Matlab 确定矩阵A是否为矩阵B的子集
对于矩阵，例如Matlab 确定矩阵A是否为矩阵B的子集,matlab,matrix,Matlab,Matrix,对于矩阵，例如 A = [... 12 34 67; 90 78 15; 10 71 24]; 我们如何有效地确定它是否是较大矩阵的子集 B = [... 12 34 67; % found 89 67 45; 90 78 15; % found 10 71 24; % found, so A is
A = [...
12 34 67;
90 78 15;
10 71 24];
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];
- 所有数字都是整数
- 矩阵非常大，即，行#>100000，列#可能在1到10之间变化（A和B相同）
ismemberismemberclear 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
Elapsed time is 1.088552 seconds.
Elapsed time is 12.154969 seconds.
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.
对于小矩阵
ismemberismember（B，A，'rows'）我把这个答案放在这里，强调需要更高性能的解决方案。只有在没有更好的解决方案时，我才会接受这个答案。对于小矩阵
ismemberismember（B，A，'rows'）我把这个答案放在这里，强调需要更高性能的解决方案。只有在没有更好的解决方案的情况下，我才会接受这个答案。使用
ismemberaBaBABA = [...
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);
使用
ismemberaBaBABA = [...
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);
您已经说过了列数您已经说过了列数看来ismember很难打败，至少使用MATLAB代码是这样。我创建了一个可以使用MEX编译器的C实现
#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;
}
ismember_mex(x, sortrows(x))
ismemberfromtoismemberismemberismember#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;
}
#包括“mex.h”
#包括
#包括
#包括
int ismember（常数双精度*y，常数双精度*x，无符号整数nrowy，无符号整数nrowx，无符号整数ncol）；
void MEX函数（整数nlhs，mxArray*plhs[]，
整数nrhs，常量mxArray*prhs[]
{
无符号整数xcol、ycol、nrowx、nrowy；
/*论据*/
常量MX数组*y；
常量MX数组*x；
如果（nrhs！=2）
{
MEXERMSGSTXT（“需要2个输入”）；
}
y=prhs[0]；
x=prhs[1]；
ycol=（无符号整数）mxGetN（y）；
nrowy=（无符号整数）mxGetM（y）；
xcol=（无符号整数）mxGetN（x）；
nrowx=（无符号整数）mxGetM（x）；
/*第一个输入必须是稀疏矩阵*/
如果（！mxidouble（y）| |！mxidouble（x））
{
MEXERMSGSTXT（“输入必须为'double'类型”）；
}
如果（xcol！=ycol）
{
MEXERMSGSTXT（“输入必须具有相同的列数”）；
}
plhs[0]=mxCreateLogicalScalar（ismember（mxGetPr（y）、mxGetPr（x）、nrowy、nrowx、ycol））；
}
int ismemberinner（常数双精度*y，常数双精度*x，无符号整数nrowy，无符号整数nrowx，无符号整数ncol）{
无符号整数from=0，to=nrowx-1，i；
对于（i=0；il&&curx[from-1]==yi；--from）
无符号整数限制=mididx；
while（curx[from]！=yi）{
const unsigned int mididx=from+（limit from）/2；
if（curx[middx]mex -O ismember_mex.c
ismember_mex(x, sortrows(x))
#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;
}