xref: /petsc/src/mat/tests/ex70.c (revision 3faff0630ddb0e5c928de8ab5c63f2cda2d2edd1)

#include <petscmat.h>

static char help[] = "Tests MatMat operations with MAT_REUSE_MATRIX and already allocated dense result.\n\n";

static PetscScalar MAGIC_NUMBER = 12345;

static PetscErrorCode CheckLocal(Mat A, Mat B, PetscScalar *a, PetscScalar *b) {
  PetscBool wA = PETSC_FALSE, wB = PETSC_FALSE;
  PetscBool wAv = PETSC_FALSE, wBv = PETSC_FALSE;
  PetscInt  lda, i, j, m, n;

  PetscFunctionBegin;
  if (a) {
    const PetscScalar *Aa;
    PetscCall(MatDenseGetArrayRead(A, &Aa));
    wA = (PetscBool)(a != Aa);
    PetscCall(MatDenseGetLDA(A, &lda));
    PetscCall(MatGetLocalSize(A, &m, &n));
    for (j = 0; j < n; j++) {
      for (i = m; i < lda; i++) {
        if (Aa[j * lda + i] != MAGIC_NUMBER) wAv = PETSC_TRUE;
      }
    }
    PetscCall(MatDenseRestoreArrayRead(A, &Aa));
  }
  if (b) {
    const PetscScalar *Bb;
    PetscCall(MatDenseGetArrayRead(B, &Bb));
    wB = (PetscBool)(b != Bb);
    PetscCall(MatDenseGetLDA(B, &lda));
    PetscCall(MatGetLocalSize(B, &m, &n));
    for (j = 0; j < n; j++) {
      for (i = m; i < lda; i++) {
        if (Bb[j * lda + i] != MAGIC_NUMBER) wBv = PETSC_TRUE;
      }
    }
    PetscCall(MatDenseRestoreArrayRead(B, &Bb));
  }
  PetscCheck(!wA && !wB, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Wrong array in first Mat? %d, Wrong array in second Mat? %d", wA, wB);
  PetscCheck(!wAv && !wBv, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Wrong data in first Mat? %d, Wrong data in second Mat? %d", wAv, wBv);
  PetscFunctionReturn(0);
}

typedef struct {
  Mat A;
  Mat P;
  Mat R;
} proj_data;

PetscErrorCode proj_destroy(void *ctx) {
  proj_data *userdata = (proj_data *)ctx;

  PetscFunctionBegin;
  PetscCheck(userdata, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Missing userdata");
  PetscCall(MatDestroy(&userdata->A));
  PetscCall(MatDestroy(&userdata->P));
  PetscCall(MatDestroy(&userdata->R));
  PetscCall(PetscFree(userdata));
  PetscFunctionReturn(0);
}

PetscErrorCode proj_mult(Mat S, Vec X, Vec Y) {
  Mat        A, R, P;
  Vec        Ax, Ay;
  Vec        Px, Py;
  proj_data *userdata;

  PetscFunctionBegin;
  PetscCall(MatShellGetContext(S, &userdata));
  PetscCheck(userdata, PetscObjectComm((PetscObject)S), PETSC_ERR_PLIB, "Missing userdata");
  A = userdata->A;
  R = userdata->R;
  P = userdata->P;
  PetscCheck(A, PetscObjectComm((PetscObject)S), PETSC_ERR_PLIB, "Missing matrix");
  PetscCheck(R || P, PetscObjectComm((PetscObject)S), PETSC_ERR_PLIB, "Missing projectors");
  PetscCheck(!R || !P, PetscObjectComm((PetscObject)S), PETSC_ERR_PLIB, "Both projectors");
  PetscCall(MatCreateVecs(A, &Ax, &Ay));
  if (R) {
    PetscCall(MatCreateVecs(R, &Py, &Px));
  } else {
    PetscCall(MatCreateVecs(P, &Px, &Py));
  }
  PetscCall(VecCopy(X, Px));
  if (P) {
    PetscCall(MatMult(P, Px, Py));
  } else {
    PetscCall(MatMultTranspose(R, Px, Py));
  }
  PetscCall(VecCopy(Py, Ax));
  PetscCall(MatMult(A, Ax, Ay));
  PetscCall(VecCopy(Ay, Py));
  if (P) {
    PetscCall(MatMultTranspose(P, Py, Px));
  } else {
    PetscCall(MatMult(R, Py, Px));
  }
  PetscCall(VecCopy(Px, Y));
  PetscCall(VecDestroy(&Px));
  PetscCall(VecDestroy(&Py));
  PetscCall(VecDestroy(&Ax));
  PetscCall(VecDestroy(&Ay));
  PetscFunctionReturn(0);
}

PetscErrorCode MyPtShellPMultSymbolic(Mat S, Mat P, Mat PtAP, void **ctx) {
  proj_data *userdata;

  PetscFunctionBegin;
  PetscCall(PetscNew(&userdata));
  PetscCall(MatShellSetContext(PtAP, userdata));
  *ctx = (void *)userdata;
  PetscFunctionReturn(0);
}

PetscErrorCode MyPtShellPMultNumeric(Mat S, Mat P, Mat PtAP, void *ctx) {
  Mat        A;
  proj_data *userdata = (proj_data *)ctx;

  PetscFunctionBegin;
  PetscCall(MatShellGetContext(S, &A));
  PetscCall(PetscObjectReference((PetscObject)A));
  PetscCall(PetscObjectReference((PetscObject)P));
  PetscCall(MatDestroy(&userdata->A));
  PetscCall(MatDestroy(&userdata->P));
  PetscCall(MatDestroy(&userdata->R));
  userdata->A = A;
  userdata->P = P;
  PetscCall(MatShellSetOperation(PtAP, MATOP_MULT, (void (*)(void))proj_mult));
  PetscCall(MatSetUp(PtAP));
  PetscCall(MatAssemblyBegin(PtAP, MAT_FINAL_ASSEMBLY));
  PetscCall(MatAssemblyEnd(PtAP, MAT_FINAL_ASSEMBLY));
  PetscFunctionReturn(0);
}

PetscErrorCode MyRShellRtMultSymbolic(Mat S, Mat R, Mat RARt, void **ctx) {
  proj_data *userdata;

  PetscFunctionBegin;
  PetscCall(PetscNew(&userdata));
  PetscCall(MatShellSetContext(RARt, userdata));
  *ctx = (void *)userdata;
  PetscFunctionReturn(0);
}

PetscErrorCode MyRShellRtMultNumeric(Mat S, Mat R, Mat RARt, void *ctx) {
  Mat        A;
  proj_data *userdata = (proj_data *)ctx;

  PetscFunctionBegin;
  PetscCall(MatShellGetContext(S, &A));
  PetscCall(PetscObjectReference((PetscObject)A));
  PetscCall(PetscObjectReference((PetscObject)R));
  PetscCall(MatDestroy(&userdata->A));
  PetscCall(MatDestroy(&userdata->P));
  PetscCall(MatDestroy(&userdata->R));
  userdata->A = A;
  userdata->R = R;
  PetscCall(MatShellSetOperation(RARt, MATOP_MULT, (void (*)(void))proj_mult));
  PetscCall(MatSetUp(RARt));
  PetscCall(MatAssemblyBegin(RARt, MAT_FINAL_ASSEMBLY));
  PetscCall(MatAssemblyEnd(RARt, MAT_FINAL_ASSEMBLY));
  PetscFunctionReturn(0);
}

PetscErrorCode MyMatShellMatMultNumeric(Mat S, Mat B, Mat C, void *ctx) {
  Mat A;

  PetscFunctionBegin;
  PetscCall(MatShellGetContext(S, &A));
  PetscCall(MatMatMult(A, B, MAT_REUSE_MATRIX, PETSC_DEFAULT, &C));
  PetscFunctionReturn(0);
}

PetscErrorCode MyMatTransposeShellMatMultNumeric(Mat S, Mat B, Mat C, void *ctx) {
  Mat A;

  PetscFunctionBegin;
  PetscCall(MatShellGetContext(S, &A));
  PetscCall(MatTransposeMatMult(A, B, MAT_REUSE_MATRIX, PETSC_DEFAULT, &C));
  PetscFunctionReturn(0);
}

PetscErrorCode MyMatShellMatTransposeMultNumeric(Mat S, Mat B, Mat C, void *ctx) {
  Mat A;

  PetscFunctionBegin;
  PetscCall(MatShellGetContext(S, &A));
  PetscCall(MatMatTransposeMult(A, B, MAT_REUSE_MATRIX, PETSC_DEFAULT, &C));
  PetscFunctionReturn(0);
}

int main(int argc, char **args) {
  Mat          X, B, A, Bt, T, T2, PtAP = NULL, RARt = NULL, R = NULL;
  Vec          r, l, rs, ls;
  PetscInt     m, n, k, M = 10, N = 10, K = 5, ldx = 3, ldb = 5, ldr = 4;
  const char  *deft = MATAIJ;
  char         mattype[256];
  PetscBool    flg, symm = PETSC_FALSE, testtt = PETSC_TRUE, testnest = PETSC_TRUE, testtranspose = PETSC_TRUE, testcircular = PETSC_FALSE, local = PETSC_TRUE;
  PetscBool    testhtranspose = PETSC_FALSE; /* Hermitian transpose is not handled correctly and generates an error */
  PetscBool    xgpu = PETSC_FALSE, bgpu = PETSC_FALSE, testshellops = PETSC_FALSE, testproj = PETSC_TRUE, testrart = PETSC_TRUE, testmatmatt = PETSC_TRUE, testmattmat = PETSC_TRUE;
  PetscScalar *dataX = NULL, *dataB = NULL, *dataR = NULL, *dataBt = NULL;
  PetscScalar *aX, *aB, *aBt;
  PetscReal    err;

  PetscFunctionBeginUser;
  PetscCall(PetscInitialize(&argc, &args, NULL, help));
  PetscCall(PetscOptionsGetInt(NULL, NULL, "-N", &N, NULL));
  PetscCall(PetscOptionsGetInt(NULL, NULL, "-M", &M, NULL));
  PetscCall(PetscOptionsGetInt(NULL, NULL, "-K", &K, NULL));
  PetscCall(PetscOptionsGetBool(NULL, NULL, "-symm", &symm, NULL));
  PetscCall(PetscOptionsGetBool(NULL, NULL, "-local", &local, NULL));
  PetscCall(PetscOptionsGetInt(NULL, NULL, "-ldx", &ldx, NULL));
  PetscCall(PetscOptionsGetInt(NULL, NULL, "-ldb", &ldb, NULL));
  PetscCall(PetscOptionsGetInt(NULL, NULL, "-ldr", &ldr, NULL));
  PetscCall(PetscOptionsGetBool(NULL, NULL, "-testtranspose", &testtranspose, NULL));
  PetscCall(PetscOptionsGetBool(NULL, NULL, "-testnest", &testnest, NULL));
  PetscCall(PetscOptionsGetBool(NULL, NULL, "-testtt", &testtt, NULL));
  PetscCall(PetscOptionsGetBool(NULL, NULL, "-testcircular", &testcircular, NULL));
  PetscCall(PetscOptionsGetBool(NULL, NULL, "-testshellops", &testshellops, NULL));
  PetscCall(PetscOptionsGetBool(NULL, NULL, "-testproj", &testproj, NULL));
  PetscCall(PetscOptionsGetBool(NULL, NULL, "-testrart", &testrart, NULL));
  PetscCall(PetscOptionsGetBool(NULL, NULL, "-testmatmatt", &testmatmatt, NULL));
  PetscCall(PetscOptionsGetBool(NULL, NULL, "-testmattmat", &testmattmat, NULL));
  PetscCall(PetscOptionsGetBool(NULL, NULL, "-xgpu", &xgpu, NULL));
  PetscCall(PetscOptionsGetBool(NULL, NULL, "-bgpu", &bgpu, NULL));
  PetscCall(PetscOptionsGetScalar(NULL, NULL, "-magic_number", &MAGIC_NUMBER, NULL));
  if (M != N) testproj = PETSC_FALSE;

  PetscCall(MatCreate(PETSC_COMM_WORLD, &A));
  PetscCall(MatSetSizes(A, PETSC_DECIDE, PETSC_DECIDE, M, N));
  PetscCall(MatSetType(A, MATAIJ));
  PetscCall(MatSetUp(A));
  PetscCall(MatSetRandom(A, NULL));
  if (M == N && symm) {
    Mat AT;

