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CUBLAS: incorrect inversion for a matrix with a zero support rod

Since CUDA 5.5, the CUBLAS library contains procedures for batch factorization and matrix inversion ( cublas<t>getrfBatchedand, cublas<t>getriBatchedaccordingly).

Guided by the documentation, I wrote test code to invert the N x N matrix using these routines. The code gives the correct conclusion only if the matrix has all non-zero reference points. Setting any zero to zero leads to incorrect results. I checked the results using MATLAB.

I understand that I provide the basic row matrices as input, while CUBLAS expects the main column matrices, but that does not matter, since it will only carry the result. Of course, I also tested at the main input of the column, but I got the same behavior.

I got confused as it cublas<t>getriBatchedexpects an array of information about summary exchanges to be found as input P, which is the result of cublas<t>getrfBatched. Thus, if any zero reference points are eliminated by the exchange of lines, then the inversion procedure should process it automatically.

How to invert matrices containing zero hinge using CUBLAS?

The following is an example of self-compilation with various test cases:

#include <cstdio>
#include <cstdlib>
#include <cuda_runtime.h>
#include <cublas_v2.h>

#define cudacall(call)                                                                                                          \
    do                                                                                                                          \
    {                                                                                                                           \
        cudaError_t err = (call);                                                                                               \
        if(cudaSuccess != err)                                                                                                  \
        {                                                                                                                       \
            fprintf(stderr,"CUDA Error:\nFile = %s\nLine = %d\nReason = %s\n", __FILE__, __LINE__, cudaGetErrorString(err));    \
            cudaDeviceReset();                                                                                                  \
            exit(EXIT_FAILURE);                                                                                                 \
        }                                                                                                                       \
    }                                                                                                                           \
    while (0)

#define cublascall(call)                                                                                        \
    do                                                                                                          \
    {                                                                                                           \
        cublasStatus_t status = (call);                                                                         \
        if(CUBLAS_STATUS_SUCCESS != status)                                                                     \
        {                                                                                                       \
            fprintf(stderr,"CUBLAS Error:\nFile = %s\nLine = %d\nCode = %d\n", __FILE__, __LINE__, status);     \
            cudaDeviceReset();                                                                                  \
            exit(EXIT_FAILURE);                                                                                 \
        }                                                                                                       \
                                                                                                                \
    }                                                                                                           \
    while(0)


void invert_device(float* src_d, float* dst_d, int n)
{
    cublasHandle_t handle;
    cublascall(cublasCreate_v2(&handle));

    int batchSize = 1;

    int *P, *INFO;

    cudacall(cudaMalloc<int>(&P,n * batchSize * sizeof(int)));
    cudacall(cudaMalloc<int>(&INFO,batchSize * sizeof(int)));

    int lda = n;

    float *A[] = { src_d };
    float** A_d;
    cudacall(cudaMalloc<float*>(&A_d,sizeof(A)));
    cudacall(cudaMemcpy(A_d,A,sizeof(A),cudaMemcpyHostToDevice));

    cublascall(cublasSgetrfBatched(handle,n,A_d,lda,P,INFO,batchSize));

    int INFOh = 0;
    cudacall(cudaMemcpy(&INFOh,INFO,sizeof(int),cudaMemcpyDeviceToHost));

    if(INFOh == n)
    {
        fprintf(stderr, "Factorization Failed: Matrix is singular\n");
        cudaDeviceReset();
        exit(EXIT_FAILURE);
    }

    float* C[] = { dst_d };
    float** C_d;
    cudacall(cudaMalloc<float*>(&C_d,sizeof(C)));
    cudacall(cudaMemcpy(C_d,C,sizeof(C),cudaMemcpyHostToDevice));

    cublascall(cublasSgetriBatched(handle,n,A_d,lda,P,C_d,lda,INFO,batchSize));

    cudacall(cudaMemcpy(&INFOh,INFO,sizeof(int),cudaMemcpyDeviceToHost));

    if(INFOh != 0)
    {
        fprintf(stderr, "Inversion Failed: Matrix is singular\n");
        cudaDeviceReset();
        exit(EXIT_FAILURE);
    }

    cudaFree(P), cudaFree(INFO), cublasDestroy_v2(handle);
}

void invert(float* src, float* dst, int n)
{
    float* src_d, *dst_d;

    cudacall(cudaMalloc<float>(&src_d,n * n * sizeof(float)));
    cudacall(cudaMemcpy(src_d,src,n * n * sizeof(float),cudaMemcpyHostToDevice));
    cudacall(cudaMalloc<float>(&dst_d,n * n * sizeof(float)));

    invert_device(src_d,dst_d,n);

    cudacall(cudaMemcpy(dst,dst_d,n * n * sizeof(float),cudaMemcpyDeviceToHost));

    cudaFree(src_d), cudaFree(dst_d);
}

void test_invert()
{
    const int n = 3;

    //Random matrix with full pivots
    float full_pivots[n*n] = { 0.5, 3, 4, 
                                1, 3, 10, 
                                4 , 9, 16 };

    //Almost same as above matrix with first pivot zero
    float zero_pivot[n*n] = { 0, 3, 4, 
                              1, 3, 10,
                              4 , 9, 16 };

    float zero_pivot_col_major[n*n] = { 0, 1, 4, 
                                        3, 3, 9,
                                        4 , 10, 16 };

    float another_zero_pivot[n*n] = { 0, 3, 4, 
                                      1, 5, 6,
                                      9, 8, 2 };

    float another_full_pivot[n * n] = { 22, 3, 4, 
                                        1, 5, 6,
                                        9, 8, 2 };

    float singular[n*n] = {1,2,3,
                           4,5,6,
                           7,8,9};


    //Select matrix by setting "a"
    float* a = zero_pivot;  

    fprintf(stdout, "Input:\n\n");
    for(int i=0; i<n; i++)
    {
        for(int j=0; j<n; j++)
            fprintf(stdout,"%f\t",a[i*n+j]);
        fprintf(stdout,"\n");
    }

    fprintf(stdout,"\n\n");

    invert(a,a,n);

    fprintf(stdout, "Inverse:\n\n");
    for(int i=0; i<n; i++)
    {
        for(int j=0; j<n; j++)
            fprintf(stdout,"%f\t",a[i*n+j]);
        fprintf(stdout,"\n");
    }

}

int main()
{
    test_invert();

    int n;  scanf("%d",&n);
    return 0;
}
+2
1

, CUBLAS cublas<t>getrfBatched (n) , 3<=n<=16, " ", .

"-" A, , n < 17, 17x17 ( Matlab):

 LU = getrf( [A 0 ; 0 I]);

, cublas<t>getriBatched :

 invA = getri( LU(1:3,1:3) )

( n = 17, getri , 3x3 invA.)

, , , 3x3 zero_pivot zero_pivot_war :

$ cat t340.cu
#include <cstdio>
#include <cstdlib>
#include <cuda_runtime.h>
#include <cublas_v2.h>

#define cudacall(call)                                                                                                          \
    do                                                                                                                          \
    {                                                                                                                           \
        cudaError_t err = (call);                                                                                               \
        if(cudaSuccess != err)                                                                                                  \
        {                                                                                                                       \
            fprintf(stderr,"CUDA Error:\nFile = %s\nLine = %d\nReason = %s\n", __FILE__, __LINE__, cudaGetErrorString(err));    \
            cudaDeviceReset();                                                                                                  \
            exit(EXIT_FAILURE);                                                                                                 \
        }                                                                                                                       \
    }                                                                                                                           \
    while (0)

#define cublascall(call)                                                                                        \
    do                                                                                                          \
    {                                                                                                           \
        cublasStatus_t status = (call);                                                                         \
        if(CUBLAS_STATUS_SUCCESS != status)                                                                     \
        {                                                                                                       \
            fprintf(stderr,"CUBLAS Error:\nFile = %s\nLine = %d\nCode = %d\n", __FILE__, __LINE__, status);     \
            cudaDeviceReset();                                                                                  \
            exit(EXIT_FAILURE);                                                                                 \
        }                                                                                                       \
                                                                                                                \
    }                                                                                                           \
    while(0)


void invert_device(float* src_d, float* dst_d, int n)
{
    cublasHandle_t handle;
    cublascall(cublasCreate_v2(&handle));

    int batchSize = 1;

    int *P, *INFO;

    cudacall(cudaMalloc<int>(&P,17 * batchSize * sizeof(int)));
    cudacall(cudaMalloc<int>(&INFO,batchSize * sizeof(int)));

    int lda = 17;

    float *A[] = { src_d };
    float** A_d;
    cudacall(cudaMalloc<float*>(&A_d,sizeof(A)));
    cudacall(cudaMemcpy(A_d,A,sizeof(A),cudaMemcpyHostToDevice));

    cublascall(cublasSgetrfBatched(handle,17,A_d,lda,P,INFO,batchSize));

    int INFOh = 0;
    cudacall(cudaMemcpy(&INFOh,INFO,sizeof(int),cudaMemcpyDeviceToHost));

    if(INFOh == 17)
    {
        fprintf(stderr, "Factorization Failed: Matrix is singular\n");
        cudaDeviceReset();
        exit(EXIT_FAILURE);
    }

    float* C[] = { dst_d };
    float** C_d;
    cudacall(cudaMalloc<float*>(&C_d,sizeof(C)));
    cudacall(cudaMemcpy(C_d,C,sizeof(C),cudaMemcpyHostToDevice));

    cublascall(cublasSgetriBatched(handle,n,A_d,lda,P,C_d,n,INFO,batchSize));

    cudacall(cudaMemcpy(&INFOh,INFO,sizeof(int),cudaMemcpyDeviceToHost));

    if(INFOh != 0)
    {
        fprintf(stderr, "Inversion Failed: Matrix is singular\n");
        cudaDeviceReset();
        exit(EXIT_FAILURE);
    }

    cudaFree(P), cudaFree(INFO), cublasDestroy_v2(handle);
}

void invert(float* src, float* dst, int n)
{
    float* src_d, *dst_d;

    cudacall(cudaMalloc<float>(&src_d,17 * 17 * sizeof(float)));
    cudacall(cudaMemcpy(src_d,src,17 * 17 * sizeof(float),cudaMemcpyHostToDevice));
    cudacall(cudaMalloc<float>(&dst_d,n * n * sizeof(float)));

    invert_device(src_d,dst_d,n);

    cudacall(cudaMemcpy(dst,dst_d,n * n * sizeof(float),cudaMemcpyDeviceToHost));

    cudaFree(src_d), cudaFree(dst_d);
}

void test_invert()
{
    const int n = 3;

    //Random matrix with full pivots
/*    float full_pivots[n*n] = { 0.5, 3, 4,
                                1, 3, 10,
                                4 , 9, 16 };

    //Almost same as above matrix with first pivot zero
    float zero_pivot[n*n] = { 0, 3, 4,
                              1, 3, 10,
                              4 , 9, 16 };

    float zero_pivot_col_major[n*n] = { 0, 1, 4,
                                        3, 3, 9,
                                        4 , 10, 16 };
*/
    float zero_pivot_war[17*17] = {
                                        0,3,4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
                                        1,3,10,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
                                        4,9,16,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
                                        0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,
                                        0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,
                                        0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,
                                        0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,
                                        0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,
                                        0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,
                                        0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,
                                        0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,
                                        0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,
                                        0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,
                                        0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,
                                        0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,
                                        0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,
                                        0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1 };
/*
    float another_zero_pivot[n*n] = { 0, 3, 4,
                                      1, 5, 6,
                                      9, 8, 2 };

    float another_full_pivot[n * n] = { 22, 3, 4,
                                        1, 5, 6,
                                        9, 8, 2 };

    float singular[n*n] = {1,2,3,
                           4,5,6,
                           7,8,9};
*/
    float result[n*n];

    //Select matrix by setting "a"
    float* a = zero_pivot_war;

    fprintf(stdout, "Input:\n\n");
    for(int i=0; i<n; i++)
    {
        for(int j=0; j<n; j++)
            fprintf(stdout,"%f\t",a[i*17+j]);
        fprintf(stdout,"\n");
    }

    fprintf(stdout,"\n\n");

    invert(a,result,n);

    fprintf(stdout, "Inverse:\n\n");
    for(int i=0; i<n; i++)
    {
        for(int j=0; j<n; j++)
            fprintf(stdout,"%f\t",result[i*n+j]);
        fprintf(stdout,"\n");
    }

}

int main()
{
    test_invert();

//    int n;  scanf("%d",&n);
    return 0;
}
$ nvcc -arch=sm_20 -o t340 t340.cu -lcublas
$ cuda-memcheck ./t340
========= CUDA-MEMCHECK
Input:

0.000000        3.000000        4.000000
1.000000        3.000000        10.000000
4.000000        9.000000        16.000000


Inverse:

-0.700000       -0.200000       0.300000
0.400000        -0.266667       0.066667
-0.050000       0.200000        -0.050000
========= ERROR SUMMARY: 0 errors
$

.

CUBLAS. , , CUDA 5.5, CUDA 6.0 RC. , NVIDIA (, CUBLAS), NVIDIA developer.nvidia.com ( ).

+2

Source: https://habr.com/ru/post/1532447/

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