Python matplotlib.pylab.grid() Examples

def plot_metrics(metric_list, save_path=None):
    # runs through each test case and adds a set of bars to a plot.  Saves

    f, (ax1) = plt.subplots(1, 1)
    plt.grid(True)

    print_metrics(metric_list)

    bar_metrics(metric_list[0], ax1, index=0)
    bar_metrics(metric_list[1], ax1, index=1)
    bar_metrics(metric_list[2], ax1, index=2)

    if save_path is None:
        save_path = "img/bar_" + key + ".png"

    plt.savefig(save_path, dpi=400) 

def plot_clustering(x, y, title, mx=None, ymax=None, xmin=None, km=None):
    pylab.figure(num=None, figsize=(8, 6))
    if km:
        pylab.scatter(x, y, s=50, c=km.predict(list(zip(x, y))))
    else:
        pylab.scatter(x, y, s=50)

    pylab.title(title)
    pylab.xlabel("Occurrence word 1")
    pylab.ylabel("Occurrence word 2")

    pylab.autoscale(tight=True)
    pylab.ylim(ymin=0, ymax=1)
    pylab.xlim(xmin=0, xmax=1)
    pylab.grid(True, linestyle='-', color='0.75')

    return pylab 

def plot(traj, x, y, **kwargs):
    """ Create a matplotlib plot of property x against property y

    Args:
        x,y (str): names of the properties
        **kwargs (dict): kwargs for :meth:`matplotlib.pylab.plot`

    Returns:
        List[matplotlib.lines.Lines2D]: the lines that were plotted

    """
    from matplotlib import pylab
    xl = yl = None
    if type(x) is str:
        strx = x
        x = getattr(traj, x)
        xl = '%s / %s' % (strx, getattr(x, 'units', 'dimensionless'))
    if type(y) is str:
        stry = y
        y = getattr(traj, y)
        yl = '%s / %s' % (stry, getattr(y, 'units', 'dimensionless'))
    plt = pylab.plot(x, y, **kwargs)
    pylab.xlabel(xl); pylab.ylabel(yl); pylab.grid()
    return plt 

def plot_performance_profiles(problems, solvers):
    """
    Plot performance profiles in matplotlib for specified problems and solvers
    """
    # Remove OSQP polish solver
    solvers = solvers.copy()
    for s in solvers:
        if "polish" in s:
            solvers.remove(s)

    df = pd.read_csv('./results/%s/performance_profiles.csv' % problems)
    plt.figure(0)
    for solver in solvers:
        plt.plot(df["tau"], df[solver], label=solver)
    plt.xlim(1., 10000.)
    plt.ylim(0., 1.)
    plt.xlabel(r'Performance ratio $\tau$')
    plt.ylabel('Ratio of problems solved')
    plt.xscale('log')
    plt.legend()
    plt.grid()
    plt.show(block=False)
    results_file = './results/%s/%s.png' % (problems, problems)
    print("Saving plots to %s" % results_file)
    plt.savefig(results_file) 

def plot_roc(auc_score, name, tpr, fpr, label=None):
    pylab.clf()
    pylab.figure(num=None, figsize=(5, 4))
    pylab.grid(True)
    pylab.plot([0, 1], [0, 1], 'k--')
    pylab.plot(fpr, tpr)
    pylab.fill_between(fpr, tpr, alpha=0.5)
    pylab.xlim([0.0, 1.0])
    pylab.ylim([0.0, 1.0])
    pylab.xlabel('False Positive Rate')
    pylab.ylabel('True Positive Rate')
    pylab.title('ROC curve (AUC = %0.2f) / %s' %
                (auc_score, label), verticalalignment="bottom")
    pylab.legend(loc="lower right")
    filename = name.replace(" ", "_")
    pylab.savefig(
        os.path.join(CHART_DIR, "roc_" + filename + ".png"), bbox_inches="tight") 

