Updated figure 14 sizing & added figure 1 plotting

Author: Paul Mannix

.gitignore

@@ -7,6 +7,10 @@ __pycache__/
 *.h5
 *.vtr
 *.npy
+*.txt
+*.plt
+*.dat
+*.zip
 
 # Ouptut images & Movies
 *.png

Paper_Figures/Plot_Fig1_Beaume_solutions.py

@@ -0,0 +1,214 @@
+"""
+This script generates a bifurcation diagram and spatial solutions for a
+planar bifurcation problem. It reads data from specified files, processes
+the data, and creates contour plots to visualize the results. The script
+uses Matplotlib for plotting and NumPy for numerical operations.
+
+To run this script, ensure you have the required libraries installed:
+- numpy
+- matplotlib
+You can install them using pip:
+pip install numpy matplotlib
+
+To execute the script, run the following command in your terminal:
+python plot_solutions.py
+"""
+
+import numpy as np
+import matplotlib.pyplot as plt
+from matplotlib.gridspec import GridSpec
+from matplotlib.colors import ListedColormap, BoundaryNorm
+
+# Uncomment the following lines to use LaTeX for text rendering
+plt.rcParams.update({
+    "text.usetex": True,
+    "font.family": "sans-serif",
+    "font.sans-serif": "Helvetica",
+    'text.latex.preamble': r'\usepackage{amsfonts}'
+})
+
+
+def cmap(Z, RES=12):
+    """
+    Generate a custom colormap and normalization for visualizing data.
+
+    This function creates a colormap based on the 'RdBu_r' colormap, with a 
+    specified number of levels. The color corresponding to the value 0 is 
+    replaced with white to emphasize the zero level. The function also 
+    returns the levels and a normalization object for mapping data values 
+    to the colormap.
+
+    Parameters:
+    -----------
+    Z : numpy.ndarray
+        A 2D array of data values for which the colormap will be created. 
+        The maximum absolute value in `Z` determines the range of the colormap.
+    RES : int, optional
+        The number of levels in the colormap. Default is 12. It must be even.
+        This parameter is used to create evenly spaced levels for the colormap.
+    Returns:
+    --------
+    levels : numpy.ndarray
+        An array of evenly spaced levels for the colormap, symmetric around 0.
+    custom_cmap : matplotlib.colors.ListedColormap
+        A custom colormap with the color corresponding to 0 replaced by white.
+    norm : matplotlib.colors.BoundaryNorm
+        A normalization object for mapping data values to the colormap.
+
+    Notes:
+    ------
+    - The function assumes that the input array `Z` is 2D and contains numeric 
+      values.
+
+    Example:
+    --------
+    >>> import numpy as np
+    >>> Z = np.random.randn(10, 10)
+    >>> levels, custom_cmap, norm = cmap(Z)
+    """
+
+    print(np.asarray([min(Z.flatten()), max(Z.flatten())]))
+    Max = np.max(abs(Z))
+
+    assert RES % 2 == 0  # ensure RES is even
+
+    # Define levels (must include 0)
+    levels = np.linspace(-Max, Max, RES)
+
+    # Create RdBu_r colormap with 12 colors
+    original_cmap = plt.get_cmap('RdBu_r', len(levels) - 1)
+    colors = original_cmap(np.arange(original_cmap.N))
+
+    # Find the index of the bin that contains 0
+    # Since levels are symmetric, 0 will be in the middle bin
+    zero_bin_index = (len(levels) - 1) // 2  # e.g., 6 if 12 bins
+
+    # Replace that color with white
+    colors[zero_bin_index] = [1, 1, 1, 1]  # RGBA for white
+    custom_cmap = ListedColormap(colors)
+
+    # Create normalization
+    norm = BoundaryNorm(levels, custom_cmap.N)
+
+    return levels, custom_cmap, norm
+
+
+def transform(file):
+    """
+    Transforms data from a file into structured arrays for plotting.
+
+    This function reads data from a file, extracts specific columns, and reshapes
+    the data into 2D arrays suitable for plotting. It also removes an offset from
+    the computed values.
+
+    Args:
+        file (str): Path to the file containing the data. The file should be in a
+                    format readable by `numpy.loadtxt` and contain at least 5 columns.
+
+    Returns:
+        tuple: A tuple containing three 2D numpy arrays:
+            - X (numpy.ndarray): 2D array of x-coordinates (reshaped from column 1).
+            - Z (numpy.ndarray): 2D array of z-coordinates (reshaped from column 2).
+            - T (numpy.ndarray): 2D array of transformed values (computed from column 5).
+    """
+    # Load data from the file
+    data = np.loadtxt(file)
+
+    # Extract columns for plotting (column 1, column 2, and computed value for color)
+    x = data[:, 0]  # Column 1 - but python is zero-indexed
+    z = data[:, 1]  # Column 2
+    t = data[:, 4]  # Column 5
+
+    Nz = 17
+    Nx = 500
+    X = np.zeros((Nz, Nx))
+    Z = np.zeros((Nz, Nx))
+    T = np.zeros((Nz, Nx))
+    for i in range(Nx):
+        X[:, i] = x[i*Nz:(i+1)*Nz]
+        Z[:, i] = z[i*Nz:(i+1)*Nz]
+        T[:, i] = t[i*Nz:(i+1)*Nz]
+
+    T += (Z - 1/2)  # Remove the offset
+
+    # Print file and max/min
+    print(file, np.asarray([min(T.flatten()), max(T.flatten())]), '\n')
+
+    return X, Z, T
+
+
+print('Load above')
+dir = '/home/pmannix/Spatial_Localisation/SpectralDoubleDiffusiveConvection/Paper_Data/Beamue2011_Data/'
+
+# ~~~~~~~~~~~~~~~~~~~~~~ # ~~~~~~~~~~~~~~~~~~~~~~~~
+
+fig = plt.figure(figsize=(16, 6), layout='constrained')
+
+# Create a GridSpec with custom width ratios
+gs = GridSpec(6, 2, figure=fig, width_ratios=[0.5, 1.5])  # Adjust width_ratios as needed
+
+# Create the left column as a single subplot
+ax = fig.add_subplot(gs[:, 0])
+
+# Create the right column subplots
+axs = np.empty((6, 1), dtype=object)
+for i in range(6):
+    axs[i, 0] = fig.add_subplot(gs[i, 1], aspect=.75)
+
+
+# A) Bifurcation diagram
+# ~~~~~~~~~~~~~~~~~~~~~~ # ~~~~~~~~~~~~~~~~~~~~~~~~
+
+# Load data from bifdiag1.dat and bifdiag2.dat
+data1 = np.loadtxt(dir + 'Planarfigure1_2/bifdiag1.dat')
+data2 = np.loadtxt(dir + 'Planarfigure1_2/bifdiag2.dat')
+
+# Extract columns for plotting (column 2 and column 7, zero-indexed)
+x1, y1 = data1[:, 1], data1[:, 6]
+x2, y2 = data2[:, 1], data2[:, 6]
+
+# Create the plot
+ax.plot(x1, y1, 'k-', linewidth=2, label=r'$L^{1-}_{10}$')
+ax.plot(x2, y2, 'k:', linewidth=2, label=r'$L^{1+}_{10}$')
+
+# Add labels, legend, and title
+ax.set_xlabel(r'$Ra_T$', fontsize=30)
+ax.set_ylabel(r'$\mathcal{E}$', fontsize=30)
+
+# Show the plot
+ax.set_xlim(2660, 2800)
+ax.set_ylim(0, 290)
+ax.tick_params(axis='both', which='major', labelsize=20)
+
+E = np.array([35-2, 65-4, 90-3,   25-3, 50-3, 75])
+Ra= np.array([2700-4, 2700-7, 2700-7,   2710-6, 2700-6, 2700-6])
+letters = [r'1',r'2',r'3', r'a',r'b',r'c']
+for i, xy in enumerate(zip(Ra, E)):
+    ax.annotate(letters[i], xy=xy, textcoords='data', fontsize=15)
+
+# B) Spatial solutions
+# ~~~~~~~~~~~~~~~~~~~~~~ # ~~~~~~~~~~~~~~~~~~~~~~~~
+
+files = ['Planarfigure2_2/SOL_sn1.plt','Planarfigure2_2/SOL_sn2.plt',
+        'Planarfigure2_2/SOL_sn3.plt','Planarfigure2_2/SOL_sna.plt',
+        'Planarfigure2_2/SOL_snb.plt','Planarfigure2_2/SOL_snc.plt']
+
+# Create a contour plot
+for i, file in enumerate(files):
+    X, Z, T = transform(dir + file)
+    levels, custom_cmap, norm = cmap(T)
+    axs[::-1, 0][i].contour(X, Z, T, levels=levels, cmap=custom_cmap, norm=norm)
+    axs[::-1, 0][i].contourf(X, Z, T, levels=levels, cmap=custom_cmap, norm=norm)
+    axs[::-1, 0][i].set_xticks([])
+    axs[::-1, 0][i].set_yticks([])
+
+
+letters = [r'1',r'2',r'3', r'a',r'b',r'c']
+for i, letter in enumerate(letters):
+    axs[::-1, 0][i].annotate(letter, xy=(-0.025, 0.5), xycoords='axes fraction', fontsize=20, color='k')
+
+# ~~~~~~~~~~~~~~~~~~~~~ # ~~~~~~~~~~~~~~~~~~~~~~~~
+
+# Save the figure
+plt.savefig('planar_bifurcation_diagram.png', dpi=100)
+plt.show()

Paper_Figures/Plot_figures_l11_snaking.py

@@ -372,7 +372,7 @@ def Psi_Plot(Y_FOLD, N_r_FOLD, N_fm_FOLD, axs):
 
 # L = 11 Ras=150 extra detail
 # ~~~~~~~~~~~~~~~~~~~~~~ # ~~~~~~~~~~~~~~~~~~~~~~~~
-fig, axs = plt.subplots(nrows=5, ncols=2, figsize=(16, 8), layout='constrained')
+fig, axs = plt.subplots(nrows=5, ncols=2, figsize=((2/3)*16,(5/12)*10), layout='constrained')
 
 # remove the underlying Axes in the middle column
 for axl in axs[:, 0]: