-
Notifications
You must be signed in to change notification settings - Fork 5
/
helper.jl
245 lines (195 loc) · 5.99 KB
/
helper.jl
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
include("helper/parameter_scheduling.jl")
include("helper/interpolations.jl")
# Indexing #
#----------#
function transposedims(v, transpositions, inplace=true)
perm = get_perm(ndims(v), transpositions)
if inplace
return PermutedDimsArray(v, perm)
else
return permutedims(v, perm)
end
end
function transposedims(v, transpositions::T, inplace=true) where T <: Tuple{<:Number, <:Number}
return transposedims(v, [transpositions], inplace)
end
function get_perm(n, transpositions)
perm = collect(1:n)
for t in transpositions
perm[[t[1], t[2]]] .= perm[t[2]], perm[t[1]]
end
return perm
end
function light_argmax(x, dims)
return argmax.(eachslice(x, dims=dimsexcept(x, dims), drop=false))
end
function getindex_slices(x, dims, i)
return getindex.(eachslice(x, dims=dimsexcept(x, dims), drop=false), i)
end
"""
Like selectdim, but follow broadcasting rules. If the size of the
dimension is 1, return the whole array.
"""
function selectdim_broadcasty(A::AbstractArray, d::Integer, i::Int)
size(A, d) == 1 && return A
return selectdim(A, d, i)
end
# https://stackoverflow.com/a/69470628/4828492
function extend_dims(A, which_dim, n=1)
s = [size(A)...]
for _ in 1:n
insert!(s,which_dim,1)
end
return reshape(A, s...)
end
function extend_dims(A, dims::NTuple{N,T}) where {N, T <: Tuple}
return reduce((A, dn)->extend_dims(A, dn...), dims, init=A)
end
function pad_dims(A, left, right)
s = Int[ones(left)..., size(A)..., ones(right)...]
return reshape(A, s...)
end
function pad_dims(A; left=0, right=0, ndims_new=-1)
if ndims_new != -1
if right == 0
right = ndims_new - ndims(A) - left
else
left = ndims_new - ndims(A) - right
end
end
return pad_dims(A, left, right)
end
e_vec(n, i) = [i==j for j=1:n]
# Slicing #
#---------#
struct DimsExcept{T}
dims::T
end
function dimsexcept(A::AbstractArray{T, N}, dims::NTuple{M}) where {T,N,M}
return NTuple{N-M,Int}(i for i=1:N if i ∉ dims)
end
dimsexcept(A, dim::Int) = dimsexcept(A, (dim,))
dimsexcept(A, dims::DimsExcept) = dimsexcept(A, dims.dims)
#= in jail until they can be made to work fast=#
Base.eachslice(A, dims, drop=true) = eachslice(A; dims, drop)
Base.eachslice(A, dims::DimsExcept, drop=true) = eachslice(A; dims=dimsexcept(A, dims), drop)
_eachslice_catchRef(Ai; dims, drop) = eachslice(Ai; dims, drop)
_eachslice_catchRef(Ai::Ref; dims, drop) = Ai
function broadcastslices(f, dims, A...; args=[])
return f.(eachslice.(A; dims, drop=false)..., Ref.(args)...)
end
function broadcastslices(f, dims::DimsExcept, A...; args=[])
return broadcastslices(f, dimsexcept(A[1], dims), A...; args)
end
#=
function eachslice_asview_along(A::AbstractArray, dims)
nd = ndims(A)
longdims = ntuple(d -> d in dims ? 1 : size(A,d), nd)
sliced = .!in.(1:nd, Ref(dims))
#[view(A, ntuple(d -> sliced[d] ? Colon() : (idx[d]:idx[d]), nd)...) for idx in CartesianIndices(longdims)]
return (view(A, ntuple(d -> (idx[d] : (sliced[d] ? size(A,d) : idx[d])), nd)...) for idx in CartesianIndices(longdims))
end
eachslice_asview(A::AbstractArray, dims) = eachslice_asview_along(A, dimsexcept(A, dims))
=#
# Rootfinding and Maximization #
#------------------------------#
function isquasiconvex(v)
v_last = v[1]
increasing = v[2] >= v[1]
for v_i in v[2:end]
if v_i > v_last
if !increasing
return false
end
elseif v_i < v_last
increasing = false
end
v_last = v_i
end
return true
end
function _get_right_start(v::AbstractVector)
right = length(v)
while right > 1 && v[right] == -Inf
right = div(right, 2)
end
return right*2
end
"Find the argmax of an array iff the array is quasiconvex"
function quasiconvex_argmax(v; right::Int=length(v))
left = 1
while right - left > 1
gap = div(right - left, 3)
middle_l = left + gap
middle_r = right - gap
@inbounds if v[middle_l] < v[middle_r]
left = middle_l + 1
else
right = middle_r - 1
end
end
return v[left] > v[right] ? left : right
end
"""
For each pre-utility state, maximize utility + post-utility value,
over the post-utility states.
"""
function k1_argmax!(V_prec, k1, V, u)
n = length(k1)
@assert ispow2(n-1)
k1[1] = 1
V_prec[1] = u[1][1] + V[1]
k1[end] = argmax_sum(u[end], V, 1, n)
V_prec[end] = u[end][k1[end]] + V[k1[end]]
segment_length = div(n-1, 2)
while segment_length >= 1
i = 1
while i < n - 1
k1_lb = k1[i]
i += segment_length
k1_ub = k1[i+segment_length]
k1[i] = argmax_sum(u[i], V, k1_lb, min(k1_ub,i))
V_prec[i] = u[i][k1[i]] + V[k1[i]]
i += segment_length
end
segment_length = div(segment_length, 2)
#TODO figure out how to do for non-power-of-two vector lengths
end
return k1
end
"Maximize over the sum of two vectors"
function argmax_sum(u_sub, V_sub, lb, ub)
max = -Inf
argmax = lb
@inbounds for i=lb:ub
val = u_sub[i] + V_sub[i]
if val > max
max = val
argmax = i
end
end
return argmax
end
#######################
# Gumbel Distribution #
#######################
const EULER_GAMMA = 0.57721566490153286060 |> FLOAT_PRECISION
##############################
# Exponential Approximations #
##############################
const fastexp = Base.Math.exp_fast
const fastlog = log
##########
# Macros #
##########
macro print(ex)
return :(println($(esc(ex))))
end
##########
# Fields #
##########
"Get all fields of the components of a struct."
subfieldnames(::T) where T = reduce(vcat, collect.(fieldnames.(collect(T.types))))
"Get a subfield of an object, by searching through the fields of its fields."
hasfield(T, s) = s in fieldnames(T)
fieldvalues(obj::T) where T = getfield.(Ref(obj), collect(fieldnames(T)))