如何使用MAGMA搭配NVIDIA GPU卡代替CPU LAPACKE逆大矩阵

Question

I need to inverse large matrices and I would like to modify my current LAPACKE version routine in order to exploit the powerfull of a GPU NVIDIA Card.

Indeed, my LAPACKE routines works well for relative small matrices but not for large matrices.

Below thr implementation of this LAPACKE routine:

 #include <mkl.h>

// Passing Matrixes by Reference
void matrix_inverse_lapack(vector<vector<double>> const &F_matrix, vector<vector<double>> &F_output) {

  // Index for loop and arrays
  int i, j, ip, idx;

  // Size of F_matrix
  int N = F_matrix.size();

  int *IPIV = new int[N];

 // Output Diagonal block
  double *diag = new double[N];

  for (i = 0; i<N; i++){
    for (j = 0; j<N; j++){
      idx = i*N + j;
      arr[idx] = F_matrix[i][j];
    }
  }

  // LAPACKE routines
  int info1 = LAPACKE_dgetrf(LAPACK_ROW_MAJOR, N, N, arr, N, IPIV);
  int info2 = LAPACKE_dgetri(LAPACK_ROW_MAJOR, N, arr, N, IPIV);

 for (i = 0; i<N; i++){
    for (j = 0; j<N; j++){
      idx = i*N + j;
      F_output[i][j] = arr[idx];
    }
  }

  delete[] IPIV;
  delete[] arr;
}

with is called like this to inverse CO_CL matrix:

matrix_inverse_lapack(CO_CL, CO_CL);

with CO_CL defined by:

vector<vector<double>> CO_CL(lsize*(2*Dim_x+Dim_y), vector<double>(lsize*(2*Dim_x+Dim_y), 0));

How can I use MAGMA for NVIDIA for inversing matrix in my case instead of using LAPACKE?

UPDATE 1: I have donwloaded magma-2.6.1 and firstly, I have to modify the original Makefile:

CXX = icpc -std=c++11 -O3 -xHost
CXXFLAGS = -Wall -c -I${MKLROOT}/include -I/opt/intel/oneapi/compiler/latest/linux/compiler/include -qopenmp -qmkl=parallel
LDFLAGS = -L${MKLROOT}/lib -Wl,-rpath,${MKLROOT}/lib -Wl,-rpath,${MKLROOT}/../compiler/lib -qopenmp -qmkl
SOURCES = main_intel.cpp XSAF_C_intel.cpp
EXECUTABLE = main_intel.exe

I didn't see mkl headers in magma-2.6.1 : nvcc and MKL are compatibles?

Answer 1

Try using magma sgetri gpu - inverse matrix in single precision, GPU interface. This function computes in single precision the inverse A^−1 of an m × m matrix A.

magma_ssetmatrix ( m, m, a,m, d_a ,m, queue ); // copy a -> d_a
magmablas_slacpy ( MagmaFull ,m,m,d_a ,m,d_r ,m, queue ); // d_a - >d_r
// find the inverse matrix : d_a *X=I using the LU factorization
// with partial pivoting and row interchanges computed by
// magma_sgetrf_gpu ; row i is interchanged with row piv (i);
// d_a -mxm matrix ; d_a is overwritten by the inverse
gpu_time = magma_sync_wtime ( NULL );
magma sgetrf gpu( m, m, d a, m, piv, &info);
magma sgetri gpu(m,d a,m,piv,dwork,ldwork,&info);

The official documentation of NVIDIA contains quite a lot of examples, so you may also take a look at them: