Distributing uneven workload using MPI - fortran

I've got an Array
A(1:n_max)
which I would like to scatter with MPI in order to evaluate some f(A(j)). However the evaluation of f(A(1)) takes 0.35s and the evaluation of f(A(n_max)) takes 15s. I have different ideas on how to tackle it, but I'm not sure which is the best:
Some Master/Slave work load distributing.
Along the lines of this: http://www.hpc.cam.ac.uk/using-clusters/compiling-and-development/parallel-programming-mpi-example
I reorder A with Reshape(Transpose(Reshape(A)), which would turn
array([ 0, 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])
into
array([[ 0, 33, 66, 1, 34, 67, 2, 35, 68, 3, 36, 69, 4, 37, 70, 5, 38,
71, 6, 39, 72, 7, 40, 73, 8, 41, 74, 9, 42, 75, 10, 43, 76, 11,
44, 77, 12, 45, 78, 13, 46, 79, 14, 47, 80, 15, 48, 81, 16, 49, 82,
17, 50, 83, 18, 51, 84, 19, 52, 85, 20, 53, 86, 21, 54, 87, 22, 55,
88, 23, 56, 89, 24, 57, 90, 25, 58, 91, 26, 59, 92, 27, 60, 93, 28,
61, 94, 29, 62, 95, 30, 63, 96, 31, 64, 97, 32, 65, 98]])
which I then could distribute using scatter and gather. The problem is, that one process would have to run f(A(0)), f(A(33)) and f(A(66)), while another has to run f(A(32)), f(A(65)) and f(A(98)).
Sadly the run times in between rise monotonic, but not linear.
I'm hoping for some of your Ideas
What do you recommend?


If the order of execution is important (e.g. caches) you could split the array in contiguous groups of different sizes but almost equal workloads and distribute them with MPI_SCATTERV.
If the end of the array is to heavy (in case of work load) you could also split the array and use the same approach twice.
If the order of execution is not important and you have reordering doesn't take to much time I would prefer your second approach.
If you have always an array like this, you should think about the first solution but only send the interval limits instead of all numbers inside the interval. This makes especially sense if you are bandwidth-bound in your communication.

Related

How to concat a tensor in pytorch?

What I want to do is something like this:
import torch
a = torch.arange(120).reshape(2, 3, 4, 5)
b = torch.cat(list(a), dim=2)
I want to know:
I have to convert tensor to a list, will this cause performance not good?
Even performance is OK, can I do this just with tensor?

You want to:
Reduce the number of copies: in this specific scenario, copies need to be made since we are rearranging the layout of our underlying data.
Reduce or remove any torch.Tensor -> non-torch.Tensor conversions: this will be a pain point when working with a GPU since you're transferring data in and out of the device.
You can perform the same operation by permuting the axes such that axis=0 goes to axis=-2 (the before the last axis), then flattening the last two axes:
>>> a.permute(1,2,0,3).flatten(-2)
tensor([[[ 0, 1, 2, 3, 4, 60, 61, 62, 63, 64],
[ 5, 6, 7, 8, 9, 65, 66, 67, 68, 69],
[ 10, 11, 12, 13, 14, 70, 71, 72, 73, 74],
[ 15, 16, 17, 18, 19, 75, 76, 77, 78, 79]],
[[ 20, 21, 22, 23, 24, 80, 81, 82, 83, 84],
[ 25, 26, 27, 28, 29, 85, 86, 87, 88, 89],
[ 30, 31, 32, 33, 34, 90, 91, 92, 93, 94],
[ 35, 36, 37, 38, 39, 95, 96, 97, 98, 99]],
[[ 40, 41, 42, 43, 44, 100, 101, 102, 103, 104],
[ 45, 46, 47, 48, 49, 105, 106, 107, 108, 109],
[ 50, 51, 52, 53, 54, 110, 111, 112, 113, 114],
[ 55, 56, 57, 58, 59, 115, 116, 117, 118, 119]]])

Implementing GIFT-COFB algorithm using Cryptol- list problem

I'm already new to Haskell with Cryptol dialect, also I'm irritated because I can't use loops...
I would like to implement array like this one... Initialization Matrix but I have the only idea to get every 4th element starting by [0] index and load this new list to S0. Similarly starting by 1 index of the list and load to new S1 array every 4th element.

Cryptol's type system is designed so that these sorts of bit splits that you find in crypto algorithms is almost trivial to express. And in fact, lack of loops is a plus, not a detriment, once you get used to that style.
There could be multiple ways to code your "initialization" code. But here's how I would go about it:
load : {a} [128][a] -> [4][32][a]
load(elts) = reverse (transpose cols)
where cols : [32][4][a]
cols = split elts
Note that the type here is more general than what you need, but it allows for easier testing. Here's what I get at the cryptol prompt:
Main> :set base=10
Main> load [127, 126 .. 0]
Showing a specific instance of polymorphic result:
* Using '7' for type argument 'a' of 'Main::load'
[[124, 120, 116, 112, 108, 104, 100, 96, 92, 88, 84, 80, 76, 72,
68, 64, 60, 56, 52, 48, 44, 40, 36, 32, 28, 24, 20, 16, 12, 8, 4,
0],
[125, 121, 117, 113, 109, 105, 101, 97, 93, 89, 85, 81, 77, 73, 69,
65, 61, 57, 53, 49, 45, 41, 37, 33, 29, 25, 21, 17, 13, 9, 5, 1],
[126, 122, 118, 114, 110, 106, 102, 98, 94, 90, 86, 82, 78, 74, 70,
66, 62, 58, 54, 50, 46, 42, 38, 34, 30, 26, 22, 18, 14, 10, 6, 2],
[127, 123, 119, 115, 111, 107, 103, 99, 95, 91, 87, 83, 79, 75, 71,
67, 63, 59, 55, 51, 47, 43, 39, 35, 31, 27, 23, 19, 15, 11, 7, 3]]
This is a little hard to read, so here it is formatted:
[[124, 120, 116, 112, 108, 104, 100, 96, 92, 88, 84, 80, 76, 72, 68, 64, 60, 56, 52, 48, 44, 40, 36, 32, 28, 24, 20, 16, 12, 8, 4, 0],
[125, 121, 117, 113, 109, 105, 101, 97, 93, 89, 85, 81, 77, 73, 69, 65, 61, 57, 53, 49, 45, 41, 37, 33, 29, 25, 21, 17, 13, 9, 5, 1],
[126, 122, 118, 114, 110, 106, 102, 98, 94, 90, 86, 82, 78, 74, 70, 66, 62, 58, 54, 50, 46, 42, 38, 34, 30, 26, 22, 18, 14, 10, 6, 2],
[127, 123, 119, 115, 111, 107, 103, 99, 95, 91, 87, 83, 79, 75, 71, 67, 63, 59, 55, 51, 47, 43, 39, 35, 31, 27, 23, 19, 15, 11, 7, 3]]
which is exactly the structure you wanted. Now we can specialize:
loadBits : [128] -> [4][32]
loadBits(vector) = reverse (transpose cols)
where cols : [32][4]
cols = split vector
Note that the code is exactly the same as before, we just made it specific to the type you wanted.
Hope this gets you started!

Copy selected values (via view) from boost::multi_array to another array (C++)

How can I copy (deep-copy) a selcted range (view) from a boost::multi_array to another array?

The values can be copied via =operator.
#include <iostream>
#include <string>
#include <boost/multi_array.hpp>
template<typename T>
void initArray(T& to_initialize)
{
int value = 0;
for(size_t i=0;i<to_initialize.shape()[0];++i){
for(size_t j=0;j<to_initialize.shape()[1];++j){
to_initialize[i][j]=value;
++value;
}
}
}
template<typename T>
void printArray(T& to_print, std::string additional_text)
{
std::cout<<"**************"<<additional_text<<"*****************"<<std::endl;
for(size_t i=0;i<to_print.shape()[0];++i){
for(size_t j=0;j<to_print.shape()[1];++j){
std::cout<<to_print[i][j]<<", ";
}
std::cout<<std::endl;
}
std::cout<<"*******************************"<<std::endl;
}
int main()
{
auto big_array = boost::multi_array<double, 2>(boost::extents[10][10]);
initArray(big_array);
printArray(big_array, "initial big array");
using range = boost::multi_array_types::index_range;
boost::multi_array<double, 2>::index_gen indices;
boost::multi_array<double, 2>::array_view<2>::type big_array_view = big_array[ indices[range(0,2)][range(0,4)] ];
auto small_array = boost::multi_array<double, 2>(boost::extents[2][4]);
small_array = big_array_view; //Deep Copy
printArray(small_array, "small array after copy");
big_array_view[0][0]=999; // Does not affect small_array
printArray(big_array, "big array after modifying");
printArray(small_array, "small array is not affected after modifying big array");
}
Output is:
**************initial big array*****************
0, 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,
*******************************
**************small array after copy*****************
0, 1, 2, 3,
10, 11, 12, 13,
*******************************
**************big array after modifying*****************
999, 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,
*******************************
**************small array is not affected after modifying big array*****************
0, 1, 2, 3,
10, 11, 12, 13,
*******************************

numpy memory erros on all possible combinations

I have been using _list = np.unique(np.stack(np.meshgrid(*_load), -1).reshape(-1, len(_load)), axis=0) to generate a list of all possible combinations, which worked fine on list of list that look like,
[[1, 2, 3], [8, 4, 5, 6, 7], [8, 4, 5, 6, 7], [8, 4, 5, 6, 7], [8, 4, 5, 6, 7], [9, 10, 11, 12, 13, 14], [9, 10, 11, 12, 13, 14], [9, 10, 11, 12, 13, 14], [9, 10, 11, 12, 13, 14], [9, 10, 11, 12, 13, 14]]
Howeveer, if I want to find all possibles on something like
[[3, 4, 69, 134, 39, 42, 46, 15, 99, 20, 120, 123, 93], [130, 5, 7, 139, 14, 143, 33, 48, 50, 51, 52, 53, 55, 58, 60, 62, 67, 84, 85, 87, 91, 105, 106, 107, 111, 121, 127], [130, 5, 7, 139, 14, 143, 33, 48, 50, 51, 52, 53, 55, 58, 60, 62, 67, 84, 85, 87, 91, 105, 106, 107, 111, 121, 127], [1, 132, 133, 135, 138, 11, 12, 142, 16, 147, 24, 25, 27, 28, 29, 30, 31, 35, 36, 40, 47, 54, 57, 63, 66, 68, 70, 71, 72, 140, 76, 81, 83, 88, 90, 92, 144, 98, 100, 103, 109, 110, 112, 114, 118, 122], [1, 132, 133, 135, 138, 11, 12, 142, 16, 147, 24, 25, 27, 28, 29, 30, 31, 35, 36, 40, 47, 54, 57, 63, 66, 68, 70, 71, 72, 140, 76, 81, 83, 88, 90, 92, 144, 98, 100, 103, 109, 110, 112, 114, 118, 122], [128, 129, 2, 131, 6, 8, 9, 10, 13, 141, 17, 18, 19, 21, 22, 23, 26, 32, 34, 37, 38, 41, 43, 44, 45, 49, 137, 56, 59, 61, 64, 65, 73, 74, 75, 77, 78, 79, 80, 82, 86, 89, 94, 95, 96, 97, 101, 102, 145, 104, 108, 146, 113, 115, 116, 117, 119, 136, 124, 125, 126], [128, 129, 2, 131, 6, 8, 9, 10, 13, 141, 17, 18, 19, 21, 22, 23, 26, 32, 34, 37, 38, 41, 43, 44, 45, 49, 137, 56, 59, 61, 64, 65, 73, 74, 75, 77, 78, 79, 80, 82, 86, 89, 94, 95, 96, 97, 101, 102, 145, 104, 108, 146, 113, 115, 116, 117, 119, 136, 124, 125, 126], [128, 129, 2, 131, 6, 8, 9, 10, 13, 141, 17, 18, 19, 21, 22, 23, 26, 32, 34, 37, 38, 41, 43, 44, 45, 49, 137, 56, 59, 61, 64, 65, 73, 74, 75, 77, 78, 79, 80, 82, 86, 89, 94, 95, 96, 97, 101, 102, 145, 104, 108, 146, 113, 115, 116, 117, 119, 136, 124, 125, 126], [128, 129, 2, 131, 6, 8, 9, 10, 13, 141, 17, 18, 19, 21, 22, 23, 26, 32, 34, 37, 38, 41, 43, 44, 45, 49, 137, 56, 59, 61, 64, 65, 73, 74, 75, 77, 78, 79, 80, 82, 86, 89, 94, 95, 96, 97, 101, 102, 145, 104, 108, 146, 113, 115, 116, 117, 119, 136, 124, 125, 126]]
I get a MemoryError in python, obviously I need to change my approach, any ideas? I was thinking I would need to end up writing the intermittent events to file, but I don't know how to get these built ins to do that.

