Important: Please read the installation page for details about how to install the toolboxes. $\newcommand{\dotp}[2]{\langle #1, #2 \rangle}$ $\newcommand{\enscond}[2]{\lbrace #1, #2 \rbrace}$ $\newcommand{\pd}[2]{ \frac{ \partial #1}{\partial #2} }$ $\newcommand{\umin}[1]{\underset{#1}{\min}\;}$ $\newcommand{\umax}[1]{\underset{#1}{\max}\;}$ $\newcommand{\umin}[1]{\underset{#1}{\min}\;}$ $\newcommand{\uargmin}[1]{\underset{#1}{argmin}\;}$ $\newcommand{\norm}[1]{\|#1\|}$ $\newcommand{\abs}[1]{\left|#1\right|}$ $\newcommand{\choice}[1]{ \left\{ \begin{array}{l} #1 \end{array} \right. }$ $\newcommand{\pa}[1]{\left(#1\right)}$ $\newcommand{\diag}[1]{{diag}\left( #1 \right)}$ $\newcommand{\qandq}{\quad\text{and}\quad}$ $\newcommand{\qwhereq}{\quad\text{where}\quad}$ $\newcommand{\qifq}{ \quad \text{if} \quad }$ $\newcommand{\qarrq}{ \quad \Longrightarrow \quad }$ $\newcommand{\ZZ}{\mathbb{Z}}$ $\newcommand{\CC}{\mathbb{C}}$ $\newcommand{\RR}{\mathbb{R}}$ $\newcommand{\EE}{\mathbb{E}}$ $\newcommand{\Zz}{\mathcal{Z}}$ $\newcommand{\Ww}{\mathcal{W}}$ $\newcommand{\Vv}{\mathcal{V}}$ $\newcommand{\Nn}{\mathcal{N}}$ $\newcommand{\NN}{\mathcal{N}}$ $\newcommand{\Hh}{\mathcal{H}}$ $\newcommand{\Bb}{\mathcal{B}}$ $\newcommand{\Ee}{\mathcal{E}}$ $\newcommand{\Cc}{\mathcal{C}}$ $\newcommand{\Gg}{\mathcal{G}}$ $\newcommand{\Ss}{\mathcal{S}}$ $\newcommand{\Pp}{\mathcal{P}}$ $\newcommand{\Ff}{\mathcal{F}}$ $\newcommand{\Xx}{\mathcal{X}}$ $\newcommand{\Mm}{\mathcal{M}}$ $\newcommand{\Ii}{\mathcal{I}}$ $\newcommand{\Dd}{\mathcal{D}}$ $\newcommand{\Ll}{\mathcal{L}}$ $\newcommand{\Tt}{\mathcal{T}}$ $\newcommand{\si}{\sigma}$ $\newcommand{\al}{\alpha}$ $\newcommand{\la}{\lambda}$ $\newcommand{\ga}{\gamma}$ $\newcommand{\Ga}{\Gamma}$ $\newcommand{\La}{\Lambda}$ $\newcommand{\si}{\sigma}$ $\newcommand{\Si}{\Sigma}$ $\newcommand{\be}{\beta}$ $\newcommand{\de}{\delta}$ $\newcommand{\De}{\Delta}$ $\newcommand{\phi}{\varphi}$ $\newcommand{\th}{\theta}$ $\newcommand{\om}{\omega}$ $\newcommand{\Om}{\Omega}$
This numerical tour study image denoising using non-local means. This algorithm has been introduced for denoising purposes in BuaCoMoA05
using PyPlot
using NtToolBox
This numerical tour is dedicated to the study of the structure of patches in images.
Size $N = n \times n$ of the image.
n = 128
128
We load a noisy image $f_0\in \RR^N$.
c = [100, 200]
f0 = load_image("NtToolBox/src/data/lena.png")
f0 = rescale(f0[c[1] - Base.div(n, 2) + 1 : c[1] + Base.div(n, 2), c[2] - Base.div(n, 2) + 1 : c[2] + Base.div(n, 2)])
128×128 Array{Float32,2}: 0.362205 0.362205 0.354331 0.401575 … 0.354331 0.362205 0.362205 0.385827 0.354331 0.346457 0.362205 0.417323 0.385827 0.401575 0.338583 0.338583 0.362205 0.346457 0.377953 0.385827 0.401575 0.346457 0.338583 0.354331 0.362205 0.362205 0.362205 0.362205 0.385827 0.338583 0.338583 0.354331 0.370079 0.377953 0.338583 0.370079 0.362205 0.385827 0.354331 … 0.354331 0.385827 0.346457 0.330709 0.354331 0.385827 0.346457 0.362205 0.377953 0.346457 0.354331 0.362205 0.362205 0.354331 0.393701 0.362205 0.346457 0.346457 0.354331 0.354331 0.354331 0.330709 0.393701 0.362205 0.385827 0.354331 0.385827 0.354331 0.330709 0.330709 0.385827 0.354331 0.354331 0.338583 0.377953 … 0.354331 0.354331 0.362205 0.354331 0.354331 0.385827 0.362205 0.330709 0.338583 0.346457 0.362205 0.370079 0.370079 0.385827 0.338583 0.362205 0.330709 ⋮ ⋱ ⋮ 0.283465 0.291339 0.409449 0.354331 0.669291 0.669291 0.692913 0.291339 0.322835 0.527559 0.409449 0.677165 0.669291 0.685039 0.346457 0.385827 0.417323 0.377953 0.692913 0.72441 0.72441 0.472441 0.370079 0.377953 0.354331 0.645669 0.72441 0.732284 0.582677 0.425197 0.409449 0.448819 … 0.574803 0.637795 0.700787 0.464567 0.401575 0.496063 0.448819 0.622047 0.566929 0.574803 0.464567 0.417323 0.456693 0.409449 0.677165 0.669291 0.582677 0.559055 0.464567 0.440945 0.385827 0.661417 0.692913 0.669291 0.543307 0.433071 0.401575 0.480315 0.685039 0.692913 0.608924 0.480315 0.330709 0.472441 0.566929 … 0.645669 0.582677 0.566929 0.464567 0.393701 0.496063 0.488189 0.535433 0.496063 0.653543 0.464567 0.503937 0.425197 0.322835 0.551181 0.608924 0.629921
Display $f_0$.
figure(figsize = (5, 5))
imageplot(f0)
Noise level $\si$.
sigma = .04
0.04
Generate a noisy image $f=f_0+\epsilon$ where $\epsilon \times \Nn(0,\si^2\text{Id}_N)$.
using Distributions
f = f0 .+ sigma.*rand(Normal(), n, n)
128×128 Array{Float64,2}: 0.310121 0.331575 0.421916 0.41914 … 0.404933 0.373489 0.366263 0.371062 0.375166 0.367454 0.298638 0.409829 0.324649 0.391277 0.338717 0.337497 0.350857 0.322122 0.305613 0.443315 0.328793 0.358469 0.408959 0.302386 0.420562 0.36485 0.386978 0.353269 0.366528 0.307268 0.334106 0.41304 0.394557 0.403713 0.349689 0.301808 0.372549 0.383443 0.387839 … 0.337633 0.398922 0.343062 0.271791 0.389746 0.422243 0.281307 0.326126 0.359733 0.318974 0.397233 0.429843 0.395194 0.403108 0.402998 0.382453 0.380637 0.375241 0.388268 0.349711 0.427031 0.301518 0.44367 0.255511 0.369202 0.334936 0.424085 0.340765 0.33009 0.321673 0.33002 0.39084 0.361636 0.372712 0.314115 … 0.438289 0.320409 0.350257 0.341601 0.383261 0.4244 0.366063 0.322722 0.400725 0.360035 0.352725 0.376963 0.435233 0.383157 0.370172 0.409228 0.294399 ⋮ ⋱ ⋮ 0.28303 0.312103 0.44081 0.345268 0.659962 0.706894 0.771867 0.301504 0.379728 0.581491 0.440036 0.663047 0.651876 0.648853 0.345021 0.388229 0.447937 0.416182 0.657772 0.74391 0.703863 0.49896 0.403568 0.364329 0.346948 0.67903 0.667091 0.72686 0.626079 0.425512 0.424497 0.492793 … 0.575927 0.607786 0.731195 0.434764 0.447411 0.443906 0.453921 0.680113 0.624357 0.586979 0.505774 0.428263 0.488337 0.428573 0.711711 0.630046 0.585115 0.528377 0.459281 0.439019 0.44862 0.666042 0.737301 0.679758 0.5479 0.433398 0.463395 0.496517 0.657626 0.757109 0.694726 0.441499 0.33134 0.540048 0.567202 … 0.644774 0.634769 0.64582 0.432999 0.321467 0.467588 0.485594 0.508329 0.498877 0.628629 0.460332 0.480376 0.394749 0.291599 0.494321 0.5831 0.570823
Display $f$.
figure(figsize = (5,5))
imageplot(clamP(f))
We denote $w$ to be the half width of the patches, and $w_1=2w+1$ the full width.
w = 3
w1 = 2*w + 1
7
We set up large $(n,n,w_1,w_1)$ matrices to index the the X and Y position of the pixel to extract.
Location of pixels to extract.
include("ndgrid.jl") # Il ne faut pas oublier de mettre ndgrid.jl dans le package et exporter la fonction meshgrid.
(X, Y) = meshgrid(1 : n, 1 : n)
(dX, dY) = meshgrid(-w : w, -w : w)
dX = reshape(dX, (1, 1, w1, w1))
dY = reshape(dY, (1, 1, w1, w1))
X = repeat(X, inner = [1, 1, w1, w1]) + repeat(dX, inner = [n, n, 1, 1])
Y = repeat(Y, inner = [1, 1, w1, w1]) + repeat(dY, inner = [n, n, 1, 1])
128×128×7×7 Array{Int64,4}: [:, :, 1, 1] = -2 -2 -2 -2 -2 -2 -2 -2 … -2 -2 -2 -2 -2 -2 -2 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3 … 3 3 3 3 3 3 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 8 8 8 8 8 8 8 8 … 8 8 8 8 8 8 8 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 ⋮ ⋮ ⋱ ⋮ 114 114 114 114 114 114 114 114 114 114 114 114 114 114 114 115 115 115 115 115 115 115 115 115 115 115 115 115 115 115 116 116 116 116 116 116 116 116 116 116 116 116 116 116 116 117 117 117 117 117 117 117 117 117 117 117 117 117 117 117 118 118 118 118 118 118 118 118 … 118 118 118 118 118 118 118 119 119 119 119 119 119 119 119 119 119 119 119 119 119 119 120 120 120 120 120 120 120 120 120 120 120 120 120 120 120 121 121 121 121 121 121 121 121 121 121 121 121 121 121 121 122 122 122 122 122 122 122 122 122 122 122 122 122 122 122 123 123 123 123 123 123 123 123 … 123 123 123 123 123 123 123 124 124 124 124 124 124 124 124 124 124 124 124 124 124 124 125 125 125 125 125 125 125 125 125 125 125 125 125 125 125 [:, :, 2, 1] = -1 -1 -1 -1 -1 -1 -1 -1 … -1 -1 -1 -1 -1 -1 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 4 4 4 4 4 4 4 4 … 4 4 4 4 4 4 4 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 9 9 9 9 9 9 9 9 … 9 9 9 9 9 9 9 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 ⋮ ⋮ ⋱ ⋮ 115 115 115 115 115 115 115 115 115 115 115 115 115 115 115 116 116 116 116 116 116 116 116 116 116 116 116 116 116 116 117 117 117 117 117 117 117 117 117 117 117 117 117 117 117 118 118 118 118 118 118 118 118 118 118 118 118 118 118 118 119 119 119 119 119 119 119 119 … 119 119 119 119 119 119 119 120 120 120 120 120 120 120 120 120 120 120 120 120 120 120 121 121 121 121 121 121 121 121 121 121 121 121 121 121 121 122 122 122 122 122 122 122 122 122 122 122 122 122 122 122 123 123 123 123 123 123 123 123 123 123 123 123 123 123 123 124 124 124 124 124 124 124 124 … 124 124 124 124 124 124 124 125 125 125 125 125 125 125 125 125 125 125 125 125 125 125 126 126 126 126 126 126 126 126 126 126 126 126 126 126 126 [:, :, 3, 1] = 0 0 0 0 0 0 0 0 … 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 5 5 5 5 5 5 5 5 … 5 5 5 5 5 5 5 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 10 10 10 10 10 10 10 10 … 10 10 10 10 10 10 10 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 ⋮ ⋮ ⋱ ⋮ 116 116 116 116 116 116 116 116 116 116 116 116 116 116 116 117 117 117 117 117 117 117 117 117 117 117 117 117 117 117 118 118 118 118 118 118 118 118 118 118 118 118 118 118 118 119 119 119 119 119 119 119 119 119 119 119 119 119 119 119 120 120 120 120 120 120 120 120 … 120 120 120 120 120 120 120 121 121 121 121 121 121 121 121 121 121 121 121 121 121 121 122 122 122 122 122 122 122 122 122 122 122 122 122 122 122 123 123 123 123 123 123 123 123 123 123 123 123 123 123 123 124 124 124 124 124 124 124 124 124 124 124 124 124 124 124 125 125 125 125 125 125 125 125 … 125 125 125 125 125 125 125 126 126 126 126 126 126 126 126 126 126 126 126 126 126 126 127 127 127 127 127 127 127 127 127 127 127 127 127 127 127 [:, :, 4, 1] = 1 1 1 1 1 1 1 1 … 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 6 6 6 6 6 6 6 6 … 6 6 6 6 6 6 6 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 11 11 11 11 11 11 11 11 … 11 11 11 11 11 11 11 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 ⋮ ⋮ ⋱ ⋮ 117 117 117 117 117 117 117 117 117 117 117 117 117 117 117 118 118 118 118 118 118 118 118 118 118 118 118 118 118 118 119 119 119 119 119 119 119 119 119 119 119 119 119 119 119 120 120 120 120 120 120 120 120 120 120 120 120 120 120 120 121 121 121 121 121 121 121 121 … 121 121 121 121 121 121 121 122 122 122 122 122 122 122 122 122 122 122 122 122 122 122 123 123 123 123 123 123 123 123 123 123 123 123 123 123 123 124 124 124 124 124 124 124 124 124 124 124 124 124 124 124 125 125 125 125 125 125 125 125 125 125 125 125 125 125 125 126 126 126 126 126 126 126 126 … 126 126 126 126 126 126 126 127 127 127 127 127 127 127 127 127 127 127 127 127 127 127 128 128 128 128 128 128 128 128 128 128 128 128 128 128 128 [:, :, 5, 1] = 2 2 2 2 2 2 2 2 … 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 7 7 7 7 7 7 7 7 … 7 7 7 7 7 7 7 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 12 12 12 12 12 12 12 12 … 12 12 12 12 12 12 12 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 ⋮ ⋮ ⋱ ⋮ 118 118 118 118 118 118 118 118 118 118 118 118 118 118 118 119 119 119 119 119 119 119 119 119 119 119 119 119 119 119 120 120 120 120 120 120 120 120 120 120 120 120 120 120 120 121 121 121 121 121 121 121 121 121 121 121 121 121 121 121 122 122 122 122 122 122 122 122 … 122 122 122 122 122 122 122 123 123 123 123 123 123 123 123 123 123 123 123 123 123 123 124 124 124 124 124 124 124 124 124 124 124 124 124 124 124 125 125 125 125 125 125 125 125 125 125 125 125 125 125 125 126 126 126 126 126 126 126 126 126 126 126 126 126 126 126 127 127 127 127 127 127 127 127 … 127 127 127 127 127 127 127 128 128 128 128 128 128 128 128 128 128 128 128 128 128 128 129 129 129 129 129 129 129 129 129 129 129 129 129 129 129 [:, :, 6, 1] = 3 3 3 3 3 3 3 3 … 3 3 3 3 3 3 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 8 8 8 8 8 8 8 8 … 8 8 8 8 8 8 8 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 13 13 13 13 13 13 13 13 … 13 13 13 13 13 13 13 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 ⋮ ⋮ ⋱ ⋮ 119 119 119 119 119 119 119 119 119 119 119 119 119 119 119 120 120 120 120 120 120 120 120 120 120 120 120 120 120 120 121 121 121 121 121 121 121 121 121 121 121 121 121 121 121 122 122 122 122 122 122 122 122 122 122 122 122 122 122 122 123 123 123 123 123 123 123 123 … 123 123 123 123 123 123 123 124 124 124 124 124 124 124 124 124 124 124 124 124 124 124 125 125 125 125 125 125 125 125 125 125 125 125 125 125 125 126 126 126 126 126 126 126 126 126 126 126 126 126 126 126 127 127 127 127 127 127 127 127 127 127 127 127 127 127 127 128 128 128 128 128 128 128 128 … 128 128 128 128 128 128 128 129 129 129 129 129 129 129 129 129 129 129 129 129 129 129 130 130 130 130 130 130 130 130 130 130 130 130 130 130 130 [:, :, 7, 1] = 4 4 4 4 4 4 4 4 … 4 4 4 4 4 4 4 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 9 9 9 9 9 9 9 9 … 9 9 9 9 9 9 9 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 14 14 14 14 14 14 14 14 … 14 14 14 14 14 14 14 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 ⋮ ⋮ ⋱ ⋮ 120 120 120 120 120 120 120 120 120 120 120 120 120 120 120 121 121 121 121 121 121 121 121 121 121 121 121 121 121 121 122 122 122 122 122 122 122 122 122 122 122 122 122 122 122 123 123 123 123 123 123 123 123 123 123 123 123 123 123 123 124 124 124 124 124 124 124 124 … 124 124 124 124 124 124 124 125 125 125 125 125 125 125 125 125 125 125 125 125 125 125 126 126 126 126 126 126 126 126 126 126 126 126 126 126 126 127 127 127 127 127 127 127 127 127 127 127 127 127 127 127 128 128 128 128 128 128 128 128 128 128 128 128 128 128 128 129 129 129 129 129 129 129 129 … 129 129 129 129 129 129 129 130 130 130 130 130 130 130 130 130 130 130 130 130 130 130 131 131 131 131 131 131 131 131 131 131 131 131 131 131 131 [:, :, 1, 2] = -2 -2 -2 -2 -2 -2 -2 -2 … -2 -2 -2 -2 -2 -2 -2 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3 … 3 3 3 3 3 3 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 8 8 8 8 8 8 8 8 … 8 8 8 8 8 8 8 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 ⋮ ⋮ ⋱ ⋮ 114 114 114 114 114 114 114 114 114 114 114 114 114 114 114 115 115 115 115 115 115 115 115 115 115 115 115 115 115 115 116 116 116 116 116 116 116 116 116 116 116 116 116 116 116 117 117 117 117 117 117 117 117 117 117 117 117 117 117 117 118 118 118 118 118 118 118 118 … 118 118 118 118 118 118 118 119 119 119 119 119 119 119 119 119 119 119 119 119 119 119 120 120 120 120 120 120 120 120 120 120 120 120 120 120 120 121 121 121 121 121 121 121 121 121 121 121 121 121 121 121 122 122 122 122 122 122 122 122 122 122 122 122 122 122 122 123 123 123 123 123 123 123 123 … 123 123 123 123 123 123 123 124 124 124 124 124 124 124 124 124 124 124 124 124 124 124 125 125 125 125 125 125 125 125 125 125 125 125 125 125 125 [:, :, 2, 2] = -1 -1 -1 -1 -1 -1 -1 -1 … -1 -1 -1 -1 -1 -1 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 4 4 4 4 4 4 4 4 … 4 4 4 4 4 4 4 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 9 9 9 9 9 9 9 9 … 9 9 9 9 9 9 9 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 ⋮ ⋮ ⋱ ⋮ 115 115 115 115 115 115 115 115 115 115 115 115 115 115 115 116 116 116 116 116 116 116 116 116 116 116 116 116 116 116 117 117 117 117 117 117 117 117 117 117 117 117 117 117 117 118 118 118 118 118 118 118 118 118 118 118 118 118 118 118 119 119 119 119 119 119 119 119 … 119 119 119 119 119 119 119 120 120 120 120 120 120 120 120 120 120 120 120 120 120 120 121 121 121 121 121 121 121 121 121 121 121 121 121 121 121 122 122 122 122 122 122 122 122 122 122 122 122 122 122 122 123 123 123 123 123 123 123 123 123 123 123 123 123 123 123 124 124 124 124 124 124 124 124 … 124 124 124 124 124 124 124 125 125 125 125 125 125 125 125 125 125 125 125 125 125 125 126 126 126 126 126 126 126 126 126 126 126 126 126 126 126 [:, :, 3, 2] = 0 0 0 0 0 0 0 0 … 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 5 5 5 5 5 5 5 5 … 5 5 5 5 5 5 5 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 10 10 10 10 10 10 10 10 … 10 10 10 10 10 10 10 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 ⋮ ⋮ ⋱ ⋮ 116 116 116 116 116 116 116 116 116 116 116 116 116 116 116 117 117 117 117 117 117 117 117 117 117 117 117 117 117 117 118 118 118 118 118 118 118 118 118 118 118 118 118 118 118 119 119 119 119 119 119 119 119 119 119 119 119 119 119 119 120 120 120 120 120 120 120 120 … 120 120 120 120 120 120 120 121 121 121 121 121 121 121 121 121 121 121 121 121 121 121 122 122 122 122 122 122 122 122 122 122 122 122 122 122 122 123 123 123 123 123 123 123 123 123 123 123 123 123 123 123 124 124 124 124 124 124 124 124 124 124 124 124 124 124 124 125 125 125 125 125 125 125 125 … 125 125 125 125 125 125 125 126 126 126 126 126 126 126 126 126 126 126 126 126 126 126 127 127 127 127 127 127 127 127 127 127 127 127 127 127 127 [:, :, 4, 2] = 1 1 1 1 1 1 1 1 … 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 6 6 6 6 6 6 6 6 … 6 6 6 6 6 6 6 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 11 11 11 11 11 11 11 11 … 11 11 11 11 11 11 11 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 ⋮ ⋮ ⋱ ⋮ 117 117 117 117 117 117 117 117 117 117 117 117 117 117 117 118 118 118 118 118 118 118 118 118 118 118 118 118 118 118 119 119 119 119 119 119 119 119 119 119 119 119 119 119 119 120 120 120 120 120 120 120 120 120 120 120 120 120 120 120 121 121 121 121 121 121 121 121 … 121 121 121 121 121 121 121 122 122 122 122 122 122 122 122 122 122 122 122 122 122 122 123 123 123 123 123 123 123 123 123 123 123 123 123 123 123 124 124 124 124 124 124 124 124 124 124 124 124 124 124 124 125 125 125 125 125 125 125 125 125 125 125 125 125 125 125 126 126 126 126 126 126 126 126 … 126 126 126 126 126 126 126 127 127 127 127 127 127 127 127 127 127 127 127 127 127 127 128 128 128 128 128 128 128 128 128 128 128 128 128 128 128 [:, :, 5, 2] = 2 2 2 2 2 2 2 2 … 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 7 7 7 7 7 7 7 7 … 7 7 7 7 7 7 7 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 12 12 12 12 12 12 12 12 … 12 12 12 12 12 12 12 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 ⋮ ⋮ ⋱ ⋮ 118 118 118 118 118 118 118 118 118 118 118 118 118 118 118 119 119 119 119 119 119 119 119 119 119 119 119 119 119 119 120 120 120 120 120 120 120 120 120 120 120 120 120 120 120 121 121 121 121 121 121 121 121 121 121 121 121 121 121 121 122 122 122 122 122 122 122 122 … 122 122 122 122 122 122 122 123 123 123 123 123 123 123 123 123 123 123 123 123 123 123 124 124 124 124 124 124 124 124 124 124 124 124 124 124 124 125 125 125 125 125 125 125 125 125 125 125 125 125 125 125 126 126 126 126 126 126 126 126 126 126 126 126 126 126 126 127 127 127 127 127 127 127 127 … 127 127 127 127 127 127 127 128 128 128 128 128 128 128 128 128 128 128 128 128 128 128 129 129 129 129 129 129 129 129 129 129 129 129 129 129 129 [:, :, 6, 2] = 3 3 3 3 3 3 3 3 … 3 3 3 3 3 3 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 8 8 8 8 8 8 8 8 … 8 8 8 8 8 8 8 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 13 13 13 13 13 13 13 13 … 13 13 13 13 13 13 13 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 ⋮ ⋮ ⋱ ⋮ 119 119 119 119 119 119 119 119 119 119 119 119 119 119 119 120 120 120 120 120 120 120 120 120 120 120 120 120 120 120 121 121 121 121 121 121 121 121 121 121 121 121 121 121 121 122 122 122 122 122 122 122 122 122 122 122 122 122 122 122 123 123 123 123 123 123 123 123 … 123 123 123 123 123 123 123 124 124 124 124 124 124 124 124 124 124 124 124 124 124 124 125 125 125 125 125 125 125 125 125 125 125 125 125 125 125 126 126 126 126 126 126 126 126 126 126 126 126 126 126 126 127 127 127 127 127 127 127 127 127 127 127 127 127 127 127 128 128 128 128 128 128 128 128 … 128 128 128 128 128 128 128 129 129 129 129 129 129 129 129 129 129 129 129 129 129 129 130 130 130 130 130 130 130 130 130 130 130 130 130 130 130 [:, :, 7, 2] = 4 4 4 4 4 4 4 4 … 4 4 4 4 4 4 4 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 9 9 9 9 9 9 9 9 … 9 9 9 9 9 9 9 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 14 14 14 14 14 14 14 14 … 14 14 14 14 14 14 14 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 ⋮ ⋮ ⋱ ⋮ 120 120 120 120 120 120 120 120 120 120 120 120 120 120 120 121 121 121 121 121 121 121 121 121 121 121 121 121 121 121 122 122 122 122 122 122 122 122 122 122 122 122 122 122 122 123 123 123 123 123 123 123 123 123 123 123 123 123 123 123 124 124 124 124 124 124 124 124 … 124 124 124 124 124 124 124 125 125 125 125 125 125 125 125 125 125 125 125 125 125 125 126 126 126 126 126 126 126 126 126 126 126 126 126 126 126 127 127 127 127 127 127 127 127 127 127 127 127 127 127 127 128 128 128 128 128 128 128 128 128 128 128 128 128 128 128 129 129 129 129 129 129 129 129 … 129 129 129 129 129 129 129 130 130 130 130 130 130 130 130 130 130 130 130 130 130 130 131 131 131 131 131 131 131 131 131 131 131 131 131 131 131 [:, :, 1, 3] = -2 -2 -2 -2 -2 -2 -2 -2 … -2 -2 -2 -2 -2 -2 -2 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3 … 3 3 3 3 3 3 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 8 8 8 8 8 8 8 8 … 8 8 8 8 8 8 8 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 ⋮ ⋮ ⋱ ⋮ 114 114 114 114 114 114 114 114 114 114 114 114 114 114 114 115 115 115 115 115 115 115 115 115 115 115 115 115 115 115 116 116 116 116 116 116 116 116 116 116 116 116 116 116 116 117 117 117 117 117 117 117 117 117 117 117 117 117 117 117 118 118 118 118 118 118 118 118 … 118 118 118 118 118 118 118 119 119 119 119 119 119 119 119 119 119 119 119 119 119 119 120 120 120 120 120 120 120 120 120 120 120 120 120 120 120 121 121 121 121 121 121 121 121 121 121 121 121 121 121 121 122 122 122 122 122 122 122 122 122 122 122 122 122 122 122 123 123 123 123 123 123 123 123 … 123 123 123 123 123 123 123 124 124 124 124 124 124 124 124 124 124 124 124 124 124 124 125 125 125 125 125 125 125 125 125 125 125 125 125 125 125 [:, :, 2, 3] = -1 -1 -1 -1 -1 -1 -1 -1 … -1 -1 -1 -1 -1 -1 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 4 4 4 4 4 4 4 4 … 4 4 4 4 4 4 4 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 9 9 9 9 9 9 9 9 … 9 9 9 9 9 9 9 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 ⋮ ⋮ ⋱ ⋮ 115 115 115 115 115 115 115 115 115 115 115 115 115 115 115 116 116 116 116 116 116 116 116 116 116 116 116 116 116 116 117 117 117 117 117 117 117 117 117 117 117 117 117 117 117 118 118 118 118 118 118 118 118 118 118 118 118 118 118 118 119 119 119 119 119 119 119 119 … 119 119 119 119 119 119 119 120 120 120 120 120 120 120 120 120 120 120 120 120 120 120 121 121 121 121 121 121 121 121 121 121 121 121 121 121 121 122 122 122 122 122 122 122 122 122 122 122 122 122 122 122 123 123 123 123 123 123 123 123 123 123 123 123 123 123 123 124 124 124 124 124 124 124 124 … 124 124 124 124 124 124 124 125 125 125 125 125 125 125 125 125 125 125 125 125 125 125 126 126 126 126 126 126 126 126 126 126 126 126 126 126 126 [:, :, 3, 3] = 0 0 0 0 0 0 0 0 … 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 5 5 5 5 5 5 5 5 … 5 5 5 5 5 5 5 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 10 10 10 10 10 10 10 10 … 10 10 10 10 10 10 10 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 ⋮ ⋮ ⋱ ⋮ 116 116 116 116 116 116 116 116 116 116 116 116 116 116 116 117 117 117 117 117 117 117 117 117 117 117 117 117 117 117 118 118 118 118 118 118 118 118 118 118 118 118 118 118 118 119 119 119 119 119 119 119 119 119 119 119 119 119 119 119 120 120 120 120 120 120 120 120 … 120 120 120 120 120 120 120 121 121 121 121 121 121 121 121 121 121 121 121 121 121 121 122 122 122 122 122 122 122 122 122 122 122 122 122 122 122 123 123 123 123 123 123 123 123 123 123 123 123 123 123 123 124 124 124 124 124 124 124 124 124 124 124 124 124 124 124 125 125 125 125 125 125 125 125 … 125 125 125 125 125 125 125 126 126 126 126 126 126 126 126 126 126 126 126 126 126 126 127 127 127 127 127 127 127 127 127 127 127 127 127 127 127 [:, :, 4, 3] = 1 1 1 1 1 1 1 1 … 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 6 6 6 6 6 6 6 6 … 6 6 6 6 6 6 6 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 11 11 11 11 11 11 11 11 … 11 11 11 11 11 11 11 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 ⋮ ⋮ ⋱ ⋮ 117 117 117 117 117 117 117 117 117 117 117 117 117 117 117 118 118 118 118 118 118 118 118 118 118 118 118 118 118 118 119 119 119 119 119 119 119 119 119 119 119 119 119 119 119 120 120 120 120 120 120 120 120 120 120 120 120 120 120 120 121 121 121 121 121 121 121 121 … 121 121 121 121 121 121 121 122 122 122 122 122 122 122 122 122 122 122 122 122 122 122 123 123 123 123 123 123 123 123 123 123 123 123 123 123 123 124 124 124 124 124 124 124 124 124 124 124 124 124 124 124 125 125 125 125 125 125 125 125 125 125 125 125 125 125 125 126 126 126 126 126 126 126 126 … 126 126 126 126 126 126 126 127 127 127 127 127 127 127 127 127 127 127 127 127 127 127 128 128 128 128 128 128 128 128 128 128 128 128 128 128 128 [:, :, 5, 3] = 2 2 2 2 2 2 2 2 … 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 7 7 7 7 7 7 7 7 … 7 7 7 7 7 7 7 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 12 12 12 12 12 12 12 12 … 12 12 12 12 12 12 12 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 ⋮ ⋮ ⋱ ⋮ 118 118 118 118 118 118 118 118 118 118 118 118 118 118 118 119 119 119 119 119 119 119 119 119 119 119 119 119 119 119 120 120 120 120 120 120 120 120 120 120 120 120 120 120 120 121 121 121 121 121 121 121 121 121 121 121 121 121 121 121 122 122 122 122 122 122 122 122 … 122 122 122 122 122 122 122 123 123 123 123 123 123 123 123 123 123 123 123 123 123 123 124 124 124 124 124 124 124 124 124 124 124 124 124 124 124 125 125 125 125 125 125 125 125 125 125 125 125 125 125 125 126 126 126 126 126 126 126 126 126 126 126 126 126 126 126 127 127 127 127 127 127 127 127 … 127 127 127 127 127 127 127 128 128 128 128 128 128 128 128 128 128 128 128 128 128 128 129 129 129 129 129 129 129 129 129 129 129 129 129 129 129 [:, :, 6, 3] = 3 3 3 3 3 3 3 3 … 3 3 3 3 3 3 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 8 8 8 8 8 8 8 8 … 8 8 8 8 8 8 8 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 13 13 13 13 13 13 13 13 … 13 13 13 13 13 13 13 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 ⋮ ⋮ ⋱ ⋮ 119 119 119 119 119 119 119 119 119 119 119 119 119 119 119 120 120 120 120 120 120 120 120 120 120 120 120 120 120 120 121 121 121 121 121 121 121 121 121 121 121 121 121 121 121 122 122 122 122 122 122 122 122 122 122 122 122 122 122 122 123 123 123 123 123 123 123 123 … 123 123 123 123 123 123 123 124 124 124 124 124 124 124 124 124 124 124 124 124 124 124 125 125 125 125 125 125 125 125 125 125 125 125 125 125 125 126 126 126 126 126 126 126 126 126 126 126 126 126 126 126 127 127 127 127 127 127 127 127 127 127 127 127 127 127 127 128 128 128 128 128 128 128 128 … 128 128 128 128 128 128 128 129 129 129 129 129 129 129 129 129 129 129 129 129 129 129 130 130 130 130 130 130 130 130 130 130 130 130 130 130 130 [:, :, 7, 3] = 4 4 4 4 4 4 4 4 … 4 4 4 4 4 4 4 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 9 9 9 9 9 9 9 9 … 9 9 9 9 9 9 9 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 14 14 14 14 14 14 14 14 … 14 14 14 14 14 14 14 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 ⋮ ⋮ ⋱ ⋮ 120 120 120 120 120 120 120 120 120 120 120 120 120 120 120 121 121 121 121 121 121 121 121 121 121 121 121 121 121 121 122 122 122 122 122 122 122 122 122 122 122 122 122 122 122 123 123 123 123 123 123 123 123 123 123 123 123 123 123 123 124 124 124 124 124 124 124 124 … 124 124 124 124 124 124 124 125 125 125 125 125 125 125 125 125 125 125 125 125 125 125 126 126 126 126 126 126 126 126 126 126 126 126 126 126 126 127 127 127 127 127 127 127 127 127 127 127 127 127 127 127 128 128 128 128 128 128 128 128 128 128 128 128 128 128 128 129 129 129 129 129 129 129 129 … 129 129 129 129 129 129 129 130 130 130 130 130 130 130 130 130 130 130 130 130 130 130 131 131 131 131 131 131 131 131 131 131 131 131 131 131 131 [:, :, 1, 4] = -2 -2 -2 -2 -2 -2 -2 -2 … -2 -2 -2 -2 -2 -2 -2 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3 … 3 3 3 3 3 3 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 8 8 8 8 8 8 8 8 … 8 8 8 8 8 8 8 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 ⋮ ⋮ ⋱ ⋮ 114 114 114 114 114 114 114 114 114 114 114 114 114 114 114 115 115 115 115 115 115 115 115 115 115 115 115 115 115 115 116 116 116 116 116 116 116 116 116 116 116 116 116 116 116 117 117 117 117 117 117 117 117 117 117 117 117 117 117 117 118 118 118 118 118 118 118 118 … 118 118 118 118 118 118 118 119 119 119 119 119 119 119 119 119 119 119 119 119 119 119 120 120 120 120 120 120 120 120 120 120 120 120 120 120 120 121 121 121 121 121 121 121 121 121 121 121 121 121 121 121 122 122 122 122 122 122 122 122 122 122 122 122 122 122 122 123 123 123 123 123 123 123 123 … 123 123 123 123 123 123 123 124 124 124 124 124 124 124 124 124 124 124 124 124 124 124 125 125 125 125 125 125 125 125 125 125 125 125 125 125 125 [:, :, 2, 4] = -1 -1 -1 -1 -1 -1 -1 -1 … -1 -1 -1 -1 -1 -1 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 4 4 4 4 4 4 4 4 … 4 4 4 4 4 4 4 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 9 9 9 9 9 9 9 9 … 9 9 9 9 9 9 9 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 ⋮ ⋮ ⋱ ⋮ 115 115 115 115 115 115 115 115 115 115 115 115 115 115 115 116 116 116 116 116 116 116 116 116 116 116 116 116 116 116 117 117 117 117 117 117 117 117 117 117 117 117 117 117 117 118 118 118 118 118 118 118 118 118 118 118 118 118 118 118 119 119 119 119 119 119 119 119 … 119 119 119 119 119 119 119 120 120 120 120 120 120 120 120 120 120 120 120 120 120 120 121 121 121 121 121 121 121 121 121 121 121 121 121 121 121 122 122 122 122 122 122 122 122 122 122 122 122 122 122 122 123 123 123 123 123 123 123 123 123 123 123 123 123 123 123 124 124 124 124 124 124 124 124 … 124 124 124 124 124 124 124 125 125 125 125 125 125 125 125 125 125 125 125 125 125 125 126 126 126 126 126 126 126 126 126 126 126 126 126 126 126 [:, :, 3, 4] = 0 0 0 0 0 0 0 0 … 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 5 5 5 5 5 5 5 5 … 5 5 5 5 5 5 5 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 10 10 10 10 10 10 10 10 … 10 10 10 10 10 10 10 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 ⋮ ⋮ ⋱ ⋮ 116 116 116 116 116 116 116 116 116 116 116 116 116 116 116 117 117 117 117 117 117 117 117 117 117 117 117 117 117 117 118 118 118 118 118 118 118 118 118 118 118 118 118 118 118 119 119 119 119 119 119 119 119 119 119 119 119 119 119 119 120 120 120 120 120 120 120 120 … 120 120 120 120 120 120 120 121 121 121 121 121 121 121 121 121 121 121 121 121 121 121 122 122 122 122 122 122 122 122 122 122 122 122 122 122 122 123 123 123 123 123 123 123 123 123 123 123 123 123 123 123 124 124 124 124 124 124 124 124 124 124 124 124 124 124 124 125 125 125 125 125 125 125 125 … 125 125 125 125 125 125 125 126 126 126 126 126 126 126 126 126 126 126 126 126 126 126 127 127 127 127 127 127 127 127 127 127 127 127 127 127 127 [:, :, 4, 4] = 1 1 1 1 1 1 1 1 … 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 6 6 6 6 6 6 6 6 … 6 6 6 6 6 6 6 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 11 11 11 11 11 11 11 11 … 11 11 11 11 11 11 11 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 ⋮ ⋮ ⋱ ⋮ 117 117 117 117 117 117 117 117 117 117 117 117 117 117 117 118 118 118 118 118 118 118 118 118 118 118 118 118 118 118 119 119 119 119 119 119 119 119 119 119 119 119 119 119 119 120 120 120 120 120 120 120 120 120 120 120 120 120 120 120 121 121 121 121 121 121 121 121 … 121 121 121 121 121 121 121 122 122 122 122 122 122 122 122 122 122 122 122 122 122 122 123 123 123 123 123 123 123 123 123 123 123 123 123 123 123 124 124 124 124 124 124 124 124 124 124 124 124 124 124 124 125 125 125 125 125 125 125 125 125 125 125 125 125 125 125 126 126 126 126 126 126 126 126 … 126 126 126 126 126 126 126 127 127 127 127 127 127 127 127 127 127 127 127 127 127 127 128 128 128 128 128 128 128 128 128 128 128 128 128 128 128 [:, :, 5, 4] = 2 2 2 2 2 2 2 2 … 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 7 7 7 7 7 7 7 7 … 7 7 7 7 7 7 7 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 12 12 12 12 12 12 12 12 … 12 12 12 12 12 12 12 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 ⋮ ⋮ ⋱ ⋮ 118 118 118 118 118 118 118 118 118 118 118 118 118 118 118 119 119 119 119 119 119 119 119 119 119 119 119 119 119 119 120 120 120 120 120 120 120 120 120 120 120 120 120 120 120 121 121 121 121 121 121 121 121 121 121 121 121 121 121 121 122 122 122 122 122 122 122 122 … 122 122 122 122 122 122 122 123 123 123 123 123 123 123 123 123 123 123 123 123 123 123 124 124 124 124 124 124 124 124 124 124 124 124 124 124 124 125 125 125 125 125 125 125 125 125 125 125 125 125 125 125 126 126 126 126 126 126 126 126 126 126 126 126 126 126 126 127 127 127 127 127 127 127 127 … 127 127 127 127 127 127 127 128 128 128 128 128 128 128 128 128 128 128 128 128 128 128 129 129 129 129 129 129 129 129 129 129 129 129 129 129 129 [:, :, 6, 4] = 3 3 3 3 3 3 3 3 … 3 3 3 3 3 3 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 8 8 8 8 8 8 8 8 … 8 8 8 8 8 8 8 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 13 13 13 13 13 13 13 13 … 13 13 13 13 13 13 13 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 ⋮ ⋮ ⋱ ⋮ 119 119 119 119 119 119 119 119 119 119 119 119 119 119 119 120 120 120 120 120 120 120 120 120 120 120 120 120 120 120 121 121 121 121 121 121 121 121 121 121 121 121 121 121 121 122 122 122 122 122 122 122 122 122 122 122 122 122 122 122 123 123 123 123 123 123 123 123 … 123 123 123 123 123 123 123 124 124 124 124 124 124 124 124 124 124 124 124 124 124 124 125 125 125 125 125 125 125 125 125 125 125 125 125 125 125 126 126 126 126 126 126 126 126 126 126 126 126 126 126 126 127 127 127 127 127 127 127 127 127 127 127 127 127 127 127 128 128 128 128 128 128 128 128 … 128 128 128 128 128 128 128 129 129 129 129 129 129 129 129 129 129 129 129 129 129 129 130 130 130 130 130 130 130 130 130 130 130 130 130 130 130 [:, :, 7, 4] = 4 4 4 4 4 4 4 4 … 4 4 4 4 4 4 4 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 9 9 9 9 9 9 9 9 … 9 9 9 9 9 9 9 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 14 14 14 14 14 14 14 14 … 14 14 14 14 14 14 14 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 ⋮ ⋮ ⋱ ⋮ 120 120 120 120 120 120 120 120 120 120 120 120 120 120 120 121 121 121 121 121 121 121 121 121 121 121 121 121 121 121 122 122 122 122 122 122 122 122 122 122 122 122 122 122 122 123 123 123 123 123 123 123 123 123 123 123 123 123 123 123 124 124 124 124 124 124 124 124 … 124 124 124 124 124 124 124 125 125 125 125 125 125 125 125 125 125 125 125 125 125 125 126 126 126 126 126 126 126 126 126 126 126 126 126 126 126 127 127 127 127 127 127 127 127 127 127 127 127 127 127 127 128 128 128 128 128 128 128 128 128 128 128 128 128 128 128 129 129 129 129 129 129 129 129 … 129 129 129 129 129 129 129 130 130 130 130 130 130 130 130 130 130 130 130 130 130 130 131 131 131 131 131 131 131 131 131 131 131 131 131 131 131 [:, :, 1, 5] = -2 -2 -2 -2 -2 -2 -2 -2 … -2 -2 -2 -2 -2 -2 -2 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3 … 3 3 3 3 3 3 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 8 8 8 8 8 8 8 8 … 8 8 8 8 8 8 8 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 ⋮ ⋮ ⋱ ⋮ 114 114 114 114 114 114 114 114 114 114 114 114 114 114 114 115 115 115 115 115 115 115 115 115 115 115 115 115 115 115 116 116 116 116 116 116 116 116 116 116 116 116 116 116 116 117 117 117 117 117 117 117 117 117 117 117 117 117 117 117 118 118 118 118 118 118 118 118 … 118 118 118 118 118 118 118 119 119 119 119 119 119 119 119 119 119 119 119 119 119 119 120 120 120 120 120 120 120 120 120 120 120 120 120 120 120 121 121 121 121 121 121 121 121 121 121 121 121 121 121 121 122 122 122 122 122 122 122 122 122 122 122 122 122 122 122 123 123 123 123 123 123 123 123 … 123 123 123 123 123 123 123 124 124 124 124 124 124 124 124 124 124 124 124 124 124 124 125 125 125 125 125 125 125 125 125 125 125 125 125 125 125 [:, :, 2, 5] = -1 -1 -1 -1 -1 -1 -1 -1 … -1 -1 -1 -1 -1 -1 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 4 4 4 4 4 4 4 4 … 4 4 4 4 4 4 4 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 9 9 9 9 9 9 9 9 … 9 9 9 9 9 9 9 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 ⋮ ⋮ ⋱ ⋮ 115 115 115 115 115 115 115 115 115 115 115 115 115 115 115 116 116 116 116 116 116 116 116 116 116 116 116 116 116 116 117 117 117 117 117 117 117 117 117 117 117 117 117 117 117 118 118 118 118 118 118 118 118 118 118 118 118 118 118 118 119 119 119 119 119 119 119 119 … 119 119 119 119 119 119 119 120 120 120 120 120 120 120 120 120 120 120 120 120 120 120 121 121 121 121 121 121 121 121 121 121 121 121 121 121 121 122 122 122 122 122 122 122 122 122 122 122 122 122 122 122 123 123 123 123 123 123 123 123 123 123 123 123 123 123 123 124 124 124 124 124 124 124 124 … 124 124 124 124 124 124 124 125 125 125 125 125 125 125 125 125 125 125 125 125 125 125 126 126 126 126 126 126 126 126 126 126 126 126 126 126 126 [:, :, 3, 5] = 0 0 0 0 0 0 0 0 … 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 5 5 5 5 5 5 5 5 … 5 5 5 5 5 5 5 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 10 10 10 10 10 10 10 10 … 10 10 10 10 10 10 10 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 ⋮ ⋮ ⋱ ⋮ 116 116 116 116 116 116 116 116 116 116 116 116 116 116 116 117 117 117 117 117 117 117 117 117 117 117 117 117 117 117 118 118 118 118 118 118 118 118 118 118 118 118 118 118 118 119 119 119 119 119 119 119 119 119 119 119 119 119 119 119 120 120 120 120 120 120 120 120 … 120 120 120 120 120 120 120 121 121 121 121 121 121 121 121 121 121 121 121 121 121 121 122 122 122 122 122 122 122 122 122 122 122 122 122 122 122 123 123 123 123 123 123 123 123 123 123 123 123 123 123 123 124 124 124 124 124 124 124 124 124 124 124 124 124 124 124 125 125 125 125 125 125 125 125 … 125 125 125 125 125 125 125 126 126 126 126 126 126 126 126 126 126 126 126 126 126 126 127 127 127 127 127 127 127 127 127 127 127 127 127 127 127 [:, :, 4, 5] = 1 1 1 1 1 1 1 1 … 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 6 6 6 6 6 6 6 6 … 6 6 6 6 6 6 6 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 11 11 11 11 11 11 11 11 … 11 11 11 11 11 11 11 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 ⋮ ⋮ ⋱ ⋮ 117 117 117 117 117 117 117 117 117 117 117 117 117 117 117 118 118 118 118 118 118 118 118 118 118 118 118 118 118 118 119 119 119 119 119 119 119 119 119 119 119 119 119 119 119 120 120 120 120 120 120 120 120 120 120 120 120 120 120 120 121 121 121 121 121 121 121 121 … 121 121 121 121 121 121 121 122 122 122 122 122 122 122 122 122 122 122 122 122 122 122 123 123 123 123 123 123 123 123 123 123 123 123 123 123 123 124 124 124 124 124 124 124 124 124 124 124 124 124 124 124 125 125 125 125 125 125 125 125 125 125 125 125 125 125 125 126 126 126 126 126 126 126 126 … 126 126 126 126 126 126 126 127 127 127 127 127 127 127 127 127 127 127 127 127 127 127 128 128 128 128 128 128 128 128 128 128 128 128 128 128 128 [:, :, 5, 5] = 2 2 2 2 2 2 2 2 … 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 7 7 7 7 7 7 7 7 … 7 7 7 7 7 7 7 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 12 12 12 12 12 12 12 12 … 12 12 12 12 12 12 12 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 ⋮ ⋮ ⋱ ⋮ 118 118 118 118 118 118 118 118 118 118 118 118 118 118 118 119 119 119 119 119 119 119 119 119 119 119 119 119 119 119 120 120 120 120 120 120 120 120 120 120 120 120 120 120 120 121 121 121 121 121 121 121 121 121 121 121 121 121 121 121 122 122 122 122 122 122 122 122 … 122 122 122 122 122 122 122 123 123 123 123 123 123 123 123 123 123 123 123 123 123 123 124 124 124 124 124 124 124 124 124 124 124 124 124 124 124 125 125 125 125 125 125 125 125 125 125 125 125 125 125 125 126 126 126 126 126 126 126 126 126 126 126 126 126 126 126 127 127 127 127 127 127 127 127 … 127 127 127 127 127 127 127 128 128 128 128 128 128 128 128 128 128 128 128 128 128 128 129 129 129 129 129 129 129 129 129 129 129 129 129 129 129 [:, :, 6, 5] = 3 3 3 3 3 3 3 3 … 3 3 3 3 3 3 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 8 8 8 8 8 8 8 8 … 8 8 8 8 8 8 8 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 13 13 13 13 13 13 13 13 … 13 13 13 13 13 13 13 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 ⋮ ⋮ ⋱ ⋮ 119 119 119 119 119 119 119 119 119 119 119 119 119 119 119 120 120 120 120 120 120 120 120 120 120 120 120 120 120 120 121 121 121 121 121 121 121 121 121 121 121 121 121 121 121 122 122 122 122 122 122 122 122 122 122 122 122 122 122 122 123 123 123 123 123 123 123 123 … 123 123 123 123 123 123 123 124 124 124 124 124 124 124 124 124 124 124 124 124 124 124 125 125 125 125 125 125 125 125 125 125 125 125 125 125 125 126 126 126 126 126 126 126 126 126 126 126 126 126 126 126 127 127 127 127 127 127 127 127 127 127 127 127 127 127 127 128 128 128 128 128 128 128 128 … 128 128 128 128 128 128 128 129 129 129 129 129 129 129 129 129 129 129 129 129 129 129 130 130 130 130 130 130 130 130 130 130 130 130 130 130 130 [:, :, 7, 5] = 4 4 4 4 4 4 4 4 … 4 4 4 4 4 4 4 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 9 9 9 9 9 9 9 9 … 9 9 9 9 9 9 9 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 14 14 14 14 14 14 14 14 … 14 14 14 14 14 14 14 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 ⋮ ⋮ ⋱ ⋮ 120 120 120 120 120 120 120 120 120 120 120 120 120 120 120 121 121 121 121 121 121 121 121 121 121 121 121 121 121 121 122 122 122 122 122 122 122 122 122 122 122 122 122 122 122 123 123 123 123 123 123 123 123 123 123 123 123 123 123 123 124 124 124 124 124 124 124 124 … 124 124 124 124 124 124 124 125 125 125 125 125 125 125 125 125 125 125 125 125 125 125 126 126 126 126 126 126 126 126 126 126 126 126 126 126 126 127 127 127 127 127 127 127 127 127 127 127 127 127 127 127 128 128 128 128 128 128 128 128 128 128 128 128 128 128 128 129 129 129 129 129 129 129 129 … 129 129 129 129 129 129 129 130 130 130 130 130 130 130 130 130 130 130 130 130 130 130 131 131 131 131 131 131 131 131 131 131 131 131 131 131 131 [:, :, 1, 6] = -2 -2 -2 -2 -2 -2 -2 -2 … -2 -2 -2 -2 -2 -2 -2 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3 … 3 3 3 3 3 3 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 8 8 8 8 8 8 8 8 … 8 8 8 8 8 8 8 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 ⋮ ⋮ ⋱ ⋮ 114 114 114 114 114 114 114 114 114 114 114 114 114 114 114 115 115 115 115 115 115 115 115 115 115 115 115 115 115 115 116 116 116 116 116 116 116 116 116 116 116 116 116 116 116 117 117 117 117 117 117 117 117 117 117 117 117 117 117 117 118 118 118 118 118 118 118 118 … 118 118 118 118 118 118 118 119 119 119 119 119 119 119 119 119 119 119 119 119 119 119 120 120 120 120 120 120 120 120 120 120 120 120 120 120 120 121 121 121 121 121 121 121 121 121 121 121 121 121 121 121 122 122 122 122 122 122 122 122 122 122 122 122 122 122 122 123 123 123 123 123 123 123 123 … 123 123 123 123 123 123 123 124 124 124 124 124 124 124 124 124 124 124 124 124 124 124 125 125 125 125 125 125 125 125 125 125 125 125 125 125 125 [:, :, 2, 6] = -1 -1 -1 -1 -1 -1 -1 -1 … -1 -1 -1 -1 -1 -1 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 4 4 4 4 4 4 4 4 … 4 4 4 4 4 4 4 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 9 9 9 9 9 9 9 9 … 9 9 9 9 9 9 9 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 ⋮ ⋮ ⋱ ⋮ 115 115 115 115 115 115 115 115 115 115 115 115 115 115 115 116 116 116 116 116 116 116 116 116 116 116 116 116 116 116 117 117 117 117 117 117 117 117 117 117 117 117 117 117 117 118 118 118 118 118 118 118 118 118 118 118 118 118 118 118 119 119 119 119 119 119 119 119 … 119 119 119 119 119 119 119 120 120 120 120 120 120 120 120 120 120 120 120 120 120 120 121 121 121 121 121 121 121 121 121 121 121 121 121 121 121 122 122 122 122 122 122 122 122 122 122 122 122 122 122 122 123 123 123 123 123 123 123 123 123 123 123 123 123 123 123 124 124 124 124 124 124 124 124 … 124 124 124 124 124 124 124 125 125 125 125 125 125 125 125 125 125 125 125 125 125 125 126 126 126 126 126 126 126 126 126 126 126 126 126 126 126 [:, :, 3, 6] = 0 0 0 0 0 0 0 0 … 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 5 5 5 5 5 5 5 5 … 5 5 5 5 5 5 5 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 10 10 10 10 10 10 10 10 … 10 10 10 10 10 10 10 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 ⋮ ⋮ ⋱ ⋮ 116 116 116 116 116 116 116 116 116 116 116 116 116 116 116 117 117 117 117 117 117 117 117 117 117 117 117 117 117 117 118 118 118 118 118 118 118 118 118 118 118 118 118 118 118 119 119 119 119 119 119 119 119 119 119 119 119 119 119 119 120 120 120 120 120 120 120 120 … 120 120 120 120 120 120 120 121 121 121 121 121 121 121 121 121 121 121 121 121 121 121 122 122 122 122 122 122 122 122 122 122 122 122 122 122 122 123 123 123 123 123 123 123 123 123 123 123 123 123 123 123 124 124 124 124 124 124 124 124 124 124 124 124 124 124 124 125 125 125 125 125 125 125 125 … 125 125 125 125 125 125 125 126 126 126 126 126 126 126 126 126 126 126 126 126 126 126 127 127 127 127 127 127 127 127 127 127 127 127 127 127 127 [:, :, 4, 6] = 1 1 1 1 1 1 1 1 … 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 6 6 6 6 6 6 6 6 … 6 6 6 6 6 6 6 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 11 11 11 11 11 11 11 11 … 11 11 11 11 11 11 11 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 ⋮ ⋮ ⋱ ⋮ 117 117 117 117 117 117 117 117 117 117 117 117 117 117 117 118 118 118 118 118 118 118 118 118 118 118 118 118 118 118 119 119 119 119 119 119 119 119 119 119 119 119 119 119 119 120 120 120 120 120 120 120 120 120 120 120 120 120 120 120 121 121 121 121 121 121 121 121 … 121 121 121 121 121 121 121 122 122 122 122 122 122 122 122 122 122 122 122 122 122 122 123 123 123 123 123 123 123 123 123 123 123 123 123 123 123 124 124 124 124 124 124 124 124 124 124 124 124 124 124 124 125 125 125 125 125 125 125 125 125 125 125 125 125 125 125 126 126 126 126 126 126 126 126 … 126 126 126 126 126 126 126 127 127 127 127 127 127 127 127 127 127 127 127 127 127 127 128 128 128 128 128 128 128 128 128 128 128 128 128 128 128 [:, :, 5, 6] = 2 2 2 2 2 2 2 2 … 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 7 7 7 7 7 7 7 7 … 7 7 7 7 7 7 7 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 12 12 12 12 12 12 12 12 … 12 12 12 12 12 12 12 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 ⋮ ⋮ ⋱ ⋮ 118 118 118 118 118 118 118 118 118 118 118 118 118 118 118 119 119 119 119 119 119 119 119 119 119 119 119 119 119 119 120 120 120 120 120 120 120 120 120 120 120 120 120 120 120 121 121 121 121 121 121 121 121 121 121 121 121 121 121 121 122 122 122 122 122 122 122 122 … 122 122 122 122 122 122 122 123 123 123 123 123 123 123 123 123 123 123 123 123 123 123 124 124 124 124 124 124 124 124 124 124 124 124 124 124 124 125 125 125 125 125 125 125 125 125 125 125 125 125 125 125 126 126 126 126 126 126 126 126 126 126 126 126 126 126 126 127 127 127 127 127 127 127 127 … 127 127 127 127 127 127 127 128 128 128 128 128 128 128 128 128 128 128 128 128 128 128 129 129 129 129 129 129 129 129 129 129 129 129 129 129 129 [:, :, 6, 6] = 3 3 3 3 3 3 3 3 … 3 3 3 3 3 3 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 8 8 8 8 8 8 8 8 … 8 8 8 8 8 8 8 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 13 13 13 13 13 13 13 13 … 13 13 13 13 13 13 13 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 ⋮ ⋮ ⋱ ⋮ 119 119 119 119 119 119 119 119 119 119 119 119 119 119 119 120 120 120 120 120 120 120 120 120 120 120 120 120 120 120 121 121 121 121 121 121 121 121 121 121 121 121 121 121 121 122 122 122 122 122 122 122 122 122 122 122 122 122 122 122 123 123 123 123 123 123 123 123 … 123 123 123 123 123 123 123 124 124 124 124 124 124 124 124 124 124 124 124 124 124 124 125 125 125 125 125 125 125 125 125 125 125 125 125 125 125 126 126 126 126 126 126 126 126 126 126 126 126 126 126 126 127 127 127 127 127 127 127 127 127 127 127 127 127 127 127 128 128 128 128 128 128 128 128 … 128 128 128 128 128 128 128 129 129 129 129 129 129 129 129 129 129 129 129 129 129 129 130 130 130 130 130 130 130 130 130 130 130 130 130 130 130 [:, :, 7, 6] = 4 4 4 4 4 4 4 4 … 4 4 4 4 4 4 4 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 9 9 9 9 9 9 9 9 … 9 9 9 9 9 9 9 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 14 14 14 14 14 14 14 14 … 14 14 14 14 14 14 14 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 ⋮ ⋮ ⋱ ⋮ 120 120 120 120 120 120 120 120 120 120 120 120 120 120 120 121 121 121 121 121 121 121 121 121 121 121 121 121 121 121 122 122 122 122 122 122 122 122 122 122 122 122 122 122 122 123 123 123 123 123 123 123 123 123 123 123 123 123 123 123 124 124 124 124 124 124 124 124 … 124 124 124 124 124 124 124 125 125 125 125 125 125 125 125 125 125 125 125 125 125 125 126 126 126 126 126 126 126 126 126 126 126 126 126 126 126 127 127 127 127 127 127 127 127 127 127 127 127 127 127 127 128 128 128 128 128 128 128 128 128 128 128 128 128 128 128 129 129 129 129 129 129 129 129 … 129 129 129 129 129 129 129 130 130 130 130 130 130 130 130 130 130 130 130 130 130 130 131 131 131 131 131 131 131 131 131 131 131 131 131 131 131 [:, :, 1, 7] = -2 -2 -2 -2 -2 -2 -2 -2 … -2 -2 -2 -2 -2 -2 -2 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3 … 3 3 3 3 3 3 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 8 8 8 8 8 8 8 8 … 8 8 8 8 8 8 8 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 ⋮ ⋮ ⋱ ⋮ 114 114 114 114 114 114 114 114 114 114 114 114 114 114 114 115 115 115 115 115 115 115 115 115 115 115 115 115 115 115 116 116 116 116 116 116 116 116 116 116 116 116 116 116 116 117 117 117 117 117 117 117 117 117 117 117 117 117 117 117 118 118 118 118 118 118 118 118 … 118 118 118 118 118 118 118 119 119 119 119 119 119 119 119 119 119 119 119 119 119 119 120 120 120 120 120 120 120 120 120 120 120 120 120 120 120 121 121 121 121 121 121 121 121 121 121 121 121 121 121 121 122 122 122 122 122 122 122 122 122 122 122 122 122 122 122 123 123 123 123 123 123 123 123 … 123 123 123 123 123 123 123 124 124 124 124 124 124 124 124 124 124 124 124 124 124 124 125 125 125 125 125 125 125 125 125 125 125 125 125 125 125 [:, :, 2, 7] = -1 -1 -1 -1 -1 -1 -1 -1 … -1 -1 -1 -1 -1 -1 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 4 4 4 4 4 4 4 4 … 4 4 4 4 4 4 4 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 9 9 9 9 9 9 9 9 … 9 9 9 9 9 9 9 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 ⋮ ⋮ ⋱ ⋮ 115 115 115 115 115 115 115 115 115 115 115 115 115 115 115 116 116 116 116 116 116 116 116 116 116 116 116 116 116 116 117 117 117 117 117 117 117 117 117 117 117 117 117 117 117 118 118 118 118 118 118 118 118 118 118 118 118 118 118 118 119 119 119 119 119 119 119 119 … 119 119 119 119 119 119 119 120 120 120 120 120 120 120 120 120 120 120 120 120 120 120 121 121 121 121 121 121 121 121 121 121 121 121 121 121 121 122 122 122 122 122 122 122 122 122 122 122 122 122 122 122 123 123 123 123 123 123 123 123 123 123 123 123 123 123 123 124 124 124 124 124 124 124 124 … 124 124 124 124 124 124 124 125 125 125 125 125 125 125 125 125 125 125 125 125 125 125 126 126 126 126 126 126 126 126 126 126 126 126 126 126 126 [:, :, 3, 7] = 0 0 0 0 0 0 0 0 … 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 5 5 5 5 5 5 5 5 … 5 5 5 5 5 5 5 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 10 10 10 10 10 10 10 10 … 10 10 10 10 10 10 10 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 ⋮ ⋮ ⋱ ⋮ 116 116 116 116 116 116 116 116 116 116 116 116 116 116 116 117 117 117 117 117 117 117 117 117 117 117 117 117 117 117 118 118 118 118 118 118 118 118 118 118 118 118 118 118 118 119 119 119 119 119 119 119 119 119 119 119 119 119 119 119 120 120 120 120 120 120 120 120 … 120 120 120 120 120 120 120 121 121 121 121 121 121 121 121 121 121 121 121 121 121 121 122 122 122 122 122 122 122 122 122 122 122 122 122 122 122 123 123 123 123 123 123 123 123 123 123 123 123 123 123 123 124 124 124 124 124 124 124 124 124 124 124 124 124 124 124 125 125 125 125 125 125 125 125 … 125 125 125 125 125 125 125 126 126 126 126 126 126 126 126 126 126 126 126 126 126 126 127 127 127 127 127 127 127 127 127 127 127 127 127 127 127 [:, :, 4, 7] = 1 1 1 1 1 1 1 1 … 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 6 6 6 6 6 6 6 6 … 6 6 6 6 6 6 6 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 11 11 11 11 11 11 11 11 … 11 11 11 11 11 11 11 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 ⋮ ⋮ ⋱ ⋮ 117 117 117 117 117 117 117 117 117 117 117 117 117 117 117 118 118 118 118 118 118 118 118 118 118 118 118 118 118 118 119 119 119 119 119 119 119 119 119 119 119 119 119 119 119 120 120 120 120 120 120 120 120 120 120 120 120 120 120 120 121 121 121 121 121 121 121 121 … 121 121 121 121 121 121 121 122 122 122 122 122 122 122 122 122 122 122 122 122 122 122 123 123 123 123 123 123 123 123 123 123 123 123 123 123 123 124 124 124 124 124 124 124 124 124 124 124 124 124 124 124 125 125 125 125 125 125 125 125 125 125 125 125 125 125 125 126 126 126 126 126 126 126 126 … 126 126 126 126 126 126 126 127 127 127 127 127 127 127 127 127 127 127 127 127 127 127 128 128 128 128 128 128 128 128 128 128 128 128 128 128 128 [:, :, 5, 7] = 2 2 2 2 2 2 2 2 … 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 7 7 7 7 7 7 7 7 … 7 7 7 7 7 7 7 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 12 12 12 12 12 12 12 12 … 12 12 12 12 12 12 12 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 ⋮ ⋮ ⋱ ⋮ 118 118 118 118 118 118 118 118 118 118 118 118 118 118 118 119 119 119 119 119 119 119 119 119 119 119 119 119 119 119 120 120 120 120 120 120 120 120 120 120 120 120 120 120 120 121 121 121 121 121 121 121 121 121 121 121 121 121 121 121 122 122 122 122 122 122 122 122 … 122 122 122 122 122 122 122 123 123 123 123 123 123 123 123 123 123 123 123 123 123 123 124 124 124 124 124 124 124 124 124 124 124 124 124 124 124 125 125 125 125 125 125 125 125 125 125 125 125 125 125 125 126 126 126 126 126 126 126 126 126 126 126 126 126 126 126 127 127 127 127 127 127 127 127 … 127 127 127 127 127 127 127 128 128 128 128 128 128 128 128 128 128 128 128 128 128 128 129 129 129 129 129 129 129 129 129 129 129 129 129 129 129 [:, :, 6, 7] = 3 3 3 3 3 3 3 3 … 3 3 3 3 3 3 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 8 8 8 8 8 8 8 8 … 8 8 8 8 8 8 8 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 13 13 13 13 13 13 13 13 … 13 13 13 13 13 13 13 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 ⋮ ⋮ ⋱ ⋮ 119 119 119 119 119 119 119 119 119 119 119 119 119 119 119 120 120 120 120 120 120 120 120 120 120 120 120 120 120 120 121 121 121 121 121 121 121 121 121 121 121 121 121 121 121 122 122 122 122 122 122 122 122 122 122 122 122 122 122 122 123 123 123 123 123 123 123 123 … 123 123 123 123 123 123 123 124 124 124 124 124 124 124 124 124 124 124 124 124 124 124 125 125 125 125 125 125 125 125 125 125 125 125 125 125 125 126 126 126 126 126 126 126 126 126 126 126 126 126 126 126 127 127 127 127 127 127 127 127 127 127 127 127 127 127 127 128 128 128 128 128 128 128 128 … 128 128 128 128 128 128 128 129 129 129 129 129 129 129 129 129 129 129 129 129 129 129 130 130 130 130 130 130 130 130 130 130 130 130 130 130 130 [:, :, 7, 7] = 4 4 4 4 4 4 4 4 … 4 4 4 4 4 4 4 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 9 9 9 9 9 9 9 9 … 9 9 9 9 9 9 9 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 14 14 14 14 14 14 14 14 … 14 14 14 14 14 14 14 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 ⋮ ⋮ ⋱ ⋮ 120 120 120 120 120 120 120 120 120 120 120 120 120 120 120 121 121 121 121 121 121 121 121 121 121 121 121 121 121 121 122 122 122 122 122 122 122 122 122 122 122 122 122 122 122 123 123 123 123 123 123 123 123 123 123 123 123 123 123 123 124 124 124 124 124 124 124 124 … 124 124 124 124 124 124 124 125 125 125 125 125 125 125 125 125 125 125 125 125 125 125 126 126 126 126 126 126 126 126 126 126 126 126 126 126 126 127 127 127 127 127 127 127 127 127 127 127 127 127 127 127 128 128 128 128 128 128 128 128 128 128 128 128 128 128 128 129 129 129 129 129 129 129 129 … 129 129 129 129 129 129 129 130 130 130 130 130 130 130 130 130 130 130 130 130 130 130 131 131 131 131 131 131 131 131 131 131 131 131 131 131 131
We handle boundary condition by reflexion
X[X .< 1] = 2 .- X[X .< 1]
Y[Y .< 1] = 2 .- Y[Y .< 1]
X[X .> n] = 2*n .- X[X .> n]
Y[Y .> n] = 2*n .- Y[Y .> n]
5376-element Array{Int64,1}: 127 127 127 127 127 127 127 127 127 127 127 127 127 ⋮ 127 126 125 127 126 125 127 126 125 127 126 125
Patch extractor operator.
I = X .+ (Y .- 1)*n
for i in 1 : Base.div(n, w)
for j in 1 : Base.div(n, w)
I[i, j, :, :] = transpose(I[i, j, :, :])
end
end
#function patch(f)
# P = zeros(n, n, w1, w1)
# for i in 1:length(f[:, 1])
# for j in 1:length(f[1, :])
# P[i, j, :, :] = f[I[i, j, :, :]]
# end
# end
# return P
#end
function patch(f)
return f[I]
end
patch (generic function with 1 method)
Define the patch matrix $P$ of size $(n,n,w_1,w_1)$. Each $P(i,j,:,:)$ represent an $(w_1,w_1)$ patch extracted around pixel $(i,j)$ in the image.
P = patch(f)
128×128×7×7 Array{Float64,4}: [:, :, 1, 1] = 0.420562 0.322122 0.298638 0.41914 … 0.428573 0.44862 0.496517 0.302386 0.350857 0.367454 0.421916 0.488337 0.439019 0.463395 0.408959 0.337497 0.375166 0.331575 0.428263 0.459281 0.433398 0.358469 0.338717 0.371062 0.310121 0.505774 0.528377 0.5479 0.408959 0.337497 0.375166 0.331575 0.428263 0.459281 0.433398 0.302386 0.350857 0.367454 0.421916 … 0.488337 0.439019 0.463395 0.420562 0.322122 0.298638 0.41914 0.428573 0.44862 0.496517 0.314689 0.435777 0.426165 0.384639 0.386027 0.432706 0.462501 0.353112 0.374979 0.379442 0.39974 0.491674 0.4753 0.440267 0.411506 0.357536 0.324394 0.411828 0.382523 0.478623 0.35104 0.28269 0.387966 0.392045 0.384901 … 0.288662 0.340924 0.319882 0.343019 0.361621 0.385085 0.343604 0.31774 0.343886 0.280956 0.310331 0.372574 0.361015 0.324292 0.231817 0.140795 0.167252 ⋮ ⋱ ⋮ 0.311386 0.404238 0.378485 0.391925 0.678462 0.628793 0.558204 0.335594 0.425717 0.348991 0.366602 0.605747 0.701104 0.535028 0.399874 0.34165 0.318672 0.358747 0.676218 0.685461 0.607727 0.400662 0.341967 0.414842 0.401868 0.592331 0.697516 0.758275 0.376995 0.348963 0.397058 0.386276 … 0.643912 0.553756 0.658808 0.46093 0.392605 0.314303 0.369719 0.654399 0.564135 0.66532 0.394611 0.366495 0.345775 0.415111 0.664339 0.64814 0.638867 0.433254 0.423843 0.420242 0.396661 0.654127 0.646679 0.598602 0.352568 0.335699 0.456157 0.515873 0.764299 0.699749 0.633151 0.321294 0.37938 0.366803 0.391863 … 0.774945 0.734123 0.750186 0.416089 0.38532 0.400952 0.439291 0.630456 0.653461 0.70249 0.353797 0.407809 0.443295 0.459563 0.572147 0.629985 0.629921 [:, :, 2, 1] = 0.322122 0.298638 0.41914 0.298638 … 0.488337 0.439019 0.463395 0.350857 0.367454 0.421916 0.367454 0.428263 0.459281 0.433398 0.337497 0.375166 0.331575 0.375166 0.505774 0.528377 0.5479 0.338717 0.371062 0.310121 0.371062 0.428263 0.459281 0.433398 0.337497 0.375166 0.331575 0.375166 0.488337 0.439019 0.463395 0.350857 0.367454 0.421916 0.367454 … 0.428573 0.44862 0.496517 0.322122 0.298638 0.41914 0.298638 0.386027 0.432706 0.462501 0.435777 0.426165 0.384639 0.426165 0.491674 0.4753 0.440267 0.374979 0.379442 0.39974 0.379442 0.382523 0.478623 0.35104 0.357536 0.324394 0.411828 0.324394 0.288662 0.340924 0.319882 0.387966 0.392045 0.384901 0.392045 … 0.31774 0.343886 0.280956 0.361621 0.385085 0.343604 0.385085 0.231817 0.140795 0.167252 0.372574 0.361015 0.324292 0.361015 0.202242 0.232939 0.217961 ⋮ ⋱ ⋮ 0.335594 0.425717 0.348991 0.366602 0.605747 0.701104 0.535028 0.399874 0.34165 0.318672 0.358747 0.676218 0.685461 0.607727 0.400662 0.341967 0.414842 0.401868 0.592331 0.697516 0.758275 0.376995 0.348963 0.397058 0.386276 0.643912 0.553756 0.658808 0.46093 0.392605 0.314303 0.369719 … 0.654399 0.564135 0.66532 0.394611 0.366495 0.345775 0.415111 0.664339 0.64814 0.638867 0.433254 0.423843 0.420242 0.396661 0.654127 0.646679 0.598602 0.352568 0.335699 0.456157 0.515873 0.764299 0.699749 0.633151 0.321294 0.37938 0.366803 0.391863 0.774945 0.734123 0.750186 0.416089 0.38532 0.400952 0.439291 … 0.630456 0.653461 0.70249 0.353797 0.407809 0.443295 0.459563 0.572147 0.629985 0.629921 0.36485 0.305613 0.409829 0.404933 0.711711 0.666042 0.657626 [:, :, 3, 1] = 0.298638 0.41914 0.298638 0.322122 … 0.428263 0.459281 0.433398 0.367454 0.421916 0.367454 0.350857 0.505774 0.528377 0.5479 0.375166 0.331575 0.375166 0.337497 0.428263 0.459281 0.433398 0.371062 0.310121 0.371062 0.338717 0.488337 0.439019 0.463395 0.375166 0.331575 0.375166 0.337497 0.428573 0.44862 0.496517 0.367454 0.421916 0.367454 0.350857 … 0.386027 0.432706 0.462501 0.298638 0.41914 0.298638 0.322122 0.491674 0.4753 0.440267 0.426165 0.384639 0.426165 0.435777 0.382523 0.478623 0.35104 0.379442 0.39974 0.379442 0.374979 0.288662 0.340924 0.319882 0.324394 0.411828 0.324394 0.357536 0.31774 0.343886 0.280956 0.392045 0.384901 0.392045 0.387966 … 0.231817 0.140795 0.167252 0.385085 0.343604 0.385085 0.361621 0.202242 0.232939 0.217961 0.361015 0.324292 0.361015 0.372574 0.149172 0.188722 0.150437 ⋮ ⋱ ⋮ 0.399874 0.34165 0.318672 0.358747 0.676218 0.685461 0.607727 0.400662 0.341967 0.414842 0.401868 0.592331 0.697516 0.758275 0.376995 0.348963 0.397058 0.386276 0.643912 0.553756 0.658808 0.46093 0.392605 0.314303 0.369719 0.654399 0.564135 0.66532 0.394611 0.366495 0.345775 0.415111 … 0.664339 0.64814 0.638867 0.433254 0.423843 0.420242 0.396661 0.654127 0.646679 0.598602 0.352568 0.335699 0.456157 0.515873 0.764299 0.699749 0.633151 0.321294 0.37938 0.366803 0.391863 0.774945 0.734123 0.750186 0.416089 0.38532 0.400952 0.439291 0.630456 0.653461 0.70249 0.353797 0.407809 0.443295 0.459563 … 0.572147 0.629985 0.629921 0.36485 0.305613 0.409829 0.404933 0.711711 0.666042 0.657626 0.386978 0.443315 0.324649 0.373489 0.630046 0.737301 0.757109 [:, :, 4, 1] = 0.41914 0.298638 0.322122 0.420562 … 0.505774 0.528377 0.5479 0.421916 0.367454 0.350857 0.302386 0.428263 0.459281 0.433398 0.331575 0.375166 0.337497 0.408959 0.488337 0.439019 0.463395 0.310121 0.371062 0.338717 0.358469 0.428573 0.44862 0.496517 0.331575 0.375166 0.337497 0.408959 0.386027 0.432706 0.462501 0.421916 0.367454 0.350857 0.302386 … 0.491674 0.4753 0.440267 0.41914 0.298638 0.322122 0.420562 0.382523 0.478623 0.35104 0.384639 0.426165 0.435777 0.314689 0.288662 0.340924 0.319882 0.39974 0.379442 0.374979 0.353112 0.31774 0.343886 0.280956 0.411828 0.324394 0.357536 0.411506 0.231817 0.140795 0.167252 0.384901 0.392045 0.387966 0.28269 … 0.202242 0.232939 0.217961 0.343604 0.385085 0.361621 0.343019 0.149172 0.188722 0.150437 0.324292 0.361015 0.372574 0.310331 0.0651754 0.174348 0.272203 ⋮ ⋱ ⋮ 0.400662 0.341967 0.414842 0.401868 0.592331 0.697516 0.758275 0.376995 0.348963 0.397058 0.386276 0.643912 0.553756 0.658808 0.46093 0.392605 0.314303 0.369719 0.654399 0.564135 0.66532 0.394611 0.366495 0.345775 0.415111 0.664339 0.64814 0.638867 0.433254 0.423843 0.420242 0.396661 … 0.654127 0.646679 0.598602 0.352568 0.335699 0.456157 0.515873 0.764299 0.699749 0.633151 0.321294 0.37938 0.366803 0.391863 0.774945 0.734123 0.750186 0.416089 0.38532 0.400952 0.439291 0.630456 0.653461 0.70249 0.353797 0.407809 0.443295 0.459563 0.572147 0.629985 0.629921 0.36485 0.305613 0.409829 0.404933 … 0.711711 0.666042 0.657626 0.386978 0.443315 0.324649 0.373489 0.630046 0.737301 0.757109 0.353269 0.328793 0.391277 0.366263 0.585115 0.679758 0.694726 [:, :, 5, 1] = 0.298638 0.322122 0.420562 0.41304 … 0.428263 0.459281 0.433398 0.367454 0.350857 0.302386 0.334106 0.488337 0.439019 0.463395 0.375166 0.337497 0.408959 0.307268 0.428573 0.44862 0.496517 0.371062 0.338717 0.358469 0.366528 0.386027 0.432706 0.462501 0.375166 0.337497 0.408959 0.307268 0.491674 0.4753 0.440267 0.367454 0.350857 0.302386 0.334106 … 0.382523 0.478623 0.35104 0.298638 0.322122 0.420562 0.41304 0.288662 0.340924 0.319882 0.426165 0.435777 0.314689 0.329906 0.31774 0.343886 0.280956 0.379442 0.374979 0.353112 0.381944 0.231817 0.140795 0.167252 0.324394 0.357536 0.411506 0.352719 0.202242 0.232939 0.217961 0.392045 0.387966 0.28269 0.377169 … 0.149172 0.188722 0.150437 0.385085 0.361621 0.343019 0.330815 0.0651754 0.174348 0.272203 0.361015 0.372574 0.310331 0.374705 0.125428 0.182513 0.163869 ⋮ ⋱ ⋮ 0.376995 0.348963 0.397058 0.386276 0.643912 0.553756 0.658808 0.46093 0.392605 0.314303 0.369719 0.654399 0.564135 0.66532 0.394611 0.366495 0.345775 0.415111 0.664339 0.64814 0.638867 0.433254 0.423843 0.420242 0.396661 0.654127 0.646679 0.598602 0.352568 0.335699 0.456157 0.515873 … 0.764299 0.699749 0.633151 0.321294 0.37938 0.366803 0.391863 0.774945 0.734123 0.750186 0.416089 0.38532 0.400952 0.439291 0.630456 0.653461 0.70249 0.353797 0.407809 0.443295 0.459563 0.572147 0.629985 0.629921 0.36485 0.305613 0.409829 0.404933 0.711711 0.666042 0.657626 0.386978 0.443315 0.324649 0.373489 … 0.630046 0.737301 0.757109 0.353269 0.328793 0.391277 0.366263 0.585115 0.679758 0.694726 0.386978 0.443315 0.324649 0.373489 0.630046 0.737301 0.757109 [:, :, 6, 1] = 0.322122 0.420562 0.41304 0.387839 … 0.488337 0.439019 0.463395 0.350857 0.302386 0.334106 0.383443 0.428573 0.44862 0.496517 0.337497 0.408959 0.307268 0.372549 0.386027 0.432706 0.462501 0.338717 0.358469 0.366528 0.301808 0.491674 0.4753 0.440267 0.337497 0.408959 0.307268 0.372549 0.382523 0.478623 0.35104 0.350857 0.302386 0.334106 0.383443 … 0.288662 0.340924 0.319882 0.322122 0.420562 0.41304 0.387839 0.31774 0.343886 0.280956 0.435777 0.314689 0.329906 0.379633 0.231817 0.140795 0.167252 0.374979 0.353112 0.381944 0.36836 0.202242 0.232939 0.217961 0.357536 0.411506 0.352719 0.337017 0.149172 0.188722 0.150437 0.387966 0.28269 0.377169 0.386111 … 0.0651754 0.174348 0.272203 0.361621 0.343019 0.330815 0.305207 0.125428 0.182513 0.163869 0.372574 0.310331 0.374705 0.38899 0.21213 0.112225 0.147525 ⋮ ⋱ ⋮ 0.46093 0.392605 0.314303 0.369719 0.654399 0.564135 0.66532 0.394611 0.366495 0.345775 0.415111 0.664339 0.64814 0.638867 0.433254 0.423843 0.420242 0.396661 0.654127 0.646679 0.598602 0.352568 0.335699 0.456157 0.515873 0.764299 0.699749 0.633151 0.321294 0.37938 0.366803 0.391863 … 0.774945 0.734123 0.750186 0.416089 0.38532 0.400952 0.439291 0.630456 0.653461 0.70249 0.353797 0.407809 0.443295 0.459563 0.572147 0.629985 0.629921 0.36485 0.305613 0.409829 0.404933 0.711711 0.666042 0.657626 0.386978 0.443315 0.324649 0.373489 0.630046 0.737301 0.757109 0.353269 0.328793 0.391277 0.366263 … 0.585115 0.679758 0.694726 0.386978 0.443315 0.324649 0.373489 0.630046 0.737301 0.757109 0.36485 0.305613 0.409829 0.404933 0.711711 0.666042 0.657626 [:, :, 7, 1] = 0.420562 0.41304 0.387839 0.281307 … 0.428573 0.44862 0.496517 0.302386 0.334106 0.383443 0.422243 0.386027 0.432706 0.462501 0.408959 0.307268 0.372549 0.389746 0.491674 0.4753 0.440267 0.358469 0.366528 0.301808 0.271791 0.382523 0.478623 0.35104 0.408959 0.307268 0.372549 0.389746 0.288662 0.340924 0.319882 0.302386 0.334106 0.383443 0.422243 … 0.31774 0.343886 0.280956 0.420562 0.41304 0.387839 0.281307 0.231817 0.140795 0.167252 0.314689 0.329906 0.379633 0.375243 0.202242 0.232939 0.217961 0.353112 0.381944 0.36836 0.332942 0.149172 0.188722 0.150437 0.411506 0.352719 0.337017 0.356497 0.0651754 0.174348 0.272203 0.28269 0.377169 0.386111 0.328073 … 0.125428 0.182513 0.163869 0.343019 0.330815 0.305207 0.365998 0.21213 0.112225 0.147525 0.310331 0.374705 0.38899 0.381824 0.115181 0.0791808 0.076828 ⋮ ⋱ ⋮ 0.394611 0.366495 0.345775 0.415111 0.664339 0.64814 0.638867 0.433254 0.423843 0.420242 0.396661 0.654127 0.646679 0.598602 0.352568 0.335699 0.456157 0.515873 0.764299 0.699749 0.633151 0.321294 0.37938 0.366803 0.391863 0.774945 0.734123 0.750186 0.416089 0.38532 0.400952 0.439291 … 0.630456 0.653461 0.70249 0.353797 0.407809 0.443295 0.459563 0.572147 0.629985 0.629921 0.36485 0.305613 0.409829 0.404933 0.711711 0.666042 0.657626 0.386978 0.443315 0.324649 0.373489 0.630046 0.737301 0.757109 0.353269 0.328793 0.391277 0.366263 0.585115 0.679758 0.694726 0.386978 0.443315 0.324649 0.373489 … 0.630046 0.737301 0.757109 0.36485 0.305613 0.409829 0.404933 0.711711 0.666042 0.657626 0.353797 0.407809 0.443295 0.459563 0.572147 0.629985 0.629921 [:, :, 1, 2] = 0.302386 0.350857 0.367454 0.421916 … 0.44862 0.496517 0.567202 0.408959 0.337497 0.375166 0.331575 0.439019 0.463395 0.540048 0.358469 0.338717 0.371062 0.310121 0.459281 0.433398 0.33134 0.408959 0.337497 0.375166 0.331575 0.528377 0.5479 0.441499 0.302386 0.350857 0.367454 0.421916 0.459281 0.433398 0.33134 0.420562 0.322122 0.298638 0.41914 … 0.439019 0.463395 0.540048 0.314689 0.435777 0.426165 0.384639 0.44862 0.496517 0.567202 0.353112 0.374979 0.379442 0.39974 0.432706 0.462501 0.573065 0.411506 0.357536 0.324394 0.411828 0.4753 0.440267 0.415227 0.28269 0.387966 0.392045 0.384901 0.478623 0.35104 0.365848 0.343019 0.361621 0.385085 0.343604 … 0.340924 0.319882 0.25511 0.310331 0.372574 0.361015 0.324292 0.343886 0.280956 0.16697 0.360588 0.318909 0.373246 0.374508 0.140795 0.167252 0.0874964 ⋮ ⋱ ⋮ 0.404238 0.378485 0.391925 0.378485 0.628793 0.558204 0.607852 0.425717 0.348991 0.366602 0.348991 0.701104 0.535028 0.520682 0.34165 0.318672 0.358747 0.318672 0.685461 0.607727 0.557041 0.341967 0.414842 0.401868 0.414842 0.697516 0.758275 0.738772 0.348963 0.397058 0.386276 0.397058 … 0.553756 0.658808 0.724762 0.392605 0.314303 0.369719 0.314303 0.564135 0.66532 0.707989 0.366495 0.345775 0.415111 0.345775 0.64814 0.638867 0.702256 0.423843 0.420242 0.396661 0.420242 0.646679 0.598602 0.55668 0.335699 0.456157 0.515873 0.456157 0.699749 0.633151 0.602578 0.37938 0.366803 0.391863 0.366803 … 0.734123 0.750186 0.571596 0.38532 0.400952 0.439291 0.400952 0.653461 0.70249 0.642772 0.407809 0.443295 0.459563 0.443295 0.629985 0.629921 0.606939 [:, :, 2, 2] = 0.350857 0.367454 0.421916 0.367454 … 0.439019 0.463395 0.540048 0.337497 0.375166 0.331575 0.375166 0.459281 0.433398 0.33134 0.338717 0.371062 0.310121 0.371062 0.528377 0.5479 0.441499 0.337497 0.375166 0.331575 0.375166 0.459281 0.433398 0.33134 0.350857 0.367454 0.421916 0.367454 0.439019 0.463395 0.540048 0.322122 0.298638 0.41914 0.298638 … 0.44862 0.496517 0.567202 0.435777 0.426165 0.384639 0.426165 0.432706 0.462501 0.573065 0.374979 0.379442 0.39974 0.379442 0.4753 0.440267 0.415227 0.357536 0.324394 0.411828 0.324394 0.478623 0.35104 0.365848 0.387966 0.392045 0.384901 0.392045 0.340924 0.319882 0.25511 0.361621 0.385085 0.343604 0.385085 … 0.343886 0.280956 0.16697 0.372574 0.361015 0.324292 0.361015 0.140795 0.167252 0.0874964 0.318909 0.373246 0.374508 0.373246 0.232939 0.217961 0.26696 ⋮ ⋱ ⋮ 0.425717 0.348991 0.366602 0.348991 0.701104 0.535028 0.520682 0.34165 0.318672 0.358747 0.318672 0.685461 0.607727 0.557041 0.341967 0.414842 0.401868 0.414842 0.697516 0.758275 0.738772 0.348963 0.397058 0.386276 0.397058 0.553756 0.658808 0.724762 0.392605 0.314303 0.369719 0.314303 … 0.564135 0.66532 0.707989 0.366495 0.345775 0.415111 0.345775 0.64814 0.638867 0.702256 0.423843 0.420242 0.396661 0.420242 0.646679 0.598602 0.55668 0.335699 0.456157 0.515873 0.456157 0.699749 0.633151 0.602578 0.37938 0.366803 0.391863 0.366803 0.734123 0.750186 0.571596 0.38532 0.400952 0.439291 0.400952 … 0.653461 0.70249 0.642772 0.407809 0.443295 0.459563 0.443295 0.629985 0.629921 0.606939 0.305613 0.409829 0.404933 0.409829 0.666042 0.657626 0.644774 [:, :, 3, 2] = 0.367454 0.421916 0.367454 0.350857 … 0.459281 0.433398 0.33134 0.375166 0.331575 0.375166 0.337497 0.528377 0.5479 0.441499 0.371062 0.310121 0.371062 0.338717 0.459281 0.433398 0.33134 0.375166 0.331575 0.375166 0.337497 0.439019 0.463395 0.540048 0.367454 0.421916 0.367454 0.350857 0.44862 0.496517 0.567202 0.298638 0.41914 0.298638 0.322122 … 0.432706 0.462501 0.573065 0.426165 0.384639 0.426165 0.435777 0.4753 0.440267 0.415227 0.379442 0.39974 0.379442 0.374979 0.478623 0.35104 0.365848 0.324394 0.411828 0.324394 0.357536 0.340924 0.319882 0.25511 0.392045 0.384901 0.392045 0.387966 0.343886 0.280956 0.16697 0.385085 0.343604 0.385085 0.361621 … 0.140795 0.167252 0.0874964 0.361015 0.324292 0.361015 0.372574 0.232939 0.217961 0.26696 0.373246 0.374508 0.373246 0.318909 0.188722 0.150437 0.159322 ⋮ ⋱ ⋮ 0.34165 0.318672 0.358747 0.318672 0.685461 0.607727 0.557041 0.341967 0.414842 0.401868 0.414842 0.697516 0.758275 0.738772 0.348963 0.397058 0.386276 0.397058 0.553756 0.658808 0.724762 0.392605 0.314303 0.369719 0.314303 0.564135 0.66532 0.707989 0.366495 0.345775 0.415111 0.345775 … 0.64814 0.638867 0.702256 0.423843 0.420242 0.396661 0.420242 0.646679 0.598602 0.55668 0.335699 0.456157 0.515873 0.456157 0.699749 0.633151 0.602578 0.37938 0.366803 0.391863 0.366803 0.734123 0.750186 0.571596 0.38532 0.400952 0.439291 0.400952 0.653461 0.70249 0.642772 0.407809 0.443295 0.459563 0.443295 … 0.629985 0.629921 0.606939 0.305613 0.409829 0.404933 0.409829 0.666042 0.657626 0.644774 0.443315 0.324649 0.373489 0.324649 0.737301 0.757109 0.634769 [:, :, 4, 2] = 0.421916 0.367454 0.350857 0.302386 … 0.528377 0.5479 0.441499 0.331575 0.375166 0.337497 0.408959 0.459281 0.433398 0.33134 0.310121 0.371062 0.338717 0.358469 0.439019 0.463395 0.540048 0.331575 0.375166 0.337497 0.408959 0.44862 0.496517 0.567202 0.421916 0.367454 0.350857 0.302386 0.432706 0.462501 0.573065 0.41914 0.298638 0.322122 0.420562 … 0.4753 0.440267 0.415227 0.384639 0.426165 0.435777 0.314689 0.478623 0.35104 0.365848 0.39974 0.379442 0.374979 0.353112 0.340924 0.319882 0.25511 0.411828 0.324394 0.357536 0.411506 0.343886 0.280956 0.16697 0.384901 0.392045 0.387966 0.28269 0.140795 0.167252 0.0874964 0.343604 0.385085 0.361621 0.343019 … 0.232939 0.217961 0.26696 0.324292 0.361015 0.372574 0.310331 0.188722 0.150437 0.159322 0.374508 0.373246 0.318909 0.360588 0.174348 0.272203 0.16047 ⋮ ⋱ ⋮ 0.341967 0.414842 0.401868 0.414842 0.697516 0.758275 0.738772 0.348963 0.397058 0.386276 0.397058 0.553756 0.658808 0.724762 0.392605 0.314303 0.369719 0.314303 0.564135 0.66532 0.707989 0.366495 0.345775 0.415111 0.345775 0.64814 0.638867 0.702256 0.423843 0.420242 0.396661 0.420242 … 0.646679 0.598602 0.55668 0.335699 0.456157 0.515873 0.456157 0.699749 0.633151 0.602578 0.37938 0.366803 0.391863 0.366803 0.734123 0.750186 0.571596 0.38532 0.400952 0.439291 0.400952 0.653461 0.70249 0.642772 0.407809 0.443295 0.459563 0.443295 0.629985 0.629921 0.606939 0.305613 0.409829 0.404933 0.409829 … 0.666042 0.657626 0.644774 0.443315 0.324649 0.373489 0.324649 0.737301 0.757109 0.634769 0.328793 0.391277 0.366263 0.391277 0.679758 0.694726 0.64582 [:, :, 5, 2] = 0.367454 0.350857 0.302386 0.334106 … 0.459281 0.433398 0.33134 0.375166 0.337497 0.408959 0.307268 0.439019 0.463395 0.540048 0.371062 0.338717 0.358469 0.366528 0.44862 0.496517 0.567202 0.375166 0.337497 0.408959 0.307268 0.432706 0.462501 0.573065 0.367454 0.350857 0.302386 0.334106 0.4753 0.440267 0.415227 0.298638 0.322122 0.420562 0.41304 … 0.478623 0.35104 0.365848 0.426165 0.435777 0.314689 0.329906 0.340924 0.319882 0.25511 0.379442 0.374979 0.353112 0.381944 0.343886 0.280956 0.16697 0.324394 0.357536 0.411506 0.352719 0.140795 0.167252 0.0874964 0.392045 0.387966 0.28269 0.377169 0.232939 0.217961 0.26696 0.385085 0.361621 0.343019 0.330815 … 0.188722 0.150437 0.159322 0.361015 0.372574 0.310331 0.374705 0.174348 0.272203 0.16047 0.373246 0.318909 0.360588 0.420681 0.182513 0.163869 0.144812 ⋮ ⋱ ⋮ 0.348963 0.397058 0.386276 0.397058 0.553756 0.658808 0.724762 0.392605 0.314303 0.369719 0.314303 0.564135 0.66532 0.707989 0.366495 0.345775 0.415111 0.345775 0.64814 0.638867 0.702256 0.423843 0.420242 0.396661 0.420242 0.646679 0.598602 0.55668 0.335699 0.456157 0.515873 0.456157 … 0.699749 0.633151 0.602578 0.37938 0.366803 0.391863 0.366803 0.734123 0.750186 0.571596 0.38532 0.400952 0.439291 0.400952 0.653461 0.70249 0.642772 0.407809 0.443295 0.459563 0.443295 0.629985 0.629921 0.606939 0.305613 0.409829 0.404933 0.409829 0.666042 0.657626 0.644774 0.443315 0.324649 0.373489 0.324649 … 0.737301 0.757109 0.634769 0.328793 0.391277 0.366263 0.391277 0.679758 0.694726 0.64582 0.443315 0.324649 0.373489 0.324649 0.737301 0.757109 0.634769 [:, :, 6, 2] = 0.350857 0.302386 0.334106 0.383443 … 0.439019 0.463395 0.540048 0.337497 0.408959 0.307268 0.372549 0.44862 0.496517 0.567202 0.338717 0.358469 0.366528 0.301808 0.432706 0.462501 0.573065 0.337497 0.408959 0.307268 0.372549 0.4753 0.440267 0.415227 0.350857 0.302386 0.334106 0.383443 0.478623 0.35104 0.365848 0.322122 0.420562 0.41304 0.387839 … 0.340924 0.319882 0.25511 0.435777 0.314689 0.329906 0.379633 0.343886 0.280956 0.16697 0.374979 0.353112 0.381944 0.36836 0.140795 0.167252 0.0874964 0.357536 0.411506 0.352719 0.337017 0.232939 0.217961 0.26696 0.387966 0.28269 0.377169 0.386111 0.188722 0.150437 0.159322 0.361621 0.343019 0.330815 0.305207 … 0.174348 0.272203 0.16047 0.372574 0.310331 0.374705 0.38899 0.182513 0.163869 0.144812 0.318909 0.360588 0.420681 0.289038 0.112225 0.147525 0.0775752 ⋮ ⋱ ⋮ 0.392605 0.314303 0.369719 0.314303 0.564135 0.66532 0.707989 0.366495 0.345775 0.415111 0.345775 0.64814 0.638867 0.702256 0.423843 0.420242 0.396661 0.420242 0.646679 0.598602 0.55668 0.335699 0.456157 0.515873 0.456157 0.699749 0.633151 0.602578 0.37938 0.366803 0.391863 0.366803 … 0.734123 0.750186 0.571596 0.38532 0.400952 0.439291 0.400952 0.653461 0.70249 0.642772 0.407809 0.443295 0.459563 0.443295 0.629985 0.629921 0.606939 0.305613 0.409829 0.404933 0.409829 0.666042 0.657626 0.644774 0.443315 0.324649 0.373489 0.324649 0.737301 0.757109 0.634769 0.328793 0.391277 0.366263 0.391277 … 0.679758 0.694726 0.64582 0.443315 0.324649 0.373489 0.324649 0.737301 0.757109 0.634769 0.305613 0.409829 0.404933 0.409829 0.666042 0.657626 0.644774 [:, :, 7, 2] = 0.302386 0.334106 0.383443 0.422243 … 0.44862 0.496517 0.567202 0.408959 0.307268 0.372549 0.389746 0.432706 0.462501 0.573065 0.358469 0.366528 0.301808 0.271791 0.4753 0.440267 0.415227 0.408959 0.307268 0.372549 0.389746 0.478623 0.35104 0.365848 0.302386 0.334106 0.383443 0.422243 0.340924 0.319882 0.25511 0.420562 0.41304 0.387839 0.281307 … 0.343886 0.280956 0.16697 0.314689 0.329906 0.379633 0.375243 0.140795 0.167252 0.0874964 0.353112 0.381944 0.36836 0.332942 0.232939 0.217961 0.26696 0.411506 0.352719 0.337017 0.356497 0.188722 0.150437 0.159322 0.28269 0.377169 0.386111 0.328073 0.174348 0.272203 0.16047 0.343019 0.330815 0.305207 0.365998 … 0.182513 0.163869 0.144812 0.310331 0.374705 0.38899 0.381824 0.112225 0.147525 0.0775752 0.360588 0.420681 0.289038 0.321463 0.0791808 0.076828 0.0790067 ⋮ ⋱ ⋮ 0.366495 0.345775 0.415111 0.345775 0.64814 0.638867 0.702256 0.423843 0.420242 0.396661 0.420242 0.646679 0.598602 0.55668 0.335699 0.456157 0.515873 0.456157 0.699749 0.633151 0.602578 0.37938 0.366803 0.391863 0.366803 0.734123 0.750186 0.571596 0.38532 0.400952 0.439291 0.400952 … 0.653461 0.70249 0.642772 0.407809 0.443295 0.459563 0.443295 0.629985 0.629921 0.606939 0.305613 0.409829 0.404933 0.409829 0.666042 0.657626 0.644774 0.443315 0.324649 0.373489 0.324649 0.737301 0.757109 0.634769 0.328793 0.391277 0.366263 0.391277 0.679758 0.694726 0.64582 0.443315 0.324649 0.373489 0.324649 … 0.737301 0.757109 0.634769 0.305613 0.409829 0.404933 0.409829 0.666042 0.657626 0.644774 0.407809 0.443295 0.459563 0.443295 0.629985 0.629921 0.606939 [:, :, 1, 3] = 0.408959 0.337497 0.375166 0.331575 … 0.496517 0.567202 0.485594 0.358469 0.338717 0.371062 0.310121 0.463395 0.540048 0.467588 0.408959 0.337497 0.375166 0.331575 0.433398 0.33134 0.321467 0.302386 0.350857 0.367454 0.421916 0.5479 0.441499 0.432999 0.420562 0.322122 0.298638 0.41914 0.433398 0.33134 0.321467 0.314689 0.435777 0.426165 0.384639 … 0.463395 0.540048 0.467588 0.353112 0.374979 0.379442 0.39974 0.496517 0.567202 0.485594 0.411506 0.357536 0.324394 0.411828 0.462501 0.573065 0.297878 0.28269 0.387966 0.392045 0.384901 0.440267 0.415227 0.597624 0.343019 0.361621 0.385085 0.343604 0.35104 0.365848 0.503564 0.310331 0.372574 0.361015 0.324292 … 0.319882 0.25511 0.381689 0.360588 0.318909 0.373246 0.374508 0.280956 0.16697 0.169959 0.301081 0.382493 0.355147 0.406666 0.167252 0.0874964 0.151843 ⋮ ⋱ ⋮ 0.378485 0.391925 0.378485 0.404238 0.558204 0.607852 0.638634 0.348991 0.366602 0.348991 0.425717 0.535028 0.520682 0.698036 0.318672 0.358747 0.318672 0.34165 0.607727 0.557041 0.577087 0.414842 0.401868 0.414842 0.341967 0.758275 0.738772 0.547219 0.397058 0.386276 0.397058 0.348963 … 0.658808 0.724762 0.63977 0.314303 0.369719 0.314303 0.392605 0.66532 0.707989 0.595353 0.345775 0.415111 0.345775 0.366495 0.638867 0.702256 0.760678 0.420242 0.396661 0.420242 0.423843 0.598602 0.55668 0.655217 0.456157 0.515873 0.456157 0.335699 0.633151 0.602578 0.684568 0.366803 0.391863 0.366803 0.37938 … 0.750186 0.571596 0.526541 0.400952 0.439291 0.400952 0.38532 0.70249 0.642772 0.524163 0.443295 0.459563 0.443295 0.407809 0.629921 0.606939 0.60571 [:, :, 2, 3] = 0.337497 0.375166 0.331575 0.375166 … 0.463395 0.540048 0.467588 0.338717 0.371062 0.310121 0.371062 0.433398 0.33134 0.321467 0.337497 0.375166 0.331575 0.375166 0.5479 0.441499 0.432999 0.350857 0.367454 0.421916 0.367454 0.433398 0.33134 0.321467 0.322122 0.298638 0.41914 0.298638 0.463395 0.540048 0.467588 0.435777 0.426165 0.384639 0.426165 … 0.496517 0.567202 0.485594 0.374979 0.379442 0.39974 0.379442 0.462501 0.573065 0.297878 0.357536 0.324394 0.411828 0.324394 0.440267 0.415227 0.597624 0.387966 0.392045 0.384901 0.392045 0.35104 0.365848 0.503564 0.361621 0.385085 0.343604 0.385085 0.319882 0.25511 0.381689 0.372574 0.361015 0.324292 0.361015 … 0.280956 0.16697 0.169959 0.318909 0.373246 0.374508 0.373246 0.167252 0.0874964 0.151843 0.382493 0.355147 0.406666 0.355147 0.217961 0.26696 0.181298 ⋮ ⋱ ⋮ 0.348991 0.366602 0.348991 0.425717 0.535028 0.520682 0.698036 0.318672 0.358747 0.318672 0.34165 0.607727 0.557041 0.577087 0.414842 0.401868 0.414842 0.341967 0.758275 0.738772 0.547219 0.397058 0.386276 0.397058 0.348963 0.658808 0.724762 0.63977 0.314303 0.369719 0.314303 0.392605 … 0.66532 0.707989 0.595353 0.345775 0.415111 0.345775 0.366495 0.638867 0.702256 0.760678 0.420242 0.396661 0.420242 0.423843 0.598602 0.55668 0.655217 0.456157 0.515873 0.456157 0.335699 0.633151 0.602578 0.684568 0.366803 0.391863 0.366803 0.37938 0.750186 0.571596 0.526541 0.400952 0.439291 0.400952 0.38532 … 0.70249 0.642772 0.524163 0.443295 0.459563 0.443295 0.407809 0.629921 0.606939 0.60571 0.409829 0.404933 0.409829 0.305613 0.657626 0.644774 0.508329 [:, :, 3, 3] = 0.375166 0.331575 0.375166 0.337497 … 0.433398 0.33134 0.321467 0.371062 0.310121 0.371062 0.338717 0.5479 0.441499 0.432999 0.375166 0.331575 0.375166 0.337497 0.433398 0.33134 0.321467 0.367454 0.421916 0.367454 0.350857 0.463395 0.540048 0.467588 0.298638 0.41914 0.298638 0.322122 0.496517 0.567202 0.485594 0.426165 0.384639 0.426165 0.435777 … 0.462501 0.573065 0.297878 0.379442 0.39974 0.379442 0.374979 0.440267 0.415227 0.597624 0.324394 0.411828 0.324394 0.357536 0.35104 0.365848 0.503564 0.392045 0.384901 0.392045 0.387966 0.319882 0.25511 0.381689 0.385085 0.343604 0.385085 0.361621 0.280956 0.16697 0.169959 0.361015 0.324292 0.361015 0.372574 … 0.167252 0.0874964 0.151843 0.373246 0.374508 0.373246 0.318909 0.217961 0.26696 0.181298 0.355147 0.406666 0.355147 0.382493 0.150437 0.159322 0.177689 ⋮ ⋱ ⋮ 0.318672 0.358747 0.318672 0.34165 0.607727 0.557041 0.577087 0.414842 0.401868 0.414842 0.341967 0.758275 0.738772 0.547219 0.397058 0.386276 0.397058 0.348963 0.658808 0.724762 0.63977 0.314303 0.369719 0.314303 0.392605 0.66532 0.707989 0.595353 0.345775 0.415111 0.345775 0.366495 … 0.638867 0.702256 0.760678 0.420242 0.396661 0.420242 0.423843 0.598602 0.55668 0.655217 0.456157 0.515873 0.456157 0.335699 0.633151 0.602578 0.684568 0.366803 0.391863 0.366803 0.37938 0.750186 0.571596 0.526541 0.400952 0.439291 0.400952 0.38532 0.70249 0.642772 0.524163 0.443295 0.459563 0.443295 0.407809 … 0.629921 0.606939 0.60571 0.409829 0.404933 0.409829 0.305613 0.657626 0.644774 0.508329 0.324649 0.373489 0.324649 0.443315 0.757109 0.634769 0.498877 [:, :, 4, 3] = 0.331575 0.375166 0.337497 0.408959 … 0.5479 0.441499 0.432999 0.310121 0.371062 0.338717 0.358469 0.433398 0.33134 0.321467 0.331575 0.375166 0.337497 0.408959 0.463395 0.540048 0.467588 0.421916 0.367454 0.350857 0.302386 0.496517 0.567202 0.485594 0.41914 0.298638 0.322122 0.420562 0.462501 0.573065 0.297878 0.384639 0.426165 0.435777 0.314689 … 0.440267 0.415227 0.597624 0.39974 0.379442 0.374979 0.353112 0.35104 0.365848 0.503564 0.411828 0.324394 0.357536 0.411506 0.319882 0.25511 0.381689 0.384901 0.392045 0.387966 0.28269 0.280956 0.16697 0.169959 0.343604 0.385085 0.361621 0.343019 0.167252 0.0874964 0.151843 0.324292 0.361015 0.372574 0.310331 … 0.217961 0.26696 0.181298 0.374508 0.373246 0.318909 0.360588 0.150437 0.159322 0.177689 0.406666 0.355147 0.382493 0.301081 0.272203 0.16047 0.189698 ⋮ ⋱ ⋮ 0.414842 0.401868 0.414842 0.341967 0.758275 0.738772 0.547219 0.397058 0.386276 0.397058 0.348963 0.658808 0.724762 0.63977 0.314303 0.369719 0.314303 0.392605 0.66532 0.707989 0.595353 0.345775 0.415111 0.345775 0.366495 0.638867 0.702256 0.760678 0.420242 0.396661 0.420242 0.423843 … 0.598602 0.55668 0.655217 0.456157 0.515873 0.456157 0.335699 0.633151 0.602578 0.684568 0.366803 0.391863 0.366803 0.37938 0.750186 0.571596 0.526541 0.400952 0.439291 0.400952 0.38532 0.70249 0.642772 0.524163 0.443295 0.459563 0.443295 0.407809 0.629921 0.606939 0.60571 0.409829 0.404933 0.409829 0.305613 … 0.657626 0.644774 0.508329 0.324649 0.373489 0.324649 0.443315 0.757109 0.634769 0.498877 0.391277 0.366263 0.391277 0.328793 0.694726 0.64582 0.628629 [:, :, 5, 3] = 0.375166 0.337497 0.408959 0.307268 … 0.433398 0.33134 0.321467 0.371062 0.338717 0.358469 0.366528 0.463395 0.540048 0.467588 0.375166 0.337497 0.408959 0.307268 0.496517 0.567202 0.485594 0.367454 0.350857 0.302386 0.334106 0.462501 0.573065 0.297878 0.298638 0.322122 0.420562 0.41304 0.440267 0.415227 0.597624 0.426165 0.435777 0.314689 0.329906 … 0.35104 0.365848 0.503564 0.379442 0.374979 0.353112 0.381944 0.319882 0.25511 0.381689 0.324394 0.357536 0.411506 0.352719 0.280956 0.16697 0.169959 0.392045 0.387966 0.28269 0.377169 0.167252 0.0874964 0.151843 0.385085 0.361621 0.343019 0.330815 0.217961 0.26696 0.181298 0.361015 0.372574 0.310331 0.374705 … 0.150437 0.159322 0.177689 0.373246 0.318909 0.360588 0.420681 0.272203 0.16047 0.189698 0.355147 0.382493 0.301081 0.427255 0.163869 0.144812 0.163406 ⋮ ⋱ ⋮ 0.397058 0.386276 0.397058 0.348963 0.658808 0.724762 0.63977 0.314303 0.369719 0.314303 0.392605 0.66532 0.707989 0.595353 0.345775 0.415111 0.345775 0.366495 0.638867 0.702256 0.760678 0.420242 0.396661 0.420242 0.423843 0.598602 0.55668 0.655217 0.456157 0.515873 0.456157 0.335699 … 0.633151 0.602578 0.684568 0.366803 0.391863 0.366803 0.37938 0.750186 0.571596 0.526541 0.400952 0.439291 0.400952 0.38532 0.70249 0.642772 0.524163 0.443295 0.459563 0.443295 0.407809 0.629921 0.606939 0.60571 0.409829 0.404933 0.409829 0.305613 0.657626 0.644774 0.508329 0.324649 0.373489 0.324649 0.443315 … 0.757109 0.634769 0.498877 0.391277 0.366263 0.391277 0.328793 0.694726 0.64582 0.628629 0.324649 0.373489 0.324649 0.443315 0.757109 0.634769 0.498877 [:, :, 6, 3] = 0.337497 0.408959 0.307268 0.372549 … 0.463395 0.540048 0.467588 0.338717 0.358469 0.366528 0.301808 0.496517 0.567202 0.485594 0.337497 0.408959 0.307268 0.372549 0.462501 0.573065 0.297878 0.350857 0.302386 0.334106 0.383443 0.440267 0.415227 0.597624 0.322122 0.420562 0.41304 0.387839 0.35104 0.365848 0.503564 0.435777 0.314689 0.329906 0.379633 … 0.319882 0.25511 0.381689 0.374979 0.353112 0.381944 0.36836 0.280956 0.16697 0.169959 0.357536 0.411506 0.352719 0.337017 0.167252 0.0874964 0.151843 0.387966 0.28269 0.377169 0.386111 0.217961 0.26696 0.181298 0.361621 0.343019 0.330815 0.305207 0.150437 0.159322 0.177689 0.372574 0.310331 0.374705 0.38899 … 0.272203 0.16047 0.189698 0.318909 0.360588 0.420681 0.289038 0.163869 0.144812 0.163406 0.382493 0.301081 0.427255 0.391195 0.147525 0.0775752 0.274339 ⋮ ⋱ ⋮ 0.314303 0.369719 0.314303 0.392605 0.66532 0.707989 0.595353 0.345775 0.415111 0.345775 0.366495 0.638867 0.702256 0.760678 0.420242 0.396661 0.420242 0.423843 0.598602 0.55668 0.655217 0.456157 0.515873 0.456157 0.335699 0.633151 0.602578 0.684568 0.366803 0.391863 0.366803 0.37938 … 0.750186 0.571596 0.526541 0.400952 0.439291 0.400952 0.38532 0.70249 0.642772 0.524163 0.443295 0.459563 0.443295 0.407809 0.629921 0.606939 0.60571 0.409829 0.404933 0.409829 0.305613 0.657626 0.644774 0.508329 0.324649 0.373489 0.324649 0.443315 0.757109 0.634769 0.498877 0.391277 0.366263 0.391277 0.328793 … 0.694726 0.64582 0.628629 0.324649 0.373489 0.324649 0.443315 0.757109 0.634769 0.498877 0.409829 0.404933 0.409829 0.305613 0.657626 0.644774 0.508329 [:, :, 7, 3] = 0.408959 0.307268 0.372549 0.389746 … 0.496517 0.567202 0.485594 0.358469 0.366528 0.301808 0.271791 0.462501 0.573065 0.297878 0.408959 0.307268 0.372549 0.389746 0.440267 0.415227 0.597624 0.302386 0.334106 0.383443 0.422243 0.35104 0.365848 0.503564 0.420562 0.41304 0.387839 0.281307 0.319882 0.25511 0.381689 0.314689 0.329906 0.379633 0.375243 … 0.280956 0.16697 0.169959 0.353112 0.381944 0.36836 0.332942 0.167252 0.0874964 0.151843 0.411506 0.352719 0.337017 0.356497 0.217961 0.26696 0.181298 0.28269 0.377169 0.386111 0.328073 0.150437 0.159322 0.177689 0.343019 0.330815 0.305207 0.365998 0.272203 0.16047 0.189698 0.310331 0.374705 0.38899 0.381824 … 0.163869 0.144812 0.163406 0.360588 0.420681 0.289038 0.321463 0.147525 0.0775752 0.274339 0.301081 0.427255 0.391195 0.385622 0.076828 0.0790067 0.12026 ⋮ ⋱ ⋮ 0.345775 0.415111 0.345775 0.366495 0.638867 0.702256 0.760678 0.420242 0.396661 0.420242 0.423843 0.598602 0.55668 0.655217 0.456157 0.515873 0.456157 0.335699 0.633151 0.602578 0.684568 0.366803 0.391863 0.366803 0.37938 0.750186 0.571596 0.526541 0.400952 0.439291 0.400952 0.38532 … 0.70249 0.642772 0.524163 0.443295 0.459563 0.443295 0.407809 0.629921 0.606939 0.60571 0.409829 0.404933 0.409829 0.305613 0.657626 0.644774 0.508329 0.324649 0.373489 0.324649 0.443315 0.757109 0.634769 0.498877 0.391277 0.366263 0.391277 0.328793 0.694726 0.64582 0.628629 0.324649 0.373489 0.324649 0.443315 … 0.757109 0.634769 0.498877 0.409829 0.404933 0.409829 0.305613 0.657626 0.644774 0.508329 0.443295 0.459563 0.443295 0.407809 0.629921 0.606939 0.60571 [:, :, 1, 4] = 0.358469 0.338717 0.371062 0.310121 … 0.567202 0.485594 0.291599 0.408959 0.337497 0.375166 0.331575 0.540048 0.467588 0.394749 0.302386 0.350857 0.367454 0.421916 0.33134 0.321467 0.480376 0.420562 0.322122 0.298638 0.41914 0.441499 0.432999 0.460332 0.314689 0.435777 0.426165 0.384639 0.33134 0.321467 0.480376 0.353112 0.374979 0.379442 0.39974 … 0.540048 0.467588 0.394749 0.411506 0.357536 0.324394 0.411828 0.567202 0.485594 0.291599 0.28269 0.387966 0.392045 0.384901 0.573065 0.297878 0.360733 0.343019 0.361621 0.385085 0.343604 0.415227 0.597624 0.561067 0.310331 0.372574 0.361015 0.324292 0.365848 0.503564 0.354022 0.360588 0.318909 0.373246 0.374508 … 0.25511 0.381689 0.28482 0.301081 0.382493 0.355147 0.406666 0.16697 0.169959 0.289525 0.316193 0.33284 0.357185 0.293279 0.0874964 0.151843 0.324038 ⋮ ⋱ ⋮ 0.391925 0.378485 0.404238 0.311386 0.607852 0.638634 0.57404 0.366602 0.348991 0.425717 0.335594 0.520682 0.698036 0.709138 0.358747 0.318672 0.34165 0.399874 0.557041 0.577087 0.592634 0.401868 0.414842 0.341967 0.400662 0.738772 0.547219 0.586609 0.386276 0.397058 0.348963 0.376995 … 0.724762 0.63977 0.560576 0.369719 0.314303 0.392605 0.46093 0.707989 0.595353 0.678479 0.415111 0.345775 0.366495 0.394611 0.702256 0.760678 0.743508 0.396661 0.420242 0.423843 0.433254 0.55668 0.655217 0.699603 0.515873 0.456157 0.335699 0.352568 0.602578 0.684568 0.659011 0.391863 0.366803 0.37938 0.321294 … 0.571596 0.526541 0.463265 0.439291 0.400952 0.38532 0.416089 0.642772 0.524163 0.464796 0.459563 0.443295 0.407809 0.353797 0.606939 0.60571 0.46617 [:, :, 2, 4] = 0.338717 0.371062 0.310121 0.371062 … 0.540048 0.467588 0.394749 0.337497 0.375166 0.331575 0.375166 0.33134 0.321467 0.480376 0.350857 0.367454 0.421916 0.367454 0.441499 0.432999 0.460332 0.322122 0.298638 0.41914 0.298638 0.33134 0.321467 0.480376 0.435777 0.426165 0.384639 0.426165 0.540048 0.467588 0.394749 0.374979 0.379442 0.39974 0.379442 … 0.567202 0.485594 0.291599 0.357536 0.324394 0.411828 0.324394 0.573065 0.297878 0.360733 0.387966 0.392045 0.384901 0.392045 0.415227 0.597624 0.561067 0.361621 0.385085 0.343604 0.385085 0.365848 0.503564 0.354022 0.372574 0.361015 0.324292 0.361015 0.25511 0.381689 0.28482 0.318909 0.373246 0.374508 0.373246 … 0.16697 0.169959 0.289525 0.382493 0.355147 0.406666 0.355147 0.0874964 0.151843 0.324038 0.33284 0.357185 0.293279 0.357185 0.26696 0.181298 0.340597 ⋮ ⋱ ⋮ 0.366602 0.348991 0.425717 0.335594 0.520682 0.698036 0.709138 0.358747 0.318672 0.34165 0.399874 0.557041 0.577087 0.592634 0.401868 0.414842 0.341967 0.400662 0.738772 0.547219 0.586609 0.386276 0.397058 0.348963 0.376995 0.724762 0.63977 0.560576 0.369719 0.314303 0.392605 0.46093 … 0.707989 0.595353 0.678479 0.415111 0.345775 0.366495 0.394611 0.702256 0.760678 0.743508 0.396661 0.420242 0.423843 0.433254 0.55668 0.655217 0.699603 0.515873 0.456157 0.335699 0.352568 0.602578 0.684568 0.659011 0.391863 0.366803 0.37938 0.321294 0.571596 0.526541 0.463265 0.439291 0.400952 0.38532 0.416089 … 0.642772 0.524163 0.464796 0.459563 0.443295 0.407809 0.353797 0.606939 0.60571 0.46617 0.404933 0.409829 0.305613 0.36485 0.644774 0.508329 0.494321 [:, :, 3, 4] = 0.371062 0.310121 0.371062 0.338717 … 0.33134 0.321467 0.480376 0.375166 0.331575 0.375166 0.337497 0.441499 0.432999 0.460332 0.367454 0.421916 0.367454 0.350857 0.33134 0.321467 0.480376 0.298638 0.41914 0.298638 0.322122 0.540048 0.467588 0.394749 0.426165 0.384639 0.426165 0.435777 0.567202 0.485594 0.291599 0.379442 0.39974 0.379442 0.374979 … 0.573065 0.297878 0.360733 0.324394 0.411828 0.324394 0.357536 0.415227 0.597624 0.561067 0.392045 0.384901 0.392045 0.387966 0.365848 0.503564 0.354022 0.385085 0.343604 0.385085 0.361621 0.25511 0.381689 0.28482 0.361015 0.324292 0.361015 0.372574 0.16697 0.169959 0.289525 0.373246 0.374508 0.373246 0.318909 … 0.0874964 0.151843 0.324038 0.355147 0.406666 0.355147 0.382493 0.26696 0.181298 0.340597 0.357185 0.293279 0.357185 0.33284 0.159322 0.177689 0.141649 ⋮ ⋱ ⋮ 0.358747 0.318672 0.34165 0.399874 0.557041 0.577087 0.592634 0.401868 0.414842 0.341967 0.400662 0.738772 0.547219 0.586609 0.386276 0.397058 0.348963 0.376995 0.724762 0.63977 0.560576 0.369719 0.314303 0.392605 0.46093 0.707989 0.595353 0.678479 0.415111 0.345775 0.366495 0.394611 … 0.702256 0.760678 0.743508 0.396661 0.420242 0.423843 0.433254 0.55668 0.655217 0.699603 0.515873 0.456157 0.335699 0.352568 0.602578 0.684568 0.659011 0.391863 0.366803 0.37938 0.321294 0.571596 0.526541 0.463265 0.439291 0.400952 0.38532 0.416089 0.642772 0.524163 0.464796 0.459563 0.443295 0.407809 0.353797 … 0.606939 0.60571 0.46617 0.404933 0.409829 0.305613 0.36485 0.644774 0.508329 0.494321 0.373489 0.324649 0.443315 0.386978 0.634769 0.498877 0.5831 [:, :, 4, 4] = 0.310121 0.371062 0.338717 0.358469 … 0.441499 0.432999 0.460332 0.331575 0.375166 0.337497 0.408959 0.33134 0.321467 0.480376 0.421916 0.367454 0.350857 0.302386 0.540048 0.467588 0.394749 0.41914 0.298638 0.322122 0.420562 0.567202 0.485594 0.291599 0.384639 0.426165 0.435777 0.314689 0.573065 0.297878 0.360733 0.39974 0.379442 0.374979 0.353112 … 0.415227 0.597624 0.561067 0.411828 0.324394 0.357536 0.411506 0.365848 0.503564 0.354022 0.384901 0.392045 0.387966 0.28269 0.25511 0.381689 0.28482 0.343604 0.385085 0.361621 0.343019 0.16697 0.169959 0.289525 0.324292 0.361015 0.372574 0.310331 0.0874964 0.151843 0.324038 0.374508 0.373246 0.318909 0.360588 … 0.26696 0.181298 0.340597 0.406666 0.355147 0.382493 0.301081 0.159322 0.177689 0.141649 0.293279 0.357185 0.33284 0.316193 0.16047 0.189698 0.101248 ⋮ ⋱ ⋮ 0.401868 0.414842 0.341967 0.400662 0.738772 0.547219 0.586609 0.386276 0.397058 0.348963 0.376995 0.724762 0.63977 0.560576 0.369719 0.314303 0.392605 0.46093 0.707989 0.595353 0.678479 0.415111 0.345775 0.366495 0.394611 0.702256 0.760678 0.743508 0.396661 0.420242 0.423843 0.433254 … 0.55668 0.655217 0.699603 0.515873 0.456157 0.335699 0.352568 0.602578 0.684568 0.659011 0.391863 0.366803 0.37938 0.321294 0.571596 0.526541 0.463265 0.439291 0.400952 0.38532 0.416089 0.642772 0.524163 0.464796 0.459563 0.443295 0.407809 0.353797 0.606939 0.60571 0.46617 0.404933 0.409829 0.305613 0.36485 … 0.644774 0.508329 0.494321 0.373489 0.324649 0.443315 0.386978 0.634769 0.498877 0.5831 0.366263 0.391277 0.328793 0.353269 0.64582 0.628629 0.570823 [:, :, 5, 4] = 0.371062 0.338717 0.358469 0.366528 … 0.33134 0.321467 0.480376 0.375166 0.337497 0.408959 0.307268 0.540048 0.467588 0.394749 0.367454 0.350857 0.302386 0.334106 0.567202 0.485594 0.291599 0.298638 0.322122 0.420562 0.41304 0.573065 0.297878 0.360733 0.426165 0.435777 0.314689 0.329906 0.415227 0.597624 0.561067 0.379442 0.374979 0.353112 0.381944 … 0.365848 0.503564 0.354022 0.324394 0.357536 0.411506 0.352719 0.25511 0.381689 0.28482 0.392045 0.387966 0.28269 0.377169 0.16697 0.169959 0.289525 0.385085 0.361621 0.343019 0.330815 0.0874964 0.151843 0.324038 0.361015 0.372574 0.310331 0.374705 0.26696 0.181298 0.340597 0.373246 0.318909 0.360588 0.420681 … 0.159322 0.177689 0.141649 0.355147 0.382493 0.301081 0.427255 0.16047 0.189698 0.101248 0.357185 0.33284 0.316193 0.286588 0.144812 0.163406 0.288774 ⋮ ⋱ ⋮ 0.386276 0.397058 0.348963 0.376995 0.724762 0.63977 0.560576 0.369719 0.314303 0.392605 0.46093 0.707989 0.595353 0.678479 0.415111 0.345775 0.366495 0.394611 0.702256 0.760678 0.743508 0.396661 0.420242 0.423843 0.433254 0.55668 0.655217 0.699603 0.515873 0.456157 0.335699 0.352568 … 0.602578 0.684568 0.659011 0.391863 0.366803 0.37938 0.321294 0.571596 0.526541 0.463265 0.439291 0.400952 0.38532 0.416089 0.642772 0.524163 0.464796 0.459563 0.443295 0.407809 0.353797 0.606939 0.60571 0.46617 0.404933 0.409829 0.305613 0.36485 0.644774 0.508329 0.494321 0.373489 0.324649 0.443315 0.386978 … 0.634769 0.498877 0.5831 0.366263 0.391277 0.328793 0.353269 0.64582 0.628629 0.570823 0.373489 0.324649 0.443315 0.386978 0.634769 0.498877 0.5831 [:, :, 6, 4] = 0.338717 0.358469 0.366528 0.301808 … 0.540048 0.467588 0.394749 0.337497 0.408959 0.307268 0.372549 0.567202 0.485594 0.291599 0.350857 0.302386 0.334106 0.383443 0.573065 0.297878 0.360733 0.322122 0.420562 0.41304 0.387839 0.415227 0.597624 0.561067 0.435777 0.314689 0.329906 0.379633 0.365848 0.503564 0.354022 0.374979 0.353112 0.381944 0.36836 … 0.25511 0.381689 0.28482 0.357536 0.411506 0.352719 0.337017 0.16697 0.169959 0.289525 0.387966 0.28269 0.377169 0.386111 0.0874964 0.151843 0.324038 0.361621 0.343019 0.330815 0.305207 0.26696 0.181298 0.340597 0.372574 0.310331 0.374705 0.38899 0.159322 0.177689 0.141649 0.318909 0.360588 0.420681 0.289038 … 0.16047 0.189698 0.101248 0.382493 0.301081 0.427255 0.391195 0.144812 0.163406 0.288774 0.33284 0.316193 0.286588 0.386774 0.0775752 0.274339 0.268564 ⋮ ⋱ ⋮ 0.369719 0.314303 0.392605 0.46093 0.707989 0.595353 0.678479 0.415111 0.345775 0.366495 0.394611 0.702256 0.760678 0.743508 0.396661 0.420242 0.423843 0.433254 0.55668 0.655217 0.699603 0.515873 0.456157 0.335699 0.352568 0.602578 0.684568 0.659011 0.391863 0.366803 0.37938 0.321294 … 0.571596 0.526541 0.463265 0.439291 0.400952 0.38532 0.416089 0.642772 0.524163 0.464796 0.459563 0.443295 0.407809 0.353797 0.606939 0.60571 0.46617 0.404933 0.409829 0.305613 0.36485 0.644774 0.508329 0.494321 0.373489 0.324649 0.443315 0.386978 0.634769 0.498877 0.5831 0.366263 0.391277 0.328793 0.353269 … 0.64582 0.628629 0.570823 0.373489 0.324649 0.443315 0.386978 0.634769 0.498877 0.5831 0.404933 0.409829 0.305613 0.36485 0.644774 0.508329 0.494321 [:, :, 7, 4] = 0.358469 0.366528 0.301808 0.271791 … 0.567202 0.485594 0.291599 0.408959 0.307268 0.372549 0.389746 0.573065 0.297878 0.360733 0.302386 0.334106 0.383443 0.422243 0.415227 0.597624 0.561067 0.420562 0.41304 0.387839 0.281307 0.365848 0.503564 0.354022 0.314689 0.329906 0.379633 0.375243 0.25511 0.381689 0.28482 0.353112 0.381944 0.36836 0.332942 … 0.16697 0.169959 0.289525 0.411506 0.352719 0.337017 0.356497 0.0874964 0.151843 0.324038 0.28269 0.377169 0.386111 0.328073 0.26696 0.181298 0.340597 0.343019 0.330815 0.305207 0.365998 0.159322 0.177689 0.141649 0.310331 0.374705 0.38899 0.381824 0.16047 0.189698 0.101248 0.360588 0.420681 0.289038 0.321463 … 0.144812 0.163406 0.288774 0.301081 0.427255 0.391195 0.385622 0.0775752 0.274339 0.268564 0.316193 0.286588 0.386774 0.359338 0.0790067 0.12026 0.210369 ⋮ ⋱ ⋮ 0.415111 0.345775 0.366495 0.394611 0.702256 0.760678 0.743508 0.396661 0.420242 0.423843 0.433254 0.55668 0.655217 0.699603 0.515873 0.456157 0.335699 0.352568 0.602578 0.684568 0.659011 0.391863 0.366803 0.37938 0.321294 0.571596 0.526541 0.463265 0.439291 0.400952 0.38532 0.416089 … 0.642772 0.524163 0.464796 0.459563 0.443295 0.407809 0.353797 0.606939 0.60571 0.46617 0.404933 0.409829 0.305613 0.36485 0.644774 0.508329 0.494321 0.373489 0.324649 0.443315 0.386978 0.634769 0.498877 0.5831 0.366263 0.391277 0.328793 0.353269 0.64582 0.628629 0.570823 0.373489 0.324649 0.443315 0.386978 … 0.634769 0.498877 0.5831 0.404933 0.409829 0.305613 0.36485 0.644774 0.508329 0.494321 0.459563 0.443295 0.407809 0.353797 0.606939 0.60571 0.46617 [:, :, 1, 5] = 0.408959 0.337497 0.375166 0.331575 … 0.485594 0.291599 0.485594 0.302386 0.350857 0.367454 0.421916 0.467588 0.394749 0.467588 0.420562 0.322122 0.298638 0.41914 0.321467 0.480376 0.321467 0.314689 0.435777 0.426165 0.384639 0.432999 0.460332 0.432999 0.353112 0.374979 0.379442 0.39974 0.321467 0.480376 0.321467 0.411506 0.357536 0.324394 0.411828 … 0.467588 0.394749 0.467588 0.28269 0.387966 0.392045 0.384901 0.485594 0.291599 0.485594 0.343019 0.361621 0.385085 0.343604 0.297878 0.360733 0.297878 0.310331 0.372574 0.361015 0.324292 0.597624 0.561067 0.597624 0.360588 0.318909 0.373246 0.374508 0.503564 0.354022 0.503564 0.301081 0.382493 0.355147 0.406666 … 0.381689 0.28482 0.381689 0.316193 0.33284 0.357185 0.293279 0.169959 0.289525 0.169959 0.352788 0.346671 0.335288 0.353417 0.151843 0.324038 0.151843 ⋮ ⋱ ⋮ 0.378485 0.404238 0.311386 0.364438 0.638634 0.57404 0.638634 0.348991 0.425717 0.335594 0.356753 0.698036 0.709138 0.698036 0.318672 0.34165 0.399874 0.394656 0.577087 0.592634 0.577087 0.414842 0.341967 0.400662 0.383294 0.547219 0.586609 0.547219 0.397058 0.348963 0.376995 0.321868 … 0.63977 0.560576 0.63977 0.314303 0.392605 0.46093 0.325514 0.595353 0.678479 0.595353 0.345775 0.366495 0.394611 0.335777 0.760678 0.743508 0.760678 0.420242 0.423843 0.433254 0.393593 0.655217 0.699603 0.655217 0.456157 0.335699 0.352568 0.463578 0.684568 0.659011 0.684568 0.366803 0.37938 0.321294 0.400054 … 0.526541 0.463265 0.526541 0.400952 0.38532 0.416089 0.404387 0.524163 0.464796 0.524163 0.443295 0.407809 0.353797 0.352219 0.60571 0.46617 0.60571 [:, :, 2, 5] = 0.337497 0.375166 0.331575 0.375166 … 0.467588 0.394749 0.467588 0.350857 0.367454 0.421916 0.367454 0.321467 0.480376 0.321467 0.322122 0.298638 0.41914 0.298638 0.432999 0.460332 0.432999 0.435777 0.426165 0.384639 0.426165 0.321467 0.480376 0.321467 0.374979 0.379442 0.39974 0.379442 0.467588 0.394749 0.467588 0.357536 0.324394 0.411828 0.324394 … 0.485594 0.291599 0.485594 0.387966 0.392045 0.384901 0.392045 0.297878 0.360733 0.297878 0.361621 0.385085 0.343604 0.385085 0.597624 0.561067 0.597624 0.372574 0.361015 0.324292 0.361015 0.503564 0.354022 0.503564 0.318909 0.373246 0.374508 0.373246 0.381689 0.28482 0.381689 0.382493 0.355147 0.406666 0.355147 … 0.169959 0.289525 0.169959 0.33284 0.357185 0.293279 0.357185 0.151843 0.324038 0.151843 0.346671 0.335288 0.353417 0.335288 0.181298 0.340597 0.181298 ⋮ ⋱ ⋮ 0.348991 0.425717 0.335594 0.356753 0.698036 0.709138 0.698036 0.318672 0.34165 0.399874 0.394656 0.577087 0.592634 0.577087 0.414842 0.341967 0.400662 0.383294 0.547219 0.586609 0.547219 0.397058 0.348963 0.376995 0.321868 0.63977 0.560576 0.63977 0.314303 0.392605 0.46093 0.325514 … 0.595353 0.678479 0.595353 0.345775 0.366495 0.394611 0.335777 0.760678 0.743508 0.760678 0.420242 0.423843 0.433254 0.393593 0.655217 0.699603 0.655217 0.456157 0.335699 0.352568 0.463578 0.684568 0.659011 0.684568 0.366803 0.37938 0.321294 0.400054 0.526541 0.463265 0.526541 0.400952 0.38532 0.416089 0.404387 … 0.524163 0.464796 0.524163 0.443295 0.407809 0.353797 0.352219 0.60571 0.46617 0.60571 0.409829 0.305613 0.36485 0.394557 0.508329 0.494321 0.508329 [:, :, 3, 5] = 0.375166 0.331575 0.375166 0.337497 … 0.321467 0.480376 0.321467 0.367454 0.421916 0.367454 0.350857 0.432999 0.460332 0.432999 0.298638 0.41914 0.298638 0.322122 0.321467 0.480376 0.321467 0.426165 0.384639 0.426165 0.435777 0.467588 0.394749 0.467588 0.379442 0.39974 0.379442 0.374979 0.485594 0.291599 0.485594 0.324394 0.411828 0.324394 0.357536 … 0.297878 0.360733 0.297878 0.392045 0.384901 0.392045 0.387966 0.597624 0.561067 0.597624 0.385085 0.343604 0.385085 0.361621 0.503564 0.354022 0.503564 0.361015 0.324292 0.361015 0.372574 0.381689 0.28482 0.381689 0.373246 0.374508 0.373246 0.318909 0.169959 0.289525 0.169959 0.355147 0.406666 0.355147 0.382493 … 0.151843 0.324038 0.151843 0.357185 0.293279 0.357185 0.33284 0.181298 0.340597 0.181298 0.335288 0.353417 0.335288 0.346671 0.177689 0.141649 0.177689 ⋮ ⋱ ⋮ 0.318672 0.34165 0.399874 0.394656 0.577087 0.592634 0.577087 0.414842 0.341967 0.400662 0.383294 0.547219 0.586609 0.547219 0.397058 0.348963 0.376995 0.321868 0.63977 0.560576 0.63977 0.314303 0.392605 0.46093 0.325514 0.595353 0.678479 0.595353 0.345775 0.366495 0.394611 0.335777 … 0.760678 0.743508 0.760678 0.420242 0.423843 0.433254 0.393593 0.655217 0.699603 0.655217 0.456157 0.335699 0.352568 0.463578 0.684568 0.659011 0.684568 0.366803 0.37938 0.321294 0.400054 0.526541 0.463265 0.526541 0.400952 0.38532 0.416089 0.404387 0.524163 0.464796 0.524163 0.443295 0.407809 0.353797 0.352219 … 0.60571 0.46617 0.60571 0.409829 0.305613 0.36485 0.394557 0.508329 0.494321 0.508329 0.324649 0.443315 0.386978 0.403713 0.498877 0.5831 0.498877 [:, :, 4, 5] = 0.331575 0.375166 0.337497 0.408959 … 0.432999 0.460332 0.432999 0.421916 0.367454 0.350857 0.302386 0.321467 0.480376 0.321467 0.41914 0.298638 0.322122 0.420562 0.467588 0.394749 0.467588 0.384639 0.426165 0.435777 0.314689 0.485594 0.291599 0.485594 0.39974 0.379442 0.374979 0.353112 0.297878 0.360733 0.297878 0.411828 0.324394 0.357536 0.411506 … 0.597624 0.561067 0.597624 0.384901 0.392045 0.387966 0.28269 0.503564 0.354022 0.503564 0.343604 0.385085 0.361621 0.343019 0.381689 0.28482 0.381689 0.324292 0.361015 0.372574 0.310331 0.169959 0.289525 0.169959 0.374508 0.373246 0.318909 0.360588 0.151843 0.324038 0.151843 0.406666 0.355147 0.382493 0.301081 … 0.181298 0.340597 0.181298 0.293279 0.357185 0.33284 0.316193 0.177689 0.141649 0.177689 0.353417 0.335288 0.346671 0.352788 0.189698 0.101248 0.189698 ⋮ ⋱ ⋮ 0.414842 0.341967 0.400662 0.383294 0.547219 0.586609 0.547219 0.397058 0.348963 0.376995 0.321868 0.63977 0.560576 0.63977 0.314303 0.392605 0.46093 0.325514 0.595353 0.678479 0.595353 0.345775 0.366495 0.394611 0.335777 0.760678 0.743508 0.760678 0.420242 0.423843 0.433254 0.393593 … 0.655217 0.699603 0.655217 0.456157 0.335699 0.352568 0.463578 0.684568 0.659011 0.684568 0.366803 0.37938 0.321294 0.400054 0.526541 0.463265 0.526541 0.400952 0.38532 0.416089 0.404387 0.524163 0.464796 0.524163 0.443295 0.407809 0.353797 0.352219 0.60571 0.46617 0.60571 0.409829 0.305613 0.36485 0.394557 … 0.508329 0.494321 0.508329 0.324649 0.443315 0.386978 0.403713 0.498877 0.5831 0.498877 0.391277 0.328793 0.353269 0.349689 0.628629 0.570823 0.628629 [:, :, 5, 5] = 0.375166 0.337497 0.408959 0.307268 … 0.321467 0.480376 0.321467 0.367454 0.350857 0.302386 0.334106 0.467588 0.394749 0.467588 0.298638 0.322122 0.420562 0.41304 0.485594 0.291599 0.485594 0.426165 0.435777 0.314689 0.329906 0.297878 0.360733 0.297878 0.379442 0.374979 0.353112 0.381944 0.597624 0.561067 0.597624 0.324394 0.357536 0.411506 0.352719 … 0.503564 0.354022 0.503564 0.392045 0.387966 0.28269 0.377169 0.381689 0.28482 0.381689 0.385085 0.361621 0.343019 0.330815 0.169959 0.289525 0.169959 0.361015 0.372574 0.310331 0.374705 0.151843 0.324038 0.151843 0.373246 0.318909 0.360588 0.420681 0.181298 0.340597 0.181298 0.355147 0.382493 0.301081 0.427255 … 0.177689 0.141649 0.177689 0.357185 0.33284 0.316193 0.286588 0.189698 0.101248 0.189698 0.335288 0.346671 0.352788 0.384075 0.163406 0.288774 0.163406 ⋮ ⋱ ⋮ 0.397058 0.348963 0.376995 0.321868 0.63977 0.560576 0.63977 0.314303 0.392605 0.46093 0.325514 0.595353 0.678479 0.595353 0.345775 0.366495 0.394611 0.335777 0.760678 0.743508 0.760678 0.420242 0.423843 0.433254 0.393593 0.655217 0.699603 0.655217 0.456157 0.335699 0.352568 0.463578 … 0.684568 0.659011 0.684568 0.366803 0.37938 0.321294 0.400054 0.526541 0.463265 0.526541 0.400952 0.38532 0.416089 0.404387 0.524163 0.464796 0.524163 0.443295 0.407809 0.353797 0.352219 0.60571 0.46617 0.60571 0.409829 0.305613 0.36485 0.394557 0.508329 0.494321 0.508329 0.324649 0.443315 0.386978 0.403713 … 0.498877 0.5831 0.498877 0.391277 0.328793 0.353269 0.349689 0.628629 0.570823 0.628629 0.324649 0.443315 0.386978 0.403713 0.498877 0.5831 0.498877 [:, :, 6, 5] = 0.337497 0.408959 0.307268 0.372549 … 0.467588 0.394749 0.467588 0.350857 0.302386 0.334106 0.383443 0.485594 0.291599 0.485594 0.322122 0.420562 0.41304 0.387839 0.297878 0.360733 0.297878 0.435777 0.314689 0.329906 0.379633 0.597624 0.561067 0.597624 0.374979 0.353112 0.381944 0.36836 0.503564 0.354022 0.503564 0.357536 0.411506 0.352719 0.337017 … 0.381689 0.28482 0.381689 0.387966 0.28269 0.377169 0.386111 0.169959 0.289525 0.169959 0.361621 0.343019 0.330815 0.305207 0.151843 0.324038 0.151843 0.372574 0.310331 0.374705 0.38899 0.181298 0.340597 0.181298 0.318909 0.360588 0.420681 0.289038 0.177689 0.141649 0.177689 0.382493 0.301081 0.427255 0.391195 … 0.189698 0.101248 0.189698 0.33284 0.316193 0.286588 0.386774 0.163406 0.288774 0.163406 0.346671 0.352788 0.384075 0.353846 0.274339 0.268564 0.274339 ⋮ ⋱ ⋮ 0.314303 0.392605 0.46093 0.325514 0.595353 0.678479 0.595353 0.345775 0.366495 0.394611 0.335777 0.760678 0.743508 0.760678 0.420242 0.423843 0.433254 0.393593 0.655217 0.699603 0.655217 0.456157 0.335699 0.352568 0.463578 0.684568 0.659011 0.684568 0.366803 0.37938 0.321294 0.400054 … 0.526541 0.463265 0.526541 0.400952 0.38532 0.416089 0.404387 0.524163 0.464796 0.524163 0.443295 0.407809 0.353797 0.352219 0.60571 0.46617 0.60571 0.409829 0.305613 0.36485 0.394557 0.508329 0.494321 0.508329 0.324649 0.443315 0.386978 0.403713 0.498877 0.5831 0.498877 0.391277 0.328793 0.353269 0.349689 … 0.628629 0.570823 0.628629 0.324649 0.443315 0.386978 0.403713 0.498877 0.5831 0.498877 0.409829 0.305613 0.36485 0.394557 0.508329 0.494321 0.508329 [:, :, 7, 5] = 0.408959 0.307268 0.372549 0.389746 … 0.485594 0.291599 0.485594 0.302386 0.334106 0.383443 0.422243 0.297878 0.360733 0.297878 0.420562 0.41304 0.387839 0.281307 0.597624 0.561067 0.597624 0.314689 0.329906 0.379633 0.375243 0.503564 0.354022 0.503564 0.353112 0.381944 0.36836 0.332942 0.381689 0.28482 0.381689 0.411506 0.352719 0.337017 0.356497 … 0.169959 0.289525 0.169959 0.28269 0.377169 0.386111 0.328073 0.151843 0.324038 0.151843 0.343019 0.330815 0.305207 0.365998 0.181298 0.340597 0.181298 0.310331 0.374705 0.38899 0.381824 0.177689 0.141649 0.177689 0.360588 0.420681 0.289038 0.321463 0.189698 0.101248 0.189698 0.301081 0.427255 0.391195 0.385622 … 0.163406 0.288774 0.163406 0.316193 0.286588 0.386774 0.359338 0.274339 0.268564 0.274339 0.352788 0.384075 0.353846 0.369752 0.12026 0.210369 0.12026 ⋮ ⋱ ⋮ 0.345775 0.366495 0.394611 0.335777 0.760678 0.743508 0.760678 0.420242 0.423843 0.433254 0.393593 0.655217 0.699603 0.655217 0.456157 0.335699 0.352568 0.463578 0.684568 0.659011 0.684568 0.366803 0.37938 0.321294 0.400054 0.526541 0.463265 0.526541 0.400952 0.38532 0.416089 0.404387 … 0.524163 0.464796 0.524163 0.443295 0.407809 0.353797 0.352219 0.60571 0.46617 0.60571 0.409829 0.305613 0.36485 0.394557 0.508329 0.494321 0.508329 0.324649 0.443315 0.386978 0.403713 0.498877 0.5831 0.498877 0.391277 0.328793 0.353269 0.349689 0.628629 0.570823 0.628629 0.324649 0.443315 0.386978 0.403713 … 0.498877 0.5831 0.498877 0.409829 0.305613 0.36485 0.394557 0.508329 0.494321 0.508329 0.443295 0.407809 0.353797 0.352219 0.60571 0.46617 0.60571 [:, :, 1, 6] = 0.302386 0.350857 0.367454 0.421916 … 0.291599 0.485594 0.567202 0.420562 0.322122 0.298638 0.41914 0.394749 0.467588 0.540048 0.314689 0.435777 0.426165 0.384639 0.480376 0.321467 0.33134 0.353112 0.374979 0.379442 0.39974 0.460332 0.432999 0.441499 0.411506 0.357536 0.324394 0.411828 0.480376 0.321467 0.33134 0.28269 0.387966 0.392045 0.384901 … 0.394749 0.467588 0.540048 0.343019 0.361621 0.385085 0.343604 0.291599 0.485594 0.567202 0.310331 0.372574 0.361015 0.324292 0.360733 0.297878 0.573065 0.360588 0.318909 0.373246 0.374508 0.561067 0.597624 0.415227 0.301081 0.382493 0.355147 0.406666 0.354022 0.503564 0.365848 0.316193 0.33284 0.357185 0.293279 … 0.28482 0.381689 0.25511 0.352788 0.346671 0.335288 0.353417 0.289525 0.169959 0.16697 0.258723 0.332644 0.354601 0.432126 0.324038 0.151843 0.0874964 ⋮ ⋱ ⋮ 0.404238 0.311386 0.364438 0.41035 0.57404 0.638634 0.607852 0.425717 0.335594 0.356753 0.293823 0.709138 0.698036 0.520682 0.34165 0.399874 0.394656 0.39226 0.592634 0.577087 0.557041 0.341967 0.400662 0.383294 0.453116 0.586609 0.547219 0.738772 0.348963 0.376995 0.321868 0.369058 … 0.560576 0.63977 0.724762 0.392605 0.46093 0.325514 0.415748 0.678479 0.595353 0.707989 0.366495 0.394611 0.335777 0.346071 0.743508 0.760678 0.702256 0.423843 0.433254 0.393593 0.383522 0.699603 0.655217 0.55668 0.335699 0.352568 0.463578 0.350728 0.659011 0.684568 0.602578 0.37938 0.321294 0.400054 0.367017 … 0.463265 0.526541 0.571596 0.38532 0.416089 0.404387 0.391201 0.464796 0.524163 0.642772 0.407809 0.353797 0.352219 0.388549 0.46617 0.60571 0.606939 [:, :, 2, 6] = 0.350857 0.367454 0.421916 0.367454 … 0.394749 0.467588 0.540048 0.322122 0.298638 0.41914 0.298638 0.480376 0.321467 0.33134 0.435777 0.426165 0.384639 0.426165 0.460332 0.432999 0.441499 0.374979 0.379442 0.39974 0.379442 0.480376 0.321467 0.33134 0.357536 0.324394 0.411828 0.324394 0.394749 0.467588 0.540048 0.387966 0.392045 0.384901 0.392045 … 0.291599 0.485594 0.567202 0.361621 0.385085 0.343604 0.385085 0.360733 0.297878 0.573065 0.372574 0.361015 0.324292 0.361015 0.561067 0.597624 0.415227 0.318909 0.373246 0.374508 0.373246 0.354022 0.503564 0.365848 0.382493 0.355147 0.406666 0.355147 0.28482 0.381689 0.25511 0.33284 0.357185 0.293279 0.357185 … 0.289525 0.169959 0.16697 0.346671 0.335288 0.353417 0.335288 0.324038 0.151843 0.0874964 0.332644 0.354601 0.432126 0.354601 0.340597 0.181298 0.26696 ⋮ ⋱ ⋮ 0.425717 0.335594 0.356753 0.293823 0.709138 0.698036 0.520682 0.34165 0.399874 0.394656 0.39226 0.592634 0.577087 0.557041 0.341967 0.400662 0.383294 0.453116 0.586609 0.547219 0.738772 0.348963 0.376995 0.321868 0.369058 0.560576 0.63977 0.724762 0.392605 0.46093 0.325514 0.415748 … 0.678479 0.595353 0.707989 0.366495 0.394611 0.335777 0.346071 0.743508 0.760678 0.702256 0.423843 0.433254 0.393593 0.383522 0.699603 0.655217 0.55668 0.335699 0.352568 0.463578 0.350728 0.659011 0.684568 0.602578 0.37938 0.321294 0.400054 0.367017 0.463265 0.526541 0.571596 0.38532 0.416089 0.404387 0.391201 … 0.464796 0.524163 0.642772 0.407809 0.353797 0.352219 0.388549 0.46617 0.60571 0.606939 0.305613 0.36485 0.394557 0.337633 0.494321 0.508329 0.644774 [:, :, 3, 6] = 0.367454 0.421916 0.367454 0.350857 … 0.480376 0.321467 0.33134 0.298638 0.41914 0.298638 0.322122 0.460332 0.432999 0.441499 0.426165 0.384639 0.426165 0.435777 0.480376 0.321467 0.33134 0.379442 0.39974 0.379442 0.374979 0.394749 0.467588 0.540048 0.324394 0.411828 0.324394 0.357536 0.291599 0.485594 0.567202 0.392045 0.384901 0.392045 0.387966 … 0.360733 0.297878 0.573065 0.385085 0.343604 0.385085 0.361621 0.561067 0.597624 0.415227 0.361015 0.324292 0.361015 0.372574 0.354022 0.503564 0.365848 0.373246 0.374508 0.373246 0.318909 0.28482 0.381689 0.25511 0.355147 0.406666 0.355147 0.382493 0.289525 0.169959 0.16697 0.357185 0.293279 0.357185 0.33284 … 0.324038 0.151843 0.0874964 0.335288 0.353417 0.335288 0.346671 0.340597 0.181298 0.26696 0.354601 0.432126 0.354601 0.332644 0.141649 0.177689 0.159322 ⋮ ⋱ ⋮ 0.34165 0.399874 0.394656 0.39226 0.592634 0.577087 0.557041 0.341967 0.400662 0.383294 0.453116 0.586609 0.547219 0.738772 0.348963 0.376995 0.321868 0.369058 0.560576 0.63977 0.724762 0.392605 0.46093 0.325514 0.415748 0.678479 0.595353 0.707989 0.366495 0.394611 0.335777 0.346071 … 0.743508 0.760678 0.702256 0.423843 0.433254 0.393593 0.383522 0.699603 0.655217 0.55668 0.335699 0.352568 0.463578 0.350728 0.659011 0.684568 0.602578 0.37938 0.321294 0.400054 0.367017 0.463265 0.526541 0.571596 0.38532 0.416089 0.404387 0.391201 0.464796 0.524163 0.642772 0.407809 0.353797 0.352219 0.388549 … 0.46617 0.60571 0.606939 0.305613 0.36485 0.394557 0.337633 0.494321 0.508329 0.644774 0.443315 0.386978 0.403713 0.398922 0.5831 0.498877 0.634769 [:, :, 4, 6] = 0.421916 0.367454 0.350857 0.302386 … 0.460332 0.432999 0.441499 0.41914 0.298638 0.322122 0.420562 0.480376 0.321467 0.33134 0.384639 0.426165 0.435777 0.314689 0.394749 0.467588 0.540048 0.39974 0.379442 0.374979 0.353112 0.291599 0.485594 0.567202 0.411828 0.324394 0.357536 0.411506 0.360733 0.297878 0.573065 0.384901 0.392045 0.387966 0.28269 … 0.561067 0.597624 0.415227 0.343604 0.385085 0.361621 0.343019 0.354022 0.503564 0.365848 0.324292 0.361015 0.372574 0.310331 0.28482 0.381689 0.25511 0.374508 0.373246 0.318909 0.360588 0.289525 0.169959 0.16697 0.406666 0.355147 0.382493 0.301081 0.324038 0.151843 0.0874964 0.293279 0.357185 0.33284 0.316193 … 0.340597 0.181298 0.26696 0.353417 0.335288 0.346671 0.352788 0.141649 0.177689 0.159322 0.432126 0.354601 0.332644 0.258723 0.101248 0.189698 0.16047 ⋮ ⋱ ⋮ 0.341967 0.400662 0.383294 0.453116 0.586609 0.547219 0.738772 0.348963 0.376995 0.321868 0.369058 0.560576 0.63977 0.724762 0.392605 0.46093 0.325514 0.415748 0.678479 0.595353 0.707989 0.366495 0.394611 0.335777 0.346071 0.743508 0.760678 0.702256 0.423843 0.433254 0.393593 0.383522 … 0.699603 0.655217 0.55668 0.335699 0.352568 0.463578 0.350728 0.659011 0.684568 0.602578 0.37938 0.321294 0.400054 0.367017 0.463265 0.526541 0.571596 0.38532 0.416089 0.404387 0.391201 0.464796 0.524163 0.642772 0.407809 0.353797 0.352219 0.388549 0.46617 0.60571 0.606939 0.305613 0.36485 0.394557 0.337633 … 0.494321 0.508329 0.644774 0.443315 0.386978 0.403713 0.398922 0.5831 0.498877 0.634769 0.328793 0.353269 0.349689 0.343062 0.570823 0.628629 0.64582 [:, :, 5, 6] = 0.367454 0.350857 0.302386 0.334106 … 0.480376 0.321467 0.33134 0.298638 0.322122 0.420562 0.41304 0.394749 0.467588 0.540048 0.426165 0.435777 0.314689 0.329906 0.291599 0.485594 0.567202 0.379442 0.374979 0.353112 0.381944 0.360733 0.297878 0.573065 0.324394 0.357536 0.411506 0.352719 0.561067 0.597624 0.415227 0.392045 0.387966 0.28269 0.377169 … 0.354022 0.503564 0.365848 0.385085 0.361621 0.343019 0.330815 0.28482 0.381689 0.25511 0.361015 0.372574 0.310331 0.374705 0.289525 0.169959 0.16697 0.373246 0.318909 0.360588 0.420681 0.324038 0.151843 0.0874964 0.355147 0.382493 0.301081 0.427255 0.340597 0.181298 0.26696 0.357185 0.33284 0.316193 0.286588 … 0.141649 0.177689 0.159322 0.335288 0.346671 0.352788 0.384075 0.101248 0.189698 0.16047 0.354601 0.332644 0.258723 0.305229 0.288774 0.163406 0.144812 ⋮ ⋱ ⋮ 0.348963 0.376995 0.321868 0.369058 0.560576 0.63977 0.724762 0.392605 0.46093 0.325514 0.415748 0.678479 0.595353 0.707989 0.366495 0.394611 0.335777 0.346071 0.743508 0.760678 0.702256 0.423843 0.433254 0.393593 0.383522 0.699603 0.655217 0.55668 0.335699 0.352568 0.463578 0.350728 … 0.659011 0.684568 0.602578 0.37938 0.321294 0.400054 0.367017 0.463265 0.526541 0.571596 0.38532 0.416089 0.404387 0.391201 0.464796 0.524163 0.642772 0.407809 0.353797 0.352219 0.388549 0.46617 0.60571 0.606939 0.305613 0.36485 0.394557 0.337633 0.494321 0.508329 0.644774 0.443315 0.386978 0.403713 0.398922 … 0.5831 0.498877 0.634769 0.328793 0.353269 0.349689 0.343062 0.570823 0.628629 0.64582 0.443315 0.386978 0.403713 0.398922 0.5831 0.498877 0.634769 [:, :, 6, 6] = 0.350857 0.302386 0.334106 0.383443 … 0.394749 0.467588 0.540048 0.322122 0.420562 0.41304 0.387839 0.291599 0.485594 0.567202 0.435777 0.314689 0.329906 0.379633 0.360733 0.297878 0.573065 0.374979 0.353112 0.381944 0.36836 0.561067 0.597624 0.415227 0.357536 0.411506 0.352719 0.337017 0.354022 0.503564 0.365848 0.387966 0.28269 0.377169 0.386111 … 0.28482 0.381689 0.25511 0.361621 0.343019 0.330815 0.305207 0.289525 0.169959 0.16697 0.372574 0.310331 0.374705 0.38899 0.324038 0.151843 0.0874964 0.318909 0.360588 0.420681 0.289038 0.340597 0.181298 0.26696 0.382493 0.301081 0.427255 0.391195 0.141649 0.177689 0.159322 0.33284 0.316193 0.286588 0.386774 … 0.101248 0.189698 0.16047 0.346671 0.352788 0.384075 0.353846 0.288774 0.163406 0.144812 0.332644 0.258723 0.305229 0.397625 0.268564 0.274339 0.0775752 ⋮ ⋱ ⋮ 0.392605 0.46093 0.325514 0.415748 0.678479 0.595353 0.707989 0.366495 0.394611 0.335777 0.346071 0.743508 0.760678 0.702256 0.423843 0.433254 0.393593 0.383522 0.699603 0.655217 0.55668 0.335699 0.352568 0.463578 0.350728 0.659011 0.684568 0.602578 0.37938 0.321294 0.400054 0.367017 … 0.463265 0.526541 0.571596 0.38532 0.416089 0.404387 0.391201 0.464796 0.524163 0.642772 0.407809 0.353797 0.352219 0.388549 0.46617 0.60571 0.606939 0.305613 0.36485 0.394557 0.337633 0.494321 0.508329 0.644774 0.443315 0.386978 0.403713 0.398922 0.5831 0.498877 0.634769 0.328793 0.353269 0.349689 0.343062 … 0.570823 0.628629 0.64582 0.443315 0.386978 0.403713 0.398922 0.5831 0.498877 0.634769 0.305613 0.36485 0.394557 0.337633 0.494321 0.508329 0.644774 [:, :, 7, 6] = 0.302386 0.334106 0.383443 0.422243 … 0.291599 0.485594 0.567202 0.420562 0.41304 0.387839 0.281307 0.360733 0.297878 0.573065 0.314689 0.329906 0.379633 0.375243 0.561067 0.597624 0.415227 0.353112 0.381944 0.36836 0.332942 0.354022 0.503564 0.365848 0.411506 0.352719 0.337017 0.356497 0.28482 0.381689 0.25511 0.28269 0.377169 0.386111 0.328073 … 0.289525 0.169959 0.16697 0.343019 0.330815 0.305207 0.365998 0.324038 0.151843 0.0874964 0.310331 0.374705 0.38899 0.381824 0.340597 0.181298 0.26696 0.360588 0.420681 0.289038 0.321463 0.141649 0.177689 0.159322 0.301081 0.427255 0.391195 0.385622 0.101248 0.189698 0.16047 0.316193 0.286588 0.386774 0.359338 … 0.288774 0.163406 0.144812 0.352788 0.384075 0.353846 0.369752 0.268564 0.274339 0.0775752 0.258723 0.305229 0.397625 0.349684 0.210369 0.12026 0.0790067 ⋮ ⋱ ⋮ 0.366495 0.394611 0.335777 0.346071 0.743508 0.760678 0.702256 0.423843 0.433254 0.393593 0.383522 0.699603 0.655217 0.55668 0.335699 0.352568 0.463578 0.350728 0.659011 0.684568 0.602578 0.37938 0.321294 0.400054 0.367017 0.463265 0.526541 0.571596 0.38532 0.416089 0.404387 0.391201 … 0.464796 0.524163 0.642772 0.407809 0.353797 0.352219 0.388549 0.46617 0.60571 0.606939 0.305613 0.36485 0.394557 0.337633 0.494321 0.508329 0.644774 0.443315 0.386978 0.403713 0.398922 0.5831 0.498877 0.634769 0.328793 0.353269 0.349689 0.343062 0.570823 0.628629 0.64582 0.443315 0.386978 0.403713 0.398922 … 0.5831 0.498877 0.634769 0.305613 0.36485 0.394557 0.337633 0.494321 0.508329 0.644774 0.407809 0.353797 0.352219 0.388549 0.46617 0.60571 0.606939 [:, :, 1, 7] = 0.420562 0.322122 0.298638 0.41914 … 0.485594 0.567202 0.496517 0.314689 0.435777 0.426165 0.384639 0.467588 0.540048 0.463395 0.353112 0.374979 0.379442 0.39974 0.321467 0.33134 0.433398 0.411506 0.357536 0.324394 0.411828 0.432999 0.441499 0.5479 0.28269 0.387966 0.392045 0.384901 0.321467 0.33134 0.433398 0.343019 0.361621 0.385085 0.343604 … 0.467588 0.540048 0.463395 0.310331 0.372574 0.361015 0.324292 0.485594 0.567202 0.496517 0.360588 0.318909 0.373246 0.374508 0.297878 0.573065 0.462501 0.301081 0.382493 0.355147 0.406666 0.597624 0.415227 0.440267 0.316193 0.33284 0.357185 0.293279 0.503564 0.365848 0.35104 0.352788 0.346671 0.335288 0.353417 … 0.381689 0.25511 0.319882 0.258723 0.332644 0.354601 0.432126 0.169959 0.16697 0.280956 0.38013 0.356753 0.306655 0.410987 0.151843 0.0874964 0.167252 ⋮ ⋱ ⋮ 0.311386 0.364438 0.41035 0.338129 0.638634 0.607852 0.558204 0.335594 0.356753 0.293823 0.385394 0.698036 0.520682 0.535028 0.399874 0.394656 0.39226 0.385214 0.577087 0.557041 0.607727 0.400662 0.383294 0.453116 0.357385 0.547219 0.738772 0.758275 0.376995 0.321868 0.369058 0.421469 … 0.63977 0.724762 0.658808 0.46093 0.325514 0.415748 0.380033 0.595353 0.707989 0.66532 0.394611 0.335777 0.346071 0.342621 0.760678 0.702256 0.638867 0.433254 0.393593 0.383522 0.340241 0.655217 0.55668 0.598602 0.352568 0.463578 0.350728 0.371003 0.684568 0.602578 0.633151 0.321294 0.400054 0.367017 0.435339 … 0.526541 0.571596 0.750186 0.416089 0.404387 0.391201 0.376272 0.524163 0.642772 0.70249 0.353797 0.352219 0.388549 0.359756 0.60571 0.606939 0.629921 [:, :, 2, 7] = 0.322122 0.298638 0.41914 0.298638 … 0.467588 0.540048 0.463395 0.435777 0.426165 0.384639 0.426165 0.321467 0.33134 0.433398 0.374979 0.379442 0.39974 0.379442 0.432999 0.441499 0.5479 0.357536 0.324394 0.411828 0.324394 0.321467 0.33134 0.433398 0.387966 0.392045 0.384901 0.392045 0.467588 0.540048 0.463395 0.361621 0.385085 0.343604 0.385085 … 0.485594 0.567202 0.496517 0.372574 0.361015 0.324292 0.361015 0.297878 0.573065 0.462501 0.318909 0.373246 0.374508 0.373246 0.597624 0.415227 0.440267 0.382493 0.355147 0.406666 0.355147 0.503564 0.365848 0.35104 0.33284 0.357185 0.293279 0.357185 0.381689 0.25511 0.319882 0.346671 0.335288 0.353417 0.335288 … 0.169959 0.16697 0.280956 0.332644 0.354601 0.432126 0.354601 0.151843 0.0874964 0.167252 0.356753 0.306655 0.410987 0.306655 0.181298 0.26696 0.217961 ⋮ ⋱ ⋮ 0.335594 0.356753 0.293823 0.385394 0.698036 0.520682 0.535028 0.399874 0.394656 0.39226 0.385214 0.577087 0.557041 0.607727 0.400662 0.383294 0.453116 0.357385 0.547219 0.738772 0.758275 0.376995 0.321868 0.369058 0.421469 0.63977 0.724762 0.658808 0.46093 0.325514 0.415748 0.380033 … 0.595353 0.707989 0.66532 0.394611 0.335777 0.346071 0.342621 0.760678 0.702256 0.638867 0.433254 0.393593 0.383522 0.340241 0.655217 0.55668 0.598602 0.352568 0.463578 0.350728 0.371003 0.684568 0.602578 0.633151 0.321294 0.400054 0.367017 0.435339 0.526541 0.571596 0.750186 0.416089 0.404387 0.391201 0.376272 … 0.524163 0.642772 0.70249 0.353797 0.352219 0.388549 0.359756 0.60571 0.606939 0.629921 0.36485 0.394557 0.337633 0.326126 0.508329 0.644774 0.657626 [:, :, 3, 7] = 0.298638 0.41914 0.298638 0.322122 … 0.321467 0.33134 0.433398 0.426165 0.384639 0.426165 0.435777 0.432999 0.441499 0.5479 0.379442 0.39974 0.379442 0.374979 0.321467 0.33134 0.433398 0.324394 0.411828 0.324394 0.357536 0.467588 0.540048 0.463395 0.392045 0.384901 0.392045 0.387966 0.485594 0.567202 0.496517 0.385085 0.343604 0.385085 0.361621 … 0.297878 0.573065 0.462501 0.361015 0.324292 0.361015 0.372574 0.597624 0.415227 0.440267 0.373246 0.374508 0.373246 0.318909 0.503564 0.365848 0.35104 0.355147 0.406666 0.355147 0.382493 0.381689 0.25511 0.319882 0.357185 0.293279 0.357185 0.33284 0.169959 0.16697 0.280956 0.335288 0.353417 0.335288 0.346671 … 0.151843 0.0874964 0.167252 0.354601 0.432126 0.354601 0.332644 0.181298 0.26696 0.217961 0.306655 0.410987 0.306655 0.356753 0.177689 0.159322 0.150437 ⋮ ⋱ ⋮ 0.399874 0.394656 0.39226 0.385214 0.577087 0.557041 0.607727 0.400662 0.383294 0.453116 0.357385 0.547219 0.738772 0.758275 0.376995 0.321868 0.369058 0.421469 0.63977 0.724762 0.658808 0.46093 0.325514 0.415748 0.380033 0.595353 0.707989 0.66532 0.394611 0.335777 0.346071 0.342621 … 0.760678 0.702256 0.638867 0.433254 0.393593 0.383522 0.340241 0.655217 0.55668 0.598602 0.352568 0.463578 0.350728 0.371003 0.684568 0.602578 0.633151 0.321294 0.400054 0.367017 0.435339 0.526541 0.571596 0.750186 0.416089 0.404387 0.391201 0.376272 0.524163 0.642772 0.70249 0.353797 0.352219 0.388549 0.359756 … 0.60571 0.606939 0.629921 0.36485 0.394557 0.337633 0.326126 0.508329 0.644774 0.657626 0.386978 0.403713 0.398922 0.359733 0.498877 0.634769 0.757109 [:, :, 4, 7] = 0.41914 0.298638 0.322122 0.420562 … 0.432999 0.441499 0.5479 0.384639 0.426165 0.435777 0.314689 0.321467 0.33134 0.433398 0.39974 0.379442 0.374979 0.353112 0.467588 0.540048 0.463395 0.411828 0.324394 0.357536 0.411506 0.485594 0.567202 0.496517 0.384901 0.392045 0.387966 0.28269 0.297878 0.573065 0.462501 0.343604 0.385085 0.361621 0.343019 … 0.597624 0.415227 0.440267 0.324292 0.361015 0.372574 0.310331 0.503564 0.365848 0.35104 0.374508 0.373246 0.318909 0.360588 0.381689 0.25511 0.319882 0.406666 0.355147 0.382493 0.301081 0.169959 0.16697 0.280956 0.293279 0.357185 0.33284 0.316193 0.151843 0.0874964 0.167252 0.353417 0.335288 0.346671 0.352788 … 0.181298 0.26696 0.217961 0.432126 0.354601 0.332644 0.258723 0.177689 0.159322 0.150437 0.410987 0.306655 0.356753 0.38013 0.189698 0.16047 0.272203 ⋮ ⋱ ⋮ 0.400662 0.383294 0.453116 0.357385 0.547219 0.738772 0.758275 0.376995 0.321868 0.369058 0.421469 0.63977 0.724762 0.658808 0.46093 0.325514 0.415748 0.380033 0.595353 0.707989 0.66532 0.394611 0.335777 0.346071 0.342621 0.760678 0.702256 0.638867 0.433254 0.393593 0.383522 0.340241 … 0.655217 0.55668 0.598602 0.352568 0.463578 0.350728 0.371003 0.684568 0.602578 0.633151 0.321294 0.400054 0.367017 0.435339 0.526541 0.571596 0.750186 0.416089 0.404387 0.391201 0.376272 0.524163 0.642772 0.70249 0.353797 0.352219 0.388549 0.359756 0.60571 0.606939 0.629921 0.36485 0.394557 0.337633 0.326126 … 0.508329 0.644774 0.657626 0.386978 0.403713 0.398922 0.359733 0.498877 0.634769 0.757109 0.353269 0.349689 0.343062 0.318974 0.628629 0.64582 0.694726 [:, :, 5, 7] = 0.298638 0.322122 0.420562 0.41304 … 0.321467 0.33134 0.433398 0.426165 0.435777 0.314689 0.329906 0.467588 0.540048 0.463395 0.379442 0.374979 0.353112 0.381944 0.485594 0.567202 0.496517 0.324394 0.357536 0.411506 0.352719 0.297878 0.573065 0.462501 0.392045 0.387966 0.28269 0.377169 0.597624 0.415227 0.440267 0.385085 0.361621 0.343019 0.330815 … 0.503564 0.365848 0.35104 0.361015 0.372574 0.310331 0.374705 0.381689 0.25511 0.319882 0.373246 0.318909 0.360588 0.420681 0.169959 0.16697 0.280956 0.355147 0.382493 0.301081 0.427255 0.151843 0.0874964 0.167252 0.357185 0.33284 0.316193 0.286588 0.181298 0.26696 0.217961 0.335288 0.346671 0.352788 0.384075 … 0.177689 0.159322 0.150437 0.354601 0.332644 0.258723 0.305229 0.189698 0.16047 0.272203 0.306655 0.356753 0.38013 0.386695 0.163406 0.144812 0.163869 ⋮ ⋱ ⋮ 0.376995 0.321868 0.369058 0.421469 0.63977 0.724762 0.658808 0.46093 0.325514 0.415748 0.380033 0.595353 0.707989 0.66532 0.394611 0.335777 0.346071 0.342621 0.760678 0.702256 0.638867 0.433254 0.393593 0.383522 0.340241 0.655217 0.55668 0.598602 0.352568 0.463578 0.350728 0.371003 … 0.684568 0.602578 0.633151 0.321294 0.400054 0.367017 0.435339 0.526541 0.571596 0.750186 0.416089 0.404387 0.391201 0.376272 0.524163 0.642772 0.70249 0.353797 0.352219 0.388549 0.359756 0.60571 0.606939 0.629921 0.36485 0.394557 0.337633 0.326126 0.508329 0.644774 0.657626 0.386978 0.403713 0.398922 0.359733 … 0.498877 0.634769 0.757109 0.353269 0.349689 0.343062 0.318974 0.628629 0.64582 0.694726 0.386978 0.403713 0.398922 0.359733 0.498877 0.634769 0.757109 [:, :, 6, 7] = 0.322122 0.420562 0.41304 0.387839 … 0.467588 0.540048 0.463395 0.435777 0.314689 0.329906 0.379633 0.485594 0.567202 0.496517 0.374979 0.353112 0.381944 0.36836 0.297878 0.573065 0.462501 0.357536 0.411506 0.352719 0.337017 0.597624 0.415227 0.440267 0.387966 0.28269 0.377169 0.386111 0.503564 0.365848 0.35104 0.361621 0.343019 0.330815 0.305207 … 0.381689 0.25511 0.319882 0.372574 0.310331 0.374705 0.38899 0.169959 0.16697 0.280956 0.318909 0.360588 0.420681 0.289038 0.151843 0.0874964 0.167252 0.382493 0.301081 0.427255 0.391195 0.181298 0.26696 0.217961 0.33284 0.316193 0.286588 0.386774 0.177689 0.159322 0.150437 0.346671 0.352788 0.384075 0.353846 … 0.189698 0.16047 0.272203 0.332644 0.258723 0.305229 0.397625 0.163406 0.144812 0.163869 0.356753 0.38013 0.386695 0.312281 0.274339 0.0775752 0.147525 ⋮ ⋱ ⋮ 0.46093 0.325514 0.415748 0.380033 0.595353 0.707989 0.66532 0.394611 0.335777 0.346071 0.342621 0.760678 0.702256 0.638867 0.433254 0.393593 0.383522 0.340241 0.655217 0.55668 0.598602 0.352568 0.463578 0.350728 0.371003 0.684568 0.602578 0.633151 0.321294 0.400054 0.367017 0.435339 … 0.526541 0.571596 0.750186 0.416089 0.404387 0.391201 0.376272 0.524163 0.642772 0.70249 0.353797 0.352219 0.388549 0.359756 0.60571 0.606939 0.629921 0.36485 0.394557 0.337633 0.326126 0.508329 0.644774 0.657626 0.386978 0.403713 0.398922 0.359733 0.498877 0.634769 0.757109 0.353269 0.349689 0.343062 0.318974 … 0.628629 0.64582 0.694726 0.386978 0.403713 0.398922 0.359733 0.498877 0.634769 0.757109 0.36485 0.394557 0.337633 0.326126 0.508329 0.644774 0.657626 [:, :, 7, 7] = 0.420562 0.41304 0.387839 0.281307 … 0.485594 0.567202 0.496517 0.314689 0.329906 0.379633 0.375243 0.297878 0.573065 0.462501 0.353112 0.381944 0.36836 0.332942 0.597624 0.415227 0.440267 0.411506 0.352719 0.337017 0.356497 0.503564 0.365848 0.35104 0.28269 0.377169 0.386111 0.328073 0.381689 0.25511 0.319882 0.343019 0.330815 0.305207 0.365998 … 0.169959 0.16697 0.280956 0.310331 0.374705 0.38899 0.381824 0.151843 0.0874964 0.167252 0.360588 0.420681 0.289038 0.321463 0.181298 0.26696 0.217961 0.301081 0.427255 0.391195 0.385622 0.177689 0.159322 0.150437 0.316193 0.286588 0.386774 0.359338 0.189698 0.16047 0.272203 0.352788 0.384075 0.353846 0.369752 … 0.163406 0.144812 0.163869 0.258723 0.305229 0.397625 0.349684 0.274339 0.0775752 0.147525 0.38013 0.386695 0.312281 0.454245 0.12026 0.0790067 0.076828 ⋮ ⋱ ⋮ 0.394611 0.335777 0.346071 0.342621 0.760678 0.702256 0.638867 0.433254 0.393593 0.383522 0.340241 0.655217 0.55668 0.598602 0.352568 0.463578 0.350728 0.371003 0.684568 0.602578 0.633151 0.321294 0.400054 0.367017 0.435339 0.526541 0.571596 0.750186 0.416089 0.404387 0.391201 0.376272 … 0.524163 0.642772 0.70249 0.353797 0.352219 0.388549 0.359756 0.60571 0.606939 0.629921 0.36485 0.394557 0.337633 0.326126 0.508329 0.644774 0.657626 0.386978 0.403713 0.398922 0.359733 0.498877 0.634769 0.757109 0.353269 0.349689 0.343062 0.318974 0.628629 0.64582 0.694726 0.386978 0.403713 0.398922 0.359733 … 0.498877 0.634769 0.757109 0.36485 0.394557 0.337633 0.326126 0.508329 0.644774 0.657626 0.353797 0.352219 0.388549 0.359756 0.60571 0.606939 0.629921
Display some example of patches.