    PetscCall(MatTranspose(A, MAT_INITIAL_MATRIX, &AT));
    PetscCall(MatAXPY(A, 1.0, AT, DIFFERENT_NONZERO_PATTERN));
    PetscCall(MatDestroy(&AT));
    PetscCall(MatSetOption(A, MAT_SYMMETRIC, PETSC_TRUE));
  }
  PetscCall(MatViewFromOptions(A, NULL, "-A_init_view"));
  PetscOptionsBegin(PETSC_COMM_WORLD, "", "", "");
  PetscCall(PetscOptionsFList("-A_mat_type", "Matrix type", "MatSetType", MatList, deft, mattype, 256, &flg));
  PetscOptionsEnd();
  if (flg) {
    Mat A2;

    PetscCall(MatDuplicate(A, MAT_COPY_VALUES, &A2));
    PetscCall(MatConvert(A, mattype, MAT_INPLACE_MATRIX, &A));
    PetscCall(MatMultEqual(A, A2, 10, &flg));
    if (!flg) {
      Mat AE, A2E;

      PetscCall(PetscPrintf(PETSC_COMM_WORLD, "Error with convert\n"));
      PetscCall(MatComputeOperator(A, MATDENSE, &AE));
      PetscCall(MatComputeOperator(A2, MATDENSE, &A2E));
      PetscCall(MatView(AE, NULL));
      PetscCall(MatView(A2E, NULL));
      PetscCall(MatAXPY(A2E, -1.0, A, SAME_NONZERO_PATTERN));
      PetscCall(MatView(A2E, NULL));
      PetscCall(MatDestroy(&A2E));
      PetscCall(MatDestroy(&AE));
    }
    PetscCall(MatDestroy(&A2));
  }
  PetscCall(MatViewFromOptions(A, NULL, "-A_view"));

  PetscCall(MatGetLocalSize(A, &m, &n));
  if (local) {
    PetscInt i;

    PetscCall(PetscMalloc1((m + ldx) * K, &dataX));
    PetscCall(PetscMalloc1((n + ldb) * K, &dataB));
    for (i = 0; i < (m + ldx) * K; i++) dataX[i] = MAGIC_NUMBER;
    for (i = 0; i < (n + ldb) * K; i++) dataB[i] = MAGIC_NUMBER;
  }
  PetscCall(MatCreateDense(PETSC_COMM_WORLD, n, PETSC_DECIDE, N, K, dataB, &B));
  PetscCall(MatCreateDense(PETSC_COMM_WORLD, m, PETSC_DECIDE, M, K, dataX, &X));
  if (local) {
    PetscCall(MatDenseSetLDA(X, m + ldx));
    PetscCall(MatDenseSetLDA(B, n + ldb));
  }
  PetscCall(MatGetLocalSize(B, NULL, &k));
  if (local) {
    PetscInt i;

    PetscCall(PetscMalloc1((k + ldr) * N, &dataBt));
    for (i = 0; i < (k + ldr) * N; i++) dataBt[i] = MAGIC_NUMBER;
  }
  PetscCall(MatCreateDense(PETSC_COMM_WORLD, k, n, K, N, dataBt, &Bt));
  if (local) PetscCall(MatDenseSetLDA(Bt, k + ldr));

  /* store pointer to dense data for testing */
  PetscCall(MatDenseGetArrayRead(B, (const PetscScalar **)&dataB));
  PetscCall(MatDenseGetArrayRead(X, (const PetscScalar **)&dataX));
  PetscCall(MatDenseGetArrayRead(Bt, (const PetscScalar **)&dataBt));
  aX  = dataX;
  aB  = dataB;
  aBt = dataBt;
  PetscCall(MatDenseRestoreArrayRead(Bt, (const PetscScalar **)&dataBt));
  PetscCall(MatDenseRestoreArrayRead(B, (const PetscScalar **)&dataB));
  PetscCall(MatDenseRestoreArrayRead(X, (const PetscScalar **)&dataX));
  if (local) {
    dataX  = aX;
    dataB  = aB;
    dataBt = aBt;
  }

  PetscCall(MatSetRandom(X, NULL));
  PetscCall(MatSetRandom(B, NULL));
  PetscCall(MatSetRandom(Bt, NULL));
  PetscCall(CheckLocal(X, NULL, aX, NULL));
  PetscCall(CheckLocal(Bt, B, aBt, aB));

  /* convert to CUDA if needed */
  if (bgpu) {
    PetscCall(MatConvert(B, MATDENSECUDA, MAT_INPLACE_MATRIX, &B));
    PetscCall(MatConvert(Bt, MATDENSECUDA, MAT_INPLACE_MATRIX, &Bt));
  }
  if (xgpu) PetscCall(MatConvert(X, MATDENSECUDA, MAT_INPLACE_MATRIX, &X));
  PetscCall(CheckLocal(B, X, aB, aX));

