Mercurial > repos > public > sbplib_julia

annotate Notes.md @ 1167:fd80e9a0ef99 feature/boundary_conditions

Find changesets by keywords (author, files, the commit message), revision number or hash, or revset expression.
Make use of discretize in sat functions
author Vidar Stiernström <vidar.stiernstrom@it.uu.se>
date Wed, 07 Dec 2022 21:56:00 +0100
parents 6757cc9ba22e
children ea2e8254820a
Ignore whitespace changes - Everywhere: Within whitespace: At end of lines:
rev   line source
318
0c8d4a734c4f Add some todos and add a Notes.md file
Jonatan Werpers <jonatan@werpers.com>
parents:
diff changeset
1 # Notes
0c8d4a734c4f Add some todos and add a Notes.md file
Jonatan Werpers <jonatan@werpers.com>
parents:
diff changeset
2
1137
6757cc9ba22e Update notes
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 1050
diff changeset
3 ## Boundary Conditions and SATs
6757cc9ba22e Update notes
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 1050
diff changeset
4
6757cc9ba22e Update notes
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 1050
diff changeset
5 Types for boundary conditions:
6757cc9ba22e Update notes
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 1050
diff changeset
6
6757cc9ba22e Update notes
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 1050
diff changeset
7 * abstract type `BoundaryDataType`
6757cc9ba22e Update notes
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 1050
diff changeset
8 * abstract type `BoundaryCondition{T<:BoundaryDataType}`
6757cc9ba22e Update notes
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 1050
diff changeset
9 * concrete types `ConstantBoundaryData <: BoundaryDataType` and similar
6757cc9ba22e Update notes
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 1050
diff changeset
10 * concrete types `NeumannCondition{BDT<:BoundaryDataType} <: BoundaryCondition{BDT}` and similar
6757cc9ba22e Update notes
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 1050
diff changeset
11 The concrete `BoundaryDataType` subtypes are "thin types" wrapping the boundary data, and are used to indicate how the boundary data should be used in e.g. sat routines. The concrete `BoundaryCondition{BDT}` subtypes are used for assembling the tensors used to construct e.g. a SAT.
6757cc9ba22e Update notes
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 1050
diff changeset
12
6757cc9ba22e Update notes
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 1050
diff changeset
13 SAT methods:
6757cc9ba22e Update notes
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 1050
diff changeset
14 There are multiple options for what the SAT methods could return.
6757cc9ba22e Update notes
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 1050
diff changeset
15 * (Current) a function which returns a `LazyTensorApplication`, e.g. `f = sat(grid,op,bc)`. The the resulting `LazyTensorApplication` can then be added to scheme i.e. `scheme = op*u + f(u)`. This is how one typically would write the SAT in the litterature. Depdending on the type of data in the BC, e.g. time-depdendent etc one can return f(u,t).
6757cc9ba22e Update notes
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 1050
diff changeset
16 * `LazyTensor`s `closure, penalty = sat(grid,op,bc)` like in the matlab version. Probably the most general one. Up to the user to make use of the returned `LazyTensor`s. One can for example then easily include the closures to the operator and have eg. `D = (op + closure)*u`.
6757cc9ba22e Update notes
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 1050
diff changeset
17 * A `LazyTensor` for closure, and a `LazyArray` for `penalty*data`. Mix of the above.
6757cc9ba22e Update notes
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 1050
diff changeset
18
6757cc9ba22e Update notes
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 1050
diff changeset
19 It is not clear if any of these are preferable as it currently stands.
6757cc9ba22e Update notes
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 1050
diff changeset
20
654
d26231227b89 Add a bunch of notes on reading and storing operators and how to implement variable second derivatives
Jonatan Werpers <jonatan@werpers.com>
parents: 606
diff changeset
21 ## Reading operators
d26231227b89 Add a bunch of notes on reading and storing operators and how to implement variable second derivatives
Jonatan Werpers <jonatan@werpers.com>
parents: 606
diff changeset
22
d26231227b89 Add a bunch of notes on reading and storing operators and how to implement variable second derivatives
Jonatan Werpers <jonatan@werpers.com>
parents: 606
diff changeset
23 Jonatan's suggestion is to add methods to `Laplace`, `SecondDerivative` and
d26231227b89 Add a bunch of notes on reading and storing operators and how to implement variable second derivatives
Jonatan Werpers <jonatan@werpers.com>
parents: 606
diff changeset
24 similar functions that take in a filename from which to read stencils. These
d26231227b89 Add a bunch of notes on reading and storing operators and how to implement variable second derivatives
Jonatan Werpers <jonatan@werpers.com>
parents: 606
diff changeset
25 methods encode how to use the structure in a file to build the particular
d26231227b89 Add a bunch of notes on reading and storing operators and how to implement variable second derivatives
Jonatan Werpers <jonatan@werpers.com>
parents: 606
diff changeset
26 operator. The filename should be a keyword argument and could have a default
d26231227b89 Add a bunch of notes on reading and storing operators and how to implement variable second derivatives
Jonatan Werpers <jonatan@werpers.com>
parents: 606
diff changeset
27 value.
d26231227b89 Add a bunch of notes on reading and storing operators and how to implement variable second derivatives
Jonatan Werpers <jonatan@werpers.com>
parents: 606
diff changeset
28
d26231227b89 Add a bunch of notes on reading and storing operators and how to implement variable second derivatives
Jonatan Werpers <jonatan@werpers.com>
parents: 606
diff changeset
29 * This allows easy creation of operators without the user having to handle stencils.
d26231227b89 Add a bunch of notes on reading and storing operators and how to implement variable second derivatives
Jonatan Werpers <jonatan@werpers.com>
parents: 606
diff changeset
30 * The user can easily switch between sets of operators by changing the file stecils are read from.
d26231227b89 Add a bunch of notes on reading and storing operators and how to implement variable second derivatives
Jonatan Werpers <jonatan@werpers.com>
parents: 606
diff changeset
31
d26231227b89 Add a bunch of notes on reading and storing operators and how to implement variable second derivatives
Jonatan Werpers <jonatan@werpers.com>
parents: 606
diff changeset
32 Grids for optimized operators could be created by reading from a .toml file in
d26231227b89 Add a bunch of notes on reading and storing operators and how to implement variable second derivatives
Jonatan Werpers <jonatan@werpers.com>
parents: 606
diff changeset
33 a similar fashion as for the operators. The grid can then be used in a
d26231227b89 Add a bunch of notes on reading and storing operators and how to implement variable second derivatives
Jonatan Werpers <jonatan@werpers.com>
parents: 606
diff changeset
34 `Laplace` method which dispatches on the grid type and knows how to read the
d26231227b89 Add a bunch of notes on reading and storing operators and how to implement variable second derivatives
Jonatan Werpers <jonatan@werpers.com>
parents: 606
diff changeset
35 optimized operators. The method would also make sure the operators match the
d26231227b89 Add a bunch of notes on reading and storing operators and how to implement variable second derivatives
Jonatan Werpers <jonatan@werpers.com>
parents: 606
diff changeset
36 grid.
d26231227b89 Add a bunch of notes on reading and storing operators and how to implement variable second derivatives
Jonatan Werpers <jonatan@werpers.com>
parents: 606
diff changeset
37
d26231227b89 Add a bunch of notes on reading and storing operators and how to implement variable second derivatives
Jonatan Werpers <jonatan@werpers.com>
parents: 606
diff changeset
38 Idea: Make the current upper case methods lower case. Add types with the upper
d26231227b89 Add a bunch of notes on reading and storing operators and how to implement variable second derivatives
Jonatan Werpers <jonatan@werpers.com>
parents: 606
diff changeset
39 case names. These types are tensor mappings for the operator but also contain
d26231227b89 Add a bunch of notes on reading and storing operators and how to implement variable second derivatives
Jonatan Werpers <jonatan@werpers.com>
parents: 606
diff changeset
40 the associated operators as fields. For example:
d26231227b89 Add a bunch of notes on reading and storing operators and how to implement variable second derivatives
Jonatan Werpers <jonatan@werpers.com>
parents: 606
diff changeset
41
d26231227b89 Add a bunch of notes on reading and storing operators and how to implement variable second derivatives
Jonatan Werpers <jonatan@werpers.com>
parents: 606
diff changeset
42 ```julia
d26231227b89 Add a bunch of notes on reading and storing operators and how to implement variable second derivatives
Jonatan Werpers <jonatan@werpers.com>
parents: 606
diff changeset
43 L = Laplace(grid)
d26231227b89 Add a bunch of notes on reading and storing operators and how to implement variable second derivatives
Jonatan Werpers <jonatan@werpers.com>
parents: 606
diff changeset
44 L.H
d26231227b89 Add a bunch of notes on reading and storing operators and how to implement variable second derivatives
Jonatan Werpers <jonatan@werpers.com>
parents: 606
diff changeset
45 L.Hi
d26231227b89 Add a bunch of notes on reading and storing operators and how to implement variable second derivatives
Jonatan Werpers <jonatan@werpers.com>
parents: 606
diff changeset
46 L.e
d26231227b89 Add a bunch of notes on reading and storing operators and how to implement variable second derivatives
Jonatan Werpers <jonatan@werpers.com>
parents: 606
diff changeset
47 L.d
d26231227b89 Add a bunch of notes on reading and storing operators and how to implement variable second derivatives
Jonatan Werpers <jonatan@werpers.com>
parents: 606
diff changeset
48 L.M
d26231227b89 Add a bunch of notes on reading and storing operators and how to implement variable second derivatives
Jonatan Werpers <jonatan@werpers.com>
parents: 606
diff changeset
49
d26231227b89 Add a bunch of notes on reading and storing operators and how to implement variable second derivatives
Jonatan Werpers <jonatan@werpers.com>
parents: 606
diff changeset
50 wave = L - L.Hi∘L.e'∘L.d
d26231227b89 Add a bunch of notes on reading and storing operators and how to implement variable second derivatives
Jonatan Werpers <jonatan@werpers.com>
parents: 606
diff changeset
51 ```
d26231227b89 Add a bunch of notes on reading and storing operators and how to implement variable second derivatives
Jonatan Werpers <jonatan@werpers.com>
parents: 606
diff changeset
52
d26231227b89 Add a bunch of notes on reading and storing operators and how to implement variable second derivatives
Jonatan Werpers <jonatan@werpers.com>
parents: 606
diff changeset
53 These types could also contain things like borrowing and such.
d26231227b89 Add a bunch of notes on reading and storing operators and how to implement variable second derivatives
Jonatan Werpers <jonatan@werpers.com>
parents: 606
diff changeset
54
d26231227b89 Add a bunch of notes on reading and storing operators and how to implement variable second derivatives
Jonatan Werpers <jonatan@werpers.com>
parents: 606
diff changeset
55 ## Storage of operators
d26231227b89 Add a bunch of notes on reading and storing operators and how to implement variable second derivatives
Jonatan Werpers <jonatan@werpers.com>
parents: 606
diff changeset
56 We need to change the toml format so that it is easier to store several
d26231227b89 Add a bunch of notes on reading and storing operators and how to implement variable second derivatives
Jonatan Werpers <jonatan@werpers.com>
parents: 606
diff changeset
57 operator with different kinds of differentiations. For example there could be
d26231227b89 Add a bunch of notes on reading and storing operators and how to implement variable second derivatives
Jonatan Werpers <jonatan@werpers.com>
parents: 606
diff changeset
58 several operators of the same order but with different number of boundary
d26231227b89 Add a bunch of notes on reading and storing operators and how to implement variable second derivatives
Jonatan Werpers <jonatan@werpers.com>
parents: 606
diff changeset
59 points or different choice of boundary stencils.
d26231227b89 Add a bunch of notes on reading and storing operators and how to implement variable second derivatives
Jonatan Werpers <jonatan@werpers.com>
parents: 606
diff changeset
60
d26231227b89 Add a bunch of notes on reading and storing operators and how to implement variable second derivatives
Jonatan Werpers <jonatan@werpers.com>
parents: 606
diff changeset
61 Properties that differentiate operators should for this reason be stored in
d26231227b89 Add a bunch of notes on reading and storing operators and how to implement variable second derivatives
Jonatan Werpers <jonatan@werpers.com>
parents: 606
diff changeset
62 variables and not be section or table names.
d26231227b89 Add a bunch of notes on reading and storing operators and how to implement variable second derivatives
Jonatan Werpers <jonatan@werpers.com>
parents: 606
diff changeset
63
d26231227b89 Add a bunch of notes on reading and storing operators and how to implement variable second derivatives
Jonatan Werpers <jonatan@werpers.com>
parents: 606
diff changeset
64 Operators/sets of stencils should be stored in an [array of tables](https://toml.io/en/v1.0.0-rc.3#array-of-tables).
d26231227b89 Add a bunch of notes on reading and storing operators and how to implement variable second derivatives
Jonatan Werpers <jonatan@werpers.com>
parents: 606
diff changeset
65
d26231227b89 Add a bunch of notes on reading and storing operators and how to implement variable second derivatives
Jonatan Werpers <jonatan@werpers.com>
parents: 606
diff changeset
66 We should formalize the format and write simple and general access methods for
d26231227b89 Add a bunch of notes on reading and storing operators and how to implement variable second derivatives
Jonatan Werpers <jonatan@werpers.com>
parents: 606
diff changeset
67 getting operators/sets of stencils from the file. They should support a simple
d26231227b89 Add a bunch of notes on reading and storing operators and how to implement variable second derivatives
Jonatan Werpers <jonatan@werpers.com>
parents: 606
diff changeset
68 way to filter based on values of variables. There filters could possibly be
d26231227b89 Add a bunch of notes on reading and storing operators and how to implement variable second derivatives
Jonatan Werpers <jonatan@werpers.com>
parents: 606
diff changeset
69 implemented through keyword arguments that are sent through all the layers of
d26231227b89 Add a bunch of notes on reading and storing operators and how to implement variable second derivatives
Jonatan Werpers <jonatan@werpers.com>
parents: 606
diff changeset
70 operator creation.
d26231227b89 Add a bunch of notes on reading and storing operators and how to implement variable second derivatives
Jonatan Werpers <jonatan@werpers.com>
parents: 606
diff changeset
71
d26231227b89 Add a bunch of notes on reading and storing operators and how to implement variable second derivatives
Jonatan Werpers <jonatan@werpers.com>
parents: 606
diff changeset
72 * Remove order as a table name and put it as a variable.
d26231227b89 Add a bunch of notes on reading and storing operators and how to implement variable second derivatives
Jonatan Werpers <jonatan@werpers.com>
parents: 606
diff changeset
73
853
fe8fe3f01162 Docs touch up
Jonatan Werpers <jonatan@werpers.com>
parents: 829
diff changeset
74 ### Parsing of stencil sets
829
1de10f5b2008 Add some notes on the format of operator storage
Jonatan Werpers <jonatan@werpers.com>
parents: 775
diff changeset
75 At the moment the only parsing that can be done at the top level is conversion
1de10f5b2008 Add some notes on the format of operator storage
Jonatan Werpers <jonatan@werpers.com>
parents: 775
diff changeset
76 from the toml file to a dict of strings. This forces the user to dig through
1de10f5b2008 Add some notes on the format of operator storage
Jonatan Werpers <jonatan@werpers.com>
parents: 775
diff changeset
77 the dictionary and apply the correct parsing methods for the different parts,
1de10f5b2008 Add some notes on the format of operator storage
Jonatan Werpers <jonatan@werpers.com>
parents: 775
diff changeset
78 e.g. `parse_stencil` or `parse_tuple`. While very flexible there is a tight
1de10f5b2008 Add some notes on the format of operator storage
Jonatan Werpers <jonatan@werpers.com>
parents: 775
diff changeset
79 coupling between what is written in the file and what code is run to make data
1de10f5b2008 Add some notes on the format of operator storage
Jonatan Werpers <jonatan@werpers.com>
parents: 775
diff changeset
80 in the file usable. While this coupling is hard to avoid it should be made
1de10f5b2008 Add some notes on the format of operator storage
Jonatan Werpers <jonatan@werpers.com>
parents: 775
diff changeset
81 explicit. This could be done by putting a reference to a parsing function in
1de10f5b2008 Add some notes on the format of operator storage
Jonatan Werpers <jonatan@werpers.com>
parents: 775
diff changeset
82 the operator-storage format or somehow specifying the type of each object.
1de10f5b2008 Add some notes on the format of operator storage
Jonatan Werpers <jonatan@werpers.com>
parents: 775
diff changeset
83 This mechanism should be extensible without changing the package. Perhaps
1de10f5b2008 Add some notes on the format of operator storage
Jonatan Werpers <jonatan@werpers.com>
parents: 775
diff changeset
84 there could be a way to register parsing functions or object types for the
1de10f5b2008 Add some notes on the format of operator storage
Jonatan Werpers <jonatan@werpers.com>
parents: 775
diff changeset
85 toml.
1de10f5b2008 Add some notes on the format of operator storage
Jonatan Werpers <jonatan@werpers.com>
parents: 775
diff changeset
86
853
fe8fe3f01162 Docs touch up
Jonatan Werpers <jonatan@werpers.com>
parents: 829
diff changeset
87 If possible the goal should be for the parsing to get all the way to the
fe8fe3f01162 Docs touch up
Jonatan Werpers <jonatan@werpers.com>
parents: 829
diff changeset
88 stencils so that a user calls `read_stencil_set` and gets a
fe8fe3f01162 Docs touch up
Jonatan Werpers <jonatan@werpers.com>
parents: 829
diff changeset
89 dictionary-structure containing stencils, tuples, scalars and other types
fe8fe3f01162 Docs touch up
Jonatan Werpers <jonatan@werpers.com>
parents: 829
diff changeset
90 ready for input to the methods creating the operators.
654
d26231227b89 Add a bunch of notes on reading and storing operators and how to implement variable second derivatives
Jonatan Werpers <jonatan@werpers.com>
parents: 606
diff changeset
91
d26231227b89 Add a bunch of notes on reading and storing operators and how to implement variable second derivatives
Jonatan Werpers <jonatan@werpers.com>
parents: 606
diff changeset
92 ## Variable second derivative
d26231227b89 Add a bunch of notes on reading and storing operators and how to implement variable second derivatives
Jonatan Werpers <jonatan@werpers.com>
parents: 606
diff changeset
93
d26231227b89 Add a bunch of notes on reading and storing operators and how to implement variable second derivatives
Jonatan Werpers <jonatan@werpers.com>
parents: 606
diff changeset
94 2020-12-08 after discussion with Vidar:
d26231227b89 Add a bunch of notes on reading and storing operators and how to implement variable second derivatives
Jonatan Werpers <jonatan@werpers.com>
parents: 606
diff changeset
95 We will have to handle the variable second derivative in a new variant of
d26231227b89 Add a bunch of notes on reading and storing operators and how to implement variable second derivatives
Jonatan Werpers <jonatan@werpers.com>
parents: 606
diff changeset
96 VolumeOperator, "SecondDerivativeVariable?". Somehow it needs to know about
d26231227b89 Add a bunch of notes on reading and storing operators and how to implement variable second derivatives
Jonatan Werpers <jonatan@werpers.com>
parents: 606
diff changeset
97 the coefficients. They should be provided as an AbstractVector. Where they are
d26231227b89 Add a bunch of notes on reading and storing operators and how to implement variable second derivatives
Jonatan Werpers <jonatan@werpers.com>
parents: 606
diff changeset
98 provided is another question. It could be that you provide a reference to the
d26231227b89 Add a bunch of notes on reading and storing operators and how to implement variable second derivatives
Jonatan Werpers <jonatan@werpers.com>
parents: 606
diff changeset
99 array to the constructor of SecondDerivativeVariable. If that array is mutable
d26231227b89 Add a bunch of notes on reading and storing operators and how to implement variable second derivatives
Jonatan Werpers <jonatan@werpers.com>
parents: 606
diff changeset
100 you are free to change it whenever and the changes should propagate
d26231227b89 Add a bunch of notes on reading and storing operators and how to implement variable second derivatives
Jonatan Werpers <jonatan@werpers.com>
parents: 606
diff changeset
101 accordingly. Another option is that the counter part to "Laplace" for this
d26231227b89 Add a bunch of notes on reading and storing operators and how to implement variable second derivatives
Jonatan Werpers <jonatan@werpers.com>
parents: 606
diff changeset
102 variable second derivate returns a function or acts like a functions that
d26231227b89 Add a bunch of notes on reading and storing operators and how to implement variable second derivatives
Jonatan Werpers <jonatan@werpers.com>
parents: 606
diff changeset
103 takes an Abstract array and returns a SecondDerivativeVariable with the
d26231227b89 Add a bunch of notes on reading and storing operators and how to implement variable second derivatives
Jonatan Werpers <jonatan@werpers.com>
parents: 606
diff changeset
104 appropriate array. This would allow syntax like `D2(a)*v`. Can this be made
d26231227b89 Add a bunch of notes on reading and storing operators and how to implement variable second derivatives
Jonatan Werpers <jonatan@werpers.com>
parents: 606
diff changeset
105 performant?