figure(figsize = (5,5))
for i in 1:16
x = rand(1 : n)
y = rand(1 : n)
imageplot(P[x, y, :, :], "", [4, 4, i])
end
Since NL-means type algorithms require the computation of many distances between patches, it is advantagous to reduce the dimensionality of the patch while keeping as much as possible of information.
Target dimensionality $d$.
d = 25
25
A linear dimensionality reduction is obtained by Principal Component Analysis (PCA) that projects the data on a small number of leading direction of the covariance matrix of the patches.
Turn the patch matrix into an $(w_1*w_1,n*n)$ array, so that each $P(:,i)$ is a $w_1*w_1$ vector representing a patch.
resh = P -> transpose((reshape(P, (n*n,w1*w1))))
(::#3) (generic function with 1 method)
Operator to remove the mean of the patches to each patch.
remove_mean = Q -> Q - repeat(mean(Q, 1), inner = (w1*w1, 1))
(::#5) (generic function with 1 method)
Compute the mean and the covariance of the points cloud representing the patches.
P1 = remove_mean(resh(P))
C = P1*transpose(P1)
49×49 Array{Float64,2}: 131.936 77.2095 46.5651 … -25.4735 -23.785 -17.5533 77.2095 121.381 67.3999 -25.9776 -26.7635 -24.1005 46.5651 67.3999 112.653 -25.7255 -26.301 -26.0259 27.8702 37.7467 59.4592 -28.8331 -25.0024 -24.7251 18.1669 20.245 31.3374 -29.9974 -26.6962 -21.9355 10.1857 12.4336 14.8341 … -30.2334 -26.4507 -22.151 2.25873 6.15092 8.88626 -25.7245 -24.7144 -19.9362 67.2198 68.495 54.8283 -21.4129 -22.696 -22.7255 44.0538 55.9557 57.9443 -25.0261 -23.1991 -23.5449 25.3588 34.2606 46.9429 -29.7959 -25.3353 -22.4983 13.7735 16.8541 26.6187 … -32.7065 -28.6216 -23.1829 4.45361 7.02014 10.8829 -30.2134 -29.5932 -24.6672 -3.04818 -0.227483 2.91176 -25.7234 -25.0746 -23.5566 ⋮ ⋱ -23.8409 -29.1243 -30.1578 11.0099 6.84582 4.26891 -22.5349 -28.259 -32.66 27.1568 17.4338 14.2956 -22.1599 -25.2158 -30.0699 48.5088 35.6748 26.8608 -23.2678 -23.3726 -25.5313 … 59.2582 58.6027 46.8494 -22.7891 -22.9862 -22.1232 56.2704 71.0329 71.3181 -17.5671 -22.3694 -23.8187 6.58808 4.35664 0.887412 -20.2215 -25.1622 -28.9253 13.7246 11.0812 9.33479 -20.6776 -25.6028 -29.4684 30.9147 19.5402 17.544 -23.7535 -24.355 -28.3453 … 60.3797 38.0947 27.9536 -25.4735 -25.9776 -25.7255 115.687 69.4826 48.1777 -23.785 -26.7635 -26.301 69.4826 125.946 80.862 -17.5533 -24.1005 -26.0259 48.1777 80.862 138.289
Extract the eigenvectors, sorted by decreasing amplitude.
(D, V) = eig(C)
D = sort(D, rev = true)
I = sortperm(D)[end : -1 : 1]
V = V[I, :]
49×49 Array{Float64,2}: -0.142857 0.00288788 0.022342 0.115746 … -0.201372 0.166028 -0.142857 -0.0775719 -0.039154 -0.237704 -0.215737 0.188468 -0.142857 -0.0466216 0.0304623 0.259052 -0.193864 0.201698 -0.142857 -0.00291281 0.0788866 -0.167343 -0.129294 0.203078 -0.142857 0.0375051 0.0861557 0.0362725 -0.0335826 0.188389 -0.142857 0.0581363 0.0609241 -0.00981668 … 0.0672203 0.156301 -0.142857 0.112538 -0.0793377 -0.0184382 0.133927 0.108932 -0.142857 0.0871356 -0.0240147 -0.0699827 -0.214902 0.171969 -0.142857 0.14265 0.0539251 0.207983 -0.19236 0.18962 -0.142857 0.1124 -0.151321 -0.26095 -0.118351 0.191938 -0.142857 -0.0294305 -0.205379 0.190192 … -0.00851431 0.17653 -0.142857 -0.113902 -0.175673 -0.0191166 0.101116 0.141956 -0.142857 -0.159439 -0.0894712 0.047253 0.169903 0.0913398 ⋮ ⋱ -0.142857 0.0725956 -0.119268 0.178503 0.109989 -0.13773 -0.142857 0.00742462 -0.255754 -0.134852 0.00273088 -0.176623 -0.142857 -0.117737 -0.052603 0.268887 -0.110743 -0.197004 -0.142857 -0.146842 -0.00787113 -0.17119 … -0.19071 -0.198347 -0.142857 -0.0755484 -0.0136396 0.0525918 -0.217508 -0.182695 -0.142857 -0.0763572 -0.0337713 0.00799349 0.136338 -0.0957285 -0.142857 -0.0269051 0.0526934 0.0340267 0.0764488 -0.148111 -0.142857 -0.0278964 0.0566297 -0.10423 -0.022017 -0.18472 -0.142857 0.00434924 0.106746 0.131244 … -0.120879 -0.203753 -0.142857 0.0440216 -0.0214087 -0.221072 -0.191356 -0.206737 -0.142857 0.0768078 0.0183171 0.190107 -0.218507 -0.196315 -0.142857 -0.00464626 -0.00183453 -0.0903946 -0.207341 -0.175641
Display the decaying amplitude of the eigenvalues.
plot(D, linewidth = 2)
ylim(0, maximum(D))
show()
Display the leading eigenvectors - they look like Fourier modes.
figure(figsize = (5,5))
for i in 1:16
imageplot(abs(reshape(V[:,i], (w1,w1))), "", [4, 4, i])
end
Patch dimensionality reduction operator.
iresh = Q -> reshape(Q', (n, n, d)) # order = "F"
descriptor = f -> iresh(V[: , 1 : d]'*remove_mean(resh(P)))
remove_mean(resh(P))[1, :]
16384-element Array{Float64,1}: 0.0628797 -0.0601156 0.0433663 -0.0076114 0.0415792 -0.063938 0.0552831 -0.0501452 -0.00654325 0.0581593 -0.0670696 -0.00293932 -0.0351177 ⋮ -0.0810145 -0.10699 -0.040066 0.108777 0.0189314 0.0347488 0.0185005 -0.00987702 0.020824 0.140613 0.0938184 0.0223174
Each $H(i,j,:)$ is a $d$-dimensional descriptor of a patch.
H = descriptor(f)
H[1, 1, :]
25-element Array{Float64,1}: 1.12757e-16 0.00303514 -0.057321 0.00279343 0.0252618 -0.00510602 -0.0100753 -0.00124721 0.0147514 0.0228865 0.00793989 0.0926927 0.0949608 0.0191861 -0.0162093 0.0132067 -0.00514667 0.0530679 -0.0316565 -0.00451908 -0.0086364 -0.00777439 -0.146048 -0.00399402 -0.00891363
NL-means applies, an adaptive averaging kernel is computed from patch distances to each pixel location.
We denote $H_{i} \in \RR^d$ the descriptor at pixel $i$. We define the distance matrix $$ D_{i,j} = \frac{1}{w_1^2}\norm{H_i-H_j}^2. $$
Operator to compute the distances $(D_{i,j})_j$ between the patch around $i=(i_1,i_2)$ and all the other ones.
distance = i -> sum((H - repeat(reshape(H[i[1], i[2], :], (1, 1, length(H[i[1], i[2], :]))), inner = [n, n, 1])).^2, 3)./(w1*w1)
(::#11) (generic function with 1 method)
The non-local mean filter computes a denoised image $\tilde f$ as :
$$ \tilde f_i = \sum_j K_{i,j} f_j $$where the weights $K$ are computed as : $$ K_{i,j} = \frac{ \tilde K_{i,j} }{ \sum_{j'} \tilde K_{i,j'} } \qandq \tilde K_{i,j} = e^{-\frac{D_{i,j}}{2\tau^2}} . $$
The width $\tau$ of the Gaussian is very important and should be adapted to match the noise level.
Compute and normalize the weight.
normalize = K -> K./sum(K)
kernel = (i, tau) -> normalize(exp(-distance(i)./(2*tau^2)))
(::#15) (generic function with 1 method)
Compute a typical example of kernel for some pixel position $(x,y)$.
tau = .05
i = [83, 72]
D = distance(i)
H[i[1], i[2], :]
K = kernel(i, tau)
D
128×128×1 Array{Float64,3}: [:, :, 1] = 0.00295118 0.00227457 0.00312287 … 0.00485491 0.00488994 0.00503266 0.00259518 0.00283335 0.00222588 0.00378126 0.00465444 0.00269188 0.00309054 0.00297622 0.00237054 0.00343972 0.00366405 0.00546961 0.00230125 0.00349517 0.00192803 0.00550008 0.00633937 0.00564258 0.00321561 0.00167929 0.00294033 0.00402107 0.00260499 0.00340563 0.00397462 0.00264592 0.00322254 … 0.00382952 0.00600861 0.00397644 0.00245938 0.0020279 0.00312583 0.00476732 0.00374555 0.00489222 0.00274398 0.00164827 0.00266606 0.00464598 0.00539079 0.00396139 0.002302 0.00240738 0.0030592 0.00523817 0.00437711 0.00538495 0.00295479 0.00121129 0.00368635 0.00277393 0.00259435 0.00276076 0.00185107 0.002613 0.00297119 … 0.00439295 0.00463488 0.0042115 0.00240684 0.00180074 0.00291328 0.00338667 0.00283772 0.00312385 0.00251598 0.00311237 0.002596 0.00341123 0.00399084 0.00378708 ⋮ ⋱ ⋮ 0.00235609 0.00259432 0.00318434 0.00279742 0.00293299 0.00300645 0.00247655 0.00230713 0.00195436 0.00427163 0.00408478 0.00350959 0.0024835 0.00290693 0.00297222 0.00214986 0.00222044 0.00256405 0.00237134 0.00260013 0.00280712 0.00384583 0.00397182 0.00404456 0.00246556 0.00277591 0.00223755 … 0.00250236 0.00198627 0.00181474 0.00227777 0.00247946 0.00304085 0.00340078 0.00327795 0.00414402 0.00309858 0.0028201 0.00185638 0.00252003 0.00266765 0.00246318 0.00150065 0.00261661 0.00231011 0.00248716 0.00203596 0.0029757 0.00338383 0.00242381 0.00292186 0.00297141 0.00291344 0.00332062 0.0020981 0.00319493 0.00149648 … 0.00308626 0.00277732 0.0030444 0.00385313 0.00293589 0.00348093 0.00218025 0.00279784 0.00236452 0.00173234 0.00263913 0.00185182 0.00290722 0.00248422 0.00288259
Display the squared distance and the kernel.
figure(figsize = (10,10))
imageplot(D[:, :], "D", [1, 2, 1])
imageplot(K[:, :], "K", [1, 2, 2])
PyObject <matplotlib.text.Text object at 0x000000001EE5BF60>
We set a "locality constant" $q$ that set the maximum distance between patches to compare. This allows to speed up computation, and makes NL-means type methods semi-global (to avoid searching in all the image).
q = 14
14
Using this locality constant, we compute the distance between patches only within a window. Once again, one should be careful about boundary conditions.
#selection = i -> np.array((clamP(np.arange(i[1]-q,i[1] + q + 1), 0, n-1), clamP(np.arange(i[1]-q,i[1] + q + 1), 0, n-1)))
selection = i -> [clamP(collect(i[1] - q + 1 : i[1] + q + 1), 1, n)'; clamP(collect(i[1] - q + 1 : i[1] + q + 1), 1, n)']
(::#19) (generic function with 1 method)
Compute distance and kernel only within the window.
function distance_0(i, sel)
H1 = (H[sel[1, :],:,:])
H2 = (H1[:,sel[2, :],:])
return sum((H2 - repeat(reshape(H[i[1], i[2], :], (1, 1, length(H[i[1], i[2], :]))), inner = [length(sel[1, :]), length(sel[2, :]), 1])),
3)/(w1*w1)
end
distance = i -> distance_0(i, selection(i))
kernel = (i, tau) -> normalize(exp(-distance(i)./(2*tau^2)))
(::#23) (generic function with 1 method)
Compute a typical example of kernel for some pixel position $(x,y)$.
Display the squared distance and the kernel.
sel = selection(i)
D = distance(i)
K = kernel(i, tau)
29×29×1 Array{Float64,3}: [:, :, 1] = 0.00150359 0.00331627 6.83253e-5 … 0.00239348 0.00041119 0.000467514 0.000236781 0.00251782 0.000850111 0.00193867 0.00075818 0.00360707 0.000962478 0.000245312 0.000591722 0.000267653 0.000326701 0.000258885 0.000398922 0.00233789 0.00084619 0.000563018 0.00307985 0.00269301 0.000650247 0.000846278 0.00179653 0.000351704 … 0.000408738 0.000373752 0.00141865 0.000229179 0.000374389 0.00198729 0.00115064 0.000221269 0.00258376 0.000605844 0.00121756 0.000417504 0.000918029 0.000436057 0.00128788 0.00127099 0.000482956 0.000516951 0.000268027 0.00166792 0.000316963 0.00505622 0.00169658 0.000419005 0.00126345 … 0.000606645 0.000626355 0.00180485 0.000572404 0.000599983 0.00140198 0.00151399 0.000583443 0.00231071 0.000851272 0.000184051 0.000926002 ⋮ ⋱ 8.48065e-5 0.00193428 0.000548713 0.000547021 0.00155817 0.000667296 0.000865719 0.000783577 0.000304843 0.00126702 0.000615073 0.00132741 0.000298352 0.00206906 0.000285545 0.000262269 0.0018164 0.0030514 … 0.000155753 0.00280487 0.000379655 0.000154351 0.00500062 0.0013116 0.000273136 0.00285961 0.000776159 0.000525234 0.000862562 0.000633648 0.00242004 0.000150042 0.00169735 0.000391434 0.00240604 0.00107573 0.000451066 0.000258555 0.000806164 0.000150238 0.000748652 0.00573865 0.000229333 … 0.00143951 0.00234482 0.00066037 0.000361907 0.000626649 0.000703353 0.000698092 0.000435973 0.000642139 0.00095164 0.000179389 0.00101129 0.000239842 0.00197698 0.000370909 0.000643037 0.00420599
figure(figsize = (10,10))
imageplot(D[:, :], "D", [1, 2, 1])
imageplot(K[:, :], "K", [1, 2, 2])
PyObject <matplotlib.text.Text object at 0x0000000022CA5E10>
The NL-filtered value at pixel $(x,y)$ is obtained by averaging the values of $f$ with the weight $K$.
function NLval_0(K,sel)
f_temp = f[sel[1, :], :]
return sum(K.*f_temp[:, sel[1, :]])
end
NLval = (i, ta) -> NLval_0(kernel(i, tau), selection(i))
(::#25) (generic function with 1 method)
We apply the filter to each pixel location to perform the NL-means algorithm.
(Y, X) = meshgrid(0 : n - 1, 0 : n - 1)
function arrayfun(f, X, Y)
n = size(X)[1]
p = size(Y)[1]
R = zeros(n, p)
for k in 1:n
for l in 1:p
R[k,l] = f(k,l)
end
end
return R
end
NLmeans = tau -> arrayfun((i1, i2) -> NLval([i1,i2], tau), X, Y)
(::#27) (generic function with 1 method)
Display the result for some value of $\tau$.
tau = .03
figure(figsize = (5,5))
imageplot(NLmeans(tau))
#NLmeans(tau)
#n = size(X)[1]
#p = size(Y)[1]
#R = zeros(n, p)
#for k in 1:n
# for l in 1:p
# R[k,l] = f(k,l)
# end
#end
tau = .03
Exercise 1
Compute the denoising result for several values of $\tau$ in order to determine the optimal denoising that minimizes $\norm{\tilde f - f_0}$.
#run -i nt_solutions/denoisingadv_6_nl_means/exo1
include("Exos\\denoisingadv_6_nl_means\\exo1.jl")
LoadError: BoundsError: attempt to access 128×128×25 Array{Float64,3} at index [[0,0,0,0,0,0,0,0,0,0,0,0,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16],Colon(),Colon()] while loading C:\Users\Ayman\.julia\v0.5\Exos\denoisingadv_6_nl_means\exo1.jl, in expression starting on line 6 in throw_boundserror(::Array{Float64,3}, ::Tuple{Array{Int64,1},Colon,Colon}) at .\abstractarray.jl:355 in checkbounds at .\abstractarray.jl:284 [inlined] in _getindex at .\multidimensional.jl:270 [inlined] in getindex(::Array{Float64,3}, ::Array{Int64,1}, ::Colon, ::Colon) at .\abstractarray.jl:752 in distance_0 at .\In[30]:2 [inlined] in (::##19#20)(::Array{Int64,1}) at .\In[30]:8 in (::##21#22)(::Array{Int64,1}, ::Float64) at .\In[30]:9 in (::##23#24)(::Array{Int64,1}, ::Float64) at .\In[33]:6 in arrayfun(::##26#28{Float64}, ::Array{Int64,2}, ::Array{Int64,2}) at .\In[34]:9 in (::##25#27)(::Float64) at .\In[34]:15 in macro expansion; at C:\Users\Ayman\.julia\v0.5\Exos\denoisingadv_6_nl_means\exo1.jl:8 [inlined] in anonymous at .\<missing>:? in include_from_node1(::String) at .\loading.jl:488
## Insert your code here.
Display the best result.
plt.figure(figsize = (5,5))
imageplot(clamp(fNL))
Exercise 2
Explore the influence of the $q$ and $w$ parameters.
run -i nt_solutions/denoisingadv_6_nl_means/exo2
## Insert your code here.