E_2(d)$")
    if method in ["afnn"]:
        ax.plot(dimension_seq[:-1], E1, "bo-", label="$E_1(d)$", color="#FF5722")
        ax.plot(dimension_seq[:-1], E2, "go-", label="$E_2(d)$", color="#f44336")

    if method in ["fnn"]:
        ax.plot(dimension_seq, 100 * f1, "bo--", label="Test I", color="#FF5722")
        ax.plot(dimension_seq, 100 * f2, "g^--", label="Test II", color="#f44336")
        ax.plot(dimension_seq, 100 * f3, "rs-", label="Test I + II", color="#852b01")

    ax.axvline(x=min_dimension, color="#E91E63", label="Optimal dimension: " + str(min_dimension))
    ax.legend(loc="upper right")

    return fig 

def plot_species(statistics, view=False, filename='speciation.svg'):
    """ Visualizes speciation throughout evolution. """
    if plt is None:
        warnings.warn("This display is not available due to a missing optional dependency (matplotlib)")
        return

    species_sizes = statistics.get_species_sizes()
    num_generations = len(species_sizes)
    curves = np.array(species_sizes).T

    fig, ax = plt.subplots()
    ax.stackplot(range(num_generations), *curves)

    plt.title("Speciation")
    plt.ylabel("Size per Species")
    plt.xlabel("Generations")

    plt.savefig(filename)

    if view:
        plt.show()

    plt.close() 

def plot_species(statistics, view=False, filename='speciation.svg'):
    """ Visualizes speciation throughout evolution. """
    if plt is None:
        warnings.warn("This display is not available due to a missing optional dependency (matplotlib)")
        return

    species_sizes = statistics.get_species_sizes()
    num_generations = len(species_sizes)
    curves = np.array(species_sizes).T

    fig, ax = plt.subplots()
    ax.stackplot(range(num_generations), *curves)

    plt.title("Speciation")
    plt.ylabel("Size per Species")
    plt.xlabel("Generations")

    plt.savefig(filename)

    if view:
        plt.show()

    plt.close() 

def plot_alignment(alignment, gs, dir=hp.logdir):
    """Plots the alignment.

    Args:
      alignment: A numpy array with shape of (encoder_steps, decoder_steps)
      gs: (int) global step.
      dir: Output path.
    """
    if not os.path.exists(dir): os.mkdir(dir)

    fig, ax = plt.subplots()
    im = ax.imshow(alignment)

    fig.colorbar(im)
    plt.title('{} Steps'.format(gs))
    plt.savefig('{}/alignment_{}.png'.format(dir, gs), format='png') 

def plot_species(statistics, view=False, filename='speciation.svg'):
    """ Visualizes speciation throughout evolution. """
    if plt is None:
        warnings.warn("This display is not available due to a missing optional dependency (matplotlib)")
        return

    species_sizes = statistics.get_species_sizes()
    num_generations = len(species_sizes)
    curves = np.array(species_sizes).T

    fig, ax = plt.subplots()
    ax.stackplot(range(num_generations), *curves)

    plt.title("Speciation")
    plt.ylabel("Size per Species")
    plt.xlabel("Generations")

    plt.savefig(filename)

    if view:
        plt.show()

    plt.close() 

def plot_species(statistics, view=False, filename='speciation.svg'):
    """ Visualizes speciation throughout evolution. """
    if plt is None:
        warnings.warn("This display is not available due to a missing optional dependency (matplotlib)")
        return

    species_sizes = statistics.get_species_sizes()
    num_generations = len(species_sizes)
    curves = np.array(species_sizes).T

    fig, ax = plt.subplots()
    ax.stackplot(range(num_generations), *curves)

    plt.title("Speciation")
    plt.ylabel("Size per Species")
    plt.xlabel("Generations")

    plt.savefig(filename)

    if view:
        plt.show()

    plt.close() 

def plot_attention(sentences, attentions, labels, **kwargs):
    fig, ax = plt.subplots(**kwargs)
    im = ax.imshow(attentions, interpolation='nearest',
                   vmin=attentions.min(), vmax=attentions.max())
    plt.colorbar(im, shrink=0.5, ticks=[0, 1])
    plt.setp(ax.get_xticklabels(), rotation=45, ha="right",
             rotation_mode="anchor")
    ax.set_yticks(range(len(labels)))
    ax.set_yticklabels(labels, fontproperties=getChineseFont())
    # Loop over data dimensions and create text annotations.
    for i in range(attentions.shape[0]):
        for j in range(attentions.shape[1]):
            text = ax.text(j, i, sentences[i][j],
                           ha="center", va="center", color="b", size=10,
                           fontproperties=getChineseFont())

    ax.set_title("Attention Visual")
    fig.tight_layout()
    plt.show() 

def generator(vis=False):
    image_list = np.array(get_training_data())
    print('{} training images in {}'.format(image_list.shape[0], DATA_FOLDER))
    index = np.arange(0, image_list.shape[0])
    while True:
        np.random.shuffle(index)
        for i in index:
            try:
                im_fn = image_list[i]
                im = cv2.imread(im_fn)
                h, w, c = im.shape
                im_info = np.array([h, w, c]).reshape([1, 3])

                _, fn = os.path.split(im_fn)
                fn, _ = os.path.splitext(fn)
                txt_fn = os.path.join(DATA_FOLDER, "label", fn + '.txt')
                if not os.path.exists(txt_fn):
                    print("Ground truth for image {} not exist!".format(im_fn))
                    continue
                bbox = load_annoataion(txt_fn)
                if len(bbox) == 0:
                    print("Ground truth for image {} empty!".format(im_fn))
                    continue

                if vis:
                    for p in bbox:
                        cv2.rectangle(im, (p[0], p[1]), (p[2], p[3]), color=(0, 0, 255), thickness=1)
                    fig, axs = plt.subplots(1, 1, figsize=(30, 30))
                    axs.imshow(im[:, :, ::-1])
                    axs.set_xticks([])
                    axs.set_yticks([])
                    plt.tight_layout()
                    plt.show()
                    plt.close()
                yield [im], bbox, im_info

            except Exception as e:
                print(e)
                continue 

def plot_species(statistics, view=False, filename='speciation.svg'):
    """ Visualizes speciation throughout evolution. """
    if plt is None:
        warnings.warn("This display is not available due to a missing optional dependency (matplotlib)")
        return

    species_sizes = statistics.get_species_sizes()
    num_generations = len(species_sizes)
    curves = np.array(species_sizes).T

    fig, ax = plt.subplots()
    ax.stackplot(range(num_generations), *curves)

    plt.title("Speciation")
    plt.ylabel("Size per Species")
    plt.xlabel("Generations")

    plt.savefig(filename)

    if view:
        plt.show()

    plt.close() 

def analyze(context=None, results=None):
        
    f, (ax1, ax2, ax3) = plt.subplots(3, sharex = True)        
    ax1.plot(results.portfolio_value, linewidth = 2.0, label = 'porfolio')
    ax1.set_title('On-Line Moving Average Reversion')
    ax1.set_ylabel('Portfolio value (USD)')
    ax1.legend(loc=0)
    ax1.grid(True)
            
    ax2.plot(results['AAPL'], color = 'b', linestyle = '-', linewidth = 2.0, label = 'AAPL')
    ax2.plot(results['MSFT'], color = 'r', linestyle = '-', linewidth = 2.0, label = 'MSFT')
    ax2.set_ylabel('stock price (USD)')
    ax2.legend(loc=0)
    ax2.grid(True)
    
    ax3.semilogy(results['step_size'], color = 'b', linestyle = '-', linewidth = 2.0, label = 'step-size')
    ax3.semilogy(results['variability'], color = 'r', linestyle = '-', linewidth = 2.0, label = 'variability')
    ax3.legend(loc=0)
    ax3.grid(True)
    
    plt.show() 

def analyze(context=None, results=None, benchmark=None):
    
    hist_size = 300
        
    f, (ax1, ax2) = plt.subplots(2, sharex = True)        
    ax1.plot(results.portfolio_value[hist_size:], linewidth = 2.0, label = 'porfolio')
    ax1.set_title('Dual Moving Average Strategy')
    ax1.set_ylabel('Portfolio value (USD)')
    ax1.legend(loc=0)
    ax1.grid(True)
    
    ax2.plot(results['AAPL'][hist_size:], linewidth = 2.0, label = 'AAPL')
    ax2.plot(results['short_mavg'][hist_size:], color = 'r', linestyle = '-', linewidth = 2.0, label = 'short mavg')
    ax2.plot(results['long_mavg'][hist_size:], color = 'g', linestyle = '-', linewidth = 2.0, label = 'long mavg')
    ax2.set_ylabel('AAPL price (USD)')
    ax2.legend(loc=0)
    ax2.grid(True)

    plt.show() 

def visualize(problem, x, fig=None, ax=None, show=True, label=True):
    with plt.style.context('ggplot'):

        if fig is None or ax is None:
            fig, ax = plt.subplots()

        # plot cities using scatter plot
        ax.scatter(problem.cities[:, 0], problem.cities[:, 1], s=250)
        if label:
            # annotate cities
            for i, c in enumerate(problem.cities):
                ax.annotate(str(i), xy=c, fontsize=10, ha="center", va="center", color="white")

        # plot the line on the path
        for i in range(len(x)):
            current = x[i]
            next_ = x[(i + 1) % len(x)]
            ax.plot(problem.cities[[current, next_], 0], problem.cities[[current, next_], 1], 'r--')

        fig.suptitle("Route length: %.4f" % problem.get_route_length(x))

        if show:
            fig.show() 

def plot_contour(self, w=0.0):
    """
      Plot contour with poles of Green's function in the self-energy 
      SelfEnergy(w) = G(w+w')W(w')
      with respect to w' = Re(w')+Im(w')
      Poles of G(w+w') are located: w+w'-(E_n-Fermi)+i*eps sign(E_n-Fermi)==0 ==> 
      w'= (E_n-Fermi) - w -i eps sign(E_n-Fermi)
    """
    try :
      import matplotlib.pyplot as plt
      from matplotlib.patches import Arc, Arrow 
    except:
      print('no matplotlib?')
      return

    fig,ax = plt.subplots()
    fe = self.fermi_energy
    ee = self.mo_energy
    iee = 0.5-np.array(ee>fe)
    eew = ee-fe-w
    ax.plot(eew, iee, 'r.', ms=10.0)
    pp = list()
    pp.append(Arc((0,0),4,4,angle=0, linewidth=2, theta1=0, theta2=90, zorder=2, color='b'))
    pp.append(Arc((0,0),4,4,angle=0, linewidth=2, theta1=180, theta2=270, zorder=2, color='b'))
    pp.append(Arrow(0,2,0,-4,width=0.2, color='b', hatch='o'))
    pp.append(Arrow(-2,0,4,0,width=0.2, color='b', hatch='o'))
    for p in pp: ax.add_patch(p)
    ax.set_aspect('equal')
    ax.grid(True, which='both')
    ax.axhline(y=0, color='k')
    ax.axvline(x=0, color='k')
    plt.ylim(-3.0,3.0)
    plt.show()