Your algorithm is fine, but your result is unrepresentable.
Note in particular that your np.unique is useless, because each load[i] contains no duplicates, so the size of the result is the product of the lengths of the lists times the number of lists
>>> np.prod([len(i) for i in second_example], dtype=np.int64) * 9
2498897217529908
Assuming optimistically that each integer is a uint8, that's 2.2 PiB (Pebibytes), which far exceeds current RAM configurations.
Even if you don't try to put the whole result in memory at once, even iterating over this is going to take a long time - assuming a generous 4GHz processor and a single clock cycle per result, you're looking at longer than a week to finish

How to use regular expression to match square brackets of values and store in python dictionary?

I have a data and want to get the results stored in a python dictionary as below:
#example mydicdata[key] = values in the brackets
#example mydicdata[0] = [""]
#example mydicdata[7] = ['0', '1', '2', '3', '4', '5', '6', '7'... ]
import re
data = "{0=[], 1=[], 2=[], 3=[], 4=[], 5=[], 6=[], 7=[0, 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, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103], 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=[0, 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, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103], 33=[], 34=[], 35=[], 36=[], 37=[], 38=[], 39=[], 40=[], 41=[], 42=[], 43=[], 44=[], 45=[], 46=[], 47=[], 48=[], 49=[], 50=[], 51=[], 52=[0, 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, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103], 53=[], 54=[], 55=[], 56=[], 57=[], 58=[], 59=[], 60=[], 61=[], 62=[], 63=[], 64=[], 65=[], 66=[], 67=[], 68=[], 69=[0, 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, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103], 70=[0, 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, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103], 71=[], 72=[], 73=[], 74=[], 75=[], 76=[], 77=[], 78=[], 79=[], 80=[], 81=[], 82=[], 83=[], 84=[], 85=[], 86=[], 87=[], 88=[88], 89=[0, 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, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103], 90=[], 91=[], 92=[], 93=[], 94=[], 95=[], 96=[], 97=[], 98=[], 99=[], 100=[], 101=[], 102=[], 103=[]}"
data = data[1:-1]
temp = re.split(r'[\d=/[[0-9?,/d?/]]]',data)
I think I'm almost there, but the result I got here is a big chunk of list 0=[]....,103[].
Could you please give me the guideline?
Thank you.

this is a way to do it without regex: your data string is almost python (just need to replace the = by :); then ast.literal_eval can turn the string into a python dictionary:
from ast import literal_eval
data = '''{ 0=[], 1=[], 2=[], 3=[], 4=[], 5=[], 6=[],
7=[0, 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, 89, 90, 91, 92,
93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103], 8=[], 9=[],
10=[], 11=[], 12=[], 13=[], 14=[], 15=[], 16=[], 17=[], 18=[]
# more data
}'''
dct = literal_eval(data.replace('=', ':'))
print dct[0] # -> []
print dct[7] # -> [0, 1, 2, 3, 4,...,100, 101, 102, 103]