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Stephan Hilb
SemiSmoothNewton.jl
Commits
ddc21ec7
Commit
ddc21ec7
authored
3 years ago
by
Stephan Hilb
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implement newest vertex adaptive refinement
parent
41dc9d35
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Changes
2
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2 changed files
src/mesh.jl
+171
-13
171 additions, 13 deletions
src/mesh.jl
src/run.jl
+109
-1
109 additions, 1 deletion
src/run.jl
with
280 additions
and
14 deletions
src/mesh.jl
+
171
−
13
View file @
ddc21ec7
...
...
@@ -6,6 +6,21 @@ using StaticArrays: SVector
struct
HMesh
vertices
::
Vector
{
SVector
{
2
,
Float64
}}
cells
::
Vector
{
NTuple
{
3
,
Int
}}
levels
::
Vector
{
Int
}
end
function
HMesh
(
mesh
::
Mesh
)
vertices
=
Vector
{
SVector
{
2
,
Float64
}}()
for
v
in
axes
(
mesh
.
vertices
,
2
)
push!
(
vertices
,
mesh
.
vertices
[
:
,
v
])
end
cells
=
Vector
{
NTuple
{
3
,
Int
}}()
for
c
in
axes
(
mesh
.
cells
,
2
)
push!
(
cells
,
NTuple
{
3
}(
mesh
.
cells
[
:
,
c
]))
end
levels
=
zeros
(
Int
,
axes
(
cells
))
return
HMesh
(
vertices
,
cells
,
levels
)
end
Base
.
show
(
io
::
IO
,
::
MIME
"text/plain"
,
x
::
HMesh
)
=
...
...
@@ -17,7 +32,7 @@ nvertices_cell(::HMesh) = 3
nvertices
(
x
::
HMesh
)
=
length
(
x
.
vertices
)
ncells
(
x
::
HMesh
)
=
length
(
x
.
cells
)
cells
(
mesh
::
HMesh
)
=
axes
(
mesh
.
cells
,
1
)
cells
(
mesh
::
HMesh
)
=
setdiff
(
axes
(
mesh
.
cells
,
1
)
,
findall
(
>
(
0
),
mesh
.
levels
))
vertices
(
mesh
::
HMesh
,
cell
)
=
mesh
.
cells
[
cell
]
function
init_hgrid
(
m
::
Int
,
n
::
Int
=
m
,
v0
=
(
0.
,
0.
),
v1
=
(
1.
,
1.
))
...
...
@@ -37,7 +52,7 @@ function init_hgrid(m::Int, n::Int = m, v0 = (0., 0.), v1 = (1., 1.))
push!
(
cells
,
(
vidx
[
I
],
vidx
[
I
+
e1
+
e2
],
vidx
[
I
+
e2
]))
end
return
HMesh
(
vertices
,
cells
)
return
HMesh
(
vertices
,
cells
,
zeros
(
Int
,
axes
(
cells
))
)
end
init_hgrid
(
img
::
Array
{
<:
Any
,
2
};
type
=:
vertex
)
=
...
...
@@ -45,6 +60,13 @@ init_hgrid(img::Array{<:Any, 2}; type=:vertex) =
init_grid
(
size
(
img
,
1
)
-
1
,
size
(
img
,
2
)
-
1
,
(
1.0
,
1.0
),
size
(
img
))
:
init_grid
(
size
(
img
,
1
),
size
(
img
,
2
),
(
0.5
,
0.5
),
size
(
img
)
.-
(
0.5
,
0.5
))
function
sub_mesh
(
hmesh
::
HMesh
,
subcells
=
cells
(
hmesh
))
cells
=
collect
(
reshape
(
reinterpret
(
Int
,
hmesh
.
cells
[
subcells
]),
3
,
:
))
# TODO: restrict vertices too
vertices
=
collect
(
reshape
(
reinterpret
(
Float64
,
hmesh
.
vertices
),
2
,
:
))
return
Mesh
(
vertices
,
cells
)
end
# 2d, simplex grid
struct
Mesh
...
...
@@ -140,8 +162,9 @@ init_grid(img::Array{<:Any, 2}; type=:vertex) =
init_grid
(
size
(
img
,
1
)
-
1
,
size
(
img
,
2
)
-
1
,
(
1.0
,
1.0
),
size
(
img
))
:
init_grid
(
size
(
img
,
1
),
size
(
img
,
2
),
(
0.5
,
0.5
),
size
(
img
)
.-
(
0.5
,
0.5
))
function
refine!
(
mesh
::
HMesh
,
marked_cells
::
Set
)
refined_cells
=
Set
{
Int
}()
# horribly implemented, please don't curse me
function
bisect!
(
mesh
::
HMesh
,
marked_cells
::
Set
)
refined_cells
=
Pair
{
Int
,
NTuple
{
2
,
Int
}}[]
# assemble edge -> cells map
edgemap
=
Dict
{
NTuple
{
2
,
Int
},
Vector
{
Int
}}()
for
cell
in
cells
(
mesh
)
...
...
@@ -156,6 +179,8 @@ function refine!(mesh::HMesh, marked_cells::Set)
edgemap
[
e3
]
=
push!
(
get!
(
edgemap
,
e3
,
[]),
cell
)
end
#return edgemap
function
refine_cell
(
c1
)
c2
=
-
1
# c1 -> c11 + c12
...
...
@@ -168,7 +193,7 @@ function refine!(mesh::HMesh, marked_cells::Set)
c2
=
c2_arr
[
begin
]
c2_vs
=
sort
(
SVector
(
vertices
(
mesh
,
c2
)))
if
c1_vs
[
end
]
!=
c2_vs
[
end
]
if
c1_vs
[
1
:
2
]
!=
c2_vs
[
1
:
2
]
# cannot refine `cellop` compatibly, recurse
refine_cell
(
c2
)
# refetch c2 because topology has changed
...
...
@@ -186,11 +211,15 @@ function refine!(mesh::HMesh, marked_cells::Set)
push!
(
mesh
.
vertices
,
xbisect
)
vbisect
=
lastindex
(
mesh
.
vertices
)
push!
(
mesh
.
cells
,
Tuple
(
sort
(
replace
(
c1_vs
,
c1_vs
[
1
]
=>
vbisect
))))
# take care to produce positively oriented cells
push!
(
mesh
.
cells
,
Tuple
(
replace
(
SVector
(
vertices
(
mesh
,
c1
)),
c1_vs
[
1
]
=>
vbisect
)))
push!
(
mesh
.
levels
,
0
)
c3
=
lastindex
(
mesh
.
cells
)
replace!
(
edgemap
[
NTuple
{
2
}(
setdiff
(
c1_vs
,
c1_vs
[
1
]))],
c1
=>
c3
)
push!
(
mesh
.
cells
,
Tuple
(
sort
(
replace
(
c1_vs
,
c1_vs
[
2
]
=>
vbisect
))))
# take care to produce positively oriented cells
push!
(
mesh
.
cells
,
Tuple
(
replace
(
SVector
(
vertices
(
mesh
,
c1
)),
c1_vs
[
2
]
=>
vbisect
)))
push!
(
mesh
.
levels
,
0
)
c4
=
lastindex
(
mesh
.
cells
)
replace!
(
edgemap
[
NTuple
{
2
}(
setdiff
(
c1_vs
,
c1_vs
[
2
]))],
c1
=>
c4
)
...
...
@@ -199,15 +228,20 @@ function refine!(mesh::HMesh, marked_cells::Set)
edgemap
[(
c1_vs
[
2
],
vbisect
)]
=
[
c3
]
edgemap
[(
c1_vs
[
3
],
vbisect
)]
=
[
c3
,
c4
]
mesh
.
levels
[
c1
]
+=
1
delete!
(
marked_cells
,
c1
)
push!
(
refined_cells
,
c1
)
push!
(
refined_cells
,
c1
=>
(
c3
,
c4
)
)
if
c2
>
0
push!
(
mesh
.
cells
,
Tuple
(
sort
(
replace
(
c2_vs
,
c1_vs
[
1
]
=>
vbisect
))))
# c1_vs is correct
# take care to produce positively oriented cells
push!
(
mesh
.
cells
,
Tuple
(
replace
(
SVector
(
vertices
(
mesh
,
c2
)),
c1_vs
[
1
]
=>
vbisect
)))
# c1_vs is correct
push!
(
mesh
.
levels
,
0
)
c5
=
lastindex
(
mesh
.
cells
)
replace!
(
edgemap
[
NTuple
{
2
}(
setdiff
(
c2_vs
,
c1_vs
[
1
]))],
c1
=>
c5
)
push!
(
mesh
.
cells
,
Tuple
(
sort
(
replace
(
c2_vs
,
c1_vs
[
2
]
=>
vbisect
))))
# c1_vs is correct
# take care to produce positively oriented cells
push!
(
mesh
.
cells
,
Tuple
(
replace
(
SVector
(
vertices
(
mesh
,
c2
)),
c1_vs
[
2
]
=>
vbisect
)))
# c1_vs is correct
push!
(
mesh
.
levels
,
0
)
c6
=
lastindex
(
mesh
.
cells
)
replace!
(
edgemap
[
NTuple
{
2
}(
setdiff
(
c2_vs
,
c1_vs
[
2
]))],
c1
=>
c6
)
...
...
@@ -216,8 +250,9 @@ function refine!(mesh::HMesh, marked_cells::Set)
push!
(
edgemap
[(
c1_vs
[
2
],
vbisect
)],
c5
)
edgemap
[(
c1_vs
[
3
],
vbisect
)]
=
[
c5
,
c6
]
mesh
.
levels
[
c2
]
+=
1
delete!
(
marked_cells
,
c2
)
push!
(
refined_cells
,
c
1
)
push!
(
refined_cells
,
c
2
=>
(
c5
,
c6
)
)
end
end
...
...
@@ -225,10 +260,103 @@ function refine!(mesh::HMesh, marked_cells::Set)
refine_cell
(
first
(
marked_cells
))
end
deleteat!
(
mesh
.
cells
,
sort
(
collect
(
refined_cells
)))
return
mesh
return
refined_cells
#deleteat!(mesh.cells, sort(collect(refined_cells)))
end
# horribly implemented, please don't curse me
function
refine!
(
hmesh
::
HMesh
,
marked_cells
::
Set
;
fs
...
)
old_mesh
=
sub_mesh
(
hmesh
)
refined_cells
=
bisect!
(
hmesh
,
marked_cells
)
extended_mesh
=
sub_mesh
(
hmesh
,
axes
(
hmesh
.
cells
,
1
))
new_mesh
=
sub_mesh
(
hmesh
)
removed_cells
=
map
(
x
->
first
(
x
),
refined_cells
)
# extended functions onto newly created cells
extended_fs
=
map
(
NamedTuple
(
fs
))
do
f
space
=
FeSpace
(
extended_mesh
,
f
.
space
.
element
,
f
.
space
.
size
)
return
FeFunction
(
space
)
end
# copy over previous data for unmodified cells
for
(
f
,
extended_f
)
in
zip
(
NamedTuple
(
fs
),
extended_fs
)
copyto!
(
extended_f
.
data
,
f
.
data
)
end
# prolong data for refined cells
for
(
old_cell
,
extended_cells
)
in
refined_cells
for
(
f
,
extended_f
)
in
zip
(
NamedTuple
(
fs
),
extended_fs
)
prolong!
(
extended_f
,
old_cell
,
extended_cells
)
end
end
# retain only non-refined cells
new_fs
=
map
(
NamedTuple
(
extended_fs
))
do
f
space
=
FeSpace
(
new_mesh
,
f
.
space
.
element
,
f
.
space
.
size
)
return
FeFunction
(
space
)
end
retained_cells
=
setdiff
(
cells
(
extended_mesh
),
removed_cells
)
@assert
(
retained_cells
==
cells
(
hmesh
))
for
(
new_cell
,
old_cell
)
in
enumerate
(
retained_cells
)
for
(
f
,
new_f
)
in
zip
(
extended_fs
,
new_fs
)
gdofs
=
f
.
space
.
dofmap
[
:
,
:
,
old_cell
]
new_gdofs
=
new_f
.
space
.
dofmap
[
:
,
:
,
new_cell
]
new_f
.
data
[
new_gdofs
]
.=
f
.
data
[
gdofs
]
end
end
return
new_fs
end
prolong!
(
new_f
,
old_cell
,
new_cells
)
=
prolong!
(
new_f
,
old_cell
,
new_cells
,
new_f
.
space
.
element
)
prolong!
(
new_f
,
old_cell
,
new_cells
,
::
DP1
)
=
prolong!
(
new_f
,
old_cell
,
new_cells
,
P1
())
function
prolong!
(
new_f
,
old_cell
,
new_cells
,
::
P1
)
old_f
=
new_f
old_cell_vs
=
collect
(
vertices
(
old_f
.
space
.
mesh
,
old_cell
))
new_cell1_vs
=
collect
(
vertices
(
new_f
.
space
.
mesh
,
new_cells
[
1
]))
new_cell2_vs
=
collect
(
vertices
(
new_f
.
space
.
mesh
,
new_cells
[
2
]))
# copy over data for common vertices
common_vs
=
intersect
(
old_cell_vs
,
new_cell1_vs
)
old_ldofs
=
indexin
(
common_vs
,
old_cell_vs
)
old_gdofs
=
old_f
.
space
.
dofmap
[
:
,
old_ldofs
,
old_cell
]
new_ldofs
=
indexin
(
common_vs
,
new_cell1_vs
)
new_gdofs
=
new_f
.
space
.
dofmap
[
:
,
new_ldofs
,
new_cells
[
1
]]
new_f
.
data
[
new_gdofs
]
.=
old_f
.
data
[
old_gdofs
]
common_vs
=
intersect
(
old_cell_vs
,
new_cell2_vs
)
old_ldofs
=
indexin
(
common_vs
,
old_cell_vs
)
old_gdofs
=
old_f
.
space
.
dofmap
[
:
,
old_ldofs
,
old_cell
]
new_ldofs
=
indexin
(
common_vs
,
new_cell2_vs
)
new_gdofs
=
new_f
.
space
.
dofmap
[
:
,
new_ldofs
,
new_cells
[
2
]]
new_f
.
data
[
new_gdofs
]
.=
old_f
.
data
[
old_gdofs
]
# vertices of bisection edge
avg_vs
=
symdiff
(
new_cell1_vs
,
new_cell2_vs
)
old_ldofs
=
indexin
(
avg_vs
,
old_cell_vs
)
old_gdofs
=
old_f
.
space
.
dofmap
[
:
,
old_ldofs
,
old_cell
]
avg_data
=
(
old_f
.
data
[
old_gdofs
[
:
,
1
]]
.+
old_f
.
data
[
old_gdofs
[
:
,
2
]])
./
2
new_gdofs
=
new_f
.
space
.
dofmap
[
:
,
3
,
new_cells
[
1
]]
new_f
.
data
[
new_gdofs
]
.=
avg_data
new_gdofs
=
new_f
.
space
.
dofmap
[
:
,
3
,
new_cells
[
2
]]
new_f
.
data
[
new_gdofs
]
.=
avg_data
end
function
prolong!
(
new_f
,
old_cell
,
new_cells
,
::
DP0
)
old_f
=
new_f
# simply copy over the data
old_gdofs
=
old_f
.
space
.
dofmap
[
:
,
1
,
old_cell
]
new_gdofs
=
new_f
.
space
.
dofmap
[
:
,
1
,
new_cells
[
1
]]
new_f
.
data
[
new_gdofs
]
.=
old_f
.
data
[
old_gdofs
]
new_gdofs
=
new_f
.
space
.
dofmap
[
:
,
1
,
new_cells
[
2
]]
new_f
.
data
[
new_gdofs
]
.=
old_f
.
data
[
old_gdofs
]
end
#function cell_contains(mesh, cell, v)
# geo = mesh.vertices[:, mesh.cells[:, cell]]
# J = jacobian(x -> geo * [1 - x[1] - x[2], x[1], x[2]], [0., 0.])
...
...
@@ -254,3 +382,33 @@ function save(filename::String, mesh::Mesh, fs...)
end
vtk_save
(
vtk
)
end
function
elmap
(
mesh
,
cell
)
A
=
SArray
{
Tuple
{
ndims_space
(
mesh
),
nvertices_cell
(
mesh
)}}(
view
(
mesh
.
vertices
,
:
,
view
(
mesh
.
cells
,
:
,
cell
)))
return
x
->
A
*
SA
[
1
-
x
[
1
]
-
x
[
2
],
x
[
1
],
x
[
2
]]
end
function
test_mesh
(
mesh
)
# assemble edge -> cells map
edgemap
=
Dict
{
NTuple
{
2
,
Int
},
Vector
{
Int
}}()
for
cell
in
cells
(
mesh
)
vs
=
sort
(
SVector
(
vertices
(
mesh
,
cell
)))
e1
=
(
vs
[
1
],
vs
[
2
])
e2
=
(
vs
[
1
],
vs
[
3
])
e3
=
(
vs
[
2
],
vs
[
3
])
edgemap
[
e1
]
=
push!
(
get!
(
edgemap
,
e1
,
[]),
cell
)
edgemap
[
e2
]
=
push!
(
get!
(
edgemap
,
e2
,
[]),
cell
)
edgemap
[
e3
]
=
push!
(
get!
(
edgemap
,
e3
,
[]),
cell
)
end
for
(
edge
,
cells
)
in
edgemap
@assert
(
length
(
cells
)
<=
2
)
end
# are cells positively oriented?
for
cell
in
cells
(
mesh
)
delmap
=
jacobian
(
elmap
(
mesh
,
cell
),
SA
[
0.
,
0.
])
@assert
(
det
(
delmap
)
>
0
)
end
end
This diff is collapsed.
Click to expand it.
src/run.jl
+
109
−
1
View file @
ddc21ec7
...
...
@@ -203,6 +203,37 @@ function estimate!(ctx::L1L2TVContext)
interpolate!
(
ctx
.
est
,
estf
;
ctx
.
g
,
ctx
.
u
,
ctx
.
p1
,
ctx
.
p2
,
ctx
.
nablau
,
w
,
nablaw
,
ctx
.
tdata
)
end
function
refine
(
ctx
::
L1L2TVContext
,
marked_cells
)
hmesh
=
HMesh
(
ctx
.
mesh
)
refined_functions
=
refine!
(
hmesh
,
Set
(
marked_cells
);
ctx
.
est
,
ctx
.
g
,
ctx
.
u
,
ctx
.
p1
,
ctx
.
p2
,
ctx
.
du
,
ctx
.
dp1
,
ctx
.
dp2
)
new_mesh
=
refined_functions
.
u
.
space
.
mesh
new_ctx
=
L1L2TVContext
(
ctx
.
name
,
new_mesh
,
ctx
.
m
;
ctx
.
T
,
ctx
.
tdata
,
ctx
.
S
,
ctx
.
alpha1
,
ctx
.
alpha2
,
ctx
.
beta
,
ctx
.
lambda
,
ctx
.
gamma1
,
ctx
.
gamma2
)
@assert
(
new_ctx
.
est
.
space
.
dofmap
==
refined_functions
.
est
.
space
.
dofmap
)
@assert
(
new_ctx
.
g
.
space
.
dofmap
==
refined_functions
.
g
.
space
.
dofmap
)
@assert
(
new_ctx
.
u
.
space
.
dofmap
==
refined_functions
.
u
.
space
.
dofmap
)
@assert
(
new_ctx
.
p1
.
space
.
dofmap
==
refined_functions
.
p1
.
space
.
dofmap
)
@assert
(
new_ctx
.
p2
.
space
.
dofmap
==
refined_functions
.
p2
.
space
.
dofmap
)
@assert
(
new_ctx
.
du
.
space
.
dofmap
==
refined_functions
.
du
.
space
.
dofmap
)
@assert
(
new_ctx
.
dp1
.
space
.
dofmap
==
refined_functions
.
dp1
.
space
.
dofmap
)
@assert
(
new_ctx
.
dp2
.
space
.
dofmap
==
refined_functions
.
dp2
.
space
.
dofmap
)
new_ctx
.
est
.
data
.=
refined_functions
.
est
.
data
new_ctx
.
g
.
data
.=
refined_functions
.
g
.
data
new_ctx
.
u
.
data
.=
refined_functions
.
u
.
data
new_ctx
.
p1
.
data
.=
refined_functions
.
p1
.
data
new_ctx
.
p2
.
data
.=
refined_functions
.
p2
.
data
new_ctx
.
du
.
data
.=
refined_functions
.
du
.
data
new_ctx
.
dp1
.
data
.=
refined_functions
.
dp1
.
data
new_ctx
.
dp2
.
data
.=
refined_functions
.
dp2
.
data
return
new_ctx
end
function
save
(
ctx
::
L1L2TVContext
,
filename
,
fs
...
)
print
(
"save ... "
)
vtk
=
vtk_mesh
(
filename
,
ctx
.
mesh
)
...
...
@@ -211,6 +242,69 @@ function save(ctx::L1L2TVContext, filename, fs...)
return
vtk
end
function
test_refine
(
mesh
=
nothing
)
m
=
1
if
isnothing
(
mesh
)
mesh
=
init_grid
(
2
,
2
)
end
T
(
tdata
,
u
)
=
u
S
(
u
,
nablau
)
=
u
ctx
=
L1L2TVContext
(
"test"
,
mesh
,
m
;
T
,
tdata
=
nothing
,
S
,
alpha1
=
0.
,
alpha2
=
5.
,
lambda
=
0.1
,
beta
=
1e-3
,
gamma1
=
1e-3
,
gamma2
=
1e-3
)
interpolate!
(
ctx
.
g
,
x
->
x
[
1
]
+
x
[
2
]
>
1.01
)
mysave
(
ctx
,
i
)
=
save
(
ctx
,
"
$
(ctx.name)_
$
(lpad(i, 5, '0')).vtu"
,
ctx
.
g
,
ctx
.
u
,
ctx
.
p1
,
ctx
.
p2
,
ctx
.
est
)
pvd
=
paraview_collection
(
"
$
(ctx.name).pvd"
)
for
i
in
1
:
10
step!
(
ctx
)
end
pvd
[
0
]
=
mysave
(
ctx
,
0
)
ctx2
=
refine
(
ctx
,
[
1
,
2
,
3
,
4
,
5
,
6
,
7
,
8
])
#interpolate!(ctx2.g, x -> x[1] + x[2] < 2.01)
#interpolate!(ctx2.g, x -> norm(x .- m) < norm(m) / 3)
#ctx2.est.data .= 0
#ctx2.g.data .= 0
#ctx2.u.data .= 0
#ctx2.p1.data .= 0
#ctx2.p2.data .= 0
#ctx2.du.data .= 0
#ctx2.dp1.data .= 0
#ctx2.dp2.data .= 0
for
i
in
1
:
10
step!
(
ctx2
)
end
pvd
[
1
]
=
mysave
(
ctx2
,
1
)
test_mesh
(
ctx2
.
mesh
)
return
ctx
,
ctx2
for
i
in
1
:
5
step!
(
ctx
)
estimate!
(
ctx
)
pvd
[
i
]
=
mysave
(
i
)
println
()
end
estmean
=
mean
(
ctx
.
est
.
data
)
marked_cells
=
findall
(
>
(
2
*
estmean
),
ctx
.
est
.
data
)
println
(
marked_cells
)
ctx
=
refine
(
ctx
,
marked_cells
)
interpolate!
(
ctx
.
g
,
x
->
norm
(
x
.-
m
)
<
norm
(
m
)
/
3
)
for
i
in
6
:
11
step!
(
ctx
)
estimate!
(
ctx
)
pvd
[
i
]
=
mysave
(
i
)
println
()
end
return
ctx
end
function
denoise
(
img
;
name
,
params
...
)
m
=
1
mesh
=
init_grid
(
img
;
type
=:
vertex
)
...
...
@@ -236,6 +330,20 @@ function denoise(img; name, params...)
pvd
[
i
]
=
save_denoise
(
i
)
println
()
end
estmean
=
mean
(
ctx
.
est
.
data
)
marked_cells
=
findall
(
>
(
2
*
estmean
),
ctx
.
est
.
data
)
test_mesh
(
ctx
.
mesh
)
println
(
marked_cells
)
ctx
=
refine
(
ctx
,
marked_cells
)
test_mesh
(
ctx
.
mesh
)
interpolate!
(
ctx
.
g
,
x
->
norm
(
x
.-
m
)
<
norm
(
m
)
/
3
)
for
i
in
6
:
20
step!
(
ctx
)
estimate!
(
ctx
)
pvd
[
i
]
=
save_denoise
(
i
)
println
()
end
return
ctx
end
...
...
@@ -266,7 +374,7 @@ function inpaint(img, imgmask; name, params...)
pvd
=
paraview_collection
(
"
$
(ctx.name).pvd"
)
pvd
[
0
]
=
save_inpaint
(
0
)
for
i
in
1
:
20
for
i
in
1
:
3
step!
(
ctx
)
estimate!
(
ctx
)
pvd
[
i
]
=
save_inpaint
(
i
)
...
...
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