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Solve the following problem using Python, implementing the functions described below, one line at a time
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Description:
 def init_heatmap(x_vec, y_vec, hist_matrix, fig, colormap='Blues', alpha=1, grid=False, colorbar=True, vmax='auto', vmin='auto', crop=True):
 """ convenience function to initialize a standard colormap in a figure """

    plt.figure(fig.number)
    ax = fig.gca()

    # set vmax and vmin
    vma = np.amax(hist_matrix) if vmax == 'auto' else vmax
    vmi = np.amin(hist_matrix) if vmin == 'auto' else vmin

    # an error check
    if vma <= vmi:
        vma = vmi + 1

    # grid the space for pcolormesh
    x_grid, y_grid = np.meshgrid(x_vec, y_vec)

    hmap = ax.pcolormesh(x_grid, y_grid, np.array(hist_matrix),
               cmap=colormap, alpha=alpha, shading='gouraud',
               vmax=vma, vmin=vmi)

    if colorbar:
        plt.colorbar(hmap)

    if not grid:
        ax.grid(False)

    if crop:
        ax.set_xlim([x_vec[0], x_vec[-1]])
        ax.set_ylim([y_vec[0], y_vec[-1]])