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I am trying to access the results of the eigenvalue decomposition of a general real matrix, using the magma_sgeev routine. My code is as follows -
#include <cstdlib>
#include <iostream>
#include <map>
#include <typeindex>
#include <typeinfo>
#include <magma_v2.h>
#include <random>
#define N 10
#define LDA N
#define LDVL N
#define LDVR N
/* Main program */
int main()
{
magma_init();
/* Locals */
int n = N, lda = LDA, ldvl = LDVL, ldvr = LDVR, info, lwork;
float wkopt;
float *work;
/* Local arrays */
float wr[N], wi[N], vl[LDVL * N], vr[LDVR * N];
float *a = (float *)malloc(LDA * N * sizeof(float));
for (int i = 0; i < LDA * N; i++)
a[i] = rand();
printf("Done populating matrix\n");
lwork = -1;
magma_sgeev_m(MagmaNoVec, MagmaNoVec, n, a, lda, wr, wi, vl, ldvl, vr, ldvr,
work, lwork, &info);
lwork = (int)work[0];
work = (float *)malloc(lwork * sizeof(float));
printf("%d\n", lwork);
magma_sgeev_m(MagmaNoVec, MagmaNoVec, n, a, lda, wr, wi, vl, ldvl, vr, ldvr,
work, lwork, &info);
for (int i = 0; i < N; i++)
printf("%f ", wr[i]);
std::cout << std::endl;
for (int i = 0; i < N; i++)
printf("%f ", wi[i]);
printf("\n");
if (info > 0)
{
printf("The algorithm failed to compute eigenvalues.\n");
exit(1);
}
exit(0);
magma_finalize();
}
As the documentation says, the arrays wr and wi hold the results of the computation. However, there are two issues with this code,
When I try to access the wr and wi, I get a segmentation fault. I am not aware of the inner workings of the magma library, what am I missing, and how do I fix it ?
When I increase the size of the matrix, for example from 5x5 to 10x10. I get a segmentation fault in the first call of magma_sgeev itself. What am I missing
TIA
For a matrix such as
A = [...
12 34 67;
90 78 15;
10 71 24];
how could we determine efficiently if it is subset of a larger matrix?
B = [...
12 34 67; % found
89 67 45;
90 78 15; % found
10 71 24; % found, so A is subset of B.
54 34 11];
Here are conditions:
all numbers are integers
matrices are so large, i.e., row# > 100000, column# may vary from 1 to 10 (same for A and B).
Edit:
It seems that ismember for the case of this question, when called only few times works just fine. My initial impression was due to previous experiences where ismember was being invoked many times inside a nested loop resulting in the worst performance.
clear all; clc
n = 200000;
k = 10;
B = randi(n,n,k);
f = randperm(n);
A = B(f(1:1000),:);
tic
assert(sum(ismember(A,B,'rows')) == size(A,1));
toc
tic
assert(all(any(all(bsxfun(#eq,B,permute(A,[3,2,1])),2),1))); %user2999345
toc
which results in:
Elapsed time is 1.088552 seconds.
Elapsed time is 12.154969 seconds.
Here are more benchmarks:
clear all; clc
n = 20000;
f = randperm(n);
k = 10;
t1 = 0;
t2 = 0;
t3 = 0;
for i=1:7
B = randi(n,n,k);
A = B(f(1:n/10),:);
%A(100,2) = 0; % to make A not submat of B
tic
b = sum(ismember(A,B,'rows')) == size(A,1);
t1 = t1+toc;
assert(b);
tic
b = ismember_mex(A,sortrows(B));
t2 = t2+toc;
assert(b);
tic
b = issubmat(A,B);
t3 = t3+toc;
assert(b);
end
George's skm's
ismember | ismember_mex | issubmat
n=20000,k=10 0.6326 0.1064 11.6899
n=1000,k=100 0.2652 0.0155 0.0577
n=1000,k=1000 1.1705 0.1582 0.2202
n=1000,k=10000 13.2470 2.0033 2.6367
*issubmat eats RAM when n or k is over 10000!
*issubmat(A,B), A is being checked as submat of B.
It seems that ismember is hard to beat, at least using MATLAB code. I created a C implementation which can be used using the MEX compiler.
#include "mex.h"
#if MX_API_VER < 0x07030000
typedef int mwIndex;
typedef int mwSize;
#endif /* MX_API_VER */
#include <math.h>
#include <stdlib.h>
#include <string.h>
int ismember(const double *y, const double *x, int yrow, int xrow, int ncol);
void mexFunction(int nlhs, mxArray *plhs[],
int nrhs, const mxArray *prhs[])
{
mwSize xcol, ycol, xrow, yrow;
/* output data */
int* result;
/* arguments */
const mxArray* y;
const mxArray* x;
if (nrhs != 2)
{
mexErrMsgTxt("2 input required.");
}
y = prhs[0];
x = prhs[1];
ycol = mxGetN(y);
yrow = mxGetM(y);
xcol = mxGetN(x);
xrow = mxGetM(x);
/* The first input must be a sparse matrix. */
if (!mxIsDouble(y) || !mxIsDouble(x))
{
mexErrMsgTxt("Input must be of type 'double'.");
}
if (xcol != ycol)
{
mexErrMsgTxt("Inputs must have the same number of columns");
}
plhs[0] = mxCreateLogicalMatrix(1, 1);
result = mxGetPr(plhs[0]);
*result = ismember(mxGetPr(y), mxGetPr(x), yrow, xrow, ycol);
}
int ismemberinner(const double *y, int idx, const double *x, int yrow, int xrow, int ncol) {
int from, to, i;
from = 0;
to = xrow-1;
for(i = 0; i < ncol; ++i) {
// Perform binary search
double yi = *(y + i * yrow + idx);
double *curx = x + i * xrow;
int l = from;
int u = to;
while(l <= u) {
int mididx = l + (u-l)/2;
if(yi < curx[mididx]) {
u = mididx-1;
}
else if(yi > curx[mididx]) {
l = mididx+1;
}
else {
// This can be further optimized by performing additional binary searches
for(from = mididx; from > l && curx[from-1] == yi; --from);
for(to = mididx; to < u && curx[to+1] == yi; ++to);
break;
}
}
if(l > u) {
return 0;
}
}
return 1;
}
int ismember(const double *y, const double *x, int yrow, int xrow, int ncol) {
int i;
for(i = 0; i < yrow; ++i) {
if(!ismemberinner(y, i, x, yrow, xrow, ncol)) {
return 0;
}
}
return 1;
}
Compile it using:
mex -O ismember_mex.c
It can be called as follows:
ismember_mex(x, sortrows(x))
First of all, it assumes that the columns of the matrices have the same size. It works by first sorting the rows of the larger matrix (x in this case, the second argument to the function). Then, a type of binary search is employed to identify whether the rows of the smaller matrix (y hereafter) are contained in x. This is done for each row of y separately (see ismember C function).
For a given row of y, it starts from the first entry and finds the range of indices (using the from and to variables) that match with the first column of x using binary search. This is repeated for the remaining entries, unless some value is not found, in which case it terminates and returns 0.
I tried implementing it this idea in MATLAB, but it didn't work that well. Regarding performance, I found that: (a) in case there are mismatches, it is usually much faster than ismember (b) in case the range of values in x and y is large, it is again faster than ismember, and (c) in case everything matches and the number of possible values in x and y is small (e.g. less than 1000), then ismember may be faster in some situations.
Finally, I want to point out that some parts of the C implementation may be further optimized.
EDIT 1
I fixed the warnings and further improved the function.
#include "mex.h"
#include <math.h>
#include <stdlib.h>
#include <string.h>
int ismember(const double *y, const double *x, unsigned int nrowy, unsigned int nrowx, unsigned int ncol);
void mexFunction(int nlhs, mxArray *plhs[],
int nrhs, const mxArray *prhs[])
{
unsigned int xcol, ycol, nrowx, nrowy;
/* arguments */
const mxArray* y;
const mxArray* x;
if (nrhs != 2)
{
mexErrMsgTxt("2 inputs required.");
}
y = prhs[0];
x = prhs[1];
ycol = (unsigned int) mxGetN(y);
nrowy = (unsigned int) mxGetM(y);
xcol = (unsigned int) mxGetN(x);
nrowx = (unsigned int) mxGetM(x);
/* The first input must be a sparse matrix. */
if (!mxIsDouble(y) || !mxIsDouble(x))
{
mexErrMsgTxt("Input must be of type 'double'.");
}
if (xcol != ycol)
{
mexErrMsgTxt("Inputs must have the same number of columns");
}
plhs[0] = mxCreateLogicalScalar(ismember(mxGetPr(y), mxGetPr(x), nrowy, nrowx, ycol));
}
int ismemberinner(const double *y, const double *x, unsigned int nrowy, unsigned int nrowx, unsigned int ncol) {
unsigned int from = 0, to = nrowx-1, i;
for(i = 0; i < ncol; ++i) {
// Perform binary search
const double yi = *(y + i * nrowy);
const double *curx = x + i * nrowx;
unsigned int l = from;
unsigned int u = to;
while(l <= u) {
const unsigned int mididx = l + (u-l)/2;
const double midx = curx[mididx];
if(yi < midx) {
u = mididx-1;
}
else if(yi > midx) {
l = mididx+1;
}
else {
{
// Binary search to identify smallest index of x that equals yi
// Equivalent to for(from = mididx; from > l && curx[from-1] == yi; --from)
unsigned int limit = mididx;
while(curx[from] != yi) {
const unsigned int mididx = from + (limit-from)/2;
if(curx[mididx] < yi) {
from = mididx+1;
}
else {
limit = mididx-1;
}
}
}
{
// Binary search to identify largest index of x that equals yi
// Equivalent to for(to = mididx; to < u && curx[to+1] == yi; ++to);
unsigned int limit = mididx;
while(curx[to] != yi) {
const unsigned int mididx = limit + (to-limit)/2;
if(curx[mididx] > yi) {
to = mididx-1;
}
else {
limit = mididx+1;
}
}
}
break;
}
}
if(l > u) {
return 0;
}
}
return 1;
}
int ismember(const double *y, const double *x, unsigned int nrowy, unsigned int nrowx, unsigned int ncol) {
unsigned int i;
for(i = 0; i < nrowy; ++i) {
if(!ismemberinner(y + i, x, nrowy, nrowx, ncol)) {
return 0;
}
}
return 1;
}
Using this version I wasn't able to identify any case where ismember is faster. Also, I noticed that one reason ismember is hard to beat is that it uses all cores of the machine! Of course, the function I provided can be optimized to do this too, but this requires much more effort.
Finally, before using my implementation I would advise you to do extensive testing. I did some testing and it seems to work, but I suggest you also do some additional testing.
For small matrices ismember should be enough, probably.
Usage: ismember(B,A,'rows')
ans =
1
0
1
1
0
I put this answer here, emphasizing on a need to solutions with higher performance. I will accept this answer only if there was no better solution.
Using ismember, if a row of A appears twice in B while another one is missing, might wrongly indicate that A is a member of B. The following solution is suitable if the rows of A and B doesn't need to be in the same order. However, I haven't tested its performance for large matrices.
A = [...
34 12 67;
90 78 15;
10 71 24];
B = [...
34 12 67; % found
89 67 45;
90 78 15; % found
10 71 24; % found, so A is subset of B.
54 34 11];
A = permute(A,[3 2 1]);
rowIdx = all(bsxfun(#eq,B,A),2);
colIdx = any(rowIdx,1);
isAMemberB = all(colIdx);
You have said number of columns <= 10. In addition, if the matrix elements are all integers representable as bytes, you could code each row into a two 64 bit integers. That would reduce the number of comparisons by a factor of 64.
For the general case, the following may not be all that much better for thin matrices, but scales very well as the matrices get fat due to the level 3 multiplication:
function yes = is_submat(A,B)
ma = size(A, 1);
mb = size(B, 1);
n = size(B, 2);
yes = false;
if ma >= mb
a = A(:,1);
b = B(:,1);
D = (0 == bsxfun(#minus, a, b'));
q = any(D, 2);
yes = all(any(D,1));
if yes && (n > 1)
A = A(q, :);
C = B*A';
za = sum(A.*A, 2);
zb = sum(B.*B, 2);
Z = sqrt(zb)*sqrt(za');
[~, ix] = max(C./Z, [], 2);
A = A(ix,:);
yes = all(A(:) == B(:));
end
end
end
In the above, I use the fact that the dot product is maximized when two unit vectors are equal.
For fat matrices (say 5000+ columns) with large numbers of unique elements the performance beats ismember quite handily, but otherwise, it is slower than ismember. For thin matrices ismember is faster by an order of magnitude.
Best case test for this function:
A = randi(50000, [10000, 10000]);
B = A(2:3:end, :);
B = B(randperm(size(B,1)),:);
fprintf('%s: %u\n', 'Number of columns', size(A,2));
fprintf('%s: %u\n', 'Element spread', 50000);
tic; is_submat(A,B); toc;
tic; all(ismember(B,A,'rows')); toc;
fprintf('________\n\n');
is_submat_test;
Number of columns: 10000
Element spread: 50000
Elapsed time is 10.713310 seconds (is_submat).
Elapsed time is 17.446682 seconds (ismember).
So I have to admit, all round ismember seems to be much better.
Edits: Edited to correct bug when there is only one column - fixing this also results in more efficient code. Also previous version did not distinguish between positive and negative numbers. Added timing tests.
I have implemented a CUDA version of inverse discrete cosine transform (IDCT), by "translating" the MATLAB built-in function idct.m into CUDA:
My implementation is cuIDCT.cu, works when m = n and both m and n are even numbers.
cuIDCT.cu
#include <stdio.h>
#include <stdlib.h>
#include <cuda.h>
#include <cufft.h>
#include <cuComplex.h>
// round up n/m
inline int iDivUp(int n, int m)
{
return (n + m - 1) / m;
}
typedef cufftComplex complex;
#define PI 3.1415926535897932384626433832795028841971693993751
__global__
void idct_ComputeWeightsKernel(const int n, complex *ww)
{
const int pos = threadIdx.x + blockIdx.x * blockDim.x;
if (pos >= n) return;
ww[pos].x = sqrtf(2*n) * cosf(pos*PI/(2*n));
ww[pos].y = sqrtf(2*n) * sinf(pos*PI/(2*n));
}
__global__
void idct_ComputeEvenKernel(const float *b, const int n, const int m, complex *ww, complex *y)
{
const int ix = threadIdx.x + blockIdx.x * blockDim.x;
const int iy = threadIdx.y + blockIdx.y * blockDim.y;
if (ix >= n || iy >= m) return;
const int pos = ix + iy*n;
// Compute precorrection factor
ww[0].x = ww[0].x / sqrtf(2);
ww[0].y = ww[0].y / sqrtf(2);
y[iy + ix*m].x = ww[iy].x * b[pos];
y[iy + ix*m].y = ww[iy].y * b[pos];
}
__global__
void Reordering_a0_Kernel(complex *y, const int n, const int m, complex *yy)
{
const int ix = threadIdx.x + blockIdx.x * blockDim.x;
const int iy = threadIdx.y + blockIdx.y * blockDim.y;
if (ix >= n || iy >= m) return;
const int pos = ix + iy*n;
yy[iy + ix*n].x = y[pos].x / (float) n;
yy[iy + ix*n].y = y[pos].y / (float) n;
}
__global__
void Reordering_a_Kernel(complex *yy, const int n, const int m, float *a)
{
const int ix = threadIdx.x + blockIdx.x * blockDim.x;
const int iy = threadIdx.y + blockIdx.y * blockDim.y;
if (ix >= n || iy >= m) return;
const int pos = ix + iy*n;
// Re-order elements of each column according to equations (5.93) and (5.94) in Jain
if (iy < n/2)
{
a[ix + 2*iy*n] = yy[pos].x;
a[ix + (2*iy+1)*n] = yy[ix + (m-iy-1)*n].x;
}
}
/**
* a = idct(b), where a is of size [n m].
* #param b, input array
* #param n, first dimension of a
* #param m, second dimension of a
* #param a, output array
*/
void cuIDCT(float *h_in, int n, int m, float *h_out) // a is of size [n m]
{
const int data_size = n * m * sizeof(float);
// device memory allocation
float *d_in, *d_out;
cudaMalloc(&d_in, data_size);
cudaMalloc(&d_out, data_size);
// transfer data from host to device
cudaMemcpy(d_in, h_in, data_size, cudaMemcpyHostToDevice);
// compute IDCT using CUDA
// begin============================================
// Compute weights
complex *ww;
cudaMalloc(&ww, n*sizeof(complex));
dim3 threads(256);
dim3 blocks(iDivUp(n, threads.x));
idct_ComputeWeightsKernel<<<blocks, threads>>>(n, ww);
complex *y;
complex *yy;
cufftHandle plan;
dim3 threads1(32, 6);
dim3 blocks2(iDivUp(n, threads1.x), iDivUp(m, threads1.y)); // for even case
int Length[1] = {m}; // for each IFFT, the length is m
cudaMalloc(&y, n*m*sizeof(complex));
idct_ComputeEvenKernel<<<blocks2, threads1>>>(d_in, n, m, ww, y);
cufftPlanMany(&plan, 1, Length,
Length, 1, m,
Length, 1, m, CUFFT_C2C, n);
cufftExecC2C(plan, y, y, CUFFT_INVERSE); // y is of size [n m]
cudaMalloc(&yy, n*m*sizeof(complex));
Reordering_a0_Kernel<<<blocks2, threads1>>>(y, n, m, yy);
Reordering_a_Kernel<<<blocks2, threads1>>>(yy, n, m, d_out);
// end============================================
// transfer result from device to host
cudaMemcpy(h_out, d_out, data_size, cudaMemcpyDeviceToHost);
// cleanup
cufftDestroy(plan);
cudaFree(ww);
cudaFree(y);
cudaFree(yy);
cudaFree(d_in);
cudaFree(d_out);
}
Then I compared the result of my CUDA IDCT (i.e. cuIDCT.cu) against MATLAB idct.m using following code:
a test main.cpp function, and
a MATLAB main function main.m to read result from CUDA and compare it against MATLAB.