def plot_pr(auc_score, precision, recall, label=None, figure_path=None):
    """绘制R/P曲线"""
    try:
        from matplotlib import pylab
        pylab.figure(num=None, figsize=(6, 5))
        pylab.xlim([0.0, 1.0])
        pylab.ylim([0.0, 1.0])
        pylab.xlabel('Recall')
        pylab.ylabel('Precision')
        pylab.title('P/R (AUC=%0.2f) / %s' % (auc_score, label))
        pylab.fill_between(recall, precision, alpha=0.5)
        pylab.grid(True, linestyle='-', color='0.75')
        pylab.plot(recall, precision, lw=1)
        pylab.savefig(figure_path)
    except Exception as e:
        print("save image error with matplotlib")
        pass 

def plot_entropy():
    pylab.clf()
    pylab.figure(num=None, figsize=(5, 4))

    title = "Entropy $H(X)$"
    pylab.title(title)
    pylab.xlabel("$P(X=$coin will show heads up$)$")
    pylab.ylabel("$H(X)$")

    pylab.xlim(xmin=0, xmax=1.1)
    x = np.arange(0.001, 1, 0.001)
    y = -x * np.log2(x) - (1 - x) * np.log2(1 - x)
    pylab.plot(x, y)
    # pylab.xticks([w*7*24 for w in [0,1,2,3,4]], ['week %i'%(w+1) for w in
    # [0,1,2,3,4]])

    pylab.autoscale(tight=True)
    pylab.grid(True)

    filename = "entropy_demo.png"
    pylab.savefig(os.path.join(CHART_DIR, filename), bbox_inches="tight") 

def plotKChart(self, misClassDict, saveFigPath):
        kList = []
        misRateList = []
        for k, misClassNum in misClassDict.iteritems():
            kList.append(k)
            misRateList.append(1.0 - 1.0/k*misClassNum)

        fig = plt.figure(saveFigPath)
        plt.plot(kList, misRateList, 'r--')
        plt.title(saveFigPath)
        plt.xlabel('k Num.')
        plt.ylabel('Misclassified Rate')
        plt.legend(saveFigPath)
        plt.grid(True)
        plt.savefig(saveFigPath)
        plt.show()

################################### PART3 TEST ########################################
# 例子 

def plot_pr_curve(pr_curve_dml, pr_curve_base, title):
    """
      Function that plots the PR-curve.

      Args:
        pr_curve: the values of precision for each recall value
        title: the title of the plot
    """
    plt.figure(figsize=(16, 9))
    plt.plot(np.arange(0.0, 1.05, 0.05),
             pr_curve_base, color='r', marker='o', linewidth=3, markersize=10)
    plt.plot(np.arange(0.0, 1.05, 0.05),
             pr_curve_dml, color='b', marker='o', linewidth=3, markersize=10)
    plt.grid(True, linestyle='dotted')
    plt.xlabel('Recall', color='k', fontsize=27)
    plt.ylabel('Precision', color='k', fontsize=27)
    plt.yticks(color='k', fontsize=20)
    plt.xticks(color='k', fontsize=20)
    plt.ylim([0.0, 1.05])
    plt.xlim([0.0, 1.0])
    plt.title(title, color='k', fontsize=27)
    plt.tight_layout()
    plt.show() 

def freq_resp(self, mode= 'dB', fs = 8000, ylim = [-100,2]):
        """

        """
        fir_d.freqz_resp_list([self.b],[1], mode, fs=fs, Npts = 1024)
        pylab.grid()
        pylab.ylim(ylim) 

def plot_pr(auc_score, name, precision, recall, label=None):
    pylab.figure(num=None, figsize=(6, 5))
    pylab.xlim([0.0, 1.0])
    pylab.ylim([0.0, 1.0])
    pylab.xlabel('Recall')
    pylab.ylabel('Precision')
    pylab.title('P/R (AUC=%0.2f) / %s' % (auc_score, label))
    pylab.fill_between(recall, precision, alpha=0.5)
    pylab.grid(True, linestyle='-', color='0.75')
    pylab.plot(recall, precision, lw=1)
    filename = name.replace(" ", "_")
    pylab.savefig(os.path.join(CHART_DIR, "pr_" + filename + ".png")) 

def plot_bias_variance(data_sizes, train_errors, test_errors, name, title):
    pylab.figure(num=None, figsize=(6, 5))
    pylab.ylim([0.0, 1.0])
    pylab.xlabel('Data set size')
    pylab.ylabel('Error')
    pylab.title("Bias-Variance for '%s'" % name)
    pylab.plot(
        data_sizes, test_errors, "--", data_sizes, train_errors, "b-", lw=1)
    pylab.legend(["test error", "train error"], loc="upper right")
    pylab.grid(True, linestyle='-', color='0.75')
    pylab.savefig(
        os.path.join(CHART_DIR, "bv_" + name.replace(" ", "_") + ".png"), bbox_inches="tight") 

def plot_k_complexity(ks, train_errors, test_errors):
    pylab.figure(num=None, figsize=(6, 5))
    pylab.ylim([0.0, 1.0])
    pylab.xlabel('k')
    pylab.ylabel('Error')
    pylab.title('Errors for for different values of $k$')
    pylab.plot(
        ks, test_errors, "--", ks, train_errors, "-", lw=1)
    pylab.legend(["test error", "train error"], loc="upper right")
    pylab.grid(True, linestyle='-', color='0.75')
    pylab.savefig(
        os.path.join(CHART_DIR, "kcomplexity.png"), bbox_inches="tight") 

def plot_feat_hist(data_name_list, filename=None):
    if len(data_name_list) > 1:
        assert filename is not None

    pylab.figure(num=None, figsize=(8, 6))
    num_rows = int(1 + (len(data_name_list) - 1) / 2)
    num_cols = int(1 if len(data_name_list) == 1 else 2)
    pylab.figure(figsize=(5 * num_cols, 4 * num_rows))

    for i in range(num_rows):
        for j in range(num_cols):
            pylab.subplot(num_rows, num_cols, 1 + i * num_cols + j)
            x, name = data_name_list[i * num_cols + j]
            pylab.title(name)
            pylab.xlabel('Value')
            pylab.ylabel('Fraction')
            # the histogram of the data
            max_val = np.max(x)
            if max_val <= 1.0:
                bins = 50
            elif max_val > 50:
                bins = 50
            else:
                bins = max_val
            n, bins, patches = pylab.hist(
                x, bins=bins, normed=1, alpha=0.75)

            pylab.grid(True)

    if not filename:
        filename = "feat_hist_%s.png" % name.replace(" ", "_")

    pylab.savefig(os.path.join(CHART_DIR, filename), bbox_inches="tight") 

def freq_resp(self, mode= 'dB', fs = 8000, ylim = [-100,2]):
        """
        Frequency response plot
        """
        iir_d.freqz_resp_cas_list([self.sos],mode,fs=fs)
        pylab.grid()
        pylab.ylim(ylim) 

def plot_values(cls, num_events, **scheduler_kwargs):
        """Method to plot simulated scheduled values during `num_events` events.

        This class requires `matplotlib package <https://matplotlib.org/>`_ to be installed:

        .. code-block:: bash

            pip install matplotlib

        Args:
            num_events (int): number of events during the simulation.
            **scheduler_kwargs : parameter scheduler configuration kwargs.

        Returns:
            matplotlib.lines.Line2D

        Examples:

            .. code-block:: python

                import matplotlib.pylab as plt

                plt.figure(figsize=(10, 7))
                LinearCyclicalScheduler.plot_values(num_events=50, param_name='lr',
                                                    start_value=1e-1, end_value=1e-3, cycle_size=10))
        """
        try:
            import matplotlib.pylab as plt
        except ImportError:
            raise RuntimeError(
                "This method requires matplotlib to be installed. "
                "Please install it with command: \n pip install matplotlib"
            )

        values = cls.simulate_values(num_events=num_events, **scheduler_kwargs)
        label = scheduler_kwargs.get("param_name", "learning rate")
        ax = plt.plot([e for e, _ in values], [v for _, v in values], label=label)
        plt.legend()
        plt.grid(which="both")
        return ax 

def plotModelResults(model, X_train, X_test,y_train,y_test, plot_intervals=False, plot_anomalies=False, scale=1.96):
    """
        Plots modelled vs fact values, prediction intervals and anomalies
    
    """
    
    prediction = model.predict(X_test)
    
    plt.figure(figsize=(15, 7))
    plt.plot(prediction, "g", label="prediction", linewidth=2.0)
    plt.plot(y_test.values, label="actual", linewidth=2.0)
    
    if plot_intervals:
        cv = cross_val_score(model, X_train, y_train, 
                                    cv=tscv, 
                                    scoring="neg_mean_squared_error")
        #mae = cv.mean() * (-1)
        deviation = np.sqrt(cv.std())
        
        lower = prediction - (scale * deviation)
        upper = prediction + (scale * deviation)
        
        plt.plot(lower, "r--", label="upper bond / lower bond", alpha=0.5)
        plt.plot(upper, "r--", alpha=0.5)
        
        if plot_anomalies:
            anomalies = np.array([np.NaN]*len(y_test))
            anomalies[y_test<lower] = y_test[y_test<lower]
            anomalies[y_test>upper] = y_test[y_test>upper]
            plt.plot(anomalies, "o", markersize=10, label = "Anomalies")
    
    error = mean_absolute_percentage_error(prediction, y_test)
    plt.title("Mean absolute percentage error {0:.2f}%".format(error))
    plt.legend(loc="best")
    plt.tight_layout()
    plt.grid(True); 

def plotCoefficients(model,X_train):
    """
        Plots sorted coefficient values of the model
    """
    
    coefs = pd.DataFrame(model.coef_, X_train.columns)
    coefs.columns = ["coef"]
    coefs["abs"] = coefs.coef.apply(np.abs)
    coefs = coefs.sort_values(by="abs", ascending=False).drop(["abs"], axis=1)
    
    plt.figure(figsize=(15, 7))
    coefs.coef.plot(kind='bar')
    plt.grid(True, axis='y')
    plt.hlines(y=0, xmin=0, xmax=len(coefs), linestyles='dashed'); 

def plot_feat_hist(data_name_list, filename=None):
    pylab.clf()
    num_rows = 1 + (len(data_name_list) - 1) / 2
    num_cols = 1 if len(data_name_list) == 1 else 2
    pylab.figure(figsize=(5 * num_cols, 4 * num_rows))

    for i in range(num_rows):
        for j in range(num_cols):
            pylab.subplot(num_rows, num_cols, 1 + i * num_cols + j)
            x, name = data_name_list[i * num_cols + j]
            pylab.title(name)
            pylab.xlabel('Value')
            pylab.ylabel('Density')
            # the histogram of the data
            max_val = np.max(x)
            if max_val <= 1.0:
                bins = 50
            elif max_val > 50:
                bins = 50
            else:
                bins = max_val
            n, bins, patches = pylab.hist(
                x, bins=bins, normed=1, facecolor='green', alpha=0.75)

            pylab.grid(True)

    if not filename:
        filename = "feat_hist_%s.png" % name

    pylab.savefig(os.path.join(CHART_DIR, filename), bbox_inches="tight") 

def plot_log():
    pylab.clf()

    x = np.arange(0.001, 1, 0.001)
    y = np.log(x)

    pylab.title('Relationship between probabilities and their logarithm')
    pylab.plot(x, y)
    pylab.grid(True)
    pylab.xlabel('P')
    pylab.ylabel('log(P)')
    filename = 'log_probs.png'
    pylab.savefig(os.path.join(CHART_DIR, filename), bbox_inches="tight") 

def plot_pr(auc_score, name, precision, recall, label=None):
    pylab.clf()
    pylab.figure(num=None, figsize=(5, 4))
    pylab.grid(True)
    pylab.fill_between(recall, precision, alpha=0.5)
    pylab.plot(recall, precision, lw=1)
    pylab.xlim([0.0, 1.0])
    pylab.ylim([0.0, 1.0])
    pylab.xlabel('Recall')
    pylab.ylabel('Precision')
    pylab.title('P/R curve (AUC = %0.2f) / %s' % (auc_score, label))
    filename = name.replace(" ", "_")
    pylab.savefig(
        os.path.join(CHART_DIR, "pr_" + filename + ".png"), bbox_inches="tight") 

def plot_pr(auc_score, name, phase, precision, recall, label=None):
    pylab.clf()
    pylab.figure(num=None, figsize=(5, 4))
    pylab.grid(True)
    pylab.fill_between(recall, precision, alpha=0.5)
    pylab.plot(recall, precision, lw=1)
    pylab.xlim([0.0, 1.0])
    pylab.ylim([0.0, 1.0])
    pylab.xlabel('Recall')
    pylab.ylabel('Precision')
    pylab.title('P/R curve (AUC=%0.2f) / %s' % (auc_score, label))
    filename = name.replace(" ", "_")
    pylab.savefig(os.path.join(CHART_DIR, "pr_%s_%s.png" %
                  (filename, phase)), bbox_inches="tight") 

def plot_log():
    pylab.clf()
    pylab.figure(num=None, figsize=(6, 5))

    x = np.arange(0.001, 1, 0.001)
    y = np.log(x)

    pylab.title('Relationship between probabilities and their logarithm')
    pylab.plot(x, y)
    pylab.grid(True)
    pylab.xlabel('P')
    pylab.ylabel('log(P)')
    filename = 'log_probs.png'
    pylab.savefig(os.path.join(CHART_DIR, filename), bbox_inches="tight") 

def plot_feat_hist(data_name_list, filename=None):
    pylab.clf()
    num_rows = 1 + (len(data_name_list) - 1) / 2
    num_cols = 1 if len(data_name_list) == 1 else 2
    pylab.figure(figsize=(5 * num_cols, 4 * num_rows))

    for i in range(num_rows):
        for j in range(num_cols):
            pylab.subplot(num_rows, num_cols, 1 + i * num_cols + j)
            x, name = data_name_list[i * num_cols + j]
            pylab.title(name)
            pylab.xlabel('Value')
            pylab.ylabel('Density')
            # the histogram of the data
            max_val = np.max(x)
            if max_val <= 1.0:
                bins = 50
            elif max_val > 50:
                bins = 50
            else:
                bins = max_val
            n, bins, patches = pylab.hist(
                x, bins=bins, normed=1, facecolor='green', alpha=0.75)

            pylab.grid(True)

    if not filename:
        filename = "feat_hist_%s.png" % name

    pylab.savefig(os.path.join(CHART_DIR, filename), bbox_inches="tight") 

def plot_bias_variance(data_sizes, train_errors, test_errors, name):
    pylab.clf()
    pylab.ylim([0.0, 1.0])
    pylab.xlabel('Data set size')
    pylab.ylabel('Error')
    pylab.title("Bias-Variance for '%s'" % name)
    pylab.plot(
        data_sizes, train_errors, "-", data_sizes, test_errors, "--", lw=1)
    pylab.legend(["train error", "test error"], loc="upper right")
    pylab.grid()
    pylab.savefig(os.path.join(CHART_DIR, "bv_" + name + ".png")) 

def plot_bias_variance(data_sizes, train_errors, test_errors, name):
    pylab.clf()
    pylab.ylim([0.0, 1.0])
    pylab.xlabel('Data set size')
    pylab.ylabel('Error')
    pylab.title("Bias-Variance for '%s'" % name)
    pylab.plot(
        data_sizes, train_errors, "-", data_sizes, test_errors, "--", lw=1)
    pylab.legend(["train error", "test error"], loc="upper right")
    pylab.grid(True)
    pylab.savefig(os.path.join(CHART_DIR, "bv_" + name + ".png")) 

def plot_simple_demo_2():
    pylab.clf()
    fig = pylab.figure(num=None, figsize=(10, 4))
    pylab.subplot(121)

    title = "Original feature space"
    pylab.title(title)
    pylab.xlabel("$X_1$")
    pylab.ylabel("$X_2$")

    x1 = np.arange(0, 10, .2)
    x2 = x1 + np.random.normal(scale=1, size=len(x1))

    good = x1 > x2
    bad = ~good

    x1g = x1[good]
    x2g = x2[good]
    pylab.scatter(x1g, x2g, edgecolor="blue", facecolor="blue")

    x1b = x1[bad]
    x2b = x2[bad]
    pylab.scatter(x1b, x2b, edgecolor="red", facecolor="white")

    pylab.grid(True)

    pylab.subplot(122)

    X = np.c_[(x1, x2)]

    pca = decomposition.PCA(n_components=1)
    Xtrans = pca.fit_transform(X)

    Xg = Xtrans[good]
    Xb = Xtrans[bad]

    pylab.scatter(
        Xg[:, 0], np.zeros(len(Xg)), edgecolor="blue", facecolor="blue")
    pylab.scatter(
        Xb[:, 0], np.zeros(len(Xb)), edgecolor="red", facecolor="white")
    title = "Transformed feature space"
    pylab.title(title)
    pylab.xlabel("$X'$")
    fig.axes[1].get_yaxis().set_visible(False)

    print(pca.explained_variance_ratio_)

    pylab.grid(True)

    pylab.autoscale(tight=True)
    filename = "pca_demo_2.png"
    pylab.savefig(os.path.join(CHART_DIR, filename), bbox_inches="tight") 

def plot(self, *args, **kwargs):
        """
        Plot the given samples from the conditional frequency distribution.
        For a cumulative plot, specify cumulative=True.
        (Requires Matplotlib to be installed.)

        :param samples: The samples to plot
        :type samples: list
        :param title: The title for the graph
        :type title: str
        :param conditions: The conditions to plot (default is all)
        :type conditions: list
        """
        try:
            from matplotlib import pylab
        except ImportError:
            raise ValueError('The plot function requires matplotlib to be installed.'
                         'See http://matplotlib.org/')

        cumulative = _get_kwarg(kwargs, 'cumulative', False)
        conditions = _get_kwarg(kwargs, 'conditions', sorted(self.conditions()))
        title = _get_kwarg(kwargs, 'title', '')
        samples = _get_kwarg(kwargs, 'samples',
                             sorted(set(v for c in conditions for v in self[c])))  # this computation could be wasted
        if not "linewidth" in kwargs:
            kwargs["linewidth"] = 2

        for condition in conditions:
            if cumulative:
                freqs = list(self[condition]._cumulative_frequencies(samples))
                ylabel = "Cumulative Counts"
                legend_loc = 'lower right'
            else:
                freqs = [self[condition][sample] for sample in samples]
                ylabel = "Counts"
                legend_loc = 'upper right'
            # percents = [f * 100 for f in freqs] only in ConditionalProbDist?
            kwargs['label'] = "%s" % condition
            pylab.plot(freqs, *args, **kwargs)

        pylab.legend(loc=legend_loc)
        pylab.grid(True, color="silver")
        pylab.xticks(range(len(samples)), [compat.text_type(s) for s in samples], rotation=90)
        if title:
            pylab.title(title)
        pylab.xlabel("Samples")
        pylab.ylabel(ylabel)
        pylab.show() 

def get_food_contour_morph(mask_video, 
                     min_area = None, 
                     n_bins = 180,
                     frac_lowess=0.1,
                     _is_debug=False):
    '''
    Identify the contour of a food patch. I tested this for the worm rig.
    It assumes the food has a semi-circular shape. 
    The food lawn is very thin so the challenge was to estimate the contour of a very dim area.
    '''
    #%%
    
    try:
        with tables.File(mask_video, 'r') as fid:
            full_data = fid.get_node('/full_data')[:5] # I am using the first two images to calculate this info
    except tables.exceptions.NoSuchNodeError:
        return None, None
        
    img = np.max(full_data[:2], axis=0)
    #dark_mask = get_dark_mask(full_data)
    
    mask = get_patch_mask(img, min_area = min_area)
    circx, circy, best_fit = mask_to_food_contour(mask, 
                                        n_bins = n_bins,
                                        frac_lowess=frac_lowess)
    
    
    if _is_debug:
        from skimage.draw import circle_perimeter
        import matplotlib.pylab as plt
        
        cpx, cpy = circle_perimeter(*best_fit[1:])
        
        plt.figure(figsize=(5,5))        
        plt.gca().xaxis.set_ticklabels([])
        plt.gca().yaxis.set_ticklabels([])
        
        (px, py) = np.where(skeletonize(mask))
        plt.imshow(img, cmap='gray')
        plt.plot(py, px, '.')
        plt.plot(cpx, cpy, '.r')
        plt.plot(circy, circx, '.')
        plt.grid('off')
    
    food_cnt = np.vstack((circy, circx)).T
    return food_cnt 

def plot_accuracy(results):
    """
    Routine to visualize the errors as well as the expected errors

    Args:
        results: the dictionary containing the errors
    """

    # retrieve the list of nvars from results
    assert 'nvars_list' in results, 'ERROR: expecting the list of nvars in the results dictionary'
    nvars_list = sorted(results['nvars_list'])

    # Set up plotting parameters
    params = {'legend.fontsize': 20,
              'figure.figsize': (12, 8),
              'axes.labelsize': 20,
              'axes.titlesize': 20,
              'xtick.labelsize': 16,
              'ytick.labelsize': 16,
              'lines.linewidth': 3
              }
    plt.rcParams.update(params)

    # create new figure
    plt.figure()
    # take x-axis limits from nvars_list + some spacning left and right
    plt.xlim([min(nvars_list) / 2, max(nvars_list) * 2])
    plt.xlabel('nvars')
    plt.ylabel('abs. error')
    plt.grid()

    # get guide for the order of accuracy, i.e. the errors to expect
    # get error for first entry in nvars_list
    id = ID(nvars=nvars_list[0])
    base_error = results[id]
    # assemble optimal errors for 2nd order method and plot
    order_guide_space = [base_error / (2 ** (2 * i)) for i in range(0, len(nvars_list))]
    plt.loglog(nvars_list, order_guide_space, color='k', ls='--', label='2nd order')

    min_err = 1E99
    max_err = 0E00
    err_list = []
    # loop over nvars, get errors and find min/max error for y-axis limits
    for nvars in nvars_list:
        id = ID(nvars=nvars)
        err = results[id]
        min_err = min(err, min_err)
        max_err = max(err, max_err)
        err_list.append(err)
    plt.loglog(nvars_list, err_list, ls=' ', marker='o', markersize=10, label='experiment')

    # adjust y-axis limits, add legend
    plt.ylim([min_err / 10, max_err * 10])
    plt.legend(loc=1, ncol=1, numpoints=1)

    # save plot as PDF, beautify
    fname = 'step_1_accuracy_test_space.png'
    plt.savefig(fname, rasterized=True, bbox_inches='tight')

    return None