I need the best way to store a three dimensional table for pixels. What I need to do is have multiple x,y tables (basically three dimensional) it is to raster multiple two dimensional pixel maps with transparency. You see I can create two dimensions easily like so:
pixels = {{},{}}
pixels[1][5] = "green" --just an example
print(pixels[1][5])
However, I cannot do this like I can in Java...
pixels = {{}, {}, {}}
pixels[1][4][3] = "red" -- [x][y][z]
print(pixels[1][4][3])
This is the functionality I want, but I have disgustingly got around this by doing this...
pixels = {}
pixels["x23,y02,z05"] = "green"
print(pixels["x23,y02,z05"]")
I just use string.sub, and string.concat to read and set the tables... I really would like the functionality of example 2 to work, however I know it might need to be implemented differently.
There are basically two ways to go about this
Auto-tables
Auto-tables generate sub-tables transparently using metatables and essentially after creating it you should be able to forget about them.
function newAutotable(dim)
local MT = {};
for i=1, dim do
MT[i] = {__index = function(t, k)
if i < dim then
t[k] = setmetatable({}, MT[i+1])
return t[k];
end
end}
end
return setmetatable({}, MT[1]);
end
-- Usage
local at = newAutotable(3);
print(at[0]) -- returns table
print(at[0][1]) -- returns table
print(at[0][1][2]) -- returns nil
at[0][1][2] = 2;
print(at[0][1][2]) -- returns value
print(at[0][1][3][3]) -- error, because only 3 dimensions set
What is not so nice about them is that they generate lots of tables -- obviously. That's some memory overhead and each level of depth increases the execution time.
What's nice about them is that they can be completely dynamic in size. You could even make them infinitely deep. Though in your use-case this is very likely not necessary and probably even a bad idea.
This structure is very suitable for non-integer indexes though, you could for example make the depth even depend on a "template structure" and so implement a transparent dynamic configuration table, but I'm getting side-tracked...
Flattened arrays
The other variant are flattened arrays. user3125367 already wrote about them, but I want to expand on this as this can be done a lot more convenient and explain a few things.
Often flattening your multi-dimensional arrays is a good idea in CG anyway, since then you can do many matrix operations very easily. Calculating a modified index is also relatively cheap in terms of processing time required. But it should be noted, although kind of obvious, that this approach only works with numeric keys and a predefined size of your matrix.
function newMdArray(X, Y, Z)
local MT = { __call = function(t, x, y, z, v)
if x>X or y>Y or z>Z or x<1 or y<1 or z<1 then return; end
local k = x + X*(y-1) + X*Y*(z-1);
if v ~= nil then t[k] = v; end
return t[k];
end };
return setmetatable({}, MT);
end
-- Usage
local mdt = newMdArray(100, 100, 100);
local v = mdt(1, 2, 3);
mdt(1, 2, 3, v*.1);
This code is taken from another answer from me: dynamic tables or arrays
It can probably be optimised a little (for example calculate X*Y in the closure) but I wanted to paste the original code here. Anyway, with this you can both easily work on the flattened structure by just using normal array indexing:
for i=1, #mdt
mdt[i] = (mdt[i] or 0)*.5
end
As well as access 3d indexes directly:
mdt(12, 13, 14, 0)
You can also easily modify the function to return a default value for missing keys by adding an __index field to the metatable or so that the table saves the matrix dimensions etc.
In addition to classic 'array in array in array' scheme, you can use benefits of Lua table internals. How? Lua table is just a mapping from key to value, and when you use it as an array, you may skip some keys and this will cost virtually nothing.
t = { }
t[1] = "Hello"
t[500000] = "World" -- does NOT allocate additional 499999 elements
So, if your data is sparse (over 50% of your 3d-points having no value), you may benefit from this:
local n_x, n_y, n_z = 1920, 1080, 1000
local n_xy = n_x * n_y
function setValue(t, x, y, z, value)
assert(x > 0 and x < n_x)
assert(y > 0 and y < n_y)
assert(z > 0 and z < n_z)
t[((z-1) * n_xy) + ((y-1) * n_z) + x] = value
end
function getValue(t, x, y, z)
assert(x > 0 and x < n_x)
assert(y > 0 and y < n_y)
assert(z > 0 and z < n_z)
return t[((z-1) * n_xy) + ((y-1) * n_z) + x]
end
t = { }
setValue(t, 1, 1, 1, "red")
setValue(t, 1, 1, 2, "green")
In your first code:
pixels = {{},{}}
is equivalent to:
pixels = {}
pixels[1] = {}
pixels[2] = {}
Here, pixels[1] is already a table, that's why you can assign a value to pixels[1][5].