main.cpp
#include "cuda_runtime.h"
#include "device_launch_parameters.h"
#include <helper_functions.h>
#include <stdlib.h>
#include <stdio.h>
// N must equal to M, and both must be even numbers
#define N 256
#define M 256
void WriteDataFile(const char *name, int w, int h, const float *in, const float *out)
{
FILE *stream;
stream = fopen(name, "wb");
float data = 202021.25f;
fwrite(&data, sizeof(float), 1, stream);
fwrite(&w, sizeof(w), 1, stream);
fwrite(&h, sizeof(h), 1, stream);
for (int i = 0; i < h; i++)
for (int j = 0; j < w; j++)
{
const int pos = j + i * h;
fwrite(in + pos, sizeof(float), 1, stream);
fwrite(out + pos, sizeof(float), 1, stream);
}
fclose(stream);
}
void cuIDCT(float *b, int n, int m, float *a);
int main()
{
// host memory allocation
float *h_in = new float [N * M];
float *h_out = new float [N * M];
float *h_temp = new float [N * M];
// input data initialization
for (int i = 0; i < N * M; i++)
{
h_in[i] = (float)rand()/(float)RAND_MAX;
h_out[i] = h_in[i];
h_temp[i] = h_in[i];
}
// please comment either one case for testing
// test case 1: use cuIDCT.cu once
// cuIDCT(h_in, N, M, h_out);
// test case 2: iteratively use cuIDCT.cu
for (int i = 0; i < 4; i++)
{
if (i % 2 == 0)
cuIDCT(h_out, N, M, h_temp);
else
cuIDCT(h_temp, N, M, h_out);
}
// write data, for further visualization using MATLAB
WriteDataFile("test.flo", N, M, h_in, h_out);
// cleanup
delete [] h_in;
delete [] h_out;
delete [] h_temp;
cudaDeviceReset();
}
main.m
clc;clear;
% read
[h_in, h_out] = read_data('test.flo');
% MATLAB result, for test case 1, comment the for-loop
matlab_out = h_in;
for i = 1:4
matlab_out = idct(matlab_out);
end
% compare
err = matlab_out - h_out;
% show
figure(1);
subplot(221); imshow(h_in, []); title('h\_in'); colorbar
subplot(222); imshow(h_out, []); title('h\_out'); colorbar
subplot(223); imshow(matlab_out, []); title('matlab\_out'); colorbar
subplot(224); imshow(err, []); title('error map'); colorbar
disp(['maximum error between CUDA and MATLAB is ' ...
num2str(max(max(abs(err))))])
I ran the code on Visual Studio 11 (i.e. VS2012) in Windows 7 with Nvidia GPU Tesla K20c, using CUDA Toolkit version 7.5, and my MATLAB version is R2015b.
My test steps:
For test case 1. Un-comment test case 1 and comment test case 2.
Run main.cpp.
Run main.m in MATLAB.
Repeat step 1 and step 2 (without any change, just re-run the code).
I repeated step 3 for 20 times. The output result is unchanged, and results in main.m are:
results of test case 1
The maximum error is 7.7152e-07.
For test case 2. Un-comment test case 2 and comment test case 1.
Run main.cpp.
Run main.m in MATLAB.
Repeat step 1 and step 2 (without any change, just re-run the code).
I repeated step 3 for 20 times. The output result is changed, and results in main.m are (not enough reputation to put all images, only wrong case is shown below):
one situation (the wrong one) of test case 2
The maximum error is 0.45341 (2 times), 0.44898 (1 time), 0.26186 (1 time), 0.26301 (1 time), and 9.5716e-07 (15 times).
From the test results, my conclusion is:
From test case 1: cuIDCT.cu is numerically correct (error ~10^-7) to idct.m.
From test case 2: recursively use of cuIDCT.cu leads to unstable result (i.e. the output changes every time when re-run the code and may sometimes be numerically wrong, error ~0.1)
My question:
From test case 1 we know cuIDCT.cu is numerically correct to idct.m. But why recursiviely use of cuIDCT.cu leads to different output result each time when re-run the code?
Any helps or suggestions are highly appreciated.
I believe the variability in your results is coming about due to this code in your idct_ComputeEvenKernel:
// Compute precorrection factor
ww[0].x = ww[0].x / sqrtf(2);
ww[0].y = ww[0].y / sqrtf(2);
It's not entirely clear what your intent is here, but it's doubtful that this code could be doing what you want. You may be confused about the CUDA execution model.
The above code will be executed by every CUDA thread that you launch for that kernel that passes the thread check:
if (ix >= n || iy >= m) return;
I believe this means 65536 threads will all execute this code in that kernel. Furthermore, the threads will execute that code in more-or-less any order (not all CUDA threads execute in lock-step). They may even step on each other as they are trying to write out their values to the location ww[0]. So the final result in ww[0] will be quite unpredictable.
When I comment out those lines of code, the results become stable for me (albeit different from what they were with those lines in place), unchanging from run to run.
I'd like to point something else out. Wherever you are calculating the .x and .y values of a complex quantity, my suggestion would be to rework the code from this (for example):
y[iy + ix*m].x = ww[iy].x * b[pos];
y[iy + ix*m].y = ww[iy].y * b[pos];
to this:
complex temp1, temp2;
temp1 = ww[iy];
temp2.x = temp1.x * b[pos];
temp2.y = temp2.y * b[pos];
y[iy + ix*m] = temp2;
At least according to my testing, the compiler doesn't seem to be making this optimization for you, and one side-effect benefit is that it's much easier to test your code with cuda-memcheck --tool initcheck .... In the first realization, the compiler will load y[iy + ix*m] as an 8 byte quantity, modify either 4 or 8 bytes of it, then store y[iy + ix*m] as an 8 byte quantity. The second realization should be more efficient (it eliminates the load of y[]), and eliminates the load of an uninitialized quantity (y[]), which the cuda-memcheck tool will report as a hazard.
This variability I'm describing should be possible whether you run either the 1-pass version of your code or the 4-pass version of your code. Therefore I think your statements about the 1-pass version being correct are suspect. I think if you run the 1-pass version enough, you will eventually see variability (although it may require varying initial memory conditions, or running on different GPU types). Even in your own results, we see that 15 out of 20 runs of the 4 pass code produce "correct" results, i.e. the residual error is ~1e-7
Here's my modified cuIDCT.cu file, modified from the version you posted here. The assumption I'm making below is that you wanted to compute the scaling on ww[0] only once, in which case we can easily handle that arithmetic as an addendum to the previous idct_ComputeWeightsKernel:
#include <stdio.h>
#include <stdlib.h>
#include <cuda.h>
#include <cufft.h>
#include <cuComplex.h>
#include <helper_cuda.h>
#include "assert.h"
// round up n/m
inline int iDivUp(int n, int m)
{
return (n + m - 1) / m;
}
typedef cufftComplex complex;
#define PI 3.1415926535897932384626433832795028841971693993751
#define cufftSafeCall(err) __cufftSafeCall(err, __FILE__, __LINE__)
inline void __cufftSafeCall(cufftResult err, const char *file, const int line)
{
if( CUFFT_SUCCESS != err) {
fprintf(stderr, "CUFFT error in file '%s', line %d\n %s\nerror %d: %s\nterminating!\n",__FILE__, __LINE__,err, \
_cudaGetErrorEnum(err)); \
cudaDeviceReset(); assert(0); \
}
}
__global__
void idct_ComputeWeightsKernel(const int n, complex *ww)
{
const int pos = threadIdx.x + blockIdx.x * blockDim.x;
if (pos >= n) return;
complex temp;
temp.x = sqrtf(2*n) * cosf(pos*PI/(2*n));
temp.y = sqrtf(2*n) * sinf(pos*PI/(2*n));
if (pos == 0) {
temp.x /= sqrtf(2);
temp.y /= sqrtf(2);}
ww[pos] = temp;
}
__global__
void idct_ComputeEvenKernel(const float *b, const int n, const int m, complex *ww, complex *y)
{
const int ix = threadIdx.x + blockIdx.x * blockDim.x;
const int iy = threadIdx.y + blockIdx.y * blockDim.y;
if (ix >= n || iy >= m) return;
const int pos = ix + iy*n;
/* handle this in idct_ComputeWeightsKernel
// Compute precorrection factor
ww[0].x = ww[0].x / sqrtf(2);
ww[0].y = ww[0].y / sqrtf(2);
*/
complex temp1, temp2;
temp1 = ww[iy];
temp2.x = temp1.x * b[pos];
temp2.y = temp1.y * b[pos];
y[iy + ix*m] = temp2;
}
__global__
void Reordering_a0_Kernel(complex *y, const int n, const int m, complex *yy)
{
const int ix = threadIdx.x + blockIdx.x * blockDim.x;
const int iy = threadIdx.y + blockIdx.y * blockDim.y;
if (ix >= n || iy >= m) return;
const int pos = ix + iy*n;
complex temp1, temp2;
temp1 = y[pos];
temp2.x = temp1.x / (float) n;
temp2.y = temp1.y / (float) n;
yy[iy + ix*n] = temp2;
}
__global__
void Reordering_a_Kernel(complex *yy, const int n, const int m, float *a)
{
const int ix = threadIdx.x + blockIdx.x * blockDim.x;
const int iy = threadIdx.y + blockIdx.y * blockDim.y;
if (ix >= n || iy >= m) return;
const int pos = ix + iy*n;
// Re-order elements of each column according to equations (5.93) and (5.94) in Jain
if (iy < n/2)
{
a[ix + 2*iy*n] = yy[pos].x;
a[ix + (2*iy+1)*n] = yy[ix + (m-iy-1)*n].x;
}
}
/**
* a = idct(b), where a is of size [n m].
