For a Lattice Boltzmann simulation of a lid-driven cavity (CFD) I'm decomposing my cubic domain into (also cubic) 8 subdomains, which are computed independently by 8 ranks. Each MPI rank is producing a VTK file for each timestep and since I'm using ParaView I want to visualize the whole thing as one cube. To be more specific about what I am trying to achieve:
I have a cube with length 8 (number of elements for each direction) => 8x8x8 = 512 elements.
Each dimension is distributed to 2 ranks, i.e. every rank handles 4x4x4 = 64 elements.
Every rank writes it's result to a file called lbm_out_<rank>.<timestep>.vts in a VTK StructuredGrid format.
I want to produce a .pvts file that collects the *.vts files and combines the files containing the subdomains to a single file that ParaView can treat as whole domain.
Unfortunately I'm facing many issues with that since I feel ParaView and VTK are extremely poorly documented and the error messages from ParaView are totally useless.
I'm having the following *.pvts file, which includes a ghost layer and:
<?xml version="1.0"?>
<VTKFile type="PStructuredGrid" version="0.1" byte_order="LittleEndian">
<PStructuredGrid WholeExtent="0 7 0 7 0 7 " GhostLevel="1">
<PPoints>
<PDataArray NumberOfComponents="3" type="Float32" />
</PPoints>
<Piece Extent="0 4 0 4 0 4" Source="lbm_out_0.0.vts"/>
<Piece Extent="3 7 0 4 0 4" Source="lbm_out_1.0.vts"/>
<Piece Extent="0 4 3 7 0 4" Source="lbm_out_2.0.vts"/>
<Piece Extent="3 7 3 7 0 4" Source="lbm_out_3.0.vts"/>
<Piece Extent="0 4 0 4 3 7" Source="lbm_out_4.0.vts"/>
<Piece Extent="3 7 0 4 3 7" Source="lbm_out_5.0.vts"/>
<Piece Extent="0 4 3 7 3 7" Source="lbm_out_6.0.vts"/>
<Piece Extent="3 7 3 7 3 7" Source="lbm_out_7.0.vts"/>
</PStructuredGrid>
</VTKFile>
Having that file, which I feel should work correctly (note that there are not parameters yet, just plain geometry information), my domain ranges are totally messed up, although each *.vts file works fine on its own. I have a screenshot attached to make things more clear:
What may be the problem? Is it possible to use legacy VTK files for this tasks? May I be doing something totally wrong? I really don't know how to accomplish this task and the resources I find in google are very limited. Thank you.
Unfortunately there is no example for vtkXMLPStructuredGridWriter class (VTK Classes not used in the Examples). So I decided to write the simplest code to generate *.vts and .pvts files for a structured grid, very similar to the case you are looking for.
The following code uses MPI and VTK to write parallel structured grid files. In this example, we have two processes which create their own .vts files and the vtkXMLPStructuredGridWriter class writes the .pvts file:
// MPI Library
#include <mpi.h>
//VTK Library
#include <vtkXMLPStructuredGridWriter.h>
#include <vtkStructuredGrid.h>
#include <vtkSmartPointer.h>
#include <vtkFloatArray.h>
#include <vtkCellData.h>
#include <vtkMPIController.h>
#include <vtkProgrammableFilter.h>
#include <vtkInformation.h>
struct Args {
vtkProgrammableFilter* pf;
int local_extent[6];
};
// function to operate on the point attribute data
void execute (void* arg) {
Args* args = reinterpret_cast<Args*>(arg);
auto info = args->pf->GetOutputInformation(0);
auto output_tmp = args->pf->GetOutput();
auto input_tmp = args->pf->GetInput();
vtkStructuredGrid* output = dynamic_cast<vtkStructuredGrid*>(output_tmp);
vtkStructuredGrid* input = dynamic_cast<vtkStructuredGrid*>(input_tmp);
output->ShallowCopy(input);
output->SetExtent(args->local_extent);
}
int main (int argc, char *argv[]) {
MPI_Init (&argc, &argv);
int myrank;
MPI_Comm_rank (MPI_COMM_WORLD, &myrank);
int lx {10}, ly{10}, lz{10}; //local dimensions of the process's grid
int dims[3] = {lx+1, ly+1, lz+1};
int global_extent[6] = {0, 2*lx, 0, ly, 0, lz};
int local_extent[6] = {myrank*lx, (myrank+1)*lx, 0, ly, 0, lz};
// Create and Initialize vtkMPIController
auto contr = vtkSmartPointer<vtkMPIController>::New();
contr->Initialize(&argc, &argv, 1);
int nranks = contr->GetNumberOfProcesses();
int rank = contr->GetLocalProcessId();
// Create grid points, allocate memory and Insert them
auto points = vtkSmartPointer<vtkPoints>::New();
points->Allocate(dims[0]*dims[1]*dims[2]);
for (int k=0; k<dims[2]; ++k)
for (int j=0; j<dims[1]; ++j)
for (int i=0; i<dims[0]; ++i)
points->InsertPoint(i + j*dims[0] + k*dims[0]*dims[1],
i+rank*(dims[0]-1), j, k);
// Create a density field. Note that the number of cells is always less than
// number of grid points by an amount of one so we use dims[i]-1
auto density = vtkSmartPointer<vtkFloatArray>::New();
density->SetNumberOfComponents(1);
density->SetNumberOfTuples((dims[0]-1)*(dims[1]-1)*(dims[2]-1));
density->SetName ("density");
int index;
for (int k=0; k<lz; ++k)
for (int j=0; j<ly; ++j)
for (int i=0; i<lx; ++i) {
index = i + j*(dims[0]-1) + k*(dims[0]-1)*(dims[1]-1);
density->SetValue(index, i+j+k);
}
// Create a vtkProgrammableFilter
auto pf = vtkSmartPointer<vtkProgrammableFilter>::New();
// Initialize an instance of Args
Args args;
args.pf = pf;
for(int i=0; i<6; ++i) args.local_extent[i] = local_extent[i];
pf->SetExecuteMethod(execute, &args);
// Create a structured grid and assign point data and cell data to it
auto structuredGrid = vtkSmartPointer<vtkStructuredGrid>::New();
structuredGrid->SetExtent(global_extent);
pf->SetInputData(structuredGrid);
structuredGrid->SetPoints(points);
structuredGrid->GetCellData()->AddArray(density);
// Create the parallel writer and call some functions
auto parallel_writer = vtkSmartPointer<vtkXMLPStructuredGridWriter>::New();
parallel_writer->SetInputConnection(pf->GetOutputPort());
parallel_writer->SetController(contr);
parallel_writer->SetFileName("test.pvts");
parallel_writer->SetNumberOfPieces(nranks);
parallel_writer->SetStartPiece(rank);
parallel_writer->SetEndPiece(rank);
parallel_writer->SetDataModeToBinary();
parallel_writer->Update();
parallel_writer->Write();
contr->Finalize();
// WARNING: it seems that MPI_Finalize is not necessary since we are using
// Finalize() function from vtkMPIController class. Uncomment the following
// line and see what happens.
// MPI_Finalize ();
return 0;
}
This code only writes some data (in this case density which is a scalar) into a file and do not render it. For visualization you will need a software like Paraview.
To run this code, you can use this CMake file:
cmake_minimum_required(VERSION 2.8)
PROJECT(PXMLStructuredGridWriter)
add_executable(PXMLStructuredGridWriter parallel_vtk.cpp)
find_package(VTK REQUIRED)
include(${VTK_USE_FILE})
target_link_libraries(PXMLStructuredGridWriter ${VTK_LIBRARIES})
find_package(MPI REQUIRED)
include_directories(${MPI_INCLUDE_PATH})
target_link_libraries(PXMLStructuredGridWriter ${MPI_LIBRARIES})
At the end you will find an xml file like this in the same directory that you have the executable:
<?xml version="1.0"?>
<VTKFile type="PStructuredGrid" version="0.1" byte_order="LittleEndian" header_type="UInt32" compressor="vtkZLibDataCompressor">
<PStructuredGrid WholeExtent="0 20 0 10 0 10" GhostLevel="2">
<PCellData>
<PDataArray type="Float32" Name="density"/>
</PCellData>
<PPoints>
<PDataArray type="Float32" Name="Points" NumberOfComponents="3"/>
</PPoints>
<Piece Extent="0 10 0 10 0 10" Source="test_0.vts"/>
<Piece Extent="10 20 0 10 0 10" Source="test_1.vts"/>
</PStructuredGrid>
</VTKFile>
Related
I came across different ways of calculating CCN (according to formula CCN = E-N+2P)
One way was to count all the lines in the code separately and the other way is to count a few lines of code as one step; lets have the following example:
1 public class SumAndAverage {
2
3 public static void main (String[] args) {
4 int sum = 0;
5 double average = 0.0;
6 String message = "";
7
8 int num = Integer.parseInt(args[0]);
9
10 if ((num < 1) || (num > 100)) {
11 message = "Invalid number entered.";
12 } else {
13 for (int i = 1; i <= num; i++) {
14 sum += i;
15 }
16 average = (double) sum / num;
17 message = "The sum is " + sum + " and the average is " + average;
18 }
19 System.out.println(message);
20 }
21}
Counting every statement we'd get 12 - 11 + 2x 1 = 3
I was wondering if I "join" lines 4,5,6,8 and count them as one step and do the same with line 16 and 17, would that be correct too? The result would be the same as no of edges would also decrease: 8 - 7 + 2*1 = 3
The right way to calculate complexity is by considering blocks of code. A block of code is where there is no chance of dissecting the execution path.
McCabe's paper mentions the below:
The tool, FLOW, was written in APL to input the source code from Fortran files on disk. FLOW would then break a Fortran job into distinct subroutines and analyze the control structure of each subroutine. It does this by breaking the Fortran subroutines into blocks that are delimited by statements that affect control flow: IF, GOTO ,referenced LABELS, DO, etc.
For other information on complexity, also read through Cyclomatic complexity as a Quality measure
I've been thinking about this but can't seem to figure it out. I need to pick a random integer between 1 to 50 (inclusive) in such a way that each of the integer in it would be equally likely. I will have to do this using a 8 sided dice and a 15 sided dice.
I've read somewhat similar questions related to random number generators with dices but I am still confused. I think it is somewhere along the line of partitioning the numbers into sets. Then, I would roll a die, and then, depending on the outcome, decide which die to roll again.
Can someone help me with this?
As a simple - not necessarily "optimal" solution, roll the 8 sided die, then the 15 sided:
8 sided 15 sided 1..50 result
1 or 2 1..15 1..15
3 or 4 1..15 16..30 (add 15 to 15-sided roll)
5 or 6 1..15 31..45 (add 30 to 15-sided roll)
7 or 8 1..5 46..50 (add 45 to 15-sided roll)
7 or 8 6..15 start again / reroll both dice
lets say you have two functions: d8(), which returns a number from 0 to 7, and d15(), which returns a number from 0 to 14. You want to write a d50() that returns a number from 0 to 49.
Of all the simple ways, this one is probably the most efficient in terms of how many dice you have to roll, and something like this will work for all combinations of dice you have and dice you want:
int d50()
{
int result;
do
{
result = d8()*8+d8(); //random from 0 to 63
} while(result >=50);
return result;
}
If you want really constant time, you can do this:
int d50()
{
int result = d15();
int result = result*15+d15(); //0 to 225
int result = result*8+d8(); //0 to 1799
return result/36; //integer division rounds down
}
This way combines dice until the number of possibilities (1800) is evenly divisible by 50, so the same number of possibilities correspond to each result. This works OK in this case, but doesn't work if the prime factors of the dice you have (2, 3, and 5 in this case), don't cover the factors of the dice you want (2, 5)
I think that you can consider each dice result as a subdivision of a bigger interval. So throwing one 8 sided dice you choose one out the 8 major interval that divide your range of value. Throwing a 15 sided dice means selecting one out the 15 sub-interval and so on.
Considering that 15 = 3*5, 8 = 2*2*2 and 50 = 2*5*5 you can choose 36 = 3*3*2*2 as an handy multiple of 50 so that:
15*15*8 = 50*36 = 1800
You can even think of expressing the numbers from 0 to 1799 in base 15 and choose ramdomly the three digits:
choice = [0-7]*15^2 + [0-14]*15^1 + [0-14]*15^0
So my proposal, with a test of the distribution, is (in the c++ language):
#include <iostream>
#include <random>
#include <map>
int main() {
std::map<int, int> hist;
int result;
std::random_device rd;
std::mt19937 gen(rd()); // initialiaze the random generator
std::uniform_int_distribution<> d8(0, 7); // istantiate the dices
std::uniform_int_distribution<> d15(0, 14);
for (int i = 0; i < 20000; ++i) { // make a lot of throws...
result = d8(gen) * 225;
result += d15(gen) * 15; // add to result
result += d15(gen);
++hist[ result / 36 + 1]; // count each result
}
for (auto p : hist) { // show the occurences of each result
std::cout << p.first << " : " << p.second << '\n';
}
return 0;
}
The output should be something like this:
1 : 387
2 : 360
3 : 377
4 : 393
5 : 402
...
48 : 379
49 : 378
50 : 420
My goal is to know how to create my own marker and use it
I'm having trouble to understand how to make the matrix matches the AR Marker PNG.
Id really love someone to either explain how this and the PNG are working together,
Actually Im a bit embarrassed as on further reading it is not hamming code,
but based on hamming code Still possibly someone familiar with hamming code might be able to help this is
(the whole tutorial link is at the bottom of the post)
The main difference with the hamming code is that the first bit (parity of bits 3 and 5) is inverted. So, ID 0 (which in hamming code is 00000) becomes 10000 in our code. The idea is to prevent a completely black rectangle from being a valid marker ID, with the goal of reducing the likelihood of false positives with objects of the environment.
As there are four possible orientations of the marker picture, we have to find the correct marker position. Remember, we introduced three parity bits for each two bits of information. With their help we can find the hamming distance for each possible marker orientation. The correct marker position will have zero hamming distance error, while the other rotations won't.
Here is a code snippet that rotates the bit matrix four times and finds the correct marker orientation:
//check all possible rotations
cv::Mat rotations[4];
int distances[4];
rotations[0] = bitMatrix;
distances[0] = hammDistMarker(rotations[0]);
std::pair<int,int> minDist(distances[0],0);
for (int i=1; i<4; i++)
{
//get the hamming distance to the nearest possible word
rotations[i] = rotate(rotations[i-1]);
distances[i] = hammDistMarker(rotations[i]);
if (distances[i] < minDist.first)
{
minDist.first = distances[i];
minDist.second = i;
}
}
This code finds the orientation of the bit matrix in such a way that it gives minimal error for the hamming distance metric. This error should be zero for correct marker ID; if it's not, it means that we encountered a wrong marker pattern (corrupted image or false-positive marker detection).
**this is the code that I think is relating to the Marker png shown
can anyone help me to understand the matrix so I can use it.
ALL diagrams, thoughts and explanations happily accepted for a non maths person to get an understanding of this quite complex problem ;P !
![the working AR marker when view from iPad][4]
//
// Marker.cpp
// Example_MarkerBasedAR
//
// Created by Ievgen Khvedchenia on 3/13/12.
// Copyright (c) 2012 Ievgen Khvedchenia. All rights reserved.
//
#include "Marker.hpp"
#include "DebugHelpers.hpp"
Marker::Marker()
: id(-1)
{
}
bool operator<(const Marker &M1,const Marker&M2)
{
return M1.id<M2.id;
}
cv::Mat Marker::rotate(cv::Mat in)
{
cv::Mat out;
in.copyTo(out);
for (int i=0;i<in.rows;i++)
{
for (int j=0;j<in.cols;j++)
{
out.at<uchar>(i,j)=in.at<uchar>(in.cols-j-1,i);
}
}
return out;
}
int Marker::hammDistMarker(cv::Mat bits)
{
int ids[4][5]=
{
{1,0,0,0,0},
{1,0,1,1,1},
{0,1,0,0,1},
{0,1,1,1,0}
};
int dist=0;
for (int y=0;y<5;y++)
{
int minSum=1e5; //hamming distance to each possible word
for (int p=0;p<4;p++)
{
int sum=0;
//now, count
for (int x=0;x<5;x++)
{
sum += bits.at<uchar>(y,x) == ids[p][x] ? 0 : 1;
}
if (minSum>sum)
minSum=sum;
}
//do the and
dist += minSum;
}
return dist;
}
int Marker::mat2id(const cv::Mat &bits)
{
int val=0;
for (int y=0;y<5;y++)
{
val<<=1;
if ( bits.at<uchar>(y,1)) val|=1;
val<<=1;
if ( bits.at<uchar>(y,3)) val|=1;
}
return val;
}
int Marker::getMarkerId(cv::Mat &markerImage,int &nRotations)
{
assert(markerImage.rows == markerImage.cols);
assert(markerImage.type() == CV_8UC1);
cv::Mat grey = markerImage;
// Threshold image
cv::threshold(grey, grey, 125, 255, cv::THRESH_BINARY | cv::THRESH_OTSU);
#ifdef SHOW_DEBUG_IMAGES
cv::showAndSave("Binary marker", grey);
#endif
//Markers are divided in 7x7 regions, of which the inner 5x5 belongs to marker info
//the external border should be entirely black
int cellSize = markerImage.rows / 7;
for (int y=0;y<7;y++)
{
int inc=6;
if (y==0 || y==6) inc=1; //for first and last row, check the whole border
for (int x=0;x<7;x+=inc)
{
int cellX = x * cellSize;
int cellY = y * cellSize;
cv::Mat cell = grey(cv::Rect(cellX,cellY,cellSize,cellSize));
int nZ = cv::countNonZero(cell);
if (nZ > (cellSize*cellSize) / 2)
{
return -1;//can not be a marker because the border element is not black!
}
}
}
cv::Mat bitMatrix = cv::Mat::zeros(5,5,CV_8UC1);
//get information(for each inner square, determine if it is black or white)
for (int y=0;y<5;y++)
{
for (int x=0;x<5;x++)
{
int cellX = (x+1)*cellSize;
int cellY = (y+1)*cellSize;
cv::Mat cell = grey(cv::Rect(cellX,cellY,cellSize,cellSize));
int nZ = cv::countNonZero(cell);
if (nZ> (cellSize*cellSize) /2)
bitMatrix.at<uchar>(y,x) = 1;
}
}
//check all possible rotations
cv::Mat rotations[4];
int distances[4];
rotations[0] = bitMatrix;
distances[0] = hammDistMarker(rotations[0]);
std::pair<int,int> minDist(distances[0],0);
for (int i=1; i<4; i++)
{
//get the hamming distance to the nearest possible word
rotations[i] = rotate(rotations[i-1]);
distances[i] = hammDistMarker(rotations[i]);
if (distances[i] < minDist.first)
{
minDist.first = distances[i];
minDist.second = i;
}
}
nRotations = minDist.second;
if (minDist.first == 0)
{
return mat2id(rotations[minDist.second]);
}
return -1;
}
void Marker::drawContour(cv::Mat& image, cv::Scalar color) const
{
float thickness = 2;
cv::line(image, points[0], points[1], color, thickness, CV_AA);
cv::line(image, points[1], points[2], color, thickness, CV_AA);
cv::line(image, points[2], points[3], color, thickness, CV_AA);
cv::line(image, points[3], points[0], color, thickness, CV_AA);
}
AR tutorial I'm working from
https://www.packtpub.com/books/content/marker-based-augmented-reality-iphone-or-ipad
I don't have an exhaustive answer, but I think I can explain enough to help your confusion since I am familiar with Hamming distance as well as matrix rotations and other transformations.
From what I can tell:
The matrix you have isn't the bitmap for that marker. It is an array of rotations.
In the algorithm as implemented in the article, the hamming distances are computed with 4 rotations of a marker. So the reason you have 4 rows in the matrix is it is 4 rotations.
I could be wrong, or have oversimplified, maybe this answer will trigger discussion and someone better will see it. I'll look closer at the algorithm and article to see if I can understand it. I made an A in Matrix Theory, but that was 18 years ago and I've frankly forgotten how to transform matrices.
I just found out a clue, but not very sure. Here is my thought:
I found the explanation of "Hamming code" via Wiki http://en.wikipedia.org/wiki/Hamming_code, and how to encode.(have no privilege to insert picture, so please visit the link above)
Here is the code from the book《Mastering OpenCV ...》:
int Marker::mat2id(const cv::Mat &bits)
{
int val=0;
for (int y=0;y<5;y++)
{
val<<=1;
if ( bits.at<uchar>(y,1)) val|=1;
val<<=1;
if ( bits.at<uchar>(y,3)) val|=1;
}
return val;
}
I think only bits 1 and 3 are data, so I took a look at the matrix:
int ids[4][5]=
{
{1,0,0,0,0},// 0,0 -> 0
{1,0,1,1,1},// 0,1 -> 1
{0,1,0,0,1},// 1,0 -> 2
{0,1,1,1,0} // 1,1 -> 3
}; ^ ^
| |
So these 4 cols should be the hamming-code of [0][1][2][3](which 2 bits can encode)
The following is my explanation( maybe incorrect~):
//(1):'d' represents data, 'p' represents parity bits. Among [d1~d4],only [d1][d2] are useful
//(2):then place [d1][d2] into [p1][p2][p4],[p1~p3] is calculated following the circle graph(?) in the Wiki webpage.
//(3):next, write the matrix from the high bits
//(4):finally, according to what the book explains:
The main difference with the hamming code is that the first bit (parity of bits
3 and 5) is inverted. So, ID 0 (which in hamming code is 00000) becomes 10000
in our code. The idea is to prevent a completely black rectangle from being a valid
marker ID, with the goal of reducing the likelihood of false positives with objects of
the environment.
//I invert the [p4] , and I got the matrix above.
origin Num d1 d2 d3 d4 p1 p2 p4 p1 d1 p2 d2 p4 p4 d2 p2 d1 p1 p4 d2 p2 d1 p1
00 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0
01 1 0 0 0 1 1 0 => 1 1 1 0 0 => 0 0 1 1 1 => 1 0 1 1 1
10 0 1 0 0 1 0 1 => 1 0 0 1 1 => 1 1 0 0 1 => 0 1 0 0 1
11 1 1 0 0 0 1 1 0 1 1 1 1 1 1 1 1 0 0 1 1 1 0
[ (1) ] [ (2) ] [ (3) ] [ (4) ]
I do not sure whether this is right, but I got the same result.
If it is true, then we can make our own markers with this matrix.
#Natalie and #mrjoltcola . Hope you can see this~
(this is my first time reply on this forum ,if there are something improper, I`d be glad to receiving advices :) ^_^ )
Can you explain to me how the accessing pixel has been done in this double loop ? how do they change rows and cols and pixel's value?
for(int i=0;i<cv_ptr->image.rows;i++)
{
float* ptr_img_A = cv_ptr->image.ptr<float>(i);
for(int j=0;j<cv_ptr->image.cols;j++)
{
*ptr_img_B=255*(*ptr_img_A)/3.5;
ptr_img_A++;
}
}
Thank you.
First of, is this the complete code or is ptr_img_B actually ptr_img_A in the first row of the inner loop?
Secondly I would recommend naming your variables by the content it has.
for(int i=0;i<cv_ptr->image.rows;i++)
{
float* row_ptr = cv_ptr->image.ptr<float>(i);
for(int j=0;j<cv_ptr->image.cols;j++)
{
*row_ptr=255*(*row_ptr)/3.5;
row_ptr++;
}
}
So basically it scales every pixel in the image with the factor of 255/3.5
Regarding the access of the pixel, it is stored in memory like this
COL
ROW 1 2 3 4
1 0 1 2 3
2 4 5 6 7
3 8 9 10 11
4 12 13 14 15
Then in order to access, for example pixel on row 3, col 2
float* row_ptr = cv_ptr->image.ptr<float>(row-1);
float value = row_ptr[col-1];
Finally I hope you will enjoy your time with openCV, it is a really nice framework :)
Thanks to user3125280, D.W. and Evgeny Kluev the question is updated.
I have a list of webpages and I must download them frequently, each webpage got a different download frequency. Based on this frequency we group the webpages in 5 groups:
Items in group 1 are downloaded once per 1 hour
items in group 2 once per 2 hours
items in group 3 once per 4 hours
items in group 4 once per 12 hours
items in group 5 once per 24 hours
This means, we must download all the group 1 webpages in 1 hour, all the group 2 in 2 hours etc.
I am trying to make an algorithm. As input, I have:
a) DATA_ARR = one array with 5 numbers. Each number represents the number of items in this group.
b) TIME_ARR = one array with 5 numbers (1, 2, 4, 12, 24) representing how often the items will be downloaded.
b) X = the total number of webpages to download per hour. This is calculated using items_in_group/download_frequently and rounded upwards. If we have 15 items in group 5, and 3 items in group 4, this will be 15/24 + 3/12 = 0.875 and rounded is 1.
Every hour my program must download at max X sites. I expect the algorithm to output something like:
Hour 1: A1 B0 C4 D5
Hour 2: A2 B1 C2 D2
...
A1 = 2nd item of 1st group
C0 = 1st item of 3rd group
My algorithm must be as efficient as possible. This means:
a) the pattern must be extendable to at least 200+ hours
b) no need to create a repeatable pattern
c) spaces are needed when possible in order to use the absolute minimum bandwidth
d) never ever download an item more often than the update frequency, no exceptions
Example:
group 1: 0 items | once per 1 hour
group 2: 3 items | once per 2 hours
group 3: 4 items | once per 4 hours
group 4: 0 items | once per 12 hours
group 5: 0 items | once per 24 hours
We calculate the number of items we can take per hour: 3/2+4/4 = 2.5. We round this upwards and it's 3.
Using pencil and paper, we can found the following solution:
Hour 1: B0 C0 B1
Hour 2: B2 C1 c2
Hour 3: B0 C3 B1
Hour 4: B2
Hour 5: B0 C0 B1
Hour 6: B2 C1 c2
Hour 7: B0 C3 B1
Hour 8: B2
Hour 9: B0 C0 B1
Hour 10: B2 C1 c2
Hour 11: B0 C3 B1
Hour 12: B2
Hour 13: B0 C0 B1
Hour 14: B2 C1 c2
and continue the above.
We take C0, C1 C2, and C3 once every 4 hours. We also take B0, B1 and B2 once every 2 hours.
Question: Please, explain to me, how to design an algorithm able to download the items, while using the absolute minimum number of downloads? Brute force is NOT a solution and the algorithm must be efficient CPU wise because the number of elements can be huge.
You may read the answer posted here: https://cs.stackexchange.com/a/19422/12497 as well as the answer posted bellow by user3125280.
You problem is a typical scheduling problem. These kinds of problems are well studied in computer science so there is a huge array of literature to consult.
The code is kind of like Deficit round robin, but with a few simplifications. First, we feed the queues ourself by adding to the data_to_process variable. Secondly, the queues just iterate through a list of values.
One difference is that this solution will get the optimal value you want, barring mathematical error.
Rough sketch: have not compiled (c++11) unix based, to spec code
#include <iostream>
#include <vector>
#include <numeric>
#include <unistd.h>
//#include <cmath> //for ceil
#define TIME_SCALE ((double)60.0) //1 for realtime speed
//Assuming you are not refreshing ints in the real case
template<typename T>
struct queue
{
const std::vector<T> data; //this will be filled with numbers
int position;
double refresh_rate; //must be refreshed ever ~ hours
double data_rate; //this many refreshes per hour
double credit; //amount of refreshes owed
queue(std::initializer_list<T> v, int r ) :
data(v), position(0), refresh_rate(r), credit(0) {
data_rate = data.size() / (double) refresh_rate;
}
int getNext() {
return data[position++ % data.size()];
}
};
double time_passed(){
static double total;
//if(total < 20){ //stop early
usleep(60000000 / TIME_SCALE); //sleep for a minute
total += 1.0 / 60.0; //add a minute
std::cout << "Time: " << total << std::endl;
return 1.0; //change to 1.0 / 60.0 for real time speed
//} else return 0;
}
int main()
{
//keep a list of the queues
std::vector<queue<int> > queues{
{{1, 2, 3}, 2},
{{1, 2, 3, 4}, 3}};
double total_data_rate = 0;
for(auto q : queues) total_data_rate += q.data_rate;
double data_to_process = 0; //how many refreshes we have to do
int queue_number = 0; //which queue we are processing
auto current_queue = &queues[0];
while(1) {
data_to_process += time_passed() * total_data_rate;
//data_to_process = ceil(data_to_process) //optional
while(data_to_process >= 1){
//data_to_process >= 0 will make the the scheduler more
//eager in the first time period (ie. everything will updated correctly
//in the first period and and following periods
if(current_queue->credit >= 1){
//don't change here though, since credit determines the weighting only,
//not how many refreshes are made
//refresh(current_queue.getNext();
std::cout << "From queue " << queue_number << " refreshed " <<
current_queue->getNext() << std::endl;
current_queue->credit -= 1;
data_to_process -= 1;
} else {
queue_number = (queue_number + 1) % queues.size();
current_queue = &queues[queue_number];
current_queue->credit += current_queue->data_rate;
}
}
}
return 0;
}
The example should now compile on gcc with --std=c++11 and give you what you want.
