Eigen: simplifying expression with Eigen intrinsics

Question

I'm trying to scale all the columns in a matrix with a corresponding value from a vector. Where this value is 0, I want to replace that column with a column from an other matrix scaled by a constant. Sounds complicated, but in Matlab it's pretty simple (but probably not fully optimized):

a(:,b ~= 0) = a(:,b ~= 0)./b(b ~= 0);
a(:,b == 0) = c(:,b == 0)*x; 

doing it with a for loop in C++ would also be pretty simple:

RowVectorXf b;
Matrix3Xf a, c;
float x;
for (int i = 0; i < b.size(); i++) {
    if (b(i) != 0) {
        a.col(i) = a.col(i) / b(i);
    } else {
        a.col(i) = c.col(i) * x;
    }
}

Is there a possibility to do this operation (faster) with Eigen intrinsics such as colwise and select?

p.s. I tried to shorten the if condition to the form

a.col(i) = (b(i) != 0) ? (a.col(i) / b(i)) : (c.col(i) * x);

But this does not compile with the error error: operands to ?: have different types ...(long listing of the types)

Edit: I added the code for testing the answers, here it is:

#include <Eigen/Dense>
#include <stdlib.h>
#include <chrono>
#include <iostream>

using namespace std;
using namespace Eigen;

void flushCache()
{
    const int size = 20 * 1024 * 1024; // Allocate 20M. Set much larger than L2
    volatile char *c = (char *) malloc(size);
    volatile int i = 8;
    for (volatile int j = 0; j < size; j++)
        c[j] = i * j;

    free((void*) c);
}

int main()
{
    Matrix3Xf a(3, 1000000);
    RowVectorXf b(1000000);
    Matrix3Xf c(3, 1000000);
    float x = 0.4;

    a.setRandom();
    b.setRandom();
    c.setRandom();

    for (int testNumber = 0; testNumber < 4; testNumber++) {
        flushCache();
        chrono::high_resolution_clock::time_point t1 = chrono::high_resolution_clock::now();
        for (int repetition = 0; repetition < 1000; repetition++) {
            switch (testNumber) {
                case 0:
                    for (int i = 0; i < b.size(); i++) {
                        if (b(i) != 0) {
                            a.col(i) = a.col(i) / b(i);
                        } else {
                            a.col(i) = c.col(i) * x;
                        }
                    }
                    break;
                case 1:
                    for (int i = 0; i < b.size(); i++) {
                        a.col(i) = (b(i) != 0) ? (a.col(i) / b(i)).eval() : (c.col(i) * x).eval();
                    }
                    break;
                case 2:
                    for (int i = 0; i < b.size(); i++) {
                        a.col(i) = (b(i) != 0) ? (a.col(i) * (1.0f / b(i))) : (c.col(i) * x);
                    }
                    break;
                case 3:
                    a = b.cwiseEqual(0.0f).replicate< 3, 1 >().select(c * x, a.cwiseQuotient(b.replicate< 3, 1 >()));
                    break;
                default:
                    break;
            }
        }

        chrono::high_resolution_clock::time_point t2 = chrono::high_resolution_clock::now();
        auto duration = chrono::duration_cast< chrono::milliseconds >(t2 - t1).count();
        cout << "duration: " << duration << "ms" << endl;
    }

    return 0;
}

Sample output is:

duration: 14391ms
duration: 15219ms
duration: 9148ms
duration: 13513ms

By the way, not using setRandom to init the variables, the output is totally different:

duration: 10255ms
duration: 11076ms
duration: 8250ms
duration: 5198ms

@chtz suggests it's because of denormalized values, but I think it's because of branch prediction. An evidance that it's because of branch prediction is, that initializing b.setZero(); leads to the same timings as not initializing.

Answer 1

a.col(i) = (b(i) != 0) ? (a.col(i) * (1.0f/b(i))) : (c.col(i) * x);

would work but only because the expressions would be of the same type, and it will likely not safe any time (a ? : expression is essentially translated to the same as an if-else branch.)

If you prefer writing it into one line, the following expression should work:

a = b.cwiseEqual(0.0f).replicate<3,1>().select(c*x, a.cwiseQuotient(b.replicate<3,1>()));

Again, I doubt it will make any significant performance difference.