[631] | 1 | import time |
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| 2 | import math |
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| 3 | import numpy as np |
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| 4 | import netCDF4 as cdf |
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| 5 | import matplotlib.tri as tri |
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| 6 | import matplotlib.pyplot as plt |
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| 7 | from unstructured import init_mesh |
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| 8 | |
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| 9 | radian=180/math.pi |
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| 10 | |
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| 11 | #------------------- Hybrid mass-based coordinate ------------- |
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| 12 | |
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| 13 | # compute hybrid coefs from distribution of mass |
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| 14 | |
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| 15 | def compute_hybrid_coefs(mass): |
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[636] | 16 | if mass.ndim==2 : |
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| 17 | nx,llm=mass.shape |
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| 18 | mass_dak = np.zeros((nx,llm)) |
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| 19 | mass_dbk = np.zeros((nx,llm)) |
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| 20 | mass_bl = np.zeros((nx,llm+1))+1. |
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| 21 | for i in range(nx): |
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| 22 | m_i = mass[i,:] |
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| 23 | dbk_i = m_i/sum(m_i) |
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| 24 | mass_dbk[i,:] = dbk_i |
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| 25 | mass_bl[i,1:]= 1.-dbk_i.cumsum() |
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| 26 | if mass.ndim==3 : |
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| 27 | nx,ny,llm=mass.shape |
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| 28 | mass_dak = np.zeros((nx,ny,llm)) |
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| 29 | mass_dbk = np.zeros((nx,ny,llm)) |
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| 30 | mass_bl = np.zeros((nx,ny,llm+1))+1. |
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| 31 | for i in range(nx): |
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| 32 | for j in range(ny): |
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| 33 | m_ij = mass[i,j,:] |
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| 34 | dbk_ij = m_ij/sum(m_ij) |
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| 35 | mass_dbk[i,j,:] = dbk_ij |
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| 36 | mass_bl[i,j,1:]= 1.-dbk_ij.cumsum() |
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| 37 | |
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[631] | 38 | return mass_bl, mass_dak, mass_dbk |
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| 39 | |
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| 40 | #----------------------- Cartesian mesh ----------------------- |
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| 41 | |
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[639] | 42 | def squeeze(dims): return np.zeros([n for n in dims if n>1]) |
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[631] | 43 | |
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| 44 | # arrays is a list of arrays |
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| 45 | # vals is a list of tuples |
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| 46 | # each tuple is stored in each array |
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| 47 | def put(ij, deg, arrays, vals): |
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| 48 | k=0 |
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| 49 | for vv in vals: # vv is a tuple of values to be stored in arrays |
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| 50 | for array,v in zip(arrays,vv): |
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| 51 | array[ij,k]=v |
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| 52 | k=k+1 |
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| 53 | deg[ij]=k |
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| 54 | |
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| 55 | class Cartesian_mesh: |
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| 56 | def __init__(self,nx,ny,llm,nqdyn,Lx,Ly,f): |
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| 57 | dx,dy = Lx/nx, Ly/ny |
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| 58 | self.dx, self.dy, self.f = dx,dy,f |
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| 59 | self.nx, self.ny, self.llm, self.nqdyn = nx,ny,llm,nqdyn |
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| 60 | self.field_z = self.field_mass |
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| 61 | # 1D coordinate arrays |
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| 62 | x=(np.arange(nx)-nx/2.)*Lx/nx |
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| 63 | y=(np.arange(ny)-ny/2.)*Ly/ny |
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| 64 | lev=np.arange(llm) |
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| 65 | levp1=np.arange(llm+1) |
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| 66 | self.x, self.y, self.lev, self.levp1 = x,y,lev,levp1 |
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| 67 | # 3D coordinate arrays |
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| 68 | self.xx,self.yy,self.ll = np.meshgrid(x,y,lev, indexing='ij') |
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| 69 | self.xxp1,self.yyp1,self.llp1 = np.meshgrid(x,y,levp1, indexing='ij') |
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| 70 | # beware conventions for indexing |
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| 71 | # Fortran order : llm,nx*ny,nqdyn / indices start at 1 |
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| 72 | # Python order : nqdyn,ny,nx,llm / indices start at 0 |
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| 73 | # indices below follow Fortran while x,y follow Python/C |
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| 74 | index=lambda x,y : ((x+(nx*(y+2*ny)))%(nx*ny))+1 |
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| 75 | indexu=lambda x,y : 2*index(x,y)-1 |
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| 76 | indexv=lambda x,y : 2*index(x,y) |
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| 77 | indices = lambda shape : np.zeros(shape,np.int32) |
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| 78 | |
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| 79 | primal_nb = indices(nx*ny) |
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| 80 | primal_edge = indices((nx*ny,4)) |
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| 81 | primal_ne = indices((nx*ny,4)) |
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| 82 | |
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| 83 | dual_nb = indices(nx*ny) |
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| 84 | dual_edge = indices((nx*ny,4)) |
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| 85 | dual_ne = indices((nx*ny,4)) |
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| 86 | dual_vertex = indices((nx*ny,4)) |
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| 87 | Riv2 = np.zeros((nx*ny,4)) |
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| 88 | |
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| 89 | left = indices(2*nx*ny) |
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| 90 | right = indices(2*nx*ny) |
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| 91 | up = indices(2*nx*ny) |
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| 92 | down = indices(2*nx*ny) |
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| 93 | le_de = np.zeros(2*nx*ny) |
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| 94 | |
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| 95 | trisk_deg = indices(2*nx*ny) |
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| 96 | trisk = indices((2*nx*ny,4)) # 4 TRiSK coefs per edge |
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| 97 | wee = np.zeros((2*nx*ny,4)) |
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| 98 | |
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| 99 | for x in range(nx): |
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| 100 | for y in range(ny): |
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| 101 | # NB : Fortran indices start at 1 |
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| 102 | # primal cells |
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| 103 | put(index(x,y)-1,primal_nb,(primal_edge,primal_ne), |
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| 104 | ((indexu(x,y),1), |
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| 105 | (indexv(x,y),1), |
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| 106 | (indexu(x-1,y),-1), |
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| 107 | (indexv(x,y-1),-1) )) |
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| 108 | # dual cells |
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| 109 | put(index(x,y)-1,dual_nb,(dual_edge,dual_vertex,dual_ne,Riv2), |
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| 110 | ((indexv(x+1,y),index(x,y),1,.25), |
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| 111 | (indexu(x,y+1),index(x+1,y),-1,.25), |
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| 112 | (indexv(x,y),index(x+1,y+1),-1,.25), |
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| 113 | (indexu(x,y),index(x,y+1),1,.25) )) |
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| 114 | # edges : |
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| 115 | # left and right are adjacent primal cells |
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| 116 | # flux is positive when going from left to right |
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| 117 | # up and down are adjacent dual cells (vertices) |
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| 118 | # circulation is positive when going from down to up |
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| 119 | # u-points |
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| 120 | ij =indexu(x,y)-1 |
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| 121 | left[ij]=index(x,y) |
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| 122 | right[ij]=index(x+1,y) |
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| 123 | down[ij]=index(x,y-1) |
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| 124 | up[ij]=index(x,y) |
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| 125 | le_de[ij]=dy/dx |
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| 126 | put(ij,trisk_deg,(trisk,wee),( |
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| 127 | (indexv(x,y),-.25), |
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| 128 | (indexv(x+1,y),-.25), |
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| 129 | (indexv(x,y-1),-.25), |
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| 130 | (indexv(x+1,y-1),-.25))) |
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| 131 | # v-points |
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| 132 | ij = indexv(x,y)-1 |
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| 133 | left[ij]=index(x,y) |
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| 134 | right[ij]=index(x,y+1) |
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| 135 | down[ij]=index(x,y) |
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| 136 | up[ij]=index(x-1,y) |
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| 137 | le_de[ij]=dx/dy |
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| 138 | put(ij,trisk_deg,(trisk,wee),( |
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| 139 | (indexu(x,y),.25), |
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| 140 | (indexu(x-1,y),.25), |
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| 141 | (indexu(x,y+1),.25), |
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| 142 | (indexu(x-1,y+1),.25))) |
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| 143 | Aiv=np.zeros(nx*ny)+dx*dy # Ai=Av=dx*dy |
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| 144 | init_mesh(llm,nqdyn,2*nx*ny,nx*ny,nx*ny,4,4,4, |
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| 145 | primal_nb,primal_edge,primal_ne, |
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| 146 | dual_nb,dual_edge,dual_ne,dual_vertex, |
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| 147 | left,right,down,up,trisk_deg,trisk, |
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| 148 | Aiv,Aiv,f+0.*Aiv,le_de,Riv2,-wee) |
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| 149 | |
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| 150 | def field_theta(self): return squeeze((self.nqdyn,self.ny,self.nx,self.llm)) |
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| 151 | def field_mass(self): return squeeze((self.ny,self.nx,self.llm)) |
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| 152 | def field_z(self): return squeeze((self.ny,self.nx,self.llm)) |
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| 153 | def field_w(self): return squeeze((self.ny,self.nx,self.llm+1)) |
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| 154 | def field_u(self): return np.zeros((self.ny,2*self.nx,self.llm)) |
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| 155 | def field_ps(self): return squeeze((self.ny,self.nx)) |
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| 156 | def ucomp(self,u): return u[:,range(0,2*self.nx,2),:] |
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| 157 | def set_ucomp(self,uv,u): uv[:,range(0,2*self.nx,2),:]=u |
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| 158 | def vcomp(self,u): return u[:,range(1,2*self.nx,2),:] |
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| 159 | |
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| 160 | #---------------------- MPAS fully unstructured mesh ------------------------ |
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| 161 | |
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| 162 | def compute_ne(num,deg,edges,left,right): |
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| 163 | ne = np.zeros_like(edges) |
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| 164 | for cell in range(num): |
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| 165 | for iedge in range(deg[cell]): |
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| 166 | edge = edges[cell,iedge]-1 |
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| 167 | if left[edge]==cell+1: ne[cell,iedge]+=1 |
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| 168 | if right[edge]==cell+1: ne[cell,iedge]-=1 |
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| 169 | if ne[cell,iedge]==0 : print 'error at cell,iedge', cell, iedge |
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| 170 | return ne |
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| 171 | |
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| 172 | def plot(tri,data): |
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| 173 | plt.figure(figsize=(12,4)) |
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| 174 | plt.gca().set_aspect('equal') |
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| 175 | plt.tricontourf(tri, data, 20) |
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| 176 | plt.colorbar() |
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| 177 | plt.ylim((-90,90)) |
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| 178 | plt.xlim((0,360)) |
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| 179 | |
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| 180 | class MPAS_Mesh: |
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| 181 | def __init__(self, gridfile, llm, nqdyn, radius, f): |
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| 182 | self.gridfile, self.llm, self.nqdyn = gridfile,llm,nqdyn |
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| 183 | self.radius, self.f = radius, f |
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| 184 | # open mesh file, get main dimensions |
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| 185 | try: |
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| 186 | nc = cdf.Dataset(gridfile, "r") |
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| 187 | except RuntimeError: |
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| 188 | print """ |
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| 189 | Unable to open grid file %s, maybe you forgot to download it ? |
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| 190 | To do so, go to the 'Python/' dir and execute './get_MPAS_grids.sh'. |
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| 191 | """ % gridfile |
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| 192 | raise |
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| 193 | |
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| 194 | def getdims(*names): return [len(nc.dimensions[name]) for name in names] |
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| 195 | def getvars(*names): |
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| 196 | for name in names : print "getvar %s ..."%name |
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| 197 | time1=time.time() |
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| 198 | ret=[nc.variables[name][:] for name in names] |
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| 199 | print "... Done in %f seconds"%(time.time()-time1) |
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| 200 | return ret |
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| 201 | primal_num, edge_num, dual_num = getdims('nCells','nEdges','nVertices') |
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| 202 | print 'Number of primal cells, dual cells and edges : %d, %d, %d '%(primal_num,dual_num,edge_num) |
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| 203 | primal_deg, trisk_deg = getvars('nEdgesOnCell','nEdgesOnEdge') |
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| 204 | dual_deg = [3 for i in range(dual_num) ] |
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| 205 | dual_deg = np.ascontiguousarray(dual_deg,dtype=np.int32) # NB : Fortran code expects 32-bit ints |
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| 206 | |
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| 207 | # get indices for stencils |
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| 208 | # primal -> vertices (unused) |
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| 209 | primal_vertex, dual_vertex = getvars('verticesOnCell','cellsOnVertex') |
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| 210 | # primal <-> edges |
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| 211 | primal_edge, left_right = getvars('edgesOnCell','cellsOnEdge') |
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| 212 | left,right = left_right[:,0], left_right[:,1] |
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| 213 | primal_ne = compute_ne(primal_num,primal_deg,primal_edge,left,right) |
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| 214 | # dual <-> edges |
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| 215 | dual_edge, down_up = getvars('edgesOnVertex','verticesOnEdge') |
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| 216 | down,up = down_up[:,0], down_up[:,1] |
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| 217 | dual_ne = compute_ne(dual_num,dual_deg,dual_edge,up,down) |
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| 218 | # primal <-> dual, edges <-> edges (TRiSK) |
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| 219 | dual_vertex, trisk = getvars('cellsOnVertex','edgesOnEdge') |
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| 220 | # get positions, lengths, surfaces and weights |
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| 221 | le,de,Ai,Av = getvars('dvEdge','dcEdge','areaCell','areaTriangle') |
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| 222 | lat_i,lon_i = getvars('latCell','lonCell') |
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| 223 | lat_v,lon_v = getvars('latVertex','lonVertex') |
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| 224 | lat_e,lon_e,angle_e = getvars('latEdge','lonEdge','angleEdge') |
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| 225 | wee,Riv2 = getvars('weightsOnEdge','kiteAreasOnVertex') |
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| 226 | |
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| 227 | # fix normalization of wee and Riv2 weights |
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| 228 | for edge1 in range(edge_num): |
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| 229 | for i in range(trisk_deg[edge1]): |
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| 230 | edge2=trisk[edge1,i]-1 # NB Fortran vs C/Python indexing |
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| 231 | wee[edge1,i] = de[edge1]*wee[edge1,i]/le[edge2] |
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| 232 | for ivertex in range(dual_num): |
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| 233 | for j in range(3): |
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| 234 | Riv2[ivertex,j]=Riv2[ivertex,j]/Av[ivertex] |
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| 235 | r=Riv2[ivertex,:] |
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| 236 | r=sum(r) |
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| 237 | if abs(r-1.)>1e-6 : print 'error with Riv2 at vertex ', ivertex |
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| 238 | |
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| 239 | max_primal_deg, max_dual_deg, max_trisk_deg = getdims('maxEdges','vertexDegree','maxEdges2') |
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| 240 | |
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| 241 | # CRITICAL : force arrays left, etc. to be contiguous in memory: |
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| 242 | left,right,up,down = [np.ascontiguousarray(x) for x in (left,right,up,down)] |
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| 243 | trisk,wee,primal_edge = [np.ascontiguousarray(x) for x in (trisk,wee,primal_edge)] |
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| 244 | |
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| 245 | print ('Max stencil sizes (div,curl,trisk) : %d, %d, %d' |
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| 246 | % (max_primal_deg, max_dual_deg, max_trisk_deg) ) |
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| 247 | |
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| 248 | r2 = radius**2 |
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| 249 | Av = r2*Av |
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| 250 | fv = f(lon_v,lat_v) # Coriolis parameter |
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| 251 | self.Ai, self.Av, self.fv = r2*Ai,Av,fv |
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| 252 | self.le, self.de, self.le_de = radius*le, radius*de, le/de |
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| 253 | self.trisk_deg, self.trisk, self.wee = trisk_deg, trisk, wee |
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| 254 | init_mesh(llm, nqdyn, edge_num, primal_num,dual_num, |
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| 255 | max_trisk_deg, max_primal_deg, max_dual_deg, |
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| 256 | primal_deg,primal_edge,primal_ne, |
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| 257 | dual_deg,dual_edge,dual_ne,dual_vertex, |
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| 258 | left,right,down,up,trisk_deg,trisk, |
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| 259 | self.Ai,self.Av,self.fv,le/de,Riv2,wee) |
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| 260 | |
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| 261 | for edge in range(edge_num): |
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| 262 | iedge = trisk[edge,0:trisk_deg[edge]] |
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| 263 | if iedge.min()<1 : |
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| 264 | print 'error' |
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| 265 | |
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| 266 | self.primal_num, self.edge_num, self.dual_num = primal_num, edge_num, dual_num |
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| 267 | def period(x) : return (x+2*math.pi)%(2*math.pi) |
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| 268 | lon_i, lon_v, lon_e = map(period, (lon_i,lon_v,lon_e)) |
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| 269 | self.lon_i, self.lat_i = lon_i, lat_i |
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| 270 | self.lon_v, self.lat_v = lon_v, lat_v |
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| 271 | self.lon_e, self.lat_e, self.angle_e = lon_e, lat_e, angle_e |
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| 272 | self.primal_deg, self.primal_vertex = primal_deg, primal_vertex |
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| 273 | self.primal = tri.Triangulation(lon_i*180./math.pi, lat_i*180./math.pi) |
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| 274 | self.dual_deg, self.dual_vertex = dual_deg, dual_vertex |
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| 275 | self.dual = tri.Triangulation(lon_v*180./math.pi, lat_v*180./math.pi) |
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| 276 | self.triedge = tri.Triangulation(lon_e*180./math.pi, lat_e*180./math.pi) |
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| 277 | self.dx = de.min() |
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| 278 | self.lon3D_i, self.ll3D = np.meshgrid(lon_i, range(llm)) |
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| 279 | self.lat3D_i, self.ll3D = np.meshgrid(lat_i, range(llm)) |
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[639] | 280 | def field_theta(self,n=1): return squeeze((n,self.nqdyn,self.primal_num,self.llm)) |
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| 281 | def field_mass(self,n=1): return squeeze((n,self.primal_num,self.llm)) |
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| 282 | def field_z(self,n=1): return squeeze((n,self.dual_num,self.llm)) |
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| 283 | def field_w(self,n=1): return squeeze((n,self.primal_num,self.llm+1)) |
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| 284 | def field_u(self,n=1): return squeeze((n,self.edge_num,self.llm)) |
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| 285 | def field_ps(self,n=1): return squeeze((n,self.primal_num,)) |
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[631] | 286 | def ucov2D(self, ulon, ulat): |
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| 287 | return self.de*(ulon*np.cos(self.angle_e)+ulat*np.sin(self.angle_e)) |
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| 288 | def ucov3D(self, ulon, ulat): |
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| 289 | ucov = np.zeros((self.edge_num,ulon.shape[1])) |
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| 290 | for edge in range(self.edge_num): |
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| 291 | angle=self.angle_e[edge] |
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| 292 | ucov[edge,:] = self.de[edge]*(ulon[edge,:]*math.cos(angle)+ulat[edge,:]*math.sin(angle)) |
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| 293 | return ucov |
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| 294 | def plot_i(self,data): |
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| 295 | plot(self.primal,data) |
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| 296 | def plot_v(self,data): |
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| 297 | plot(self.dual,data) |
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| 298 | def plot_e(self,data): |
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| 299 | plot(self.triedge,data) |
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| 300 | |
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| 301 | #-------------------------------------- Mesh partitioning ------------------------------------------# |
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| 302 | |
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| 303 | def partition_from_stencil(owner2, degree, stencil): |
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| 304 | # given a stencil dim1->dim2 and owner2 on dim2, define owner[i] on dim1 as min(stencil[i,:] if i is even, max if odd |
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| 305 | dim1, dim2= degree.dim, owner2.dim |
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| 306 | degree, stencil, n = degree.data, stencil.data, dim1.end-dim1.start |
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| 307 | cells2 = list_stencil(degree, stencil) |
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| 308 | cells2 = sorted(list(set(list(cells2)))) # list of cells for which we need to know owner2 |
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| 309 | get2 = dim2.getter(cells2) |
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| 310 | owner1, owner2, glob2loc = np.zeros(n, dtype=np.int32), get2(owner2), get2.dict |
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| 311 | for i in range(n): |
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| 312 | owners = [ owner2[glob2loc[stencil[i,j]]] for j in range(degree[i]) ] |
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| 313 | if i%2 == 0 : owner1[i] = min(owners) |
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| 314 | else : owner1[i] = max(owners) |
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| 315 | return owner1 |
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| 316 | |
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| 317 | def find_my_cells(owner): # a PArray1D containing the data returned by partition_mesh |
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| 318 | dim, comm, owner = owner.dim, owner.dim.comm, owner.data |
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| 319 | mpi_rank, mpi_size = comm.Get_rank(), comm.Get_size() |
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| 320 | cells=[set() for i in range(mpi_size)] |
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| 321 | for i in range(len(owner)): |
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| 322 | cells[owner[i]].add(dim.start+i) |
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| 323 | cells = [sorted(list(cells[i])) for i in range(mpi_size)] |
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| 324 | mycells = comm.alltoall(cells) |
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| 325 | mycells = sorted(sum(mycells, [])) # concatenate into a single list |
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| 326 | return mycells |
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| 327 | |
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| 328 | #---------------------------------- Stencil management ---------------------------------------# |
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| 329 | |
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| 330 | # Class Stencil represents an adjacency relationship (e.g. cell=>edges) |
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| 331 | # using adjacency information read from PArrays |
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| 332 | # It computes a list of "edges" adjacent to a given list of "cells" |
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| 333 | # This is used to form the sets E0 -> C0 -> E1 -> V1 -> E2 -> C1 |
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| 334 | # which are then used to form lists of global indices for V1,C1,E2 such that |
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| 335 | # C0, E0, E1 form contiguous subsets of C1, E2 starting from 0 |
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| 336 | |
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| 337 | def reindex(vertex_dict, degree, bounds): |
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| 338 | for i in range(degree.size): |
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| 339 | for j in range(degree[i]): |
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| 340 | bounds[i,j] = vertex_dict[bounds[i,j]] |
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| 341 | |
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| 342 | class Stencil_glob: |
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| 343 | def __init__(self, degree, neigh, weight=None): |
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| 344 | self.degree, self.neigh, self.weight = degree, neigh, weight |
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| 345 | def __call__(self, cells, neigh_dict=None): |
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| 346 | return Stencil(cells, self.degree, self.neigh, neigh_dict, self.weight) |
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| 347 | |
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| 348 | class Stencil: |
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| 349 | def __init__(self, cells, degree, neigh, neigh_dict, weight=None): |
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| 350 | get = degree.dim.getter(cells) |
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| 351 | mydegree, myneigh = [get(x) for x in (degree, neigh)] |
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| 352 | if not weight is None : myweight = get(weight) |
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| 353 | if neigh_dict is None : |
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| 354 | keep = lambda n : True |
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| 355 | else : # if neigh_dict is present, only neighbours in dict are retained |
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| 356 | keep = lambda n : n in neigh_dict |
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| 357 | neigh_set = list_stencil(mydegree, myneigh, keep) |
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| 358 | self.neigh_set = list(set(list(neigh_set) )) |
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| 359 | rej=0 |
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| 360 | for i in range(len(mydegree)): # keep only elements in neigh_dict, in-place |
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| 361 | k=0 |
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| 362 | for j in range(mydegree[i]): |
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| 363 | n=myneigh[i,j] |
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| 364 | if keep(n): |
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| 365 | myneigh[i,k]=n |
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| 366 | if not weight is None : myweight[i,k]=myweight[i,j] |
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| 367 | k=k+1 |
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| 368 | else: |
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| 369 | rej=rej+1 |
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| 370 | mydegree[i]=k |
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| 371 | if neigh_dict is None: |
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| 372 | neigh_dict = {j:i for i,j in enumerate(self.neigh_set)} |
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| 373 | myneigh_loc = reindex(neigh_dict, mydegree, myneigh) |
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| 374 | self.degree, self.neigh_glob, self.neigh_loc = mydegree, myneigh, myneigh_loc |
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| 375 | |
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| 376 | def progressive_iter(mylist, cell_lists): |
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| 377 | for thelist in cell_lists: |
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| 378 | mylist = mylist + list(set(thelist)-set(mylist)) |
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| 379 | yield mylist |
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| 380 | def progressive_list(*cell_lists): |
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| 381 | # cell_lists : a tuple of lists of global indices, with each list a subset of the next |
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| 382 | # returns : a list 'mylist' such that for each list 'thelist' in cell_lists, thelist = mylist[0:len(thelist)] |
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| 383 | # example : edge_list = progressive_list(E0,E1,E2) with E0,E1,E2 increasing lists of cell edges |
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| 384 | return list(progressive_iter([], cell_lists)) |
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