* #param b, input array
* #param n, first dimension of a
* #param m, second dimension of a
* #param a, output array
*/
void cuIDCT(float *h_in, int n, int m, float *h_out) // a is of size [n m]
{
const int data_size = n * m * sizeof(float);
// device memory allocation
float *d_in, *d_out;
checkCudaErrors(cudaMalloc(&d_in, data_size));
checkCudaErrors(cudaMalloc(&d_out, data_size));
// transfer data from host to device
checkCudaErrors(cudaMemcpy(d_in, h_in, data_size, cudaMemcpyHostToDevice));
// compute IDCT using CUDA
// begin============================================
// Compute weights
complex *ww;
checkCudaErrors(cudaMalloc(&ww, n*sizeof(complex)));
dim3 threads(256);
dim3 blocks(iDivUp(n, threads.x));
idct_ComputeWeightsKernel<<<blocks, threads>>>(n, ww);
complex *y;
complex *yy;
cufftHandle plan;
dim3 threads1(32, 6);
dim3 blocks2(iDivUp(n, threads1.x), iDivUp(m, threads1.y)); // for even case
int Length[1] = {m}; // for each IFFT, the length is m
checkCudaErrors(cudaMalloc(&y, n*m*sizeof(complex)));
idct_ComputeEvenKernel<<<blocks2, threads1>>>(d_in, n, m, ww, y);
cufftSafeCall(cufftPlanMany(&plan, 1, Length,
Length, 1, m,
Length, 1, m, CUFFT_C2C, n));
cufftSafeCall(cufftExecC2C(plan, y, y, CUFFT_INVERSE)); // y is of size [n m]
checkCudaErrors(cudaMalloc(&yy, n*m*sizeof(complex)));
Reordering_a0_Kernel<<<blocks2, threads1>>>(y, n, m, yy);
cudaMemset(d_out, 0, data_size);
Reordering_a_Kernel<<<blocks2, threads1>>>(yy, n, m, d_out);
// end============================================
// transfer result from device to host
checkCudaErrors(cudaMemcpy(h_out, d_out, data_size, cudaMemcpyDeviceToHost));
// cleanup
cufftDestroy(plan);
checkCudaErrors(cudaFree(ww));
checkCudaErrors(cudaFree(y));
checkCudaErrors(cudaFree(yy));
checkCudaErrors(cudaFree(d_in));
checkCudaErrors(cudaFree(d_out));
}
You'll note I threw an extra cudaMemset on d_out in there, because it helped me clean up an issue with cuda-memcheck --tool initcheck .... It shouldn't be necessary, you can delete it if you want.
Input: I have some 50000 points in a xy plane as shown in the below picture.
Now, I need to get all the possible points in a triangular ROI. How to get it. It can can be opencv or Matlab.
The below is the sample where I need to get the possible points of the triangular areas.
MATLAB has an inpolygon command: inpolygon.
For example, this code
xv = [0.1 0.4 0.15 0.1]; yv = [0 0.4 0.8 0];
x = rand(250,1); y = rand(250,1);
in = inpolygon(x,y,xv,yv);
plot(xv,yv,x(in),y(in),'r+',x(~in),y(~in),'bo')
generates a picture like this:
Something like this, in c++?
Mat plane = imread("plane.png"); // this is the 50 000 pixel plane image
// I assume your triangles are here. E.e. findContours function would save them here, but I don't know your situation.
vector<vector<Point> > triangles;
// this size is something like 1000, so here are only points that should be checkedd if they are inside some triangle
vector<Point> points;
// lets loop all rois and check if point is inside one of them
for (int j = 0; j < triangles.size(); j++) {
for (int i = 0; i < points.size(); i++) {
double test = pointPolygonTest(trigangles[j], points[i] false);
if (test < 0) {
cout << " point " << points[i] << " is outside of triangle " << j << endl;
} else if (test > 0) {
cout << " point " << points[i] << " is inside of triangle " << j << endl;
} else if (test == 0) {
cout << " point " << points[i] << " is on edge of triangle " << j << endl;
}
}
}
for more info: http://docs.opencv.org/modules/imgproc/doc/structural_analysis_and_shape_descriptors.html?highlight=pointpolygontest#pointpolygontest
here is OpenCV's example: http://docs.opencv.org/trunk/doc/tutorials/imgproc/shapedescriptors/point_polygon_test/point_polygon_test.html
In OpenCV, you can quickly filter out the points that are not in the minimal bounding rectangle for each triangle. This rectangle can be previously computed by hand or with cv::boundingRect(). The hit test is done with Rect::contains(). This is a fast operation (at least much faster than cv::pointPolygonTest)and this will filter out the points that are obviously not in any triangle. Afterward, you test the points that pass the filter with cv::pointPolygonTest().
That is:
std::vector<cv::Point> pointList;
std::vector<cv::Rect> rectList;
std::vector<std::vector<Point>> triangleList;
for (int pointIndex = 0; pointIndex < pointList.size(); pointIndex++)
{
for (int rectIndex = 0; rectIndex < rectList.size(); rectIndex++)
{
if (!rectList[rectIndex].contains(pointList[pointIndex]))
continue;
if (cv::pointPolygonTest(triangleList[rectIndex], pointList[pointIndex], false) < 0)
continue;
/* TODO Mark the point for future use */
}
}
What are good hashing functions (fast, good distribution, few collisions) for hashing 2d and 3d vectors composed of IEEE 32bit floats. I assume general 3d vectors, but algorithms assuming normals (always in [-1,1]) are also welcome. I also do not fear bit-manipulation as IEEE floats are alsways IEEE floats.
Another more general problem is hashing an Nd float-vector, where N is quite small (3-12) and constant but not known at compile time. At the moment I just take these floats as uints and XOR them together, which is probably not the best solution.
There's a spatial hash function described in Optimized Spatial Hashing for Collision Detection of Deformable Objects. They use the hash function
hash(x,y,z) = ( x p1 xor y p2 xor z
p3) mod n
where p1, p2, p3 are large
prime numbers, in our case 73856093,
19349663, 83492791, respectively. The
value n is the hash table size.
In the paper, x, y, and z are the discretized coordinates; you could probably also use the binary values of your floats.
I have two suggestions.
Assume a grid cell of size l and quantize the x, y and z co-ordinates by computing ix = floor(x/l), iy = floor(y/l), and iz = floor(z/l), where ix, iy and iz are integers. Now use the hash function defined in Optimized Spatial Hashing for Collision Detection of Deformable Objects
If you don't do the quantization, it wont be sensitive to closeness(locality).
Locality Sensitive Hashing has been mentioned for hashing higher dimensional vectors. Why not use them for 3d or 2d vectors as well? A variant of LSH using adapted for Eucledian distance metric (which is what we need for 2d and 3d vectors) is called Locality Sensitive Hashing using p-stable distributions. A very readable tutorial is here.
I wrote this in Python based on the comments seen here,
l = 5
n = 5
p1,p2,p3 = 73856093, 19349663, 83492791
x1 = [33,4,11]
x2 = [31,1,14]
x3 = [10,44,19]
def spatial_hash(x):
ix,iy,iz = np.floor(x[0]/l), np.floor(x[1]/l), np.floor(x[2]/l)
return (int(ix*p1) ^ int(iy*p2) ^ int(iz*p3)) % n
print (spatial_hash(x1))
print (spatial_hash(x2))
print (spatial_hash(x3))
It gives
1
1
3
It seemed to work.
In C++
#include <cstdlib>
#include <iostream>
#include <unordered_map>
#include <vector>
#include <random>
#include <eigen3/Eigen/Dense>
using namespace Eigen;
using namespace std;
const int HASH_SIZE = 200;
//const float MAX = 500.0;
const float L = 0.2f;
const float mmin = -1.f;
const float mmax = 1.f;
unordered_map<int, vector<Vector3d>> map ;
inline size_t hasha(Vector3d &p) {
int ix = (unsigned int)((p[0]+2.f) / L);
int iy = (unsigned int)((p[1]+2.f) / L);
int iz = (unsigned int)((p[2]+2.f) / L);
return (unsigned int)((ix * 73856093) ^ (iy * 19349663) ^ (iz * 83492791)) % HASH_SIZE;
}
int main(int argc, char** argv) {
std::default_random_engine generator;
std::uniform_real_distribution<double> distribution(-1.0,1.0);
for(size_t i=0;i<300;i++){
float x = distribution(generator);
float y = distribution(generator);
float z = distribution(generator);
Vector3d v(x,y,z);
std::cout << hasha(v) << " " << v[0] << " " << v[1] << " " << v[2] << std::endl;
map[hasha(v)].push_back(v);
vector<Vector3d> entry = map[hasha(v)];
std::cout << "size " << entry.size() << std::endl;
}
for (const auto & [ key, value ] : map) {
cout << key << std::endl;
vector<Vector3d> v = map[key];
float average = 0.0f;
for (int i=0; i<v.size(); i++){
for (int j=0; j<v.size(); j++){
if (i!=j){
Vector3d v1 = v[i];
Vector3d v2 = v[j];
std::cout << " dist " << (v1-v2).norm() << std::endl;
}
}
}
}
}