  /* Test MatDenseGetSubMatrix */
  {
    Mat B2, T3, T4;

    PetscCall(MatDuplicate(B, MAT_COPY_VALUES, &B2));
    PetscCall(MatDuplicate(B, MAT_DO_NOT_COPY_VALUES, &T4));
    PetscCall(MatSetRandom(T4, NULL));
    PetscCall(MatAXPY(B2, 1.0, T4, SAME_NONZERO_PATTERN));
    PetscCall(MatDenseGetSubMatrix(B, PETSC_DECIDE, PETSC_DECIDE, PetscMin(1, K - 1), PetscMin(2, K), &T));
    PetscCall(MatDenseGetSubMatrix(T4, PETSC_DECIDE, PETSC_DECIDE, PetscMin(1, K - 1), PetscMin(2, K), &T2));
    PetscCall(MatDenseGetSubMatrix(B2, PETSC_DECIDE, PETSC_DECIDE, PetscMin(1, K - 1), PetscMin(2, K), &T3));
    PetscCall(MatAXPY(T, 1.0, T2, SAME_NONZERO_PATTERN));
    PetscCall(MatAXPY(T3, -1.0, T, SAME_NONZERO_PATTERN));
    PetscCall(MatNorm(T3, NORM_FROBENIUS, &err));
    if (err > PETSC_SMALL) {
      PetscCall(PetscPrintf(PETSC_COMM_WORLD, "Error with MatDenseGetSubMatrix\n"));
      PetscCall(MatView(T3, NULL));
    }
    PetscCall(MatDenseRestoreSubMatrix(B, &T));
    PetscCall(MatDenseRestoreSubMatrix(T4, &T2));
    PetscCall(MatDenseRestoreSubMatrix(B2, &T3));
    PetscCall(CheckLocal(B, NULL, aB, NULL));
    PetscCall(MatDestroy(&B2));
    PetscCall(MatDestroy(&T4));
    if (N >= 2) {
      PetscCall(MatDuplicate(B, MAT_COPY_VALUES, &B2));
      PetscCall(MatDuplicate(B, MAT_DO_NOT_COPY_VALUES, &T4));
      PetscCall(MatSetRandom(T4, NULL));
      PetscCall(MatAXPY(B2, 1.0, T4, SAME_NONZERO_PATTERN));
      PetscCall(MatDenseGetSubMatrix(B, N - 2, PETSC_DECIDE, PetscMin(1, K - 1), PetscMin(2, K), &T));
      PetscCall(MatDenseGetSubMatrix(T4, N - 2, PETSC_DECIDE, PetscMin(1, K - 1), PetscMin(2, K), &T2));
      PetscCall(MatDenseGetSubMatrix(B2, N - 2, PETSC_DECIDE, PetscMin(1, K - 1), PetscMin(2, K), &T3));
      PetscCall(MatAXPY(T, 1.0, T2, SAME_NONZERO_PATTERN));
      PetscCall(MatAXPY(T3, -1.0, T, SAME_NONZERO_PATTERN));
      PetscCall(MatNorm(T3, NORM_FROBENIUS, &err));
      if (err > PETSC_SMALL) {
        PetscCall(PetscPrintf(PETSC_COMM_WORLD, "Error with MatDenseGetSubMatrix\n"));
        PetscCall(MatView(T3, NULL));
      }
      PetscCall(MatDenseRestoreSubMatrix(B, &T));
      PetscCall(MatDenseRestoreSubMatrix(T4, &T2));
      PetscCall(MatDenseRestoreSubMatrix(B2, &T3));
      PetscCall(CheckLocal(B, NULL, aB, NULL));
      PetscCall(MatDestroy(&B2));
      PetscCall(MatDestroy(&T4));
      PetscCall(MatDuplicate(B, MAT_COPY_VALUES, &B2));
      PetscCall(MatDuplicate(B, MAT_DO_NOT_COPY_VALUES, &T4));
      PetscCall(MatSetRandom(T4, NULL));
      PetscCall(MatAXPY(B2, 1.0, T4, SAME_NONZERO_PATTERN));
      PetscCall(MatDenseGetSubMatrix(B, PETSC_DECIDE, 2, PetscMin(1, K - 1), PetscMin(2, K), &T));
      PetscCall(MatDenseGetSubMatrix(T4, PETSC_DECIDE, 2, PetscMin(1, K - 1), PetscMin(2, K), &T2));
      PetscCall(MatDenseGetSubMatrix(B2, PETSC_DECIDE, 2, PetscMin(1, K - 1), PetscMin(2, K), &T3));
      PetscCall(MatAXPY(T, 1.0, T2, SAME_NONZERO_PATTERN));
      PetscCall(MatAXPY(T3, -1.0, T, SAME_NONZERO_PATTERN));
      PetscCall(MatNorm(T3, NORM_FROBENIUS, &err));
      if (err > PETSC_SMALL) {
        PetscCall(PetscPrintf(PETSC_COMM_WORLD, "Error with MatDenseGetSubMatrix\n"));
        PetscCall(MatView(T3, NULL));
      }
      PetscCall(MatDenseRestoreSubMatrix(B, &T));
      PetscCall(MatDenseRestoreSubMatrix(T4, &T2));
      PetscCall(MatDenseRestoreSubMatrix(B2, &T3));
      PetscCall(CheckLocal(B, NULL, aB, NULL));
      PetscCall(MatDestroy(&B2));
      PetscCall(MatDestroy(&T4));
    }
  }

  /* Test reusing a previously allocated dense buffer */
  PetscCall(MatMatMult(A, B, MAT_REUSE_MATRIX, PETSC_DEFAULT, &X));
  PetscCall(CheckLocal(B, X, aB, aX));
  PetscCall(MatMatMultEqual(A, B, X, 10, &flg));
  if (!flg) {
    PetscCall(PetscPrintf(PETSC_COMM_WORLD, "Error with reusage\n"));
    PetscCall(MatMatMult(A, B, MAT_INITIAL_MATRIX, PETSC_DEFAULT, &T));
    PetscCall(MatAXPY(T, -1.0, X, SAME_NONZERO_PATTERN));
    PetscCall(MatView(T, NULL));
    PetscCall(MatDestroy(&T));
  }

  /* Test MatTransposeMat and MatMatTranspose */
  if (testmattmat) {
    PetscCall(MatTransposeMatMult(A, X, MAT_REUSE_MATRIX, PETSC_DEFAULT, &B));
    PetscCall(CheckLocal(B, X, aB, aX));
    PetscCall(MatTransposeMatMultEqual(A, X, B, 10, &flg));
    if (!flg) {
      PetscCall(PetscPrintf(PETSC_COMM_WORLD, "Error with reusage (MatTransposeMat)\n"));
      PetscCall(MatTransposeMatMult(A, X, MAT_INITIAL_MATRIX, PETSC_DEFAULT, &B));
      PetscCall(MatAXPY(T, -1.0, B, SAME_NONZERO_PATTERN));
      PetscCall(MatView(T, NULL));
      PetscCall(MatDestroy(&T));
    }
  }
  if (testmatmatt) {
    PetscCall(MatMatTransposeMult(A, Bt, MAT_REUSE_MATRIX, PETSC_DEFAULT, &X));
    PetscCall(CheckLocal(Bt, X, aBt, aX));
    PetscCall(MatMatTransposeMultEqual(A, Bt, X, 10, &flg));
    if (!flg) {
      PetscCall(PetscPrintf(PETSC_COMM_WORLD, "Error with reusage (MatMatTranspose)\n"));
      PetscCall(MatMatTransposeMult(A, Bt, MAT_INITIAL_MATRIX, PETSC_DEFAULT, &T));
      PetscCall(MatAXPY(T, -1.0, X, SAME_NONZERO_PATTERN));
      PetscCall(MatView(T, NULL));
      PetscCall(MatDestroy(&T));
    }
  }

