Adapt Existing Code And Kernel Code To Perform A High Number Of 3x3 Matrix Inversion

Following a previous question ( Performing high number of 4x4 matrix inversion - PyCuda ), considering the inversion of 4x4 matrix, I would like to do the same but with 3x3 matrix.

Solution 1:

This answer will closely follow my answer on the 4x4 invert question, both in terms of answer layout and calculation method/kernel design. The formulas are described here.

First, as before, we will show a CUDA C++ version with comparison to cublas:

$ cat t432.cu
#include<iostream>#include<cublas_v2.h>#include<cstdlib>// 3x3 matrix inversion// https://stackoverflow.com/questions/1148309/inverting-a-4x4-matrix// https://ardoris.wordpress.com/2008/07/18/general-formula-for-the-inverse-of-a-3x3-matrix/// 9 threads per matrix to invert// 32 matrices per 288 thread blockconstunsigned block_size = 288;
typedefdouble mt;

#define cudaCheckErrors(msg) \
    do { \
        cudaError_t __err = cudaGetLastError(); \
        if (__err != cudaSuccess) { \
            fprintf(stderr, "Fatal error: %s (%s at %s:%d)\n", \
                msg, cudaGetErrorString(__err), \
                __FILE__, __LINE__); \
            fprintf(stderr, "*** FAILED - ABORTING\n"); \
            exit(1); \
        } \
    } while (0)#include<time.h>#include<sys/time.h>#define USECPSEC 1000000ULLlonglongdtime_usec(unsignedlonglong start){

  timeval tv;
  gettimeofday(&tv, 0);
  return ((tv.tv_sec*USECPSEC)+tv.tv_usec)-start;
}

__device__ unsigned pat[9];
constunsigned hpat[9] = {0x07584, 0x08172, 0x04251, 0x08365, 0x06280, 0x05032, 0x06473, 0x07061, 0x03140};


__device__ unsignedgetoff(unsigned &off){
  unsigned ret = off & 0x0F;
  off >>= 4;
  return ret;
}

// in-place is acceptable i.e. out == in)// T = float or double onlytemplate <typename T>
__global__ voidinv3x3(const T * __restrict__ in, T * __restrict__ out, constsize_t n){

  __shared__ T si[block_size];
  size_t idx = threadIdx.x+blockDim.x*blockIdx.x;
  T det = 1;
  if (idx < n*9)
    det = in[idx];
  unsigned sibase = (threadIdx.x / 9)*9;
  unsigned lane = threadIdx.x - sibase; // cheaper modulo
  si[threadIdx.x] = det;
  __syncthreads();
  unsigned off = pat[lane];
  T a  = si[sibase + getoff(off)];
  a   *= si[sibase + getoff(off)];
  T b  = si[sibase + getoff(off)];
  b   *= si[sibase + getoff(off)];
  a -= b;
  __syncthreads();
  if (lane == 0) si[sibase+3] = a;
  if (lane == 3) si[sibase+4] = a;
  if (lane == 6) si[sibase+5] = a;
  __syncthreads();
  det =  si[sibase]*si[sibase+3]+si[sibase+1]*si[sibase+4]+si[sibase+2]*si[sibase+5];
  if (idx < n*9)
    out[idx] = a / det;
}

size_t nr = 2048;
intmain(int argc, char *argv[]){
  if (argc > 1) nr = atoi(argv[1]);


  const mt m2[] = {1.0, 1.0, 1.0, 0.0, 0.0, 3.0, 1.0, 2.0, 2.0};
  const mt i2[] = {2.0, 0.0, -1.0, -1.0, -0.33333334, 1.0, 0.0, 0.33333334,  0.0};
  const mt m1[] = {1.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 1.0};
  const mt i1[] = {1.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 1.0};

  mt *h_d, *d_d;
  h_d = (mt *)malloc(nr*9*sizeof(mt));
  cudaMalloc(&d_d, nr*9*sizeof(mt));
  cudaMemcpyToSymbol(pat, hpat, 9*sizeof(unsigned));
  for (int i = 0; i < nr/2; i++){
    memcpy(h_d+i*2*9, m1, sizeof(m1));
    memcpy(h_d+i*2*9+9, m2, sizeof(m2));}
  cudaMemcpy(d_d, h_d, nr*9*sizeof(mt), cudaMemcpyHostToDevice);
  longlong t = dtime_usec(0);
  inv3x3<<<((nr*9)/block_size)+1, block_size>>>(d_d, d_d, nr);
  cudaDeviceSynchronize();
  t = dtime_usec(t);
  cudaMemcpy(h_d, d_d, nr*9*sizeof(mt), cudaMemcpyDeviceToHost);
  for (int i = 0; i < 2; i++){
    for (int j = 0; j < 9; j++) std::cout << h_d[i*9 + j] << ",";
    std::cout << std::endl;
    for (int j = 0; j < 9; j++) std::cout << ((i==0)?i1[j]:i2[j]) << ",";
    std::cout << std::endl;}
  std::cout << "kernel time: " << t << " microseconds" << std::endl;
  cudaError_t err = cudaGetLastError();
  if (err != cudaSuccess) std::cout << cudaGetErrorString(err) << std::endl;
  //cublasfor (int i = 0; i < nr/2; i++){
    memcpy(h_d+i*2*9, m1, sizeof(m1));
    memcpy(h_d+i*2*9+9, m2, sizeof(m2));}
  cudaMemcpy(d_d, h_d, nr*9*sizeof(mt), cudaMemcpyHostToDevice);
  cublasHandle_t h;
  cublasStatus_t cs = cublasCreate(&h);
  if (cs != CUBLAS_STATUS_SUCCESS) std::cout << "cublas create error" << std::endl;
  mt **A, **Ai, *Aid, **Ap, **Aip;
  A  = (mt **)malloc(nr*sizeof(mt *));
  Ai = (mt **)malloc(nr*sizeof(mt *));
  cudaMalloc(&Aid, nr*9*sizeof(mt));
  cudaMalloc(&Ap,  nr*sizeof(mt *));
  cudaMalloc(&Aip, nr*sizeof(mt *));
  for (int i = 0; i < nr; i++) A[i]  =  d_d + 9*i;
  for (int i = 0; i < nr; i++) Ai[i] =  Aid + 9*i;
  cudaMemcpy(Ap, A, nr*sizeof(mt *), cudaMemcpyHostToDevice);
  cudaMemcpy(Aip, Ai, nr*sizeof(mt *), cudaMemcpyHostToDevice);
  int *info;
  cudaMalloc(&info, nr*sizeof(int));
  t = dtime_usec(0);
  cs = cublasDmatinvBatched(h, 3,  Ap, 3, Aip, 3, info, nr);
  if (cs != CUBLAS_STATUS_SUCCESS) std::cout << "cublas matinv error" << std::endl;
  cudaDeviceSynchronize();
  t = dtime_usec(t);
  cudaMemcpy(h_d, Aid, nr*9*sizeof(mt), cudaMemcpyDeviceToHost);
  for (int i = 0; i < 2; i++){
    for (int j = 0; j < 9; j++) std::cout << h_d[i*9 + j] << ",";
    std::cout << std::endl;
    for (int j = 0; j < 9; j++) std::cout << ((i==0)?i1[j]:i2[j]) << ",";
    std::cout << std::endl;}
  std::cout << "cublas time: " << t << " microseconds" << std::endl;
  err = cudaGetLastError();
  if (err != cudaSuccess) std::cout << cudaGetErrorString(err) << std::endl;
  return0;
}
$ nvcc -o t432 t432.cu -lcublas
$ ./t432
1,0,0,0,1,0,0,0,1,
1,0,0,0,1,0,0,0,1,
2,-0,-1,-1,-0.333333,1,-0,0.333333,-0,
2,0,-1,-1,-0.333333,1,0,0.333333,0,
kernel time: 59 microseconds
1,0,0,0,1,0,0,0,1,
1,0,0,0,1,0,0,0,1,
2,0,-1,-1,-0.333333,1,0,0.333333,0,
2,0,-1,-1,-0.333333,1,0,0.333333,0,
cublas time: 68 microseconds
$

So this is perhaps slightly faster than cublas but not much, for this 2048 matrix test case, CUDA 10.0, Tesla P100, linux.

