A C++ CPLEX model that I have is long, and I build constraints inside functions. Say I have a function that returns a constraint:
IloConstraint f(IloInt i, IloInt j, IloNumVarArray x)
{
IloConstraint constr;
constr = (x[j]-x[i] >= 15) && (x[j]-x[i] <= 20);
return constr;
}
Is it possible to do pass a constant array instead of a variable array x, and to obtain a logical value of constraint, i.e. to do something like.
IloNumArray a(env, 5, 1, 1, 1, 1, 1);
IloConstraint c = f(1,2,a);
cout<<c.logicalValue();
You can use IloAnd
In CPLEX documentation you can read
For example, you may write:
IloAnd and(env);
and.add(constraint1);
and.add(constraint2);
and.add(constraint3);
Those lines are equivalent to :
IloAnd and = constraint1 && constraint2 && constraint3;
I couldn't find a real solution, but I have some workaround. Assuming we already have a constraint c, we create a new model with c as its constraint, and add new bounds for the variables.
bool constraintLogicalValue(IloConstraint const& constr, IloEnv env, IloNumVarArray const& x, IloNumArray const& a, unsigned int const n)
{
IloModel model(env);
IloCplex cplex_model(model);
cplex_model.setOut(env.getNullStream());
for(int i=0; i<n; ++i)
model.add(x[i]==a[i]);
model.add(constr);
return(cplex_model.solve());
}
Now we can use it in the following way:
int n;
IloEnv env;
IloModel model(env);
IloNumVarArray x (env);
...
IloNumArray a(env);
for(int i=0; i<n; ++i)
a.add(1);
IloConstraint c = f(1,2,x);
cout<<constraintLogicalValue(c, env, x, a, n);
EDIT: A problem could be an existing bounds for x, which are passed into constraintLogicalValue(). If x[i]==a[i] is out of these bonds, for some i, the model is unfeasible and we obtain false as a result, event if constr is satisfied.
Sometimes this is what we want.
Related
Below is a piece of C code run from R used to compare each row of a matrix to a vector. The number of identical values is stored in the first column of a two-column matrix.
I know it can easily be done in R (as done to check the results), but this is a first step for a more complex use case.
When openmp is not used, it works ok. When openmp is used, it give correlated (0.99) but inconsistent results.
Question1: What am I doing wrong?
Question2: I use a double for loop to fill the output matrix (ret) with zeros. What would be a better solution?
Also, inconsistencies were observed when the code was used in a package. I tried to make the code reproducible using inline, but it does not recognize the openmp statements (I tried to include 'omp.h', in the parameters of cfunction, ...).
Question3: How can we make this code work with inline?
I'm (too?) far outside my comfort zone on this topic.
library(inline)
compare <- cfunction(c(x = "integer", vec = "integer"), "
const int I = nrows(x), J = ncols(x);
SEXP ret;
PROTECT(ret = allocMatrix(INTSXP, I, 2));
int *ptx = INTEGER(x), *ptvec = INTEGER(vec), *ptret = INTEGER(ret);
for (int i=0; i<I; i++)
for (int j=0; j<2; j++)
ptret[j * I + i] = 0;
int i, j;
#pragma omp parallel for default(none) shared(ptx, ptvec, ptret) private(i,j)
for (j=0; j<J; j++)
for (i=0; i<I; i++)
if (ptx[i + I * j] == ptvec[j]) {++ptret[i];}
UNPROTECT(1);
return ret;
")
N = 3e3
M = 1e4
m = matrix(sample(c(-1:1), N*M, replace = TRUE), nc = M)
v = sample(-1:1, M, replace = TRUE)
cc = compare(m, v)
cr = rowSums(t(t(m) == v))
all.equal(cc[,1], cr)
Thanks to the comments above, I reconsidered the data race issue.
IIUC, my loop was parallelized on j (the columns). Then, each thread had its own value of i (the rows), but possible identical values across threads, that were then trying to increment ptret[i] at the same time.
To avoid this, I now loop on i first, so that only a single thread will increment each row.
Then, I realized that I could move the zero-initialization of ptret within the first loop.
It seems to work. I get identical results, increased CPU usage, and 3-4x speedup on my laptop.
I guess that solves questions 1 and 2. I will have a closer look at the inline/openmp problem.
Code below, fwiw.
#include <omp.h>
#include <R.h>
#include <Rinternals.h>
#include <stdio.h>
SEXP c_compare(SEXP x, SEXP vec)
{
const int I = nrows(x), J = ncols(x);
SEXP ret;
PROTECT(ret = allocMatrix(INTSXP, I, 2));
int *ptx = INTEGER(x), *ptvec = INTEGER(vec), *ptret = INTEGER(ret);
int i, j;
#pragma omp parallel for default(none) shared(ptx, ptvec, ptret) private(i, j)
for (i = 0; i < I; i++) {
// init ptret to zero
ptret[i] = 0;
ptret[I + i] = 0;
for (j = 0; j < J; j++)
if (ptx[i + I * j] == ptvec[j]) {
++ptret[i];
}
}
UNPROTECT(1);
return ret;
}
In a very first attempt at creating a C++ function which can be called from R using Rcpp, I have a simple function to compute a minimum spanning tree from a distance matrix using Prim's algorithm. This function has been converted into C++ from a former version in ANSI C (which works fine).
Here it is:
#include <Rcpp.h>
using namespace Rcpp;
// [[Rcpp::export]]
DataFrame primlm(const int n, NumericMatrix d)
{
double const din = 9999999.e0;
long int i1, nc, nc1;
double dlarge, dtot;
NumericVector is, l, lp, dist;
l(1) = 1;
is(1) = 1;
for (int i=2; i <= n; i++) {
is(i) = 0;
}
for (int i=2; i <= n; i++) {
dlarge = din;
i1 = i - 1;
for (int j=1; j <= i1; j++) {
for (int k=1; k <= n; k++) {
if (l(j) == k)
continue;
if (d[l(j), k] > dlarge)
continue;
if (is(k) == 1)
continue;
nc = k;
nc1 = l(j);
dlarge = d(nc1, nc);
}
}
is(nc) = 1;
l(i) = nc;
lp(i) = nc1;
dist(i) = dlarge;
}
dtot = 0.e0;
for (int i=2; i <= n; i++){
dtot += dist(i);
}
return DataFrame::create(Named("l") = l,
Named("lp") = lp,
Named("dist") = dist,
Named("dtot") = dtot);
}
When I compile this function using Rcpp under RStudio, I get two warnings, complaining that variables 'nc' and 'nc1' have not been initialized. Frankly, I could not understand that, as it seems to me that both variables are being initialized inside the third loop. Also, why there is no similar complaint about variable 'i1'?
Perhaps it comes as no surprise that, when attempting to call this function from R, using the below code, what I get is a crash of the R system!
# Read test data
df <- read.csv("zygo.csv", header=TRUE)
lonlat <- data.frame(df$Longitude, df$Latitude)
colnames(lonlat) <- c("lon", "lat")
# Compute distance matrix using geosphere library
library(geosphere)
d <- distm(lonlat, lonlat, fun=distVincentyEllipsoid)
# Calls Prim minimum spanning tree routine via Rcpp
library(Rcpp)
sourceCpp("Prim.cpp")
n <- nrow(df)
p <- primlm(n, d)
Here is the dataset I use for testing purposes:
"Scientific name",Locality,Longitude,Latitude Zygodontmys,Bush Bush
Forest,-61.05,10.4 Zygodontmys,Cerro Azul,-79.4333333333,9.15
Zygodontmys,Dividive,-70.6666666667,9.53333333333 Zygodontmys,Hato El
Frio,-63.1166666667,7.91666666667 Zygodontmys,Finca Vuelta
Larga,-63.1166666667,10.55 Zygodontmys,Isla
Cebaco,-81.1833333333,7.51666666667 Zygodontmys,Kayserberg
Airstrip,-56.4833333333,3.1 Zygodontmys,Limao,-60.5,3.93333333333
Zygodontmys,Montijo Bay,-81.0166666667,7.66666666667
Zygodontmys,Parcela 200,-67.4333333333,8.93333333333 Zygodontmys,Rio
Chico,-65.9666666667,10.3166666667 Zygodontmys,San Miguel
Island,-78.9333333333,8.38333333333
Zygodontmys,Tukuko,-72.8666666667,9.83333333333
Zygodontmys,Urama,-68.4,10.6166666667
Zygodontmys,Valledup,-72.9833333333,10.6166666667
Could anyone give me a hint?
The initializations of ncand nc1 are never reached if one of the three if statements is true. It might be that this is not possible with your data, but the compiler has no way knowing that.
However, this is not the reason for the crash. When I run your code I get:
Index out of bounds: [index=1; extent=0].
This comes from here:
NumericVector is, l, lp, dist;
l(1) = 1;
is(1) = 1;
When declaring a NumericVector you have to tell the required size if you want to assign values by index. In your case
NumericVector is(n), l(n), lp(n), dist(n);
might work. You have to analyze the C code carefully w.r.t. memory allocation and array boundaries.
Alternatively you could use the C code as is and use Rcpp to build a wrapper function, e.g.
#include <array>
#include <Rcpp.h>
using namespace Rcpp;
// One possibility for the function signature ...
double prim(const int n, double *d, double *l, double *lp, double *dist) {
....
}
// [[Rcpp::export]]
List primlm(NumericMatrix d) {
int n = d.nrow();
std::array<double, n> lp; // adjust size as needed!
std::array<double, n> dist; // adjust size as needed!
double dtot = prim(n, d.begin(), l.begin(), lp.begin(), dist.begin());
return List::create(Named("l") = l,
Named("lp") = lp,
Named("dist") = dist,
Named("dtot") = dtot);
}
Notes:
I am returning a List instead of a DataFrame since dtot is a scalar value.
The above code is meant to illustrate the idea. Most likely it will not work without adjustments!
I created a cumsum function in an R package with rcpp which will cumulatively sum a vector until it hits the user defined ceiling or floor. However, if one wants the cumsum to be bounded above, the user must still specify a floor.
Example:
a = c(1, 1, 1, 1, 1, 1, 1)
If i wanted to cumsum a and have an upper bound of 3, I could cumsum_bounded(a, lower = 1, upper = 3). I would rather not have to specify the lower bound.
My code:
#include <Rcpp.h>
#include <float.h>
#include <cmath>
using namespace Rcpp;
// [[Rcpp::export]]
NumericVector cumsum_bounded(NumericVector x, int upper, int lower) {
NumericVector res(x.size());
double acc = 0;
for (int i=0; i < x.size(); ++i) {
acc += x[i];
if (acc < lower) acc = lower;
else if (acc > upper) acc = upper;
res[i] = acc;
}
return res;
}
What I would like:
#include <Rcpp.h>
#include <float.h>
#include <cmath>
#include <climits> //for LLONG_MIN and LLONG_MAX
using namespace Rcpp;
// [[Rcpp::export]]
NumericVector cumsum_bounded(NumericVector x, long long int upper = LLONG_MAX, long long int lower = LLONG_MIN) {
NumericVector res(x.size());
double acc = 0;
for (int i=0; i < x.size(); ++i) {
acc += x[i];
if (acc < lower) acc = lower;
else if (acc > upper) acc = upper;
res[i] = acc;
}
return res;
}
In short, yes its possible but it requires finesse that involves creating an intermediary function or embedding sorting logic within the main function.
In long, Rcpp attributes only supports a limit feature set of values. These values are listed in the Rcpp FAQ 3.12 entry
String literals delimited by quotes (e.g. "foo")
Integer and Decimal numeric values (e.g. 10 or 4.5)
Pre-defined constants including:
Booleans: true and false
Null Values: R_NilValue, NA_STRING, NA_INTEGER, NA_REAL, and NA_LOGICAL.
Selected vector types can be instantiated using the
empty form of the ::create static member function.
CharacterVector, IntegerVector, and NumericVector
Matrix types instantiated using the rows, cols constructor Rcpp::Matrix n(rows,cols)
CharacterMatrix, IntegerMatrix, and NumericMatrix)
If you were to specify numerical values for LLONG_MAX and LLONG_MIN this would meet the criteria to directly use Rcpp attributes on the function. However, these values are implementation specific. Thus, it would not be ideal to hardcode them. Thus, we have to seek an outside solution: the Rcpp::Nullable<T> class to enable the default NULL value. The reason why we have to wrap the parameter type with Rcpp::Nullable<T> is that NULL is a very special and can cause heartache if not careful.
The NULL value, unlike others on the real number line, will not be used to bound your values in this case. As a result, it is the perfect candidate to use on the function call. There are two choices you then have to make: use Rcpp::Nullable<T> as the parameters on the main function or create a "logic" helper function that has the correct parameters and can be used elsewhere within your application without worry. I've opted for the later below.
#include <Rcpp.h>
#include <float.h>
#include <cmath>
#include <climits> //for LLONG_MIN and LLONG_MAX
using namespace Rcpp;
NumericVector cumsum_bounded_logic(NumericVector x,
long long int upper = LLONG_MAX,
long long int lower = LLONG_MIN) {
NumericVector res(x.size());
double acc = 0;
for (int i=0; i < x.size(); ++i) {
acc += x[i];
if (acc < lower) acc = lower;
else if (acc > upper) acc = upper;
res[i] = acc;
}
return res;
}
// [[Rcpp::export]]
NumericVector cumsum_bounded(NumericVector x,
Rcpp::Nullable<long long int> upper = R_NilValue,
Rcpp::Nullable<long long int> lower = R_NilValue) {
if(upper.isNotNull() && lower.isNotNull()){
return cumsum_bounded_logic(x, Rcpp::as< long long int >(upper), Rcpp::as< long long int >(lower));
} else if(upper.isNull() && lower.isNotNull()){
return cumsum_bounded_logic(x, LLONG_MAX, Rcpp::as< long long int >(lower));
} else if(upper.isNotNull() && lower.isNull()) {
return cumsum_bounded_logic(x, Rcpp::as< long long int >(upper), LLONG_MIN);
} else {
return cumsum_bounded_logic(x, LLONG_MAX, LLONG_MIN);
}
// Required to quiet compiler
return x;
}
Test Output
cumsum_bounded(a, 5)
## [1] 1 2 3 4 5 5 5
cumsum_bounded(a, 5, 2)
## [1] 2 3 4 5 5 5 5
can we parallelize a recursive function using MPI?
I am trying to parallelize the quick sort function, but don't know if it works in MPI because it is recursive. I also want to know where should I do the parallel region.
// quickSort.c
#include <stdio.h>
void quickSort( int[], int, int);
int partition( int[], int, int);
void main()
{
int a[] = { 7, 12, 1, -2, 0, 15, 4, 11, 9};
int i;
printf("\n\nUnsorted array is: ");
for(i = 0; i < 9; ++i)
printf(" %d ", a[i]);
quickSort( a, 0, 8);
printf("\n\nSorted array is: ");
for(i = 0; i < 9; ++i)
printf(" %d ", a[i]);
}
void quickSort( int a[], int l, int r)
{
int j;
if( l < r )
{
// divide and conquer
j = partition( a, l, r);
quickSort( a, l, j-1);
quickSort( a, j+1, r);
}
}
int partition( int a[], int l, int r) {
int pivot, i, j, t;
pivot = a[l];
i = l; j = r+1;
while( 1)
{
do ++i; while( a[i] <= pivot && i <= r );
do --j; while( a[j] > pivot );
if( i >= j ) break;
t = a[i]; a[i] = a[j]; a[j] = t;
}
t = a[l]; a[l] = a[j]; a[j] = t;
return j;
}
I would also really appreciate it if there is another simpler code for the quick sort.
Well, technically you can, but I'm afraid this would be efficient only in SMP. And does the array fit to single node? If no, then you cannot perform even the first pass of a quick-sort.
If you really need to sort an array on a parallel system using MPI, you might want to consider using merge sort instead (of course you still can use quick sort for single blocks at each node, before you begin merging the blocks).
If you still want to use quick sort, but you are confused with the recursive version, here is a sketch of non-recursive algorithm which hopefully can be parallelized a bit easier, although it's essentially the same:
std::stack<std::pair<int, int> > unsorted;
unsorted.push(std::make_pair(0, size-1));
while (!unsorted.empty()) {
std::pair<int, int> u = unsorted.top();
unsorted.pop();
m = partition(A, u.first, u.second);
// here you can send one of intervals to another node instead of
// pushing it into the stack, so it would be processed in parallel.
if (m+1 < u.second) unsorted.push(std::make_pair(m+1, u.second));
if (u.first < m-1) unsorted.push(std::make_pair(u.first, m-1));
}
Theoretically "anything" can be parallelized using MPI, but remember that MPI isn't doing any parallelization itself. It's just providing the communication layer between processes. As long as all of your sends and receives (or collective calls) match up, it's a correct program for the most part. That being said, it may not be the most efficient thing to use MPI, depending on your algorithm. If you are going to be sorting lots and lots of data (more than can fit in the memory of one node) then it could be efficient to use MPI (you probably want to take a look at the RMA chapter in that case) or some other higher level library that might make things even simpler for this type of application (UPC, Co-array Fortran, SHMEM, etc.).
I have recently begun using the Rcpp package to write some segments of my R code into C++.
Given a matrix of data, I have the following Rcpp function which calculates a kernel reweighted estimate of the covariance for some observation.
cppFunction('
NumericVector get_cov_1obs(NumericMatrix cdata, int ID, float radius){
int nrow = cdata.nrow(), ncol = cdata.ncol();
float norm_ = 0;
float w;
NumericMatrix out(ncol, ncol);
NumericMatrix outer_prod(ncol, ncol);
for (int i=0; i<ncol;i++){
for (int j=0;j<ncol;j++){
out(i,j) = 0;
outer_prod(i,j) = 0;
}
}
for (int i=0; i<nrow;i++){
w = exp( -(i-ID)*(i-ID)/(2*radius));
norm_ += w;
for (int j=0; j<ncol;j++){
for (int k=0;k<ncol;k++){
outer_prod(j,k) = cdata(i,j) * cdata(i,k);
}
}
for (int j=0; j<ncol;j++){
for (int k=0;k<ncol;k++){
out(j,k) += outer_prod(j,k)*w;
}
}
}
for (int i=0; i<ncol;i++){
for (int j=0;j<ncol;j++){
out(i,j) /= norm_;
}
}
return out;
}')
I would like to quickly estimated the kernel rewieghted covariance matricies for all observations in a dataset and store them as an array. Since Rcpp doesn't handle arrays I have written the following R function:
get_kern_cov_C = function(data, radius){
# data is data for which we wish to estimate covariances
# radius is the radius of the gaussian kernel
# calculate covariances:
kern_cov = array(0, c(ncol(data),ncol(data),nrow(data)))
for (i in 1:nrow(data)){
kern_cov[,,i] = get_cov_1obs(cdata=data, ID = i-1, radius=radius)
}
return(kern_cov)
}
This seems to work fine (and much, MUCH faster than R) however the problem is that every now and then (seemingly at random) I get an error of the following form:
Error in kern_cov[, , i] = get_cov_1obs(cdata = data, ID = i - 1, radius = radius) :
incompatible types (from X to Y)
where X is either builtin or NULL and Y is double.
I roughly understand why this is happening (I am trying to place a builtin/NULL variable into a double) but I am not sure were in the code the bug is. I suspect this might be something related to memory management as it only occurs every now and again.
You can test for NULL at the C(++) level too, and in this case probably should do that.
As to why it is occurring: I am afraid you will need to debug this.