  /* Test projection operations (PtAP and RARt) */
  if (testproj) {
    PetscCall(MatPtAP(A, B, MAT_INITIAL_MATRIX, PETSC_DEFAULT, &PtAP));
    PetscCall(MatPtAPMultEqual(A, B, PtAP, 10, &flg));
    if (!flg) {
      PetscCall(PetscPrintf(PETSC_COMM_WORLD, "Error with PtAP\n"));
      PetscCall(MatMatMult(A, B, MAT_INITIAL_MATRIX, PETSC_DEFAULT, &T));
      PetscCall(MatTransposeMatMult(B, T, MAT_INITIAL_MATRIX, PETSC_DEFAULT, &T2));
      PetscCall(MatAXPY(T2, -1.0, PtAP, SAME_NONZERO_PATTERN));
      PetscCall(MatView(T2, NULL));
      PetscCall(MatDestroy(&T2));
      PetscCall(MatDestroy(&T));
    }
    PetscCall(PetscMalloc1((k + ldr) * M, &dataR));
    PetscCall(MatCreateDense(PETSC_COMM_WORLD, PETSC_DECIDE, m, K, M, dataR, &R));
    PetscCall(MatDenseSetLDA(R, k + ldr));
    PetscCall(MatSetRandom(R, NULL));
    if (testrart) { /* fails for AIJCUSPARSE because RA operation is not defined */
      PetscCall(MatRARt(A, R, MAT_INITIAL_MATRIX, PETSC_DEFAULT, &RARt));
      PetscCall(MatRARtMultEqual(A, R, RARt, 10, &flg));
      if (!flg) {
        PetscCall(PetscPrintf(PETSC_COMM_WORLD, "Error with RARt\n"));
        PetscCall(MatMatTransposeMult(A, R, MAT_INITIAL_MATRIX, PETSC_DEFAULT, &T));
        PetscCall(MatMatMult(R, T, MAT_INITIAL_MATRIX, PETSC_DEFAULT, &T2));
        PetscCall(MatAXPY(T2, -1.0, RARt, SAME_NONZERO_PATTERN));
        PetscCall(MatView(T2, NULL));
        PetscCall(MatDestroy(&T2));
        PetscCall(MatDestroy(&T));
      }
    }
  }

  /* Test MatDenseGetColumnVec and friends */
  PetscCall(MatMatMult(A, B, MAT_REUSE_MATRIX, PETSC_DEFAULT, &X));
  PetscCall(MatMatMult(A, B, MAT_INITIAL_MATRIX, PETSC_DEFAULT, &T));
  PetscCall(MatDuplicate(T, MAT_DO_NOT_COPY_VALUES, &T2));
  for (k = 0; k < K; k++) {
    Vec Xv, Tv, T2v;

    PetscCall(MatDenseGetColumnVecRead(X, k, &Xv));
    PetscCall(MatDenseGetColumnVec(T, k, &Tv));
    PetscCall(MatDenseGetColumnVecWrite(T2, k, &T2v));
    PetscCall(VecCopy(Xv, T2v));
    PetscCall(VecAXPY(Tv, -1., Xv));
    PetscCall(MatDenseRestoreColumnVecRead(X, k, &Xv));
    PetscCall(MatDenseRestoreColumnVec(T, k, &Tv));
    PetscCall(MatDenseRestoreColumnVecWrite(T2, k, &T2v));
  }
  PetscCall(MatNorm(T, NORM_FROBENIUS, &err));
  if (err > PETSC_SMALL) {
    PetscCall(PetscPrintf(PETSC_COMM_WORLD, "Error with MatDenseGetColumnVec\n"));
    PetscCall(MatView(T, NULL));
  }
  PetscCall(MatAXPY(T2, -1., X, SAME_NONZERO_PATTERN));
  PetscCall(MatNorm(T2, NORM_FROBENIUS, &err));
  if (err > PETSC_SMALL) {
    PetscCall(PetscPrintf(PETSC_COMM_WORLD, "Error with MatDenseGetColumnVecWrite\n"));
    PetscCall(MatView(T2, NULL));
  }
  PetscCall(MatDestroy(&T));
  PetscCall(MatDestroy(&T2));

  /* Test with MatShell */
  PetscCall(MatDuplicate(A, MAT_COPY_VALUES, &T));
  PetscCall(MatConvert(T, MATSHELL, MAT_INITIAL_MATRIX, &T2));
  PetscCall(MatDestroy(&T));

  /* scale matrix */
  PetscCall(MatScale(A, 2.0));
  PetscCall(MatScale(T2, 2.0));
  PetscCall(MatCreateVecs(A, &r, &l));
  PetscCall(VecSetRandom(r, NULL));
  PetscCall(VecSetRandom(l, NULL));
  PetscCall(MatCreateVecs(T2, &rs, &