From 9f11e0b3991c53d11e69a0158d384445c27e8ca3 Mon Sep 17 00:00:00 2001
From: JanHab <Jan.Habscheid@web.de>
Date: Sat, 19 Oct 2024 14:03:52 +0200
Subject: [PATCH] Updated L2-error to take the sqrt of int (f_fine - f_h)**2

---
 examples/Data/Convergence.npz                 |  Bin 3296 -> 3296 bytes
 examples/Data/ParameterAnalysis/Molarity.npz  |  Bin 0 -> 593690 bytes
 examples/Figures/Compressibility.svg          |  366 +-
 examples/Figures/Compressibility_no_log.svg   | 3627 +++++++++++++++++
 examples/Figures/Convergence.svg              | 1143 +++---
 .../Figures/ParameterAnalysis/Molarity.svg    | 1868 +++++++++
 examples/ReproducableCode/Convergence.py      |   12 +-
 .../ParameterAnalysis/FractionsHeightLeft.py  |    4 +-
 .../ParameterAnalysis/Molarity.py             |   92 +
 examples/Visualizations/VisCompressibility.py |   72 +-
 examples/Visualizations/VisConvergence.py     |   11 +-
 .../Visualizations/VisPoissonBoltzmann.py     |   54 +
 src/__pycache__/Eq04.cpython-312.pyc          |  Bin 20364 -> 20438 bytes
 13 files changed, 6468 insertions(+), 781 deletions(-)
 create mode 100644 examples/Data/ParameterAnalysis/Molarity.npz
 create mode 100644 examples/Figures/Compressibility_no_log.svg
 create mode 100644 examples/Figures/ParameterAnalysis/Molarity.svg
 create mode 100644 examples/ReproducableCode/ParameterAnalysis/Molarity.py

diff --git a/examples/Data/Convergence.npz b/examples/Data/Convergence.npz
index bca1d9266286a4fbacd74b03f703d66d511cba12..9f5f078e34b6a481d13eef83753c0cf04a30af5d 100644
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diff --git a/examples/Data/ParameterAnalysis/Molarity.npz b/examples/Data/ParameterAnalysis/Molarity.npz
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+     <use xlink:href="#DejaVuSans-30" transform="translate(151.757812 0.78125)"/>
+     <use xlink:href="#DejaVuSans-2e" transform="translate(215.380859 0.78125)"/>
+     <use xlink:href="#DejaVuSans-31" transform="translate(247.167969 0.78125)"/>
+    </g>
+   </g>
+   <g id="line2d_91">
+    <path d="M 429.013125 15.298437 
+L 439.013125 15.298437 
+L 449.013125 15.298437 
+" style="fill: none; stroke: #2ca02c; stroke-width: 1.5; stroke-linecap: square"/>
+   </g>
+   <g id="text_47">
+    <!-- $M$: 1.0 -->
+    <g transform="translate(457.013125 18.798437) scale(0.1 -0.1)">
+     <use xlink:href="#DejaVuSans-Oblique-4d" transform="translate(0 0.78125)"/>
+     <use xlink:href="#DejaVuSans-3a" transform="translate(86.279297 0.78125)"/>
+     <use xlink:href="#DejaVuSans-20" transform="translate(119.970703 0.78125)"/>
+     <use xlink:href="#DejaVuSans-31" transform="translate(151.757812 0.78125)"/>
+     <use xlink:href="#DejaVuSans-2e" transform="translate(215.380859 0.78125)"/>
+     <use xlink:href="#DejaVuSans-30" transform="translate(247.167969 0.78125)"/>
+    </g>
+   </g>
+  </g>
+ </g>
+ <defs>
+  <clipPath id="p1c6c4362fc">
+   <rect x="43.803125" y="34.96" width="161.77" height="301.6375"/>
+  </clipPath>
+  <clipPath id="p36f7013672">
+   <rect x="286.593125" y="34.96" width="161.77" height="301.6375"/>
+  </clipPath>
+  <clipPath id="pdebe13306e">
+   <rect x="529.383125" y="34.96" width="161.77" height="301.6375"/>
+  </clipPath>
+ </defs>
+</svg>
diff --git a/examples/ReproducableCode/Convergence.py b/examples/ReproducableCode/Convergence.py
index a34ff90..2664029 100644
--- a/examples/ReproducableCode/Convergence.py
+++ b/examples/ReproducableCode/Convergence.py
@@ -58,12 +58,12 @@ p_interp1d = [interp1d(x[i], p[i]) for i in range(len(number_cells_vec))]
 # Calculate L2-error
 y_A_error_L2, y_C_error_L2, y_S_error_L2, phi_error_L2, p_error_L2 = [], [], [], [], []
 for i in range(len(number_cells_vec)-1):
-    y_A_error_L2.append(np.trapz((y_A_interp1d[i](x[i]) - y_A_interp1d[-1](x[i]))**2, x[i]))
-    y_C_error_L2.append(np.trapz((y_C_interp1d[i](x[i]) - y_C_interp1d[-1](x[i]))**2, x[i]))
-    y_S_error_L2.append(np.trapz((y_S_interp1d[i](x[i]) - y_S_interp1d[-1](x[i]))**2, x[i]))
-    phi_error_L2.append(np.trapz((phi_interp1d[i](x[i]) - phi_interp1d[-1](x[i]))**2, x[i]))
-    p_error_L2.append(np.trapz((p_interp1d[i](x[i]) - p_interp1d[-1](x[i]))**2, x[i]))
-    
+    y_A_error_L2.append(np.sqrt(np.trapz((y_A_interp1d[i](x[i]) - y_A_interp1d[-1](x[i]))**2, x[i])))
+    y_C_error_L2.append(np.sqrt(np.trapz((y_C_interp1d[i](x[i]) - y_C_interp1d[-1](x[i]))**2, x[i])))
+    y_S_error_L2.append(np.sqrt(np.trapz((y_S_interp1d[i](x[i]) - y_S_interp1d[-1](x[i]))**2, x[i])))
+    phi_error_L2.append(np.sqrt(np.trapz((phi_interp1d[i](x[i]) - phi_interp1d[-1](x[i]))**2, x[i])))
+    p_error_L2.append(np.sqrt(np.trapz((p_interp1d[i](x[i]) - p_interp1d[-1](x[i]))**2, x[i])))
+
 # Log-log plot of L2-error
 plt.figure()
 plt.loglog(number_cells_vec[:-1], y_A_error_L2, 'o-', label='$y_A$')
diff --git a/examples/ReproducableCode/ParameterAnalysis/FractionsHeightLeft.py b/examples/ReproducableCode/ParameterAnalysis/FractionsHeightLeft.py
index 9e7d8e1..c9b1ee0 100644
--- a/examples/ReproducableCode/ParameterAnalysis/FractionsHeightLeft.py
+++ b/examples/ReproducableCode/ParameterAnalysis/FractionsHeightLeft.py
@@ -21,7 +21,7 @@ del sys.path[0]
 import matplotlib.pyplot as plt
 import numpy as np
 
-# Define Parameter and buondary conditions
+# Define Parameter and boundary conditions
 phi_right = 0.0
 p_right = 0.0
 y_A_R, y_C_R = 1/3, 1/3
@@ -61,4 +61,4 @@ axs.set_xlabel('$\delta \\varphi$ [-]')
 axs.set_ylabel('$y_\\alpha$ [-]')
 axs.legend()
 fig.tight_layout()
-fig.show()
\ No newline at end of file
+fig.show()
diff --git a/examples/ReproducableCode/ParameterAnalysis/Molarity.py b/examples/ReproducableCode/ParameterAnalysis/Molarity.py
new file mode 100644
index 0000000..9d6a834
--- /dev/null
+++ b/examples/ReproducableCode/ParameterAnalysis/Molarity.py
@@ -0,0 +1,92 @@
+'''
+Jan Habscheid
+Jan.Habscheid@rwth-aachen.de
+'''
+# import the src file needed to solve the system of equations
+import sys
+import os
+
+
+# Add the src directory to the sys.path
+src_path = os.path.join(os.path.dirname(os.path.abspath(__file__)), '../../..', 'src')
+sys.path.insert(0, src_path)
+
+from Eq04 import solve_System_4eq
+
+# Remove the src directory from sys.path after import
+del sys.path[0]
+
+# Import plotting library
+import matplotlib.pyplot as plt
+import numpy as np
+
+# Define Parameter and buondary conditions
+phi_right = 0.0
+p_right = 0.0
+z_A, z_C = -1.0, 1.0
+K = 'incompressible'
+a2 = 7.5412e-4
+nR_mol = 55
+number_cells = 1024*4
+refinement_style = 'hard_log'
+rtol = 1e-8
+max_iter = 10_000
+
+Molarity = np.array([0.01, 0.1, 1.0]) # 10
+y_A_L = Molarity / nR_mol
+
+# Define left values of electric potential and values for lambda^2
+phi_left = 16.0
+Lambda2 = 8.553e-6
+y_A, y_C, y_S, phi, p, x = [], [], [], [], [], []
+
+# Solve the system for different values of phi_left
+for y_alpha_L_ in y_A_L:
+    y_A_, y_C_, phi_, p_, x_ = solve_System_4eq(phi_left, phi_right, p_right, z_A, z_C, y_alpha_L_, y_alpha_L_, K, Lambda2, a2, number_cells, relax_param=0.05, x0=0, x1=1, refinement_style=refinement_style, return_type='Vector', max_iter=max_iter, rtol=rtol)
+    y_A.append(y_A_)
+    y_C.append(y_C_)
+    y_S.append(1 - y_A_ - y_C_)
+    phi.append(phi_)
+    p.append(p_)
+    x.append(x_)
+    
+# Visualize the results
+fig, axs = plt.subplots(ncols=3, figsize=(10, 5))
+xlim = 0.1
+markers = ['--', '-', ':']
+colors = ['tab:blue', 'tab:orange', 'tab:green', 'tab:red', 'tab:purple']
+
+for i in range(len(Molarity)):
+    clr = colors[i]
+    axs[0].plot(x[i], y_A[i], color=clr)#, lw=lw)
+    axs[1].plot(x[i], y_C[i], color=clr)#, lw=lw)
+    axs[2].plot(x[i], y_S[i], color=clr)#, lw=lw)
+[axs[i].grid() for i in range(3)]
+[axs[i].set_xlim(0,xlim) for i in range(3)]
+axs[0].set_ylim(0, 1)
+axs[1].set_ylim(0, np.max(y_C))
+axs[2].set_ylim(0, 1)
+[axs[i].set_xlabel('$x$ [-]') for i in range(3)]#, fontsize=labelsize)
+# axs.set_ylabel('$y_\\alpha$ [-]')#, fontsize=labelsize)
+axs[0].set_ylabel('$y_A$ [-]')#, fontsize=labelsize)
+axs[1].set_ylabel('$y_C$ [-]')#, fontsize=labelsize)
+axs[2].set_ylabel('$y_S$ [-]')#, fontsize=labelsize)
+# axs.tick_params(axis='both')#, labelsize=labelsize)
+
+# dummy, = axs.plot(2, 0, color='grey', linestyle='--', label='$y_A$')
+# dummy, = axs.plot(2, 2, color='grey', linestyle='-', label='$y_C$')
+# dummy, = axs.plot(2, 2, color='grey', linestyle=':', label='$y_S$')
+for i in range(len(Molarity)):
+    dummy, = axs[0].plot(2, 0, color=colors[i], linestyle='-', label=f'$M$: {Molarity[i]}')
+
+lines_labels = [ax.get_legend_handles_labels() for ax in fig.axes]
+lines, labels = [sum(lol, []) for lol in zip(*lines_labels)]
+
+# Finally, the legend (that maybe you'll customize differently)
+lgnd = fig.legend(lines, labels, bbox_to_anchor=(0.7,1.05), ncol=4)
+fig.tight_layout()
+fig.savefig('../../Figures/ParameterAnalysis/Molarity.svg', bbox_inches='tight')
+fig.show()
+
+# Save the Results
+np.savez('../../Data/ParameterAnalysis/Molarity.npz', phi_right=phi_right, p_right = p_right, y_alpha_L = y_alpha_L_, z_A = z_A, z_C = z_C, number_cells=number_cells, a2=a2, phi_left=phi_left, Lambda2=Lambda2, x=x, phi=phi, y_A=y_A, y_C=y_C, y_S=y_S, p=p)
\ No newline at end of file
diff --git a/examples/Visualizations/VisCompressibility.py b/examples/Visualizations/VisCompressibility.py
index 7c20122..defcfbe 100644
--- a/examples/Visualizations/VisCompressibility.py
+++ b/examples/Visualizations/VisCompressibility.py
@@ -53,40 +53,64 @@ axs[0,1].set_xlabel('x [-]', fontsize=labelsize)
 axs[0,1].set_ylabel('$y_\\alpha$ [-]', fontsize=labelsize)
 axs[0,1].tick_params(axis='both', labelsize=labelsize)
 
-# a = plt.axes([.75, .77, .2, .2])
+
+# Scale to log-log plot by uncommenting and commenting the two sections
+# log-log plot
 # for i in range(len(K_vec)):
 #     clr = colors[i]
-#     a.plot(x[i], y_S[i], markers[0], color=clr, lw=lw)
-# axs[0,1].plot(0, 0.1, color='grey', linestyle='--', label='Solvent')
-# a.set_xlim(0,xlim)
-# a.grid()
-# a.set_xlabel('$x [-]$', fontsize=labelsize)
-# a.set_ylabel('$y_S$ [-]', fontsize=labelsize)
-# a.tick_params(axis='both', labelsize=labelsize)
-
-
-for i in range(len(K_vec)):
+#     axs[1,1].plot(x[i], y_A[i] * n[i], markers[0], color=clr, lw=lw)
+#     axs[1,1].plot(x[i], y_C[i] * n[i], markers[1], color=clr, lw=lw)
+# axs[1,1].set_xscale('log')
+# axs[1,1].set_yscale('log')
+# axs[1,1].set_xlim(0,xlim)
+# axs[1,1].grid()
+# axs[1,1].set_xlabel('log(x) [-]', fontsize=labelsize)
+# axs[1,1].set_ylabel('log($n_\\alpha$) [-]', fontsize=labelsize)
+# axs[1,1].tick_params(axis='both', labelsize=labelsize)
+
+# linear plot
+for i in range(len(K_vec)-1):
     clr = colors[i]
     axs[1,1].plot(x[i], y_A[i] * n[i], markers[0], color=clr, lw=lw)
-    axs[1,1].plot(x[i], y_C[i] * n[i], markers[1], color=clr, lw=lw)
-axs[1,1].set_xscale('log')
-axs[1,1].set_yscale('log')
-axs[1,1].set_xlim(0,xlim)
+    # axs[1,1].plot(x[i], y_C[i] * n[i], markers[1], color=clr, lw=lw)
+axs[1,1].set_xlim(0,0.01)
 axs[1,1].grid()
-axs[1,1].set_xlabel('log(x) [-]', fontsize=labelsize)
-axs[1,1].set_ylabel('log($n_\\alpha$) [-]', fontsize=labelsize)
+axs[1,1].set_xlabel('x [-]', fontsize=labelsize)
+axs[1,1].set_ylabel('$n_A$ [-]', fontsize=labelsize)
 axs[1,1].tick_params(axis='both', labelsize=labelsize)
 
-[axs[1,0].plot(x[i], p[i], lw=lw, color=colors[i]) for i in range(len(K_vec))]
-axs[1,0].set_yscale('log')
-axs[1,0].set_xlim(0,xlim)
-axs[1,0].set_ylim(1e-9, np.max(p))
+a = plt.axes([.75, .27, .2, .2])
+for i in range(len(K_vec)-1):
+    clr = colors[i]
+    a.plot(x[i], y_C[i] * n[i], markers[1], color=clr, lw=lw)
+# axs[0,1].plot(0, 0.1, color='grey', linestyle='--', label='Solvent')
+a.set_xlim(0,0.025)
+a.set_ylim(0, 1)
+a.grid()
+a.set_xlabel('$x$ [-]', fontsize=labelsize)
+a.set_ylabel('$n_C$ [-]', fontsize=labelsize)
+a.tick_params(axis='both', labelsize=labelsize)
+
+# Scale to log plot by uncommenting and commenting the two sections
+# log plot
+# [axs[1,0].plot(x[i], p[i], lw=lw, color=colors[i]) for i in range(len(K_vec))]
+# axs[1,0].set_yscale('log')
+# axs[1,0].set_xlim(0,xlim)
+# axs[1,0].set_ylim(1e-9, np.max(p))
+# axs[1,0].grid()
+# axs[1,0].set_xlabel('x [-]', fontsize=labelsize)
+# axs[1,0].set_ylabel('log($p$) [-]', fontsize=labelsize)
+# axs[1,0].tick_params(axis='both', labelsize=labelsize)
+
+# linear plot
+[axs[1,0].plot(x[i], p[i], lw=lw, color=colors[i]) for i in range(len(K_vec)-1)]
+axs[1,0].set_xlim(0,0.01)
+# axs[1,0].set_ylim(1e-9, np.max(p))
 axs[1,0].grid()
 axs[1,0].set_xlabel('x [-]', fontsize=labelsize)
-axs[1,0].set_ylabel('log($p$) [-]', fontsize=labelsize)
+axs[1,0].set_ylabel('$p$ [-]', fontsize=labelsize)
 axs[1,0].tick_params(axis='both', labelsize=labelsize)
 
-
 # order = [0, 5, 1, 6, 2, 7, 3, 4] 
 # order = [0, 5, 1, 6, 2, 3, 4] 
 order = [0, 5, 1, 4, 2, 3] 
@@ -97,5 +121,5 @@ lgnd = fig.legend([lines[i] for i in order], [labels[i] for i in order], bbox_to
 for line in lgnd.get_lines():
     line.set_linewidth(legend_width)
 fig.tight_layout()
-fig.savefig('../Figures/Compressibility.svg', bbox_inches='tight')
+fig.savefig('../Figures/Compressibility_no_log.svg', bbox_inches='tight')
 fig.show()
\ No newline at end of file
diff --git a/examples/Visualizations/VisConvergence.py b/examples/Visualizations/VisConvergence.py
index aa9c029..163dff1 100644
--- a/examples/Visualizations/VisConvergence.py
+++ b/examples/Visualizations/VisConvergence.py
@@ -26,8 +26,8 @@ p_error_inf = data['p_error_inf']
 # Reference order
 x_ref = [1e+1, 1e+5]
 O1_2_ref = [10e+4, 10e+0]
-O2_2_ref = [10e-8, 10e-16]
-O3_2_ref = [10e-8, 10e-20]
+O2_2_ref = [10e-3, 10e-11]
+# O3_2_ref = [10e-8, 10e-20]
 O1_inf_ref = [10e+4, 10e+0]
 O2_inf_ref = [10e-4, 10e-12]
 # O3_inf_ref = [10e-1, 10e-13]
@@ -46,8 +46,8 @@ axs[0].loglog(number_cells_vec[:-1], y_S_error_L2, 'o-', label='$y_S$', lw=lw, m
 axs[0].loglog(number_cells_vec[:-1], phi_error_L2, 'o-', label='$\\varphi$', lw=lw, ms=ms)
 axs[0].loglog(number_cells_vec[:-1], p_error_L2, 'o-', label='$p$', lw=lw, ms=ms)
 axs[0].loglog(x_ref, O1_2_ref, Ref_Ord_marker[0], color='tab:gray', label='$O(nx)^1$', lw=lw, ms=ms)
-# axs[0].loglog(x_ref, O2_2_ref, Ref_Ord_marker[1], color='tab:gray', label='$O(nx)^2$', lw=lw, ms=ms)
-axs[0].loglog(x_ref, O3_2_ref, Ref_Ord_marker[2], color='tab:gray', label='$O(nx)^3$', lw=lw, ms=ms)
+axs[0].loglog(x_ref, O2_2_ref, Ref_Ord_marker[1], color='tab:gray', label='$O(nx)^2$', lw=lw, ms=ms)
+# axs[0].loglog(x_ref, O3_2_ref, Ref_Ord_marker[2], color='tab:gray', label='$O(nx)^3$', lw=lw, ms=ms)
 axs[0].set_xlabel('log(nx)', fontsize=labelsize)
 axs[0].set_ylabel('log($L_2$)', fontsize=labelsize)
 axs[0].grid()
@@ -66,7 +66,8 @@ axs[1].set_ylabel('log($L_\infty$)', fontsize=labelsize)
 axs[1].grid()
 axs[1].tick_params(axis='both', labelsize=labelsize)
 
-order = [0, 5, 1, 7, 2, 6, 3, 4] 
+# order = [0, 5, 1, 7, 2, 6, 3, 4] 
+order = [0, 5, 1, 6, 2, 3, 4] 
 lines_labels = [ax.get_legend_handles_labels() for ax in fig.axes]
 lines, labels = [sum(lol, []) for lol in zip(*lines_labels)]
 lgnd = fig.legend([lines[i] for i in order], [labels[i] for i in order], bbox_to_anchor=(0.81,1.2), ncol=5, fontsize=labelsize)
diff --git a/examples/Visualizations/VisPoissonBoltzmann.py b/examples/Visualizations/VisPoissonBoltzmann.py
index 3848e55..b5c99a8 100644
--- a/examples/Visualizations/VisPoissonBoltzmann.py
+++ b/examples/Visualizations/VisPoissonBoltzmann.py
@@ -216,4 +216,58 @@ fig.legend(lines, labels, bbox_to_anchor=(0.69,1.1), ncol=6, fontsize=labelsize)
 
 fig.tight_layout()
 fig.savefig('../Figures/PoissonBoltzmann_Convergence.svg', bbox_inches='tight')
+fig.show()
+
+
+# Visualize the results - rescale to physical values
+''' 
+The dimensionless parameter were chosen to:
+Lambda2 = 8.553e-6
+a2 = 7.5412e-4
+with the following physical parameters:
+T = 293.75 [K] - Temperature
+nR = 55 [mol/l] - Reference number density
+pR = 1 [atm] - Reference pressure
+LR = 20e-9 [m] - Reference length
+chi = 80 [-] - Dielectric permittivity
+The constants:
+e0 = 1.602e-19 [As] - Dielectric constant
+k = 1.381e-23 [1/mol] - Avogadro constant
+'''
+e0 = 1.602e-19 # [As]
+k = 1.381e-23 # [J/K]
+T = 293.75 # [K]
+phi_left_vec_physical = phi_left_vec * (k*T)/e0
+fig, axs = plt.subplots(ncols=2, figsize=(30, 12))
+labelsize = 40
+lw = 6
+ms=20
+# Log-log plot of L2-error
+axs[0].plot(phi_left_vec_physical, y_A_error_L2, 'o-', label='$y_A$', lw=lw, ms=ms)
+axs[0].plot(phi_left_vec_physical, y_C_error_L2, 'o-', label='$y_C$', lw=lw, ms=ms)
+axs[0].plot(phi_left_vec_physical, y_S_error_L2, 'o-', label='$y_S$', lw=lw, ms=ms)
+axs[0].set_yscale('log')
+axs[0].set_xlabel('$\delta \\varphi [V]$', fontsize=labelsize)
+axs[0].set_ylabel('log($L_2$) [-]', fontsize=labelsize)
+axs[0].tick_params(axis='both', labelsize=labelsize)
+axs[0].grid()
+
+# Log-log plot of infinity error
+axs[1].plot(phi_left_vec_physical, y_A_error_inf, 'o-', lw=lw, ms=ms)
+axs[1].plot(phi_left_vec_physical, y_C_error_inf, 'o-', lw=lw, ms=ms)
+axs[1].plot(phi_left_vec_physical, y_S_error_inf, 'o-', lw=lw, ms=ms)
+axs[1].set_yscale('log')
+axs[1].set_xlabel('$\delta \\varphi [V]$', fontsize=labelsize)
+axs[1].set_ylabel('log($L_\infty$) [-]', fontsize=labelsize)
+axs[1].tick_params(axis='both', labelsize=labelsize)
+axs[1].grid()
+
+lines_labels = [ax.get_legend_handles_labels() for ax in fig.axes]
+lines, labels = [sum(lol, []) for lol in zip(*lines_labels)]
+
+# Finally, the legend (that maybe you'll customize differently)
+fig.legend(lines, labels, bbox_to_anchor=(0.69,1.1), ncol=6, fontsize=labelsize)
+
+fig.tight_layout()
+fig.savefig('../Figures/PoissonBoltzmann_Convergence_Rescaled_Dimensions.svg', bbox_inches='tight')
 fig.show()
\ No newline at end of file
diff --git a/src/__pycache__/Eq04.cpython-312.pyc b/src/__pycache__/Eq04.cpython-312.pyc
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-- 
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