std::max_element skip over NANs

I have a std::vector<double> that may contain several NAN values. I want to find the largest element in the vector. How can I efficiently skip the NANs in the comparison? I'd like to avoid having to call isnan on each element. any ideas?

// std::max_element([NAN,NAN,NAN,-31,-89]) = NAN 
// because NAN > -31 returns NAN.
// how can I skip all NANs in the comparison?
// test 2 below is my use case.

#include <vector>
#include <iostream>
#include <cmath>

void vector_max(std::vector<double> v, double &max, int &imax){
    std::vector<double>::iterator v_iter;
    v_iter = std::max_element(v.begin(),v.end());
    imax = std::distance(v.begin(), v_iter);
    max  = *v_iter;
}

int main(){

    std::vector<double> v_vec;
    std::vector<double>::iterator v_vec_iter;
    int imax;
    double val;

    std::cout << "test 1. " << std::endl;

    v_vec.push_back( -33.0 );
    v_vec.push_back( -124.0 );
    v_vec.push_back( -31.0 );
    v_vec.push_back( 18.4 );

    vector_max(v_vec,val,imax);
    std::cout << "max(v_vec) = " << val << std::endl;
    std::cout << "indmax(v_vec) = " << imax << std::endl;

    std::cout << "test 2: my case. " << std::endl;

    v_vec.clear();
    v_vec.push_back( NAN );
    v_vec.push_back( NAN );
    v_vec.push_back( NAN );
    v_vec.push_back( -33.0 );
    v_vec.push_back( -124.0 );
    v_vec.push_back( -31.0 );
    v_vec.push_back( 31.0 );

    vector_max(v_vec,val,imax);
    std::cout << "max(v_vec) = " << val << std::endl;
    std::cout << "indmax(v_vec) = " << imax << std::endl;

};

this returns:

test 1. 
max(v_vec) = 18.4
indmax(v_vec) = 3
test 2. 
max(v_vec) = nan
indmax(v_vec) = 0