The goal is to add as much OpenMP to the following Cholesky factor function to increase parallelization. So far, I only have one #pragma omp parallel for implemented correctly. vector<vector<double>> represents a 2-D matrix. I've already tried adding #pragma omp parallel for for
for (int i = 0; i < n; ++i), for (int k = 0; k < i; ++k), and for (int j = 0; j < k; ++j) but the parallelization goes wrong. makeMatrix(n, n) initializes a vector<vector<double>> of all zeroes of size nxn.
vector<vector<double>> cholesky_factor(vector<vector<double>> input)
{
int n = input.size();
vector<vector<double>> result = makeMatrix(n, n);
for (int i = 0; i < n; ++i)
{
for (int k = 0; k < i; ++k)
{
double value = input[i][k];
for (int j = 0; j < k; ++j)
{
value -= result[i][j] * result[k][j];
}
result[i][k] = value / result[k][k];
}
double value = input[i][i];
#pragma omp parallel for
for (int j = 0; j < i; ++j)
{
value -= result[i][j] * result[i][j];
}
result[i][i] = std::sqrt(value);
}
return result;
}
I don't think you can parallelize much more than this with this algorithm, as the ith iteration of the outer loop depends on the results of the i - 1th iteration and the kth iteration of the inner loop depends on the results of the k - 1th iteration.
vector<vector<double>> cholesky_factor(vector<vector<double>> input)
{
int n = input.size();
vector<vector<double>> result = makeMatrix(n, n);
for (int i = 0; i < n; ++i)
{
for (int k = 0; k < i; ++k)
{
double value = input[i][k];
// reduction(-: value) does the same
// (private instances of value are initialized to zero and
// added to the initial instance of value when the threads are joining
#pragma omp parallel for reduction(+: value)
for (int j = 0; j < k; ++j)
{
value -= result[i][j] * result[k][j];
}
result[i][k] = value / result[k][k];
}
double value = input[i][i];
#pragma omp parallel for reduction(+: value)
for (int j = 0; j < i; ++j)
{
value -= result[i][j] * result[i][j];
}
result[i][i] = std::sqrt(value);
}
return result;
}
Related
The goal is to add OpenMP parallelization to for (i = 0; i < n; i++) for the lower triangle solver for the form Ax=b. Expected result is exactly same as the result when there is NO parallelization added to for (i = 0; i < n; i++).
vector<vector<double>> represents a 2-D matrix. makeMatrix(int m, int n) initializes a vector<vector<double>> of all zeroes of size mxn.
Two of the most prominent tries have been left in comments.
vector<vector<double>> lowerTriangleSolver(vector<vector<double>> A, vector<vector<double>> b)
{
vector<vector<double>> x = makeMatrix(A.size(), 1);
int i, j;
int n = A.size();
double s;
//#pragma omp parallel for reduction(+: s)
//#pragma omp parallel for shared(s)
for (i = 0; i < n; i++)
{
s = 0.0;
#pragma omp parallel for
for (j = 0; j < i; j++)
{
s = s + A[i][j] * x[j][0];
}
x[i][0] = (b[i][0] - s) / A[i][i];
}
return x;
}
You could try to assign the outer loop iterations among threads, instead of the inner loop. In this way, you increase the granularity of the parallel tasks and avoid the reduction of the 's' variable.
#pragma omp parallel for
for (int i = 0; i < n; i++){
double s = 0.0;
for (int j = 0; j < i; j++){
s = s + A[i][j] * x[j][0];
}
x[i][0] = (b[i][0] - s) / A[i][i];
}
Unfortunately, that is not possible because there is a dependency between s = s + A[i][j] * x[j][0]; and x[i][0] = (b[i][0] - s) / A[i][i];, more precisely x[j][0] depends upon the x[i][0].
So you can try two approaches:
for (int i = 0; i < n; i++){
double s = 0.0;
#pragma omp parallel for reduction(+:s)
for (int j = 0; j < i; j++){
s = s + A[i][j] * x[j][0];
}
x[i][0] = (b[i][0] - s) / A[i][i];
}
or using SIMD :
for (int i = 0; i < n; i++){
double s = 0.0;
#pragma omp simd reduction(+:s)
for (int j = 0; j < i; j++){
s = s + A[i][j] * x[j][0];
}
x[i][0] = (b[i][0] - s) / A[i][i];
}
I was getting the error: "free(): corrupted unsorted chunks" when trying to run:
#pragma omp parallel for reduction(+:save) shared(save2)
for (size_t i = 0; i <= N; ++i) {
vector<float> dist = cdist(i, arestas);
vector<float> distinv(dist.size());
for (size_t j = 0; j < N(); ++j) {
if (arr[j] > 0)
arrv[j] = (1/N) + (1 / arr[j]);
else
arrv[j] = 0;
}
save = accumulate(arrv.begin(), arrv.end(), 0.0);
vector<double>::iterator iter = save2.begin() + i;
save2.insert(iter, sum);
}
I might miss the point here, but what about just doing it this way (not tested)?
vector<double> sum2(N);
#pragma omp parallel for num_threads(8)
for ( size_t i = 0; i < N; i++ ) {
double sum = 0;
for ( size_t j = 0; j < dist.size(); ++j ) {
if ( dist[j] > 0 ) {
sum += 1. / dist[j];
}
}
sum2[i] = sum;
}
There is still some room for improving this version (by removing the if statement for example, in order to help the vectorization), but unless you had some unexplained constrains in your code, I think this version is a good starting point.
I've just started studying parallel programming with OpenMP, and there is a subtle point in the nested loop. I wrote a simple matrix multiplication code, and checked the result that is correct. But actually there are several ways to parallelize this for loop, which may be different in terms of low-level detail, and I wanna ask about it.
At first, I wrote code below, which multiply two matrix A, B and assign the result to C.
for(i = 0; i < N; i++)
{
for(j = 0; j < N; j++)
{
sum = 0;
#pragma omp parallel for reduction(+:sum)
for(k = 0; k < N; k++)
{
sum += A[i][k]*B[k][j];
}
C[i][j] = sum;
}
}
It works, but it takes really long time. And I find out that because of the location of parallel directive, it will construct the parallel region N2 time. I found it by huge increase in user time when I used linux time command.
Next time, I tried code below which also worked.
#pragma omp parallel for private(i, j, k, sum)
for(i = 0; i < N; i++)
{
for(j = 0; j < N; j++)
{
sum = 0;
for(k = 0; k < N; k++)
{
sum += A[i][k]*B[k][j];
}
C[i][j] = sum;
}
}
And the elapsed time is decreased from 72.720s in sequential execution to 5.782s in parallel execution with the code above. And it is the reasonable result because I executed it with 16 cores.
But the flow of the second code is not easily drawn in my mind. I know that if we privatize all loop variables, the program will consider that nested loop as one large loop with size N3. It can be easily checked by executing the code below.
#pragma omp parallel for private(i, j, k)
for(i = 0; i < N; i++)
{
for(j = 0; j < N; j++)
{
for(k = 0; k < N; k++)
{
printf("%d, %d, %d\n", i, j, k);
}
}
}
The printf was executed N3 times.
But in my second matrix multiplication code, there is sum right before and after the innermost loop. And It bothers me to unfold the loop in my mind easily. The third code I wrote is easily unfolded in my mind.
To summarize, I want to know what really happens behind the scene in my second matrix multiplication code, especially with the change of the value of sum. Or I'll really thank you for some recommendation of tools to observe the flow of multithreads program written with OpenMP.
omp for by default only applies to the next direct loop. The inner loops are not affected at all. This means, your can think about your second version like this:
// Example for two threads
with one thread execute
{
// declare private variables "locally"
int i, j, k;
for(i = 0; i < N / 2; i++) // loop range changed
{
for(j = 0; j < N; j++)
{
sum = 0;
for(k = 0; k < N; k++)
{
sum += A[i][k]*B[k][j];
}
C[i][j] = sum;
}
}
}
with the other thread execute
{
// declare private variables "locally"
int i, j, k;
for(i = N / 2; i < N; i++) // loop range changed
{
for(j = 0; j < N; j++)
{
sum = 0;
for(k = 0; k < N; k++)
{
sum += A[i][k]*B[k][j];
}
C[i][j] = sum;
}
}
}
You can simply all reasoning about variables with OpenMP by declaring them as locally as possible. I.e. instead of the explicit declaration use:
#pragma omp parallel for
for(int i = 0; i < N; i++)
{
for(int j = 0; j < N; j++)
{
int sum = 0;
for(int k = 0; k < N; k++)
{
sum += A[i][k]*B[k][j];
}
C[i][j] = sum;
}
}
This way you the private scope of variable more easily.
In some cases it can be beneficial to apply parallelism to multiple loops.
This is done by using collapse, i.e.
#pragma omp parallel for collapse(2)
for(int i = 0; i < N; i++)
{
for(int j = 0; j < N; j++)
You can imagine this works with a transformation like:
#pragma omp parallel for
for (int ij = 0; ij < N * N; ij++)
{
int i = ij / N;
int j = ij % N;
A collapse(3) would not work for this loop because of the sum = 0 in-between.
Now is one more detail:
#pragma omp parallel for
is a shorthand for
#pragma omp parallel
#pragma omp for
The first creates the threads - the second shares the work of a loop among all threads reaching this point. This may not be of importance for the understanding now, but there are use-cases for which it matters. For instance you could write:
#pragma omp parallel
for(int i = 0; i < N; i++)
{
#pragma omp for
for(int j = 0; j < N; j++)
{
I hope this sheds some light on what happens there from a logical point of view.
I'm trying to understand the operation count of the code given below.
void add(matrix a, matrix b, matrix c, int m, int n)
{
for(int i = 0; i < m; i++)
{
count++; //for 'for' i -------(a)
for(int j = 0; j < n; j++)
{
count++; //for 'for' j -------(b)
c[i][j] = a[i][j] + b[i][j];
count++; //for assignment ------(c)
}
count++; //for last time of 'for' j ------(d)
}
count++; //for lastime of 'for' i ---------(e)
}
The variable count has been used by the author in which this code is to calculate operation count. I do know that the declarative statements (int i = 0; int j = 0) have operation count of 0.
Every time each the for loop will run it, the following expressions should do 2 operation counts for i < m; i++ when only 1 operation i < m is performed.
for(int i = 0; i < m; i++)
for(int j = 0; j < n; j++)
But the author has only calculated it once (a) and (b). Does that means i < m and j < n is not calculated in operation count?
In this line the operation count should be 2: 1 addition operation and 1 assignment operation.
c[i][j] = a[i][j] + b[i][j];
Again he has only calculated it once (c).
Because of the questions I don't know why he incremented count at (d) and (e).
//Simplified program with counting only
line void add (matrix a, matrix b, matrix c, int m, int n)
{
for(int i = 0; i < m; i++)
{
for(int j = 0; j < m; j++)
count += 2;
count += 2;
}
count++;
}
Thank you :)
I have this C++ code.
Loop goes throgh the matrix, finds the min element in each row and subtracts it from each element of corresponding row.
Variable myr is a summ of all min elements
Trying to parallel for:
int min = 0;
int myr = 0;
int temp[SIZE][SIZE];
int size = 0;
...//some initialization
omp_set_num_threads(1);
start_time = omp_get_wtime();
#ifdef _OPENMP
#pragma omp parallel for firstprivate(min, size) reduction(+:myr)
#endif
for(int i = 0; i < size; i++){
min = INFINITY;
for(int j = 0; j < size; j++){
if (temp[i][j] < min)
min = temp[i][j];
}
myr+=min;
for(int j = 0; j < size; j++)
temp[i][j]-=min;
}
end_time = omp_get_wtime();
if I set omp_set_num_threads(2); this part of code starts working slower.
My proc has 2 cores
Why code works slower with 2 threads?
There must be some aliasing or something going on. Make things simpler for OpenMP:
int const size0 = size;
#ifdef _OPENMP
#pragma omp parallel for reduction(+:myr)
#endif
for(int i = 0; i < size0; i++){
int min = INFINITY;
int * tmp = temp[i];
for(int j = 0; j < size0; j++){
if (tmp[j] < min)
min = tmp[j];
}
for(int j = 0; j < size0; j++)
tmp[j]-=min;
myr+=min;
}
That is, have most of the variables local and const if you may.
The parallel part can be reinterpreted as follows (I have used the snippet by #jens-gustedt, but to my experience it didn't make much difference):
#pragma omp parallel private(myr_private) shared(myr)
{
myr_private = 0;
#pragma omp for
for(int i = 0; i < size; i++){
int min = INFINITY;
int * tmp = temp[i];
for(int j = 0; j < size; j++){
if (tmp[j] < min)
min = tmp[j];
}
for(int j = 0; j < size; j++)
tmp[j]-=min;
myr_private+=min;
}
#pragma omp critical
{
myr+=myr_private;
}
}
(This interpretation is straight from http://www.openmp.org/mp-documents/OpenMP3.1.pdf Example A.36.2c).
If number of threads is n>1, there is overhead when #pragma omp parallel creates additional thread(s) and then in critical section, which all of the threads should wait for.
I have experimented with different matrix sizes and in my limited tests two threads are considerably faster with sizes above 1000, and start lagging behind with sizes below 500.