1 | import os |
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2 | import time |
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3 | from shallow_water_domain_avalanche import * |
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4 | from Numeric import Float, sqrt |
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5 | from config import g, epsilon |
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6 | from numpy import sin, cos, tan, array, zeros |
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7 | from scipy import linspace |
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8 | from parameters import * |
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9 | |
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10 | def analytical_sol(X,t): |
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11 | N = len(X) |
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12 | u = zeros(N,Float) |
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13 | h = zeros(N,Float) |
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14 | w = zeros(N,Float) |
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15 | z = zeros(N,Float) |
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16 | mom = zeros(N,Float) |
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17 | for i in range(N): |
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18 | # Calculate Analytical Solution at time t > 0 |
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19 | if X[i] <= -2.0*c0*t + 0.5*m*t**2.0: |
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20 | u[i] = 0.0 |
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21 | h[i] = 0.0 |
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22 | elif X[i] <= c0*t + 0.5*m*t**2.0: |
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23 | u[i] = 2.0/3.0 * (X[i]/t - c0 + m*t) |
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24 | h[i] = 1.0/(9.0*g) * (X[i]/t + 2.0*c0 - 0.5*m*t)**2.0 |
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25 | else: |
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26 | u[i] = m*t |
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27 | h[i] = h_0 |
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28 | z[i] = bed_slope*X[i] |
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29 | w[i] = h[i] + z[i] |
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30 | mom[i] = u[i]*h[i] |
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31 | return u,h,w,z,mom |
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32 | |
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33 | def height(X): |
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34 | N = len(X) |
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35 | y = zeros(N,Float) |
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36 | for i in range(N): |
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37 | if X[i]<=0.0: |
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38 | y[i] = 0.0 |
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39 | else: |
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40 | y[i] = h_0 |
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41 | return y |
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42 | |
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43 | def stage(X): |
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44 | N = len(X) |
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45 | w = zeros(N,Float) |
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46 | for i in range(N): |
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47 | if X[i]<=0.0: |
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48 | w[i] = bed_slope*X[i] |
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49 | else: |
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50 | w[i] = bed_slope*X[i] + h_0 |
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51 | return w |
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52 | |
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53 | def elevation(X): |
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54 | N = len(X) |
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55 | y=zeros(N, Float) |
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56 | for i in range(N): |
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57 | y[i] = bed_slope*X[i] |
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58 | return y |
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59 | """ |
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60 | #=========================================================================# |
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61 | #The following values are set in parameters.py |
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62 | h_0 = 10.0 # depth upstream. Note that the depth downstream is 0.0 |
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63 | L = 2000.0 # length of stream/domain |
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64 | n = 100 # number of cells |
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65 | cell_len = L/n # length of each cell |
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66 | points = zeros(n+1, Float) |
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67 | for i in range (n+1): |
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68 | points[i] = i*cell_len - 0.5*L |
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69 | |
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70 | bed_slope = 0.005 # bottom slope, positive if it is increasing bottom. |
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71 | c0 = sqrt(g*h_0) # sound speed |
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72 | m = -1.0*g*bed_slope # auxiliary variable |
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73 | #==========================================================================# |
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74 | """ |
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75 | boundary = { (0,0): 'left',(n-1,1): 'right'} |
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76 | domain = Domain(points,boundary) |
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77 | domain.order = 2 |
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78 | domain.set_timestepping_method('rk2') |
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79 | domain.set_CFL(1.0) |
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80 | domain.beta = 1.0 |
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81 | domain.set_limiter("minmod") |
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82 | |
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83 | def f_right(t): |
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84 | z_r = bed_slope*(0.5*L) |
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85 | h_r = h_0 #+ bed_slope*cell_len |
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86 | w_r = z_r + h_r |
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87 | u_r = m*t |
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88 | #['stage', 'xmomentum', 'elevation', 'height', 'velocity'] |
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89 | return [w_r, u_r*h_r, z_r, h_r, u_r] |
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90 | |
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91 | T_right = Time_boundary(domain,f_right) |
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92 | #T_right = Transmissive_boundary(domain) |
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93 | #D_right = Dirichlet_boundary([bed_slope*(0.5*L)+h_0, (m*domain.time)*h_0, bed_slope*(0.5*L), h_0, m*domain.time]) |
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94 | D_left = Dirichlet_boundary([-1.0*bed_slope*(0.5*L), 0.0, -1.0*bed_slope*(0.5*L), 0.0, 0.0]) |
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95 | domain.set_boundary({'left':D_left,'right':T_right}) |
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96 | domain.set_quantity('stage',stage) |
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97 | domain.set_quantity('elevation',elevation) |
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98 | |
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99 | X = domain.vertices |
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100 | C = domain.centroids |
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101 | |
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102 | yieldstep = finaltime = 1.0 |
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103 | t0 = time.time() |
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104 | |
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105 | while finaltime <= 1.1: |
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106 | for t in domain.evolve(yieldstep = yieldstep, finaltime = finaltime): |
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107 | domain.write_time() |
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108 | |
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109 | #The following is for computing the error and plotting the result |
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110 | Mom = domain.quantities['xmomentum'] |
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111 | Height = domain.quantities['height'] |
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112 | Stage = domain.quantities['stage'] |
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113 | Velocity = domain.quantities['velocity'] |
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114 | Elevation = domain.quantities['elevation'] |
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115 | |
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116 | #The following is for computing the error |
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117 | Uc,Hc,Wc,Zc,Mc = analytical_sol(C,domain.time) |
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118 | HeightC = Height.centroid_values |
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119 | MomC = Mom.centroid_values |
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120 | StageC = Stage.centroid_values |
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121 | VelC = Velocity.centroid_values |
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122 | ElevationC = Elevation.centroid_values |
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123 | |
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124 | print "number of cells=",n |
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125 | W_error = (1.0/n)*sum(abs(Wc-StageC)) |
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126 | M_error = (1.0/n)*sum(abs(Mc-MomC)) |
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127 | U_error = (1.0/n)*sum(abs(Uc-VelC)) |
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128 | print "stage_error %.10f" %(W_error) |
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129 | print "momentum_error %.10f"%(M_error) |
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130 | print "velocity_error %.10f" %(U_error) |
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131 | |
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132 | |
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133 | #The following is for plotting the result. |
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134 | Uv,Hv,Wv,Zv,Mv = analytical_sol(X.flat,domain.time) |
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135 | HeightV = Height.vertex_values |
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136 | MomV = Mom.vertex_values |
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137 | StageV = Stage.vertex_values |
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138 | VelV = Velocity.vertex_values |
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139 | ElevationV = Elevation.vertex_values |
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140 | from pylab import clf,plot,title,xlabel,ylabel,legend,savefig,show,hold,subplot |
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141 | hold(False) |
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142 | clf() |
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143 | |
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144 | plot1 = subplot(311) |
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145 | plot(X.flat,Wv,'b-', X.flat,StageV.flat,'k--', X.flat,ElevationV.flat,'k:') |
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146 | #plot(X.flat,Wv, X.flat,StageV.flat, X.flat,ElevationV.flat) |
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147 | #xlabel('Position') |
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148 | ylabel('Stage') |
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149 | #plot1.set_ylim([-1.0,21.0]) |
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150 | #plot1.set_xlim([-500.0,-420.0])#([-9.0e-3,9.0e-3]) |
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151 | #legend(('Analytical solution', 'Numerical solution', 'Discretized bed'), 'upper left', shadow=False) |
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152 | |
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153 | plot2 = subplot(312) |
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154 | plot(X.flat,Mv,'b-', X.flat,MomV.flat,'k--') |
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155 | #xlabel('Position') |
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156 | ylabel('Momentum') |
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157 | #plot2.set_xlim([-300.0,300.0]) |
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158 | #plot2.set_ylim([-310.0,10.0])#([-90.0,10.0]) |
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159 | #legend(('analytical solution', 'numerical solution'), 'lower right', shadow=False) |
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160 | |
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161 | plot3 = subplot(313) |
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162 | plot(X.flat,Uv,'b-', X.flat,VelV.flat,'k--') |
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163 | xlabel('Position') |
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164 | ylabel('Velocity') |
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165 | #plot3.set_xlim([-300.0,300.0]) |
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166 | #plot3.set_ylim([-45.0,5.0])#([-30.0,5.0]) |
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167 | #legend(('analytical solution', 'numerical solution'), 'lower right', shadow=False) |
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168 | |
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169 | finaltime = finaltime + 10.0 |
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170 | |
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171 | file = "B-case2-" |
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172 | file += str(n) |
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173 | file += ".eps" |
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174 | #savefig(file) |
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175 | |
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176 | show() |
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177 | |
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178 | |
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