Similar to the previous answer, here is a simplified (only 2 matrices) pycuda test case:

$ cat t14.py
import numpy as np
# import matplotlib.pyplot as pltimport pycuda.driver as cuda
from pycuda.compiler import SourceModule
import pycuda.autoinit
# kernel
kernel = SourceModule("""

__device__ unsigned getoff(unsigned &off){
  unsigned ret = off & 0x0F;
  off >>= 4;
  return ret;
}

// in-place is acceptable i.e. out == in)
// T = float or double only
const int block_size = 288;
typedef double T; // *** can set to float or double
__global__ void inv3x3(const T * __restrict__ in, T * __restrict__ out, const size_t n, const unsigned * __restrict__ pat){

  __shared__ T si[block_size];
  size_t idx = threadIdx.x+blockDim.x*blockIdx.x;
  T det = 1;
  if (idx < n*9)
    det = in[idx];
  unsigned sibase = (threadIdx.x / 9)*9;
  unsigned lane = threadIdx.x - sibase; // cheaper modulo
  si[threadIdx.x] = det;
  __syncthreads();
  unsigned off = pat[lane];
  T a  = si[sibase + getoff(off)];
  a   *= si[sibase + getoff(off)];
  T b  = si[sibase + getoff(off)];
  b   *= si[sibase + getoff(off)];
  a -= b;
  __syncthreads();
  if (lane == 0) si[sibase+3] = a;
  if (lane == 3) si[sibase+4] = a;
  if (lane == 6) si[sibase+5] = a;
  __syncthreads();
  det =  si[sibase]*si[sibase+3]+si[sibase+1]*si[sibase+4]+si[sibase+2]*si[sibase+5];
  if (idx < n*9)
    out[idx] = a / det;
}

""")
# host codedefgpuinv3x3(inp, n):
    # internal constants not to be modified
    hpat = (0x07584, 0x08172, 0x04251, 0x08365, 0x06280, 0x05032, 0x06473, 0x07061, 0x03140)
    # Convert parameters into numpy array# *** change next line between float32 and float64 to match float or double
    inpd = np.array(inp, dtype=np.float64)
    hpatd = np.array(hpat, dtype=np.uint32)
    # *** change next line between float32 and float64 to match float or double
    output = np.empty((n*9), dtype= np.float64)
    # Get kernel function
    matinv3x3 = kernel.get_function("inv3x3")
    # Define block, grid and compute
    blockDim = (288,1,1) # do not change
    gridDim = ((n/32)+1,1,1)
    # Kernel function
    matinv3x3 (
        cuda.In(inpd), cuda.Out(output), np.uint64(n), cuda.In(hpatd),
        block=blockDim, grid=gridDim)
    return output
inp = (1.0, 1.0, 1.0, 0.0, 0.0, 3.0, 1.0, 2.0, 2.0, 1.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 1.0)
n = 2
result = gpuinv3x3(inp, n)
print(result.reshape(2,3,3))
$ python t14.py
[[[ 2.         -0.         -1.        ]
  [-1.         -0.333333331.        ]
  [-0.0.33333333 -0.        ]]

 [[ 1.0.0.        ]
  [ 0.1.0.        ]
  [ 0.0.1.        ]]]
$

The above happens to be using double i.e. float64 in pycuda. Changing it to float i.e. float32 in pycuda involves changing the same 3 lines as described in this answer.