# cuSOLVER solving a overdetermined linear equation system

A is a m*n (m>n) sparse matrix and B is the right-hand-side vector of size m, solving this linear system Ax=b, i use
M = A^T.A, N = A^T.b The problem is converted to solving Mx=N. I have two equations，first solved ok , second solved failed.
at the second linear system,I used cusolverSpScsrlsvchol orcusolverSpScsrlsvqr ,all crashed and errorCode=CUSOLVER_STATUS_ALLOC_FAILED.
my Graphics is NVIDIA GeForce RTX3070 an CUDA Version 11.4

first linear system like this:

second linear system like this:

When the program crashes the device memroy like this:

I alse used the cuda samples cuSolverSp_LowlevelCholesky ,this crashed at "code=2(CUSOLVER_STATUS_ALLOC_FAILED) " cusolverSpXcsrcholAnalysis

I used Nsigh Compute profiling the function ,

cusolverSpXcsrcholAnalysisHost function worked will and compute a good solution

Can you provide a reproducer and input?

Can you try solving with a single RHS? We need to determine if the problem is with the factorization or the solving step.

data.rar (7.4 MB)

``````int nnz = 3397636;
int N = 262144;
int* csrRow = new int[N + 1];
int* csrCol = new int[nnz];
float* csrVal = new float[nnz];
float* rhsXYZ[3];
rhsXYZ[0] = new float[N];
rhsXYZ[1] = new float[N];
rhsXYZ[2] = new float[N];
FILE* f1 = fopen("mtxF1.txt", "r");
for (int i = 0; i < nnz; i++)
fscanf(f1, "%d %f\n", &csrCol[i], &csrVal[i]);
fclose(f1);
FILE* f2 = fopen("mtxF2.txt", "r");
for (int i = 0; i < N + 1; i++)
fscanf(f2, "%d\n", &csrRow[i]);
fclose(f2);
FILE* f3 = fopen("bVecRHS.txt", "r");
for (int i = 0; i < N; i++)
fscanf(f3, "%f %f %f\n", &rhsXYZ[0][i], &rhsXYZ[1][i], &rhsXYZ[2][i]);
fclose(f3);
int* dCsrRow, * dCsrCol;
float* dCsrVal;
cudaMalloc((void**)&dCsrRow, sizeof(int) * (N + 1));
cudaMalloc((void**)&dCsrCol, sizeof(int) * (nnz));
cudaMalloc((void**)&dCsrVal, sizeof(float) * (nnz));
cudaMemcpy(dCsrRow, csrRow, sizeof(int) * (N + 1), cudaMemcpyHostToDevice);
cudaMemcpy(dCsrCol, csrCol, sizeof(int) * (nnz), cudaMemcpyHostToDevice);
cudaMemcpy(dCsrVal, csrVal, sizeof(float) * (nnz), cudaMemcpyHostToDevice);
float* dBVec, *dResVec;
cudaMalloc((void**)&dBVec, sizeof(float) * (N));
cudaMalloc((void**)&dResVec, sizeof(float) * (N));
cusolverStatus_t stat;
cusolverSpHandle_t cusolverSpH = NULL;
stat = cusolverSpCreate(&cusolverSpH);
cusparseMatDescr_t descrA = NULL;
cusparseCreateMatDescr(&descrA);
cusparseSetMatType(descrA, CUSPARSE_MATRIX_TYPE_GENERAL);
cusparseSetMatIndexBase(descrA, CUSPARSE_INDEX_BASE_ZERO);
csrcholInfo_t d_info = NULL;
cusolverSpCreateCsrcholInfo(&d_info);
printf("step 10: analyze chol(A) to know structure of L\n");
stat = cusolverSpXcsrcholAnalysis(
cusolverSpH, N, nnz,
descrA, dCsrRow, dCsrCol,
d_info);
printf("step 11: workspace for chol(A)\n");
size_t size_internal = 0;
size_t size_chol = 0; // size of working space for csrlu
stat = cusolverSpScsrcholBufferInfo(
cusolverSpH, N, nnz,
descrA, dCsrVal, dCsrRow, dCsrCol,
d_info,
&size_internal,
&size_chol);
void* buffer_gpu;
cudaMalloc(&buffer_gpu, sizeof(char) * size_chol);
printf("step 12: compute A = L*L^T \n");
stat = cusolverSpScsrcholFactor(
cusolverSpH, N, nnz,
descrA, dCsrVal, dCsrRow, dCsrCol,
d_info,
buffer_gpu);
printf("step 13: check if the matrix is singular \n");
int singularity = 0;
const float tol = 1.e-7;
stat =  cusolverSpDcsrcholZeroPivot(
cusolverSpH, d_info, tol, &singularity);
if (0 <= singularity) {
fprintf(stderr, "Error: A is not invertible, singularity=%d\n", singularity);
// return 1;
}
float* resXYZ[3];
resXYZ[0] = new float[N];
resXYZ[1] = new float[N];
resXYZ[2] = new float[N];
printf("step 14: solve A*x = b \n");
for (int i = 0; i < 3; i++)
{
cudaMemcpy(dBVec, rhsXYZ[i], sizeof(float) * N, cudaMemcpyHostToDevice);
stat = cusolverSpScsrcholSolve(
cusolverSpH, N, dBVec, dResVec, d_info, buffer_gpu);
cudaMemcpy(resXYZ[i], dResVec, sizeof(float) * N, cudaMemcpyDeviceToHost);
}``````

My code and data are below，I try Reduce the size of the matrix，the cusolverSpXcsrcholAnalysis function don’t crashed ,but return CUSOLVER_STATUS_ALLOC_FAILED, this code copy form the cuda samples cuSolverSp_LowlevelCholesky version is 11.4

Solved，The required device memory space is too large,if csr matrix’s nnz=1546687, rtx2080ti,12GB can solve, if csr matrix’s nnz=6190816, rtx3090,24GB still not enough.This is incredible and very unreasonable

While it’s not as performant, you could try to use managed memory to extend usable memory

Thank you. My matrix may be much bigger than the one mentioned above. I’ll give it up for now

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