added simplified histogram

1d_diffusion.ipynb

@@ -47,7 +47,7 @@
    "metadata": {},
    "outputs": [],
    "source": [
-    "n = zeros(N);\n",
+    "n = DistributionArray{Float64}(0., 1., N);\n",
     "f = FluxArray{Float64}(N);"
    ]
   },
@@ -59,7 +59,17 @@
     {
      "data": {
       "text/plain": [
-       "1"
+       "10-element Array{Float64,1}:\n",
+       " 0.0\n",
+       " 0.0\n",
+       " 0.0\n",
+       " 0.0\n",
+       " 1.0\n",
+       " 0.0\n",
+       " 0.0\n",
+       " 0.0\n",
+       " 0.0\n",
+       " 0.0"
       ]
      },
      "execution_count": 5,
@@ -68,7 +78,8 @@
     }
    ],
    "source": [
-    "n[Integer(length(n)/2)] = 1"
+    "n.p[Integer(size(n)/2)] = 1;\n",
+    "n.p"
    ]
   },
   {
@@ -78,7 +89,7 @@
    "outputs": [],
    "source": [
     "fill_fr!(f);\n",
-    "fill_lr!(f, n);"
+    "fill_lr!(f, n.p);"
    ]
   },
   {
@@ -90,16 +101,16 @@
      "data": {
       "text/plain": [
        "10-element Array{Float64,1}:\n",
-       " 0.0                \n",
-       " 0.0                \n",
-       " 0.0                \n",
-       " 0.0                \n",
-       " 0.13816584763737239\n",
-       " 0.0                \n",
-       " 0.0                \n",
-       " 0.0                \n",
-       " 0.0                \n",
-       " 0.0                "
+       " 0.0                  \n",
+       " 0.0                  \n",
+       " 0.0                  \n",
+       " 0.0                  \n",
+       " 0.0022742765607139948\n",
+       " 0.0                  \n",
+       " 0.0                  \n",
+       " 0.0                  \n",
+       " 0.0                  \n",
+       " 0.0                  "
       ]
      },
      "execution_count": 7,
@@ -120,16 +131,16 @@
      "data": {
       "text/plain": [
        "10-element Array{Float64,1}:\n",
-       " 0.0               \n",
-       " 0.0               \n",
-       " 0.0               \n",
-       " 0.0               \n",
-       " 0.8618341523626276\n",
-       " 0.0               \n",
-       " 0.0               \n",
-       " 0.0               \n",
-       " 0.0               \n",
-       " 0.0               "
+       " 0.0              \n",
+       " 0.0              \n",
+       " 0.0              \n",
+       " 0.0              \n",
+       " 0.997725723439286\n",
+       " 0.0              \n",
+       " 0.0              \n",
+       " 0.0              \n",
+       " 0.0              \n",
+       " 0.0              "
       ]
      },
      "execution_count": 8,
@@ -189,17 +200,17 @@
      "data": {
       "text/plain": [
        "11-element Array{Float64,1}:\n",
-       "    0.0            \n",
-       "    0.0            \n",
-       "    0.0            \n",
-       "    0.0            \n",
-       "  138.1658476373724\n",
-       " -861.8341523626276\n",
-       "    0.0            \n",
-       "    0.0            \n",
-       "    0.0            \n",
-       "    0.0            \n",
-       "    0.0            "
+       "    0.0               \n",
+       "    0.0               \n",
+       "    0.0               \n",
+       "    0.0               \n",
+       "    2.2742765607139948\n",
+       " -997.725723439286    \n",
+       "    0.0               \n",
+       "    0.0               \n",
+       "    0.0               \n",
+       "    0.0               \n",
+       "    0.0               "
       ]
      },
      "execution_count": 11,
@@ -229,17 +240,17 @@
      "data": {
       "text/plain": [
        "11-element Array{Float64,1}:\n",
-       " -0.42054232430683963\n",
-       " -0.0                \n",
-       "  0.0                \n",
-       "  0.0                \n",
-       "  0.9582299402193841 \n",
-       "  9.427963410111976  \n",
-       "  0.0                \n",
-       "  0.0                \n",
-       "  0.0                \n",
-       " -0.0                \n",
-       "  0.6927609681908308 "
+       " -0.8640646960498399\n",
+       "  0.0               \n",
+       "  0.0               \n",
+       " -0.0               \n",
+       "  0.3672085709169771\n",
+       " -2.924360797089483 \n",
+       "  0.0               \n",
+       "  0.0               \n",
+       " -0.0               \n",
+       "  0.0               \n",
+       "  0.3838915655069409"
       ]
      },
      "execution_count": 13,
@@ -270,15 +281,15 @@
       "text/plain": [
        "11-element Array{Float64,1}:\n",
        "  0.0               \n",
-       " -0.0               \n",
-       "  0.0               \n",
        "  0.0               \n",
-       "  0.9582299402193841\n",
-       "  9.427963410111976 \n",
        "  0.0               \n",
+       " -0.0               \n",
+       "  0.3672085709169771\n",
+       " -2.924360797089483 \n",
        "  0.0               \n",
        "  0.0               \n",
        " -0.0               \n",
+       "  0.0               \n",
        "  0.0               "
       ]
      },

src/fp.jl

 module FP
 
-export FluxArray, size, reset!, fill_fr!, fill_lr!, fill_df!, fill_sf!, apply_bc!
+export DistributionArray
+export size
+export FluxArray, reset!, fill_fr!, fill_lr!, fill_df!, fill_sf!, apply_bc!
 
 import Base.size
 import Random.rand!
@@ -10,6 +12,35 @@ include("sample.jl")
 import .Sample
 
 
+"""
+DistributionArrays store the distribution (probablity) `p` data, together with
+the cell-center `xc` and face-center `xf` coodrdinates. This is essentially a
+cheap histogram.
+"""
+mutable struct DistributionArray{T}
+
+    xc::Array{T};
+    xf::Array{T};
+    p::Array{T};
+
+    function DistributionArray{T}(xlo::T, xhi::T, n::Integer) where T
+        p::Array{T} = zeros(n);
+
+        xf::Array{T} = collect(range(xlo, stop = xhi, length = n+1));
+        
+        dx::T = (xhi-xlo)/n;
+        xc::Array{T} = xf[1:n] .+ dx/2;
+        
+        new{T}(xc, xf, p)
+    end
+end
+
+function size(d::DistributionArray{T}) where T
+    return size(d.p, 1)
+end
+
+
+
 """
 FluxArrays store flux data as Struct-of-Arrays. These arrays are allocated and
 initialized (to zero) by the constructor (each array has length `n+1` where `n`
@@ -18,23 +49,23 @@ is the argument of the constructor).
 mutable struct FluxArray{T}
 
     # Fluxes
-    total::Array{T}
-    diffusive::Array{T}
-    stochastic::Array{T}
+    total::Array{T};
+    diffusive::Array{T};
+    stochastic::Array{T};
 
     # Left and Right sampling
-    fr::Array{T}
-    left::Array{T}
-    right::Array{T}
+    fr::Array{T};
+    left::Array{T};
+    right::Array{T};
 
     # Storage for the Dististribution object (used to sample Gaussian random variables)
-    distribution  
+    distribution;
 
     """
     Constructor: allocates memory for all fluxes, and intializes the distribution
     object. Note that `n` is the length of the corresponding 1D data array.
     """
-    function FluxArray{T}(n) where T
+    function FluxArray{T}(n::Integer) where T
         total::Array{T}      = zeros(n + 1);
         diffusive::Array{T}  = zeros(n + 1);
         stochastic::Array{T} = zeros(n + 1);