如何用Cublas或推力计算复杂载体的内积？

Question

经过长时间的搜索，我仍然无法解决这个问题。

我有两个向量：x = [a1，...，aN]，y = [b1，...，bN]。

我想计算他们的内在产品：= a1 * conj（b1）+ ... + aN * conj（bN）。 （conj（。）表示复共轭运算）

我试过了cublasCdotu，它只计算a1 * b1 + ... + aN * bN。

并且cublasCdotc返回conj（a1）* conj（b1）+ ... + conj（aN）* conj（bN）。

最后，我尝试了推力:: inner_product，它也计算了a1 * b1 + ... + aN * bN。

我的推力代码如下：

typedef thrust::complex<float> comThr;
thrust::host_vector< comThr > x( vec_size );
thrust::generate(x.begin(), x.end(), rand);

thrust::host_vector< comThr > y( vec_size );
thrust::generate(y.begin(), y.end(), rand);
comThr z = thrust::inner_product(x.begin(), x.end(), y.begin(), comThr(0.0f,0.0f) );

你能就这个问题给我一些建议吗？谢谢！

Answer 1

你可以用thrust::inner_product做到这一点。所需要的只是用户定义的二元函数，它实现了a * conj(b)，其中conj是复共轭。推力库包括所需的所有复杂运算符，因此实现是一个简单的运算符，如下所示：

  __host__ __device__
  comThr operator()(comThr a, comThr b) 
  { 
    return  a * thrust::conj(b); 
  };

一个完整的工作示例：

#include <iostream>
#include "thrust/host_vector.h"
#include "thrust/functional.h"
#include "thrust/complex.h"
#include "thrust/inner_product.h"
#include "thrust/random.h"

typedef thrust::complex<float> comThr;

struct a_dot_conj_b : public thrust::binary_function<comThr,comThr,comThr>
{
  __host__ __device__
  comThr operator()(comThr a, comThr b) 
  { 
    return  a * thrust::conj(b); 
  };
};

__host__ static __inline__ comThr rand_comThr()
{
    return comThr((float)rand()/RAND_MAX, (float)rand()/RAND_MAX);
}

int main()
{
    const int vec_size = 16;

    thrust::host_vector< comThr > x( vec_size );
    thrust::generate(x.begin(), x.end(), rand_comThr);

    thrust::host_vector< comThr > y( vec_size );
    thrust::generate(y.begin(), y.end(), rand_comThr);

    comThr z = thrust::inner_product(x.begin(), x.end(), y.begin(), comThr(0.0f,0.0f),
                                     thrust::plus<comThr>(),  a_dot_conj_b());

    comThr zref(0.0,0.0);
    for(int i=0; i<vec_size; i++) {
        comThr val = x[i] * thrust::conj(y[i]);
        std::cout << i << " " << x[i] << " op " << y[i] << " = " << val  << std::endl;
        zref += val;
    }

    std::cout << "z = " << z << " zref = " << zref << std::endl;

    return 0;
}

这将编译和运行如下：

$ nvcc -arch=sm_52 -o dotprod_thrust dotprod_thrust.cu 

$ ./dotprod_thrust 

0 (0.394383,0.840188) op (0.296032,0.61264) = (0.631482,0.00710744)
1 (0.79844,0.783099) op (0.524287,0.637552) = (0.917879,-0.0984784)
2 (0.197551,0.911647) op (0.972775,0.493583) = (0.642147,0.78932)
3 (0.76823,0.335223) op (0.771358,0.292517) = (0.690638,0.0338566)
4 (0.55397,0.277775) op (0.769914,0.526745) = (0.572826,-0.0779383)
5 (0.628871,0.477397) op (0.891529,0.400229) = (0.751725,0.173921)
6 (0.513401,0.364784) op (0.352458,0.283315) = (0.284301,-0.0168827)
7 (0.916195,0.95223) op (0.919026,0.807725) = (1.61115,0.135091)
8 (0.717297,0.635712) op (0.949327,0.0697553) = (0.725294,0.553463)
9 (0.606969,0.141603) op (0.0860558,0.525995) = (0.126716,-0.307077)
10 (0.242887,0.0163006) op (0.663227,0.192214) = (0.164222,-0.0358752)
11 (0.804177,0.137232) op (0.348893,0.890233) = (0.40274,-0.668025)
12 (0.400944,0.156679) op (0.020023,0.0641713) = (0.0180824,-0.0225919)
13 (0.108809,0.12979) op (0.0630958,0.457702) = (0.0662707,-0.0416127)
14 (0.218257,0.998924) op (0.970634,0.23828) = (0.449871,0.917584)
15 (0.839112,0.512932) op (0.85092,0.902208) = (1.17679,-0.32059)
z = (9.23213,1.02127) zref = (9.23213,1.02127)