But in you second code:
pixels = {{}, {}, {}}
Here, pixels is still a two-dimensional array (with 3 elements). It's equivalent to :
pixels = {}
pixels[1] = {}
pixels[2] = {}
pixels[3] = {}
pixels[1] is a table, but pixels[1][4] is not. What you need to do is to give pixels[1][4] a table constructor like this:
pixels = {{}, {}, {}}
pixels[1][4] = {} --initialize it to an empty table
pixels[1][4][3] = "red"
print(pixels[1][4][3])
Related
With the Julia Language, I defined a function to sample points uniformly inside the sphere of radius 3.14 using rejection sampling as follows:
function spherical_sample(N::Int64)
# generate N points uniformly distributed inside sphere
# using rejection sampling:
points = pi*(2*rand(5*N,3).-1.0)
ind = sum(points.^2,dims=2) .<= pi^2
## ideally I wouldn't have to do this:
ind_ = dropdims(ind,dims=2)
return points[ind_,:][1:N,:]
end
I found a hack for subsetting arrays:
ind = sum(points.^2,dims=2) .<= pi^2
## ideally I wouldn't have to do this:
ind_ = dropdims(ind,dims=2)
But, in principle array indexing should be a one-liner. How could I do this better in Julia?
The problem is that you are creating a 2-dimensional index vector. You can avoid it by using eachrow:
ind = sum.(eachrow(points.^2)) .<= pi^2
So that your full answer would be:
function spherical_sample(N::Int64)
points = pi*(2*rand(5*N,3).-1.0)
ind = sum.(eachrow(points.^2)) .<= pi^2
return points[ind,:][1:N,:]
end
Here is a one-liner:
points[(sum(points.^2,dims=2) .<= pi^2)[:],:][1:N, :]
Note that [:] is dropping a dimension so the BitArray can be used for indexing.
This does not answer your question directly (as you already got two suggestions), but I rather thought to hint how you could implement the whole procedure differently if you want it to be efficient.
The first point is to avoid generating 5*N rows of data - the problem is that it is very likely that it will be not enough to generate N valid samples. The point is that the probability of a valid sample in your model is ~50%, so it is possible that there will not be enough points to choose from and [1:N, :] selection will throw an error.
Below is the code I would use that avoids this problem:
function spherical_sample(N::Integer) # no need to require Int64 only here
points = 2 .* pi .* rand(N, 3) .- 1.0 # note that all operations are vectorized to avoid excessive allocations
while N > 0 # we will run the code until we have N valid rows
v = #view points[N, :] # use view to avoid allocating
if sum(x -> x^2, v) <= pi^2 # sum accepts a transformation function as a first argument
N -= 1 # row is valid - move to the previous one
else
rand!(v) # row is invalid - resample it in place
#. v = 2 * pi * v - 1.0 # again - do the computation in place via broadcasting
end
end
return points
end
This one is pretty fast, and uses StaticArrays. You can probably also implement something similar with ordinary tuples:
using StaticArrays
function sphsample(N)
T = SVector{3, Float64}
v = Vector{T}(undef, N)
n = 1
while n <= N
p = rand(T) .- 0.5
#inbounds v[n] = p .* 2π
n += (sum(abs2, p) <= 0.25)
end
return v
end
On my laptop it is ~9x faster than the solution with views.
As a simplified example, suppose I have a dataset composed of 40 sorted values. The values of this example are all integers, though this is not necessarily the case for the actual dataset.
import numpy as np
data = np.linspace(1,40,40)
I am trying to find the maximum value inside the dataset for certain window sizes. The formula to compute the window sizes yields a pattern that is best executed with arrays (in my opinion). For simplicity sake, let's say the indices denoting the window sizes are a list [1,2,3,4,5]; this corresponds to window sizes of [2,4,8,16,32] (the pattern is 2**index).
## this code looks long because I've provided docstrings
## just in case the explanation was unclear
def shapeshifter(num_col, my_array=data):
"""
This function reshapes an array to have 'num_col' columns, where
'num_col' corresponds to index.
"""
return my_array.reshape(-1, num_col)
def looper(num_col, my_array=data):
"""
This function calls 'shapeshifter' and returns a list of the
MAXimum values of each row in 'my_array' for 'num_col' columns.
The length of each row (or the number of columns per row if you
prefer) denotes the size of each window.