and here is test case output: (for non-time scaled earlier code)
Time: 0
From queue 1 refreshed 1
From queue 0 refreshed 1
From queue 1 refreshed 2
Time: 1
From queue 0 refreshed 2
From queue 0 refreshed 3
From queue 1 refreshed 3
Time: 2
From queue 0 refreshed 1
From queue 1 refreshed 4
From queue 1 refreshed 1
Time: 3
From queue 0 refreshed 2
From queue 0 refreshed 3
From queue 1 refreshed 2
Time: 4
From queue 0 refreshed 1
From queue 1 refreshed 3
From queue 0 refreshed 2
Time: 5
From queue 0 refreshed 3
From queue 1 refreshed 4
From queue 1 refreshed 1
As an extension, to answer the repeating pattern problem by allowing this scheduler to complete only the first lcm(update_rate * lcm(...refresh rates...), ceil(update_rate)) steps, and then repeating the pattern.
ALSO: this will, indeed, be unsolvable sometimes because of the requirement on hour boundaries. When I use your unsolvable example, and modify time_passed to return 0.1, the schedule is solved with updates every 1.1 hours (just not at the hour boundaries!).
It seems your constraints are all over the place. To quickly summarise my other answer:
It meets the refresh rates only on average
It does the least number of downloads at hour intervals required to fulfil the above
It was based on these (sometimes unfulfillable) constraints
Update at discrete, 1 hour intervals
Update the fewest items each time
Update each item at fixed intervals
and broke 3.
Since both the hourly interval and least-each-time constraints are not really necessary, I will give a simpler, better answer here, which breaks 2.
#include <iostream>
#include <vector>
#include <numeric>
#include <unistd.h>
#define TIME_SCALE ((double)60.0)
//Assuming you are not refreshing ints in the real case
template<typename T>
struct queue
{
const std::vector<T> data; //this is the data to refresh
int position; //this is the data we are up to
double refresh_rate; //must be refreshed every this many hours
double data_rate; //this many refreshes per hour
double credit; //is owed this many refreshes
const char* name;//a name for each queue
queue(std::initializer_list<T> v, int r, const char* n ) :
data(v), position(0), refresh_rate(r), credit(0), name(n) {
data_rate = data.size() / (double) refresh_rate;
}
void refresh() {
std::cout << "From queue " << name << " refreshed " << data[position++ % data.size()] << "\n";
}
};
double time_passed(){
static double total;
usleep(60000000 / TIME_SCALE); //sleep for a minute
total += 1.0; //add a minute
std::cout << "Time: " << total << std::endl;
return 1.0; //change to 1.0 / 60.0 for real time speed
}
int main()
{
//keep a list of the queues
std::vector<queue<int> > queues{
{{1}, 1, "A"},
{{1}, 2, "B"}};
while(1) {
auto t = time_passed();
for(queue<int>& q : queues) {
q.credit += q.data_rate * t;
while(q.credit >= 1){
q.refresh();
q.credit -= 1.0;
}
}
}
return 0;
}
It has the potential, however, to schedule many refreshes on the same hour. There is a third option as well, which breaks the hour-interval rule and updates only one at a time.
I think this is the easiest and requires the minimal number of updates (like the previous answer) but doesn't break rule 3.