d26231227b89 Add a bunch of notes on reading and storing operators and how to implement variable second derivatives
Jonatan Werpers <jonatan@werpers.com>
parents: 606
diff changeset
106
d26231227b89 Add a bunch of notes on reading and storing operators and how to implement variable second derivatives
Jonatan Werpers <jonatan@werpers.com>
parents: 606
diff changeset
107 For the 1d case we can have a constructor
d26231227b89 Add a bunch of notes on reading and storing operators and how to implement variable second derivatives
Jonatan Werpers <jonatan@werpers.com>
parents: 606
diff changeset
108 `SecondDerivativeVariable(D2::SecondDerivativeVariable, a)` that just creates
d26231227b89 Add a bunch of notes on reading and storing operators and how to implement variable second derivatives
Jonatan Werpers <jonatan@werpers.com>
parents: 606
diff changeset
109 a copy with a different `a`.
d26231227b89 Add a bunch of notes on reading and storing operators and how to implement variable second derivatives
Jonatan Werpers <jonatan@werpers.com>
parents: 606
diff changeset
110
d26231227b89 Add a bunch of notes on reading and storing operators and how to implement variable second derivatives
Jonatan Werpers <jonatan@werpers.com>
parents: 606
diff changeset
111 Apart from just the second derivative in 1D we need operators for higher
d26231227b89 Add a bunch of notes on reading and storing operators and how to implement variable second derivatives
Jonatan Werpers <jonatan@werpers.com>
parents: 606
diff changeset
112 dimensions. What happens if a=a(x,y)? Maybe this can be solved orthogonally to
d26231227b89 Add a bunch of notes on reading and storing operators and how to implement variable second derivatives
Jonatan Werpers <jonatan@werpers.com>
parents: 606
diff changeset
113 the `D2(a)*v` issue, meaning that if a constant nD version of
d26231227b89 Add a bunch of notes on reading and storing operators and how to implement variable second derivatives
Jonatan Werpers <jonatan@werpers.com>
parents: 606
diff changeset
114 SecondDerivativeVariable is available then maybe it can be wrapped to support
d26231227b89 Add a bunch of notes on reading and storing operators and how to implement variable second derivatives
Jonatan Werpers <jonatan@werpers.com>
parents: 606
diff changeset
115 function like syntax. We might have to implement `SecondDerivativeVariable`
d26231227b89 Add a bunch of notes on reading and storing operators and how to implement variable second derivatives
Jonatan Werpers <jonatan@werpers.com>
parents: 606
diff changeset
116 for N dimensions which takes a N dimensional a. If this could be easily
d26231227b89 Add a bunch of notes on reading and storing operators and how to implement variable second derivatives
Jonatan Werpers <jonatan@werpers.com>
parents: 606
diff changeset
117 closured to allow D(a) syntax we would have come a long way.
d26231227b89 Add a bunch of notes on reading and storing operators and how to implement variable second derivatives
Jonatan Werpers <jonatan@werpers.com>
parents: 606
diff changeset
118
d26231227b89 Add a bunch of notes on reading and storing operators and how to implement variable second derivatives
Jonatan Werpers <jonatan@werpers.com>
parents: 606
diff changeset
119 For `Laplace` which might use a variable D2 if it is on a curvilinear grid we
d26231227b89 Add a bunch of notes on reading and storing operators and how to implement variable second derivatives
Jonatan Werpers <jonatan@werpers.com>
parents: 606
diff changeset
120 might want to choose how to calculate the metric coefficients. They could be
d26231227b89 Add a bunch of notes on reading and storing operators and how to implement variable second derivatives
Jonatan Werpers <jonatan@werpers.com>
parents: 606
diff changeset
121 known on closed form, they could be calculated from the grid coordinates or
d26231227b89 Add a bunch of notes on reading and storing operators and how to implement variable second derivatives
Jonatan Werpers <jonatan@werpers.com>
parents: 606
diff changeset
122 they could be provided as a vector. Which way you want to do it might change
d26231227b89 Add a bunch of notes on reading and storing operators and how to implement variable second derivatives
Jonatan Werpers <jonatan@werpers.com>
parents: 606
diff changeset
123 depending on for example if you are memory bound or compute bound. This choice
d26231227b89 Add a bunch of notes on reading and storing operators and how to implement variable second derivatives
Jonatan Werpers <jonatan@werpers.com>
parents: 606
diff changeset
124 cannot be done on the grid since the grid shouldn't care about the computer
d26231227b89 Add a bunch of notes on reading and storing operators and how to implement variable second derivatives
Jonatan Werpers <jonatan@werpers.com>
parents: 606
diff changeset
125 architecture. The most sensible option seems to be to have an argument to the
d26231227b89 Add a bunch of notes on reading and storing operators and how to implement variable second derivatives
Jonatan Werpers <jonatan@werpers.com>
parents: 606
diff changeset
126 `Laplace` function which controls how the coefficients are gotten from the
d26231227b89 Add a bunch of notes on reading and storing operators and how to implement variable second derivatives
Jonatan Werpers <jonatan@werpers.com>
parents: 606
diff changeset
127 grid. The argument could for example be a function which is to be applied to
d26231227b89 Add a bunch of notes on reading and storing operators and how to implement variable second derivatives
Jonatan Werpers <jonatan@werpers.com>
parents: 606
diff changeset
128 the grid.
d26231227b89 Add a bunch of notes on reading and storing operators and how to implement variable second derivatives
Jonatan Werpers <jonatan@werpers.com>
parents: 606
diff changeset
129
d26231227b89 Add a bunch of notes on reading and storing operators and how to implement variable second derivatives
Jonatan Werpers <jonatan@werpers.com>
parents: 606
diff changeset
130 What happens if the grid or the varible coefficient is dependent on time?
d26231227b89 Add a bunch of notes on reading and storing operators and how to implement variable second derivatives
Jonatan Werpers <jonatan@werpers.com>
parents: 606
diff changeset
131 Maybe it becomes important to support `D(a)` or even `D(t,a)` syntax in a more
d26231227b89 Add a bunch of notes on reading and storing operators and how to implement variable second derivatives
Jonatan Werpers <jonatan@werpers.com>
parents: 606
diff changeset
132 general way.
d26231227b89 Add a bunch of notes on reading and storing operators and how to implement variable second derivatives
Jonatan Werpers <jonatan@werpers.com>
parents: 606
diff changeset
133
d26231227b89 Add a bunch of notes on reading and storing operators and how to implement variable second derivatives
Jonatan Werpers <jonatan@werpers.com>
parents: 606
diff changeset
134 ```
d26231227b89 Add a bunch of notes on reading and storing operators and how to implement variable second derivatives
Jonatan Werpers <jonatan@werpers.com>
parents: 606
diff changeset
135 g = TimeDependentGrid()
d26231227b89 Add a bunch of notes on reading and storing operators and how to implement variable second derivatives
Jonatan Werpers <jonatan@werpers.com>
parents: 606
diff changeset
136 L = Laplace(g)
d26231227b89 Add a bunch of notes on reading and storing operators and how to implement variable second derivatives
Jonatan Werpers <jonatan@werpers.com>
parents: 606
diff changeset
137 function Laplace(g::TimeDependentGrid)
d26231227b89 Add a bunch of notes on reading and storing operators and how to implement variable second derivatives
Jonatan Werpers <jonatan@werpers.com>
parents: 606
diff changeset
138 g_logical = logical(g) # g_logical is time independent
d26231227b89 Add a bunch of notes on reading and storing operators and how to implement variable second derivatives
Jonatan Werpers <jonatan@werpers.com>
parents: 606
diff changeset
139 ... Build a L(a) assuming we can do that ...
d26231227b89 Add a bunch of notes on reading and storing operators and how to implement variable second derivatives
Jonatan Werpers <jonatan@werpers.com>
parents: 606
diff changeset
140 a(t) = metric_coeffs(g,t)
d26231227b89 Add a bunch of notes on reading and storing operators and how to implement variable second derivatives
Jonatan Werpers <jonatan@werpers.com>
parents: 606
diff changeset
141 return t->L(a(t))
d26231227b89 Add a bunch of notes on reading and storing operators and how to implement variable second derivatives
Jonatan Werpers <jonatan@werpers.com>
parents: 606
diff changeset
142 end
d26231227b89 Add a bunch of notes on reading and storing operators and how to implement variable second derivatives
Jonatan Werpers <jonatan@werpers.com>
parents: 606
diff changeset
143 ```
d26231227b89 Add a bunch of notes on reading and storing operators and how to implement variable second derivatives
Jonatan Werpers <jonatan@werpers.com>
parents: 606
diff changeset
144
318
0c8d4a734c4f Add some todos and add a Notes.md file
Jonatan Werpers <jonatan@werpers.com>
parents:
diff changeset
145 ## Known size of range and domain?
320
d705b397aa33 Clean up Notes.md and TODO.md
Jonatan Werpers <jonatan@werpers.com>
parents: 319
diff changeset
146 Is there any reason to use a trait to differentiate between fixed size and unknown size?
d705b397aa33 Clean up Notes.md and TODO.md
Jonatan Werpers <jonatan@werpers.com>
parents: 319
diff changeset
147
379
de4746d6d126 Add some notes and todos
Jonatan Werpers <jonatan@werpers.com>
parents: 332
diff changeset
148 When do we need to know the size of the range and domain?
de4746d6d126 Add some notes and todos
Jonatan Werpers <jonatan@werpers.com>
parents: 332
diff changeset
149 * When indexing to provide boundschecking?
de4746d6d126 Add some notes and todos
Jonatan Werpers <jonatan@werpers.com>
parents: 332
diff changeset
150 * When doing specialised computations for different parts of the range/domain?
de4746d6d126 Add some notes and todos
Jonatan Werpers <jonatan@werpers.com>
parents: 332
diff changeset
151 * More?
319
05ac7d7f9176 Move research and thinking from TODO.md to Notes.md
Jonatan Werpers <jonatan@werpers.com>
parents: 318
diff changeset
152
995
1ba8a398af9c Rename types
Jonatan Werpers <jonatan@werpers.com>
parents: 866
diff changeset
153 Maybe if we should have dynamic sizing it could be only for the range. `domain_size` would not be implemented. And the `range_size` would be a function of a vector that the LazyTensor is applied to.
332
535f1bff4bcc Add some notes and some todos
Jonatan Werpers <jonatan@werpers.com>
parents: 320
diff changeset
154
319
05ac7d7f9176 Move research and thinking from TODO.md to Notes.md
Jonatan Werpers <jonatan@werpers.com>
parents: 318
diff changeset
155 ## Reasearch and thinking
995
1ba8a398af9c Rename types
Jonatan Werpers <jonatan@werpers.com>
parents: 866
diff changeset
156 - [ ] Use a trait to indicate that a LazyTensor har the same range and domain?
319
05ac7d7f9176 Move research and thinking from TODO.md to Notes.md
Jonatan Werpers <jonatan@werpers.com>
parents: 318
diff changeset
157 - [ ] Check how the native julia doc generator works
05ac7d7f9176 Move research and thinking from TODO.md to Notes.md
Jonatan Werpers <jonatan@werpers.com>
parents: 318
diff changeset
158 - [ ] Check if Vidars design docs fit in there
05ac7d7f9176 Move research and thinking from TODO.md to Notes.md
Jonatan Werpers <jonatan@werpers.com>
parents: 318
diff changeset
159 - [ ] Create a macro @lazy which replaces a binary op (+,-) by its lazy equivalent? Would be a neat way to indicate which evaluations are lazy without cluttering/confusing with special characters.
606
8f9b3eac128a Add a bunch of stuff to TODO.md and Notes.md
Jonatan Werpers <jonatan@werpers.com>
parents: 427
diff changeset
160 - [ ] Dispatch on Lower() instead of the type Lower so `::Lower` instead of `::Type{Lower}` ???
332
535f1bff4bcc Add some notes and some todos
Jonatan Werpers <jonatan@werpers.com>
parents: 320
diff changeset
161 Seems better unless there is some specific reason to use the type instead of the value.
379
de4746d6d126 Add some notes and todos
Jonatan Werpers <jonatan@werpers.com>
parents: 332
diff changeset
162 - [ ] How do we handle mixes of periodic and non-periodic grids? Seems it should be supported on the grid level and on the 1d operator level. Between there it should be transparent.
995
1ba8a398af9c Rename types
Jonatan Werpers <jonatan@werpers.com>
parents: 866
diff changeset
163 - [ ] Can we have a trait to tell if a LazyTensor is transposable?
379
de4746d6d126 Add some notes and todos
Jonatan Werpers <jonatan@werpers.com>
parents: 332
diff changeset
164 - [ ] Is it ok to have "Constructors" for abstract types which create subtypes? For example a Grids() functions that gives different kind of grids based on input?
663
f1803ab08740 Add Note on how we should treat the borrowing parameters of operators.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 654
diff changeset
165 - [ ] Figure out how to treat the borrowing parameters of operators. Include in into the struct? Expose via function dispatched on the operator type and grid?
410
26e186b565b3 Add some notes about vector valued grid functions
Jonatan Werpers <jonatan@werpers.com>
parents: 379
diff changeset
166
1050
396278072f18 Add some notes and clean up TODO.md a little bit
Jonatan Werpers <jonatan@werpers.com>
parents: 1041
diff changeset
167 ## Identifiers for regions
396278072f18 Add some notes and clean up TODO.md a little bit
Jonatan Werpers <jonatan@werpers.com>
parents: 1041
diff changeset
168 The identifiers (`Upper`, `Lower`, `Interior`) used for region indecies should probabily be included in the grid module. This allows new grid types to come with their own regions.
396278072f18 Add some notes and clean up TODO.md a little bit
Jonatan Werpers <jonatan@werpers.com>
parents: 1041
diff changeset
169
606
8f9b3eac128a Add a bunch of stuff to TODO.md and Notes.md
Jonatan Werpers <jonatan@werpers.com>
parents: 427
diff changeset
170 ## Regions and tensormappings
995
1ba8a398af9c Rename types
Jonatan Werpers <jonatan@werpers.com>
parents: 866
diff changeset
171 - [ ] Use a trait to indicate if a LazyTensor uses indices with regions.
606
8f9b3eac128a Add a bunch of stuff to TODO.md and Notes.md
Jonatan Werpers <jonatan@werpers.com>
parents: 427
diff changeset
172 The default should be that they do NOT.
8f9b3eac128a Add a bunch of stuff to TODO.md and Notes.md
Jonatan Werpers <jonatan@werpers.com>
parents: 427
diff changeset
173 - [ ] What to name this trait? Can we call it IndexStyle but not export it to avoid conflicts with Base.IndexStyle?
995
1ba8a398af9c Rename types
Jonatan Werpers <jonatan@werpers.com>
parents: 866
diff changeset
174 - [ ] Figure out repeated application of regioned LazyTensors. Maybe an instance of a tensor mapping needs to know the exact size of the range and domain for this to work?
606
8f9b3eac128a Add a bunch of stuff to TODO.md and Notes.md
Jonatan Werpers <jonatan@werpers.com>
parents: 427
diff changeset
175
1050
396278072f18 Add some notes and clean up TODO.md a little bit
Jonatan Werpers <jonatan@werpers.com>
parents: 1041
diff changeset
176 ### Ideas for information sharing functions
396278072f18 Add some notes and clean up TODO.md a little bit
Jonatan Werpers <jonatan@werpers.com>
parents: 1041
diff changeset
177 ```julia
396278072f18 Add some notes and clean up TODO.md a little bit
Jonatan Werpers <jonatan@werpers.com>
parents: 1041
diff changeset
178 using StaticArrays
396278072f18 Add some notes and clean up TODO.md a little bit
Jonatan Werpers <jonatan@werpers.com>
parents: 1041
diff changeset
179
396278072f18 Add some notes and clean up TODO.md a little bit
Jonatan Werpers <jonatan@werpers.com>
parents: 1041
diff changeset
180 function regions(op::SecondDerivativeVariable)
396278072f18 Add some notes and clean up TODO.md a little bit
Jonatan Werpers <jonatan@werpers.com>
parents: 1041
diff changeset
181 t = ntuple(i->(Interior(),),range_dim(op))
396278072f18 Add some notes and clean up TODO.md a little bit
Jonatan Werpers <jonatan@werpers.com>
parents: 1041
diff changeset
182 return Base.setindex(t, (Lower(), Interior(), Upper()), derivative_direction(op))
396278072f18 Add some notes and clean up TODO.md a little bit
Jonatan Werpers <jonatan@werpers.com>
parents: 1041
diff changeset
183 end
396278072f18 Add some notes and clean up TODO.md a little bit
Jonatan Werpers <jonatan@werpers.com>
parents: 1041
diff changeset
184
396278072f18 Add some notes and clean up TODO.md a little bit
Jonatan Werpers <jonatan@werpers.com>
parents: 1041
diff changeset
185 function regionsizes(op::SecondDerivativeVariable)
396278072f18 Add some notes and clean up TODO.md a little bit
Jonatan Werpers <jonatan@werpers.com>
parents: 1041
diff changeset
186 sz = tuple.(range_size(op))
396278072f18 Add some notes and clean up TODO.md a little bit
Jonatan Werpers <jonatan@werpers.com>
parents: 1041
diff changeset
187
396278072f18 Add some notes and clean up TODO.md a little bit
Jonatan Werpers <jonatan@werpers.com>
parents: 1041
diff changeset
188 cl = closuresize(op)
396278072f18 Add some notes and clean up TODO.md a little bit
Jonatan Werpers <jonatan@werpers.com>
parents: 1041
diff changeset
189 return Base.setindex(sz, (cl, n-2cl, cl), derivative_direction(op))
396278072f18 Add some notes and clean up TODO.md a little bit
Jonatan Werpers <jonatan@werpers.com>
parents: 1041
diff changeset
190 end
396278072f18 Add some notes and clean up TODO.md a little bit
Jonatan Werpers <jonatan@werpers.com>
parents: 1041
diff changeset
191
396278072f18 Add some notes and clean up TODO.md a little bit
Jonatan Werpers <jonatan@werpers.com>
parents: 1041
diff changeset
192
396278072f18 Add some notes and clean up TODO.md a little bit
Jonatan Werpers <jonatan@werpers.com>
parents: 1041
diff changeset
193 g = EquidistantGrid((11,9), (0.,0.), (10.,8.)) # h = 1
396278072f18 Add some notes and clean up TODO.md a little bit
Jonatan Werpers <jonatan@werpers.com>
parents: 1041
diff changeset
194 c = evalOn(g, (x,y)->x+y)
396278072f18 Add some notes and clean up TODO.md a little bit
Jonatan Werpers <jonatan@werpers.com>
parents: 1041
diff changeset
195
396278072f18 Add some notes and clean up TODO.md a little bit
Jonatan Werpers <jonatan@werpers.com>
parents: 1041
diff changeset
196 D₂ᶜ = SecondDerivativeVariable(g, c, interior_stencil, closure_stencils,1)
396278072f18 Add some notes and clean up TODO.md a little bit
Jonatan Werpers <jonatan@werpers.com>
parents: 1041
diff changeset
197 @test regions(D₂ᶜ) == (
396278072f18 Add some notes and clean up TODO.md a little bit
Jonatan Werpers <jonatan@werpers.com>
parents: 1041
diff changeset
198 (Lower(), Interior(), Upper()),
396278072f18 Add some notes and clean up TODO.md a little bit
Jonatan Werpers <jonatan@werpers.com>
parents: 1041
diff changeset
199 (Interior(),),
396278072f18 Add some notes and clean up TODO.md a little bit
Jonatan Werpers <jonatan@werpers.com>
parents: 1041
diff changeset
200 )
396278072f18 Add some notes and clean up TODO.md a little bit
Jonatan Werpers <jonatan@werpers.com>
parents: 1041
diff changeset
201 @test regionsizes(D₂ᶜ) == ((1,9,1),(9,))
396278072f18 Add some notes and clean up TODO.md a little bit
Jonatan Werpers <jonatan@werpers.com>
parents: 1041
diff changeset
202
396278072f18 Add some notes and clean up TODO.md a little bit
Jonatan Werpers <jonatan@werpers.com>
parents: 1041
diff changeset
203
396278072f18 Add some notes and clean up TODO.md a little bit
Jonatan Werpers <jonatan@werpers.com>
parents: 1041
diff changeset
204 D₂ᶜ = SecondDerivativeVariable(g, c, interior_stencil, closure_stencils,2)
396278072f18 Add some notes and clean up TODO.md a little bit
Jonatan Werpers <jonatan@werpers.com>
parents: 1041
diff changeset
205 @test regions(D₂ᶜ) == (
396278072f18 Add some notes and clean up TODO.md a little bit
Jonatan Werpers <jonatan@werpers.com>
parents: 1041
diff changeset
206 (Interior(),),
396278072f18 Add some notes and clean up TODO.md a little bit
Jonatan Werpers <jonatan@werpers.com>
parents: 1041
diff changeset
207 (Lower(), Interior(), Upper()),
396278072f18 Add some notes and clean up TODO.md a little bit
Jonatan Werpers <jonatan@werpers.com>
parents: 1041
diff changeset
208 )
396278072f18 Add some notes and clean up TODO.md a little bit
Jonatan Werpers <jonatan@werpers.com>
parents: 1041
diff changeset
209 @test regionsizes(D₂ᶜ) == ((11,),(1,7,1))
396278072f18 Add some notes and clean up TODO.md a little bit
Jonatan Werpers <jonatan@werpers.com>
parents: 1041
diff changeset
210 ```
396278072f18 Add some notes and clean up TODO.md a little bit
Jonatan Werpers <jonatan@werpers.com>
parents: 1041
diff changeset
211
396278072f18 Add some notes and clean up TODO.md a little bit
Jonatan Werpers <jonatan@werpers.com>
parents: 1041
diff changeset
212
606
8f9b3eac128a Add a bunch of stuff to TODO.md and Notes.md
Jonatan Werpers <jonatan@werpers.com>
parents: 427
diff changeset
213 ## Boundschecking and dimension checking
8f9b3eac128a Add a bunch of stuff to TODO.md and Notes.md
Jonatan Werpers <jonatan@werpers.com>
parents: 427
diff changeset
214 Does it make sense to have boundschecking only in getindex methods?
8f9b3eac128a Add a bunch of stuff to TODO.md and Notes.md
Jonatan Werpers <jonatan@werpers.com>
parents: 427
diff changeset
215 This would mean no bounds checking in applys, however any indexing that they do would be boundschecked. The only loss would be readability of errors. But users aren't really supposed to call apply directly anyway.
8f9b3eac128a Add a bunch of stuff to TODO.md and Notes.md
Jonatan Werpers <jonatan@werpers.com>
parents: 427
diff changeset
216
8f9b3eac128a Add a bunch of stuff to TODO.md and Notes.md
Jonatan Werpers <jonatan@werpers.com>
parents: 427
diff changeset
217 Preferably dimensions and sizes should be checked when lazy objects are created, for example TensorApplication, TensorComposition and so on. If dimension checks decreases performance we can make them skippable later.
8f9b3eac128a Add a bunch of stuff to TODO.md and Notes.md
Jonatan Werpers <jonatan@werpers.com>
parents: 427
diff changeset
218
410
26e186b565b3 Add some notes about vector valued grid functions
Jonatan Werpers <jonatan@werpers.com>
parents: 379
diff changeset
219 ## Vector valued grid functions
26e186b565b3 Add some notes about vector valued grid functions
Jonatan Werpers <jonatan@werpers.com>
parents: 379
diff changeset
220 Från slack konversation:
26e186b565b3 Add some notes about vector valued grid functions
Jonatan Werpers <jonatan@werpers.com>
parents: 379
diff changeset
221
26e186b565b3 Add some notes about vector valued grid functions
Jonatan Werpers <jonatan@werpers.com>
parents: 379
diff changeset
222 Jonatan Werpers:
26e186b565b3 Add some notes about vector valued grid functions
Jonatan Werpers <jonatan@werpers.com>
parents: 379
diff changeset
223 Med vektorvärda gridfunktioner vill vi ju fortfarande att grid funktionen ska vara till exempel AbstractArray{LitenVektor,2}
26e186b565b3 Add some notes about vector valued grid functions
Jonatan Werpers <jonatan@werpers.com>
parents: 379
diff changeset
224 Och att man ska kunna göra allt man vill med LitenVektor
26e186b565b3 Add some notes about vector valued grid functions
Jonatan Werpers <jonatan@werpers.com>
parents: 379
diff changeset
225 typ addera, jämföra osv
26e186b565b3 Add some notes about vector valued grid functions
Jonatan Werpers <jonatan@werpers.com>
parents: 379
diff changeset
226 Och då borde points returnera AbstractArray{LitenVektor{Float,2},2} för ett 2d nät
26e186b565b3 Add some notes about vector valued grid functions
Jonatan Werpers <jonatan@werpers.com>
parents: 379
diff changeset
227 Men det kanske bara ska vara Static arrays?
26e186b565b3 Add some notes about vector valued grid functions
Jonatan Werpers <jonatan@werpers.com>
parents: 379
diff changeset
228
26e186b565b3 Add some notes about vector valued grid functions
Jonatan Werpers <jonatan@werpers.com>
parents: 379
diff changeset
229 Vidar Stiernström:
26e186b565b3 Add some notes about vector valued grid functions
Jonatan Werpers <jonatan@werpers.com>
parents: 379
diff changeset
230 Ja, jag vet inte riktigt vad som är en rimlig representation
26e186b565b3 Add some notes about vector valued grid functions
Jonatan Werpers <jonatan@werpers.com>
parents: 379
diff changeset
231 Du menar en vektor av static arrays då?
26e186b565b3 Add some notes about vector valued grid functions
Jonatan Werpers <jonatan@werpers.com>
parents: 379
diff changeset
232
26e186b565b3 Add some notes about vector valued grid functions
Jonatan Werpers <jonatan@werpers.com>
parents: 379
diff changeset
233 Jonatan Werpers:
26e186b565b3 Add some notes about vector valued grid functions
Jonatan Werpers <jonatan@werpers.com>
parents: 379
diff changeset
234 Ja, att LitenVektor är en StaticArray
26e186b565b3 Add some notes about vector valued grid functions
Jonatan Werpers <jonatan@werpers.com>
parents: 379
diff changeset
235
26e186b565b3 Add some notes about vector valued grid functions
Jonatan Werpers <jonatan@werpers.com>
parents: 379
diff changeset
236 Vidar Stiernström:
26e186b565b3 Add some notes about vector valued grid functions
Jonatan Werpers <jonatan@werpers.com>
parents: 379
diff changeset
237 Tuplar känns typ rätt inuitivt för att representera värdet i en punkt
26e186b565b3 Add some notes about vector valued grid functions
Jonatan Werpers <jonatan@werpers.com>
parents: 379
diff changeset
238 men
26e186b565b3 Add some notes about vector valued grid functions
Jonatan Werpers <jonatan@werpers.com>
parents: 379
diff changeset
239 det suger att man inte har + och - för dem
26e186b565b3 Add some notes about vector valued grid functions
Jonatan Werpers <jonatan@werpers.com>
parents: 379
diff changeset
240
26e186b565b3 Add some notes about vector valued grid functions
Jonatan Werpers <jonatan@werpers.com>
parents: 379
diff changeset
241 Jonatan Werpers:
26e186b565b3 Add some notes about vector valued grid functions
Jonatan Werpers <jonatan@werpers.com>
parents: 379
diff changeset
242 Ja precis
26e186b565b3 Add some notes about vector valued grid functions
Jonatan Werpers <jonatan@werpers.com>
parents: 379
diff changeset
243
26e186b565b3 Add some notes about vector valued grid functions
Jonatan Werpers <jonatan@werpers.com>
parents: 379
diff changeset
244 Vidar Stiernström:
26e186b565b3 Add some notes about vector valued grid functions
Jonatan Werpers <jonatan@werpers.com>
parents: 379
diff changeset
245 så kanske är bra med static arrays i detta fall
26e186b565b3 Add some notes about vector valued grid functions
Jonatan Werpers <jonatan@werpers.com>
parents: 379
diff changeset
246
26e186b565b3 Add some notes about vector valued grid functions
Jonatan Werpers <jonatan@werpers.com>
parents: 379
diff changeset
247 Jonatan Werpers:
26e186b565b3 Add some notes about vector valued grid functions
Jonatan Werpers <jonatan@werpers.com>
parents: 379
diff changeset
248 Man vill ju kunna köra en Operator rakt på och vara klar eller?
26e186b565b3 Add some notes about vector valued grid functions
Jonatan Werpers <jonatan@werpers.com>
parents: 379
diff changeset
249
26e186b565b3 Add some notes about vector valued grid functions
Jonatan Werpers <jonatan@werpers.com>
parents: 379
diff changeset
250 Vidar Stiernström:
26e186b565b3 Add some notes about vector valued grid functions
Jonatan Werpers <jonatan@werpers.com>
parents: 379
diff changeset
251 Har inte alls tänkt på hur det vi gör funkar mot vektorvärda funktioner
26e186b565b3 Add some notes about vector valued grid functions
Jonatan Werpers <jonatan@werpers.com>
parents: 379
diff changeset
252 men känns som staticarrays är hur man vill göra det
26e186b565b3 Add some notes about vector valued grid functions
Jonatan Werpers <jonatan@werpers.com>
parents: 379
diff changeset
253 tuplar är ju immutable också
26e186b565b3 Add some notes about vector valued grid functions
Jonatan Werpers <jonatan@werpers.com>
parents: 379
diff changeset
254 blir jobbigt om man bara agerar på en komponent då
26e186b565b3 Add some notes about vector valued grid functions
Jonatan Werpers <jonatan@werpers.com>
parents: 379
diff changeset
255
26e186b565b3 Add some notes about vector valued grid functions
Jonatan Werpers <jonatan@werpers.com>
parents: 379
diff changeset
256 Jonatan Werpers:
26e186b565b3 Add some notes about vector valued grid functions
Jonatan Werpers <jonatan@werpers.com>
parents: 379
diff changeset
257 Hm…
26e186b565b3 Add some notes about vector valued grid functions
Jonatan Werpers <jonatan@werpers.com>
parents: 379
diff changeset
258 Tål att tänkas på
26e186b565b3 Add some notes about vector valued grid functions
Jonatan Werpers <jonatan@werpers.com>
parents: 379
diff changeset
259 Men det lär ju bli mer indirektion med mutables eller?
26e186b565b3 Add some notes about vector valued grid functions
Jonatan Werpers <jonatan@werpers.com>
parents: 379
diff changeset
260 Hur fungerar det?
26e186b565b3 Add some notes about vector valued grid functions
Jonatan Werpers <jonatan@werpers.com>
parents: 379
diff changeset
261 Det finns ju hur som helst både SVector och MVector i StaticArrays
26e186b565b3 Add some notes about vector valued grid functions
Jonatan Werpers <jonatan@werpers.com>
parents: 379
diff changeset
262
26e186b565b3 Add some notes about vector valued grid functions
Jonatan Werpers <jonatan@werpers.com>
parents: 379
diff changeset
263 Vidar Stiernström:
26e186b565b3 Add some notes about vector valued grid functions
Jonatan Werpers <jonatan@werpers.com>
parents: 379
diff changeset
264 När vi jobbat i c/c++ och kollat runt lite hur man brukar göra så lagrar man i princip alla sina obekanta i en lång vektor och så får man specificera i funktioerna vilken komponent man agerar på och till vilken man skriver
26e186b565b3 Add some notes about vector valued grid functions
Jonatan Werpers <jonatan@werpers.com>
parents: 379
diff changeset
265 så man lagrar grejer enl: w = [u1, v1, u2, v2, …] i 1D.
26e186b565b3 Add some notes about vector valued grid functions
Jonatan Werpers <jonatan@werpers.com>
parents: 379
diff changeset
266 Men alltså har ingen aning hur julia hanterar detta
26e186b565b3 Add some notes about vector valued grid functions
Jonatan Werpers <jonatan@werpers.com>
parents: 379
diff changeset
267
26e186b565b3 Add some notes about vector valued grid functions
Jonatan Werpers <jonatan@werpers.com>
parents: 379
diff changeset
268 Jonatan Werpers:
26e186b565b3 Add some notes about vector valued grid functions
Jonatan Werpers <jonatan@werpers.com>
parents: 379
diff changeset
269 Det vi är ute efter kanske är att en grid funcktion är en AbstractArray{T,2} where T<:NågotSomViKanRäknaMed
26e186b565b3 Add some notes about vector valued grid functions
Jonatan Werpers <jonatan@werpers.com>
parents: 379
diff changeset
270 Och så får den typen var lite vad som helst.
26e186b565b3 Add some notes about vector valued grid functions
Jonatan Werpers <jonatan@werpers.com>
parents: 379
diff changeset
271
26e186b565b3 Add some notes about vector valued grid functions
Jonatan Werpers <jonatan@werpers.com>
parents: 379
diff changeset
272 Vidar Stiernström:
26e186b565b3 Add some notes about vector valued grid functions
Jonatan Werpers <jonatan@werpers.com>
parents: 379
diff changeset
273 Tror det kan vara farligt att ha nåt som är AbstractArray{LitenArray{NDof},Dim}
26e186b565b3 Add some notes about vector valued grid functions
Jonatan Werpers <jonatan@werpers.com>
parents: 379
diff changeset
274 Jag gissar att det kompilatorn vill ha är en stor array med doubles
26e186b565b3 Add some notes about vector valued grid functions
Jonatan Werpers <jonatan@werpers.com>
parents: 379
diff changeset
275
26e186b565b3 Add some notes about vector valued grid functions
Jonatan Werpers <jonatan@werpers.com>
parents: 379
diff changeset
276 Jonatan Werpers:
26e186b565b3 Add some notes about vector valued grid functions
Jonatan Werpers <jonatan@werpers.com>
parents: 379
diff changeset
277 Och sen är det upp till den som använder grejerna att vara smart
26e186b565b3 Add some notes about vector valued grid functions
Jonatan Werpers <jonatan@werpers.com>
parents: 379
diff changeset
278 Vill man vara trixig kan man väl då imlementera SuperHaxxorGridFunction <: AbstractArray{Array{…},2} som lagrar allt linjärt eller något sånt
26e186b565b3 Add some notes about vector valued grid functions
Jonatan Werpers <jonatan@werpers.com>
parents: 379
diff changeset
279 Det kommer väl lösa sig när man börjar implementera vektorvärda saker
26e186b565b3 Add some notes about vector valued grid functions
Jonatan Werpers <jonatan@werpers.com>
parents: 379
diff changeset
280 Euler nästa!
26e186b565b3 Add some notes about vector valued grid functions
Jonatan Werpers <jonatan@werpers.com>
parents: 379
diff changeset
281 New
26e186b565b3 Add some notes about vector valued grid functions
Jonatan Werpers <jonatan@werpers.com>
parents: 379
diff changeset
282 Vidar Stiernström:
26e186b565b3 Add some notes about vector valued grid functions
Jonatan Werpers <jonatan@werpers.com>
parents: 379
diff changeset
283 Det vore skönt att inte behöva skriva såhär varje gång man testar mot en tupel :smile: @test [gp[i]...] ≈ [p[i]...] atol=5e-13
26e186b565b3 Add some notes about vector valued grid functions
Jonatan Werpers <jonatan@werpers.com>
parents: 379
diff changeset
284
26e186b565b3 Add some notes about vector valued grid functions
Jonatan Werpers <jonatan@werpers.com>
parents: 379
diff changeset
285 Jonatan Werpers:
26e186b565b3 Add some notes about vector valued grid functions
Jonatan Werpers <jonatan@werpers.com>
parents: 379
diff changeset
286 https://github.com/JuliaArrays/ArraysOfArrays.jl
26e186b565b3 Add some notes about vector valued grid functions
Jonatan Werpers <jonatan@werpers.com>
parents: 379
diff changeset
287 https://github.com/jw3126/Setfield.jl
423
10a67ac48d6e Add some notes
Jonatan Werpers <jonatan@werpers.com>
parents: 410
diff changeset
288
10a67ac48d6e Add some notes
Jonatan Werpers <jonatan@werpers.com>
parents: 410
diff changeset
289 ### Test-applikationer
10a67ac48d6e Add some notes
Jonatan Werpers <jonatan@werpers.com>
parents: 410
diff changeset
290 div och grad operationer
10a67ac48d6e Add some notes
Jonatan Werpers <jonatan@werpers.com>
parents: 410
diff changeset
291
606
8f9b3eac128a Add a bunch of stuff to TODO.md and Notes.md
Jonatan Werpers <jonatan@werpers.com>
parents: 427
diff changeset
292 Enligt Wikipedia verkar det som att `∇⋅` agerar på första dimensionen av ett tensor fält och `div()` på sista.
8f9b3eac128a Add a bunch of stuff to TODO.md and Notes.md
Jonatan Werpers <jonatan@werpers.com>
parents: 427
diff changeset
293 Om man generaliserar kanske `∇` i så fall bara lägger till en dimension i början.
8f9b3eac128a Add a bunch of stuff to TODO.md and Notes.md
Jonatan Werpers <jonatan@werpers.com>
parents: 427
diff changeset
294
8f9b3eac128a Add a bunch of stuff to TODO.md and Notes.md
Jonatan Werpers <jonatan@werpers.com>
parents: 427
diff changeset
295 Kan vi implementera `⋅`(\cdot) så att de fungerar som man vill för både tensor-fält och tensor-operatorer?
427
1c41f4fd3e61 Add some notes and todos
Jonatan Werpers <jonatan@werpers.com>
parents: 423
diff changeset
296
606
8f9b3eac128a Add a bunch of stuff to TODO.md and Notes.md
Jonatan Werpers <jonatan@werpers.com>
parents: 427
diff changeset
297 Är `∇` ett tensor-fält av tensor-operatorer? Vad är ett tensor-fält i vår kod? Är det en special-fall av en tensor-mapping?
427
1c41f4fd3e61 Add some notes and todos
Jonatan Werpers <jonatan@werpers.com>
parents: 423
diff changeset
298
606
8f9b3eac128a Add a bunch of stuff to TODO.md and Notes.md
Jonatan Werpers <jonatan@werpers.com>
parents: 427
diff changeset
299 ### Grid-funktionen
8f9b3eac128a Add a bunch of stuff to TODO.md and Notes.md
Jonatan Werpers <jonatan@werpers.com>
parents: 427
diff changeset
300 Grid-funktionon har typen `AbstractArray{T,2} where T`.
8f9b3eac128a Add a bunch of stuff to TODO.md and Notes.md
Jonatan Werpers <jonatan@werpers.com>
parents: 427
diff changeset
301 `T` kan vara lite vad som helst, tillexemel en SVector eller Array, eller tuple. TensorOperatorerna bryr sig inte om exakt vad det är, mer än att typen måste stödja de operationer som operatorn använder.
8f9b3eac128a Add a bunch of stuff to TODO.md and Notes.md
Jonatan Werpers <jonatan@werpers.com>
parents: 427
diff changeset
302
8f9b3eac128a Add a bunch of stuff to TODO.md and Notes.md
Jonatan Werpers <jonatan@werpers.com>
parents: 427
diff changeset
303 En nackdel kan vara hur man ska få ut gridfunktionen för tex andra komponenten.
427
1c41f4fd3e61 Add some notes and todos
Jonatan Werpers <jonatan@werpers.com>
parents: 423
diff changeset
304
1c41f4fd3e61 Add some notes and todos
Jonatan Werpers <jonatan@werpers.com>
parents: 423
diff changeset
305 Syntax:
1c41f4fd3e61 Add some notes and todos
Jonatan Werpers <jonatan@werpers.com>
parents: 423
diff changeset
306 ```
606
8f9b3eac128a Add a bunch of stuff to TODO.md and Notes.md
Jonatan Werpers <jonatan@werpers.com>
parents: 427
diff changeset
307 f(x̄) = x̄
8f9b3eac128a Add a bunch of stuff to TODO.md and Notes.md
Jonatan Werpers <jonatan@werpers.com>
parents: 427
diff changeset
308 gf = evalOn(g, f)
8f9b3eac128a Add a bunch of stuff to TODO.md and Notes.md
Jonatan Werpers <jonatan@werpers.com>
parents: 427
diff changeset
309 gf[2,3] # x̄ för en viss gridpunkt
8f9b3eac128a Add a bunch of stuff to TODO.md and Notes.md
Jonatan Werpers <jonatan@werpers.com>
parents: 427
diff changeset
310 gf[2,3][2] # x̄[2] för en viss gridpunkt
427
1c41f4fd3e61 Add some notes and todos
Jonatan Werpers <jonatan@werpers.com>
parents: 423
diff changeset
311 ```
1c41f4fd3e61 Add some notes and todos
Jonatan Werpers <jonatan@werpers.com>
parents: 423
diff changeset
312
606
8f9b3eac128a Add a bunch of stuff to TODO.md and Notes.md
Jonatan Werpers <jonatan@werpers.com>
parents: 427
diff changeset
313 Note: Behöver bestämma om eval on skickar in `x̄` eller `x̄...` till `f`. Eller om man kan stödja båda.
427
1c41f4fd3e61 Add some notes and todos
Jonatan Werpers <jonatan@werpers.com>
parents: 423
diff changeset
314
606
8f9b3eac128a Add a bunch of stuff to TODO.md and Notes.md
Jonatan Werpers <jonatan@werpers.com>
parents: 427
diff changeset
315 ### Tensor operatorer
8f9b3eac128a Add a bunch of stuff to TODO.md and Notes.md
Jonatan Werpers <jonatan@werpers.com>
parents: 427
diff changeset
316 Vi kan ha tensor-operatorer som agerar på ett skalärt fält och ger ett vektorfält eller tensorfält.
8f9b3eac128a Add a bunch of stuff to TODO.md and Notes.md
Jonatan Werpers <jonatan@werpers.com>
parents: 427
diff changeset
317 Vi kan också ha tensor-operatorer som agerar på ett vektorfält eller tensorfält och ger ett skalärt fält.
8f9b3eac128a Add a bunch of stuff to TODO.md and Notes.md
Jonatan Werpers <jonatan@werpers.com>
parents: 427
diff changeset
318
995
1ba8a398af9c Rename types
Jonatan Werpers <jonatan@werpers.com>
parents: 866
diff changeset
319 TBD: Just nu gör `apply_transpose` antagandet att domän-typen är samma som range-typen. Det behöver vi på något sätt bryta. Ett alternativ är låta en LazyTensor ha `T_domain` och `T_range` istället för bara `T`. Känns dock lite grötigt. Ett annat alternativ skulle vara någon typ av trait för transpose? Den skulle kunna innehålla typen som transponatet agerar på? Vet inte om det fungerar dock.
606
8f9b3eac128a Add a bunch of stuff to TODO.md and Notes.md
Jonatan Werpers <jonatan@werpers.com>
parents: 427
diff changeset
320
995
1ba8a398af9c Rename types
Jonatan Werpers <jonatan@werpers.com>
parents: 866
diff changeset
321 TBD: Vad är målet med `T`-parametern för en LazyTensor? Om vi vill kunna applicera en difference operator på vad som helst kan man inte anta att en `LazyTensor{T}` bara agerar på instanser av `T`.
427
1c41f4fd3e61 Add some notes and todos
Jonatan Werpers <jonatan@werpers.com>
parents: 423
diff changeset
322
606
8f9b3eac128a Add a bunch of stuff to TODO.md and Notes.md
Jonatan Werpers <jonatan@werpers.com>
parents: 427
diff changeset
323 Man kan implementera `∇` som en tensormapping som agerar på T och returnerar `StaticVector{N,T} where N`.
8f9b3eac128a Add a bunch of stuff to TODO.md and Notes.md
Jonatan Werpers <jonatan@werpers.com>
parents: 427
diff changeset
324 (Man skulle eventuellt också kunna låta den agera på `StaticMatrix{N,T,D} where N` och returnera `StaticMatrix{M,T,D+1}`. Frågan är om man vinner något på det...)
8f9b3eac128a Add a bunch of stuff to TODO.md and Notes.md
Jonatan Werpers <jonatan@werpers.com>
parents: 427
diff changeset
325
995
1ba8a398af9c Rename types
Jonatan Werpers <jonatan@werpers.com>
parents: 866
diff changeset
326 Skulle kunna ha en funktion `range_type(::LazyTensor, ::Type{domain_type})`
606
8f9b3eac128a Add a bunch of stuff to TODO.md and Notes.md
Jonatan Werpers <jonatan@werpers.com>
parents: 427
diff changeset
327
995
1ba8a398af9c Rename types
Jonatan Werpers <jonatan@werpers.com>
parents: 866
diff changeset
328 Kanske kan man implementera `⋅(tm::LazyTensor{R,D}, v::AbstractArray{T,D})` där T är en AbstractArray, tm på något sätt har komponenter, lika många som T har element.
606
8f9b3eac128a Add a bunch of stuff to TODO.md and Notes.md
Jonatan Werpers <jonatan@werpers.com>
parents: 427
diff changeset
329
8f9b3eac128a Add a bunch of stuff to TODO.md and Notes.md
Jonatan Werpers <jonatan@werpers.com>
parents: 427
diff changeset
330 ### Ratade alternativ:
8f9b3eac128a Add a bunch of stuff to TODO.md and Notes.md
Jonatan Werpers <jonatan@werpers.com>
parents: 427
diff changeset
331
8f9b3eac128a Add a bunch of stuff to TODO.md and Notes.md
Jonatan Werpers <jonatan@werpers.com>
parents: 427
diff changeset
332
8f9b3eac128a Add a bunch of stuff to TODO.md and Notes.md
Jonatan Werpers <jonatan@werpers.com>
parents: 427
diff changeset
333 #### 2.AbstractArray{T,2+1} where T (NOPE!)
8f9b3eac128a Add a bunch of stuff to TODO.md and Notes.md
Jonatan Werpers <jonatan@werpers.com>
parents: 427
diff changeset
334 Blir inte den här. Bryter mot alla tankar om hur grid funktioner ska fungera. Om de tillåts ha en annan dimension än nätet blir allt hemskt.
8f9b3eac128a Add a bunch of stuff to TODO.md and Notes.md
Jonatan Werpers <jonatan@werpers.com>
parents: 427
diff changeset
335
427
1c41f4fd3e61 Add some notes and todos
Jonatan Werpers <jonatan@werpers.com>
parents: 423
diff changeset
336 Man låter helt enkelt arrayen ha en extra dimension. En fördel är att man har en väldigt "native" typ. En nackdel kan vara att det eventuellt blir rörigt vilken dimension olika operatorer ska agera på. I värsta fall behöver vi "kroneckra in" de tillagda dimensionerna. Vektorfältets index kommer också att bli det första eftersom vi vill att de ska lagras kontinuerligt i minnet pga chachen. (Går kanske att lösa med en custom typ men då krånglar man till det för sig). En fördel skulle vara att man enkelt får ut olika komponenter.
1c41f4fd3e61 Add some notes and todos
Jonatan Werpers <jonatan@werpers.com>
parents: 423
diff changeset
337
1c41f4fd3e61 Add some notes and todos
Jonatan Werpers <jonatan@werpers.com>
parents: 423
diff changeset
338 Syntax:
1c41f4fd3e61 Add some notes and todos
Jonatan Werpers <jonatan@werpers.com>
parents: 423
diff changeset
339 ```
1c41f4fd3e61 Add some notes and todos
Jonatan Werpers <jonatan@werpers.com>
parents: 423
diff changeset
340 gf = eval_on_grid(g,f)
1c41f4fd3e61 Add some notes and todos
Jonatan Werpers <jonatan@werpers.com>
parents: 423
diff changeset
341 gf[:,2,3] # Hela vektorn för en gridpunkt
1c41f4fd3e61 Add some notes and todos
Jonatan Werpers <jonatan@werpers.com>
parents: 423
diff changeset
342 gf[2,2,3] # Andra komponenten av vektor fältet i en punkt.
1c41f4fd3e61 Add some notes and todos
Jonatan Werpers <jonatan@werpers.com>
parents: 423
diff changeset
343 gf[2,:,:] #
1c41f4fd3e61 Add some notes and todos
Jonatan Werpers <jonatan@werpers.com>
parents: 423
diff changeset
344 ```
1c41f4fd3e61 Add some notes and todos
Jonatan Werpers <jonatan@werpers.com>
parents: 423
diff changeset
345
1c41f4fd3e61 Add some notes and todos
Jonatan Werpers <jonatan@werpers.com>
parents: 423
diff changeset
346 ### Evaluering av funktioner på nät
1c41f4fd3e61 Add some notes and todos
Jonatan Werpers <jonatan@werpers.com>
parents: 423
diff changeset
347 Hur ska man skriva funktioner som evalueras på nätet? `f(x,y) = ...` eller `f(x̄) = ...`? Eller båda? Kan eval_on_grid se skillnad eller får användaren specificera?
1c41f4fd3e61 Add some notes and todos
Jonatan Werpers <jonatan@werpers.com>
parents: 423
diff changeset
348
1c41f4fd3e61 Add some notes and todos
Jonatan Werpers <jonatan@werpers.com>
parents: 423
diff changeset
349 ```
1c41f4fd3e61 Add some notes and todos
Jonatan Werpers <jonatan@werpers.com>
parents: 423
diff changeset
350 f(x,y) = [x^2, y^2]
1c41f4fd3e61 Add some notes and todos
Jonatan Werpers <jonatan@werpers.com>
parents: 423
diff changeset
351 f(x̄) = [x̄[1]^2, x̄[2]^2]
1c41f4fd3e61 Add some notes and todos
Jonatan Werpers <jonatan@werpers.com>
parents: 423
diff changeset
352 ```
1c41f4fd3e61 Add some notes and todos
Jonatan Werpers <jonatan@werpers.com>
parents: 423
diff changeset
353
1c41f4fd3e61 Add some notes and todos
Jonatan Werpers <jonatan@werpers.com>
parents: 423
diff changeset
354 Påverkas detta av hur vi förväntar oss kunna skapa lata gridfunktioner?
1c41f4fd3e61 Add some notes and todos
Jonatan Werpers <jonatan@werpers.com>
parents: 423
diff changeset
355
1c41f4fd3e61 Add some notes and todos
Jonatan Werpers <jonatan@werpers.com>
parents: 423
diff changeset
356 ### Komponenter som gridfunktioner
606
8f9b3eac128a Add a bunch of stuff to TODO.md and Notes.md
Jonatan Werpers <jonatan@werpers.com>
parents: 427
diff changeset
357 En viktig operation för vektor fält är att kunna få ut komponenter som grid-funktioner. Detta behöver antagligen kunna ske lazy.
427
1c41f4fd3e61 Add some notes and todos
Jonatan Werpers <jonatan@werpers.com>
parents: 423
diff changeset
358 Det finns ett par olika lösningar:
1c41f4fd3e61 Add some notes and todos
Jonatan Werpers <jonatan@werpers.com>
parents: 423
diff changeset
359 * Implementera en egen typ av view som tar hand om detta. Eller Accessors.jl?
995
1ba8a398af9c Rename types
Jonatan Werpers <jonatan@werpers.com>
parents: 866
diff changeset
360 * Använda en LazyTensor
427
1c41f4fd3e61 Add some notes and todos
Jonatan Werpers <jonatan@werpers.com>
parents: 423
diff changeset
361 * Någon typ av lazy-broadcast
1c41f4fd3e61 Add some notes and todos
Jonatan Werpers <jonatan@werpers.com>
parents: 423
diff changeset
362 * En lazy array som applicerar en funktion för varje element.
1c41f4fd3e61 Add some notes and todos
Jonatan Werpers <jonatan@werpers.com>
parents: 423
diff changeset
363
1c41f4fd3e61 Add some notes and todos
Jonatan Werpers <jonatan@werpers.com>
parents: 423
diff changeset
364 Skulle vara en fördel om det är hyffsat generiskt så att en eventuell användare kan utöka det enkelt om de har någon egen exotisk typ. Eller ska man vila helt på
1c41f4fd3e61 Add some notes and todos
Jonatan Werpers <jonatan@werpers.com>
parents: 423
diff changeset
365
1c41f4fd3e61 Add some notes and todos
Jonatan Werpers <jonatan@werpers.com>
parents: 423
diff changeset
366 Syntax:
1c41f4fd3e61 Add some notes and todos
Jonatan Werpers <jonatan@werpers.com>
parents: 423
diff changeset
367 ```
1c41f4fd3e61 Add some notes and todos
Jonatan Werpers <jonatan@werpers.com>
parents: 423
diff changeset
368 gf = eval(...)
1c41f4fd3e61 Add some notes and todos
Jonatan Werpers <jonatan@werpers.com>
parents: 423
diff changeset
369 component(gf,2) # Andra komponenten av en vektor
1c41f4fd3e61 Add some notes and todos
Jonatan Werpers <jonatan@werpers.com>
parents: 423
diff changeset
370 component(gf,2,3) # (2,3) elementet av en matris
1c41f4fd3e61 Add some notes and todos
Jonatan Werpers <jonatan@werpers.com>
parents: 423
diff changeset
371 component(gf,:,2) # Andra kolumnen av en matris
1c41f4fd3e61 Add some notes and todos
Jonatan Werpers <jonatan@werpers.com>
parents: 423
diff changeset
372 @ourview gf[:,:][2]
1c41f4fd3e61 Add some notes and todos
Jonatan Werpers <jonatan@werpers.com>
parents: 423
diff changeset
373 ```
683
841ca12f3359 Add notes about embedded grids
Jonatan Werpers <jonatan@werpers.com>
parents: 654
diff changeset
374
841ca12f3359 Add notes about embedded grids
Jonatan Werpers <jonatan@werpers.com>
parents: 654
diff changeset
375 ## Grids embedded in higher dimensions
841ca12f3359 Add notes about embedded grids
Jonatan Werpers <jonatan@werpers.com>
parents: 654
diff changeset
376
841ca12f3359 Add notes about embedded grids
Jonatan Werpers <jonatan@werpers.com>
parents: 654
diff changeset
377 For grids generated by asking for boundary grids for a regular grid, it would
841ca12f3359 Add notes about embedded grids
Jonatan Werpers <jonatan@werpers.com>
parents: 654
diff changeset
378 make sense if these grids knew they were embedded in a higher dimension. They
841ca12f3359 Add notes about embedded grids
Jonatan Werpers <jonatan@werpers.com>
parents: 654
diff changeset
379 would return coordinates in the full room. This would make sense when
841ca12f3359 Add notes about embedded grids
Jonatan Werpers <jonatan@werpers.com>
parents: 654
diff changeset
380 drawing points for example, or when evaluating functions on the boundary.
841ca12f3359 Add notes about embedded grids
Jonatan Werpers <jonatan@werpers.com>
parents: 654
diff changeset
381
841ca12f3359 Add notes about embedded grids
Jonatan Werpers <jonatan@werpers.com>
parents: 654
diff changeset
382 Implementation of this is an issue that requires some thought. Adding an extra
841ca12f3359 Add notes about embedded grids
Jonatan Werpers <jonatan@werpers.com>
parents: 654
diff changeset
383 "Embedded" type for each grid would make it easy to understand each type but
841ca12f3359 Add notes about embedded grids
Jonatan Werpers <jonatan@werpers.com>
parents: 654
diff changeset
384 contribute to "type bloat". On the other hand adapting existing types to
841ca12f3359 Add notes about embedded grids
Jonatan Werpers <jonatan@werpers.com>
parents: 654
diff changeset
385 handle embeddedness would complicate the now very simple grid types. Are there
841ca12f3359 Add notes about embedded grids
Jonatan Werpers <jonatan@werpers.com>
parents: 654
diff changeset
386 other ways of doing the implentation?
718
05d8ea88c690 Add note about performance testin
Jonatan Werpers <jonatan@werpers.com>
parents: 683
diff changeset
387
05d8ea88c690 Add note about performance testin
Jonatan Werpers <jonatan@werpers.com>
parents: 683
diff changeset
388 ## Performance measuring
05d8ea88c690 Add note about performance testin
Jonatan Werpers <jonatan@werpers.com>
parents: 683
diff changeset
389 We should be measuring performance early. How does our effective cpu and memory bandwidth utilization compare to peak performance?
05d8ea88c690 Add note about performance testin
Jonatan Werpers <jonatan@werpers.com>
parents: 683
diff changeset
390
05d8ea88c690 Add note about performance testin
Jonatan Werpers <jonatan@werpers.com>
parents: 683
diff changeset
391 We should make these test simple to run for any solver.
05d8ea88c690 Add note about performance testin
Jonatan Werpers <jonatan@werpers.com>
parents: 683
diff changeset
392
05d8ea88c690 Add note about performance testin
Jonatan Werpers <jonatan@werpers.com>
parents: 683
diff changeset
393 See [this talk](https://www.youtube.com/watch?v=vPsfZUqI4_0) for some simple ideas for defining effecive memory usage and some comparison with peak performance.
05d8ea88c690 Add note about performance testin
Jonatan Werpers <jonatan@werpers.com>
parents: 683
diff changeset
394
05d8ea88c690 Add note about performance testin
Jonatan Werpers <jonatan@werpers.com>
parents: 683
diff changeset
395
761
d7d030f8f708 Add note about adjoint as trait
Jonatan Werpers <jonatan@werpers.com>
parents: 718
diff changeset
396 ## Adjoint as a trait on the sbp_operator level?
d7d030f8f708 Add note about adjoint as trait
Jonatan Werpers <jonatan@werpers.com>
parents: 718
diff changeset
397
d7d030f8f708 Add note about adjoint as trait
Jonatan Werpers <jonatan@werpers.com>
parents: 718
diff changeset
398 It would be nice to have a way of refering to adjoints with resepct to the sbp-inner-product.
d7d030f8f708 Add note about adjoint as trait
Jonatan Werpers <jonatan@werpers.com>
parents: 718
diff changeset
399 If it was possible you could reduce the number of times you have to deal with the inner product matrix.
d7d030f8f708 Add note about adjoint as trait
Jonatan Werpers <jonatan@werpers.com>
parents: 718
diff changeset
400
d7d030f8f708 Add note about adjoint as trait
Jonatan Werpers <jonatan@werpers.com>
parents: 718
diff changeset
401 Since the LazyOperators package is sort of implementing matrix-free matrices there is no concept of inner products there at the moment. It seems to complicate large parts of the package if this was included there.
d7d030f8f708 Add note about adjoint as trait
Jonatan Werpers <jonatan@werpers.com>
parents: 718
diff changeset
402
d7d030f8f708 Add note about adjoint as trait
Jonatan Werpers <jonatan@werpers.com>
parents: 718
diff changeset
403 A different approach would be to include it as a trait for operators so that you can specify what the adjoint for that operator is.
d7d030f8f708 Add note about adjoint as trait
Jonatan Werpers <jonatan@werpers.com>
parents: 718
diff changeset
404
d7d030f8f708 Add note about adjoint as trait
Jonatan Werpers <jonatan@werpers.com>
parents: 718
diff changeset
405
775
1d166e7a9deb Add a note about the name of VolumeOperator
Jonatan Werpers <jonatan@werpers.com>
parents: 761
diff changeset
406 ## Name of the `VolumeOperator` type for constant stencils
995
1ba8a398af9c Rename types
Jonatan Werpers <jonatan@werpers.com>
parents: 866
diff changeset
407 It seems that the name is too general. The name of the method `volume_operator` makes sense. It should return different types of `LazyTensor` specialized for the grid. A suggetion for a better name is `ConstantStencilVolumeOperator`