EX:
num_col = 2
==> window_size = 2
==> check max( data[1], data[2] ),
max( data[3], data[4] ),
max( data[5], data[6] ),
.
.
.
max( data[39], data[40] )
for k rows, where k = len(my_array)//num_col
"""
my_array = shapeshifter(num_col=num_col, my_array=data)
rows = [my_array[index] for index in range(len(my_array))]
res = []
for index in range(len(rows)):
res.append( max(rows[index]) )
return res
So far, the code is fine. I checked it with the following:
check1 = looper(2)
check2 = looper(4)
print(check1)
>> [2.0, 4.0, ..., 38.0, 40.0]
print(len(check1))
>> 20
print(check2)
>> [4.0, 8.0, ..., 36.0, 40.0]
print(len(check2))
>> 10
So far so good. Now here is my problem.
def metalooper(col_ls, my_array=data):
"""
This function calls 'looper' - which calls
'shapeshifter' - for every 'col' in 'col_ls'.
EX:
j_list = [1,2,3,4,5]
==> col_ls = [2,4,8,16,32]
==> looper(2), looper(4),
looper(8), ..., looper(32)
==> shapeshifter(2), shapeshifter(4),
shapeshifter(8), ..., shapeshifter(32)
such that looper(2^j) ==> shapeshifter(2^j)
for j in j_list
"""
res = []
for col in col_ls:
res.append(looper(num_col=col))
return res
j_list = [2,4,8,16,32]
check3 = metalooper(j_list)
Running the code above provides this error:
ValueError: total size of new array must be unchanged
With 40 data points, the array can be reshaped into 2 columns of 20 rows, or 4 columns of 10 rows, or 8 columns of 5 rows, BUT at 16 columns, the array cannot be reshaped without clipping data since 40/16 ≠ integer. I believe this is the problem with my code, but I do not know how to fix it.
I am hoping there is a way to cutoff the last values in each row that do not fit in each window. If this is not possible, I am hoping I can append zeroes to fill the entries that maintain the size of the original array, so that I can remove the zeroes after. Or maybe even some complicated if - try - break block. What are some ways around this problem?
I think this will give you what you want in one step:
def windowFunc(a, window, f = np.max):
return np.array([f(i) for i in np.split(a, range(window, a.size, window))])
with default f, that will give you a array of maximums for your windows.
Generally, using np.split and range, this will let you split into a (possibly ragged) list of arrays:
def shapeshifter(num_col, my_array=data):
return np.split(my_array, range(num_col, my_array.size, num_col))
You need a list of arrays because a 2D array can't be ragged (every row needs the same number of columns)
If you really want to pad with zeros, you can use np.lib.pad:
def shapeshifter(num_col, my_array=data):
return np.lib.pad(my_array, (0, num_col - my.array.size % num_col), 'constant', constant_values = 0).reshape(-1, num_col)
Warning:
It is also technically possible to use, for example, a.resize(32,2) which will create an ndArray padded with zeros (as you requested). But there are some big caveats:
You would need to calculate the second axis because -1 tricks don't work with resize.
If the original array a is referenced by anything else, a.resize will fail with the following error:
ValueError: cannot resize an array that references or is referenced
by another array in this way. Use the resize function
The resize function (i.e. np.resize(a)) is not equivalent to a.resize, as instead of padding with zeros it will loop back to the beginning.
Since you seem to want to reference a by a number of windows, a.resize isn't very useful. But it's a rabbit hole that's easy to fall into.
EDIT:
Looping through a list is slow. If your input is long and windows are small, the windowFunc above will bog down in the for loops. This should be more efficient:
def windowFunc2(a, window, f = np.max):
tail = - (a.size % window)
if tail == 0:
return f(a.reshape(-1, window), axis = -1)
else:
body = a[:tail].reshape(-1, window)
return np.r_[f(body, axis = -1), f(a[tail:])]
Here's a generalized way to reshape with truncation:
def reshape_and_truncate(arr, shape):
desired_size_factor = np.prod([n for n in shape if n != -1])
if -1 in shape: # implicit array size
desired_size = arr.size // desired_size_factor * desired_size_factor
else:
desired_size = desired_size_factor
return arr.flat[:desired_size].reshape(shape)
Which your shapeshifter could use in place of reshape
I want to create a 2D list that can have elements of variable lengths inside, for example, if I have a 10x10 list in MATLAB, I can
define it with:
z = cell(10,10)
and start assigning some elements by doing this:
z{2}{3} = ones(3,1)
z{1}{1} = zeros(100,1)
z{1}{2} = []
z{1}{3} = randn(20,1)
...
What is the optimal way to define such empty 2D list in torch? Moreover, is there a way to exploit the tensor structure to do this?
In python, I can do something along this to define an empty 10x10 2D list:
z = [[None for j in range(10)] for i in range(10)]
My best guess for torch is doing something like
z = torch.Tensor(10,10)
for i=1,10 do
for j=1,10 do
z[{{i},{j}}] = torch.Tensor()
end
end
but, this does not work, and defining a tensor inside a tensor seems like a bad idea ...
This is a follow up to the question asked here (however in the link it is asked in python): Create 2D lists in python with variable length indexed vectors
From the documentation I've read, tensors only support primitive numeric data types. You won't be able to use tensor for your intended usage. Leverage tables.
local function makeMatrix(initialVal, ...)
local isfunc = type(initialVal) == "function"
local dimtable = {...}
local function helper(depth)
if depth == 0 then
return isfunc and initialVal() or initialVal
else
local plane = {}
for i = 1, dimtable[depth] do
plane[i] = helper(depth-1)
end
return plane
end
end
return helper(#dimtable)
end
p = makeMatrix(0, 2, 3, 5) -- makes 3D matrix of size 2x3x5 with all elements initialized to 0
makeMatrix(torch.Tensor, m ,n)
Answer from Torch's Google Group forums. Agreeing that tables is the solution:
z = {}
for i=1,10 do
z[i] = {}
for j=1,10 do
z[i][j] = torch.Tensor()
end
end
I have two array, the first one is data_array(50,210), the second one is dest_array(210,210). The goal, using data from data_array to calculate the values of dest_array at specific indicies, without using for-loop.
I do it in such way:
function [ out ] = grid_point( row,col,cg_row,cg_col,data,kernel )
ker_len2 = floor(length(kernel)/2);
op1_vals = data((row - ker_len2:row + ker_len2),(col - ker_len2:col + ker_len2));
out(cg_row,cg_col) = sum(sum(op1_vals.*kernel)); %incorre
end
function [ out ] = sm(dg_X, dg_Y)
%dg_X, dg_Y - arrays of size 210x210, the values - coordinates of data in data_array,
%index of each element - position this data at 210x210 grid
data_array = randi(100,50,210); %data array
kernel = kernel_sinc2d(17,'hamming'); %sinc kernel for calculations
ker_len2 = floor(length(kernel)/2);
%adding the padding for array, to avoid
%the errors related to boundaries of data_array
data_array = vertcat(data_array(linspace(ker_len2+1,2,ker_len2),:),...
data_array,...
data_array(linspace(size(data_array,1)-1,size(data_array,1) - ker_len2,ker_len2),:));
data_array = horzcat(data_array(:,linspace(ker_len2+1,2,ker_len2)),...
data_array,...
data_array(:,linspace(size(data_array,2)-1,(size(data_array,2) - ker_len2,ker_len2)));
%cg_X, cg_Y - arrays of indicies for X and Y directions
[cg_X,cg_Y] = meshgrid(linspace(1,210,210),linspace(1,210,210));
%for each point at grid(210x210) formed by cg_X and cg_Y,
%we should calculate the value, using the data from data_array(210,210).
%after padding, data_array will have size (50 + ker_len2*2, 210 + ker_len2*2)
dest_array = arrayfun(#(y,x,cy,cx) grid_point(y, x, cy, cx, data_array, kernel),...
dg_Y, dg_X, cg_Y, cg_X);
end
But, it seems that arrayfun cannot resolve my problem, because I use arrays with different sizes. Have somebody the ideas of this?
I am not completely sure, but judging from the title, this may be what you want:
%Your data
data_array_small = rand(50,210)
data_array_large = zeros(210,210)
%Indicating the points of interest
idx = randperm(size(data_array_large,1));
idx = idx(1:size(data_array_small,1))
%Now actually use the information:
data_array_large(idx,:) = data_array_small
Can anybody optimize following statement in Scala:
// maybe large
val someArray = Array(9, 1, 6, 2, 1, 9, 4, 5, 1, 6, 5, 0, 6)
// output a sorted list which contains unique element from the array without 0
val newList=(someArray filter (_>0)).toList.distinct.sort((e1, e2) => (e1 > e2))
Since the performance is critical, is there a better way?
Thank you.
This simple line is one of the fastest codes so far:
someArray.toList.filter (_ > 0).sortWith (_ > _).distinct
but the clear winner so far is - due to my measurement - Jed Wesley-Smith. Maybe if Rex' code is fixed, it looks different.
Typical disclaimer 1 + 2:
I modified the codes to accept an Array and return an List.
Typical benchmark considerations:
This was random data, equally distributed. For 1 Million elements, I created an Array of 1 Million ints between 0 and 1 Million. So with more or less zeros, and more or less duplicates, it might vary.
It might depend on the machine etc.. I used a single core CPU, Intel-Linux-32bit, jdk-1.6, scala 2.9.0.1
Here is the underlying benchcoat-code and the concrete code to produce the graph (gnuplot). Y-axis: time in seconds. X-axis: 100 000 to 1 000 000 elements in Array.
update:
After finding the problem with Rex' code, his code is as fast as Jed's code, but the last operation is a transformation of his Array to a List (to fullfill my benchmark-interface). Using a var result = List [Int], and result = someArray (i) :: result speeds his code up, so that it is about twice as fast as the Jed-Code.
Another, maybe interesting, finding is: If I rearrange my code in the order of filter/sort/distinct (fsd) => (dsf, dfs, fsd, ...), all 6 possibilities don't differ significantly.
I haven't measured, but I'm with Duncan, sort in place then use something like:
util.Sorting.quickSort(array)
array.foldRight(List.empty[Int]){
case (a, b) =>
if (!b.isEmpty && b(0) == a)
b
else
a :: b
}
In theory this should be pretty efficient.
Without benchmarking I can't be sure, but I imagine the following is pretty efficient:
val list = collection.SortedSet(someArray.filter(_>0) :_*).toList
Also try adding .par after someArray in your version. It's not guaranteed to be quicker, bit it might be. You should run a benchmark and experiment.
sort is deprecated. Use .sortWith(_ > _) instead.
Boxing primitives is going to give you a 10-30x performance penalty. Therefore if you really are performance limited, you're going to want to work off of raw primitive arrays:
def arrayDistinctInts(someArray: Array[Int]) = {
java.util.Arrays.sort(someArray)
var overzero = 0
var ndiff = 0
var last = 0
var i = 0
while (i < someArray.length) {
if (someArray(i)<=0) overzero = i+1
else if (someArray(i)>last) {
last = someArray(i)
ndiff += 1
}
i += 1
}
val result = new Array[Int](ndiff)
var j = 0
i = overzero
last = 0
while (i < someArray.length) {
if (someArray(i) > last) {
result(j) = someArray(i)
last = someArray(i)
j += 1
}
i += 1
}
result
}
You can get slightly better than this if you're careful (and be warned, I typed this off the top of my head; I might have typoed something, but this is the style to use), but if you find the existing version too slow, this should be at least 5x faster and possibly a lot more.
Edit (in addition to fixing up the previous code so it actually works):
If you insist on ending with a list, then you can build the list as you go. You could do this recursively, but I don't think in this case it's any clearer than the iterative version, so:
def listDistinctInts(someArray: Array[Int]): List[Int] = {
if (someArray.length == 0 || someArray(someArray.length-1) <= 0) List[Int]()
else {
java.util.Arrays.sort(someArray)
var last = someArray(someArray.length-1)
var list = last :: Nil
var i = someArray.length-2
while (i >= 0) {
if (someArray(i) < last) {
last = someArray(i)
if (last <= 0) return list;
list = last :: list
}
i -= 1
}
list
}
}
Also, if you may not destroy the original array by sorting, you are by far best off if you duplicate the array and destroy the copy (array copies of primitives are really fast).
And keep in mind that there are special-case solutions that are far faster yet depending on the nature of the data. For example, if you know that you have a long array, but the numbers will be in a small range (e.g. -100 to 100), then you can use a bitset to track which ones you've encountered.
For efficiency, depending on your value of large:
val a = someArray.toSet.filter(_>0).toArray
java.util.Arrays.sort(a) // quicksort, mutable data structures bad :-)
res15: Array[Int] = Array(1, 2, 4, 5, 6, 9)
Note that this does the sort using qsort on an unboxed array.
I'm not in a position to measure, but some more suggestions...
Sorting the array in place before converting to a list might well be more efficient, and you might look at removing dups from the sorted list manually, as they will be grouped together. The cost of removing 0's before or after the sort will also depend on their ratio to the other entries.
How about adding everything to a sorted set?
val a = scala.collection.immutable.SortedSet(someArray filter (0 !=): _*)
Of course, you should benchmark the code to check what is faster, and, more importantly, that this is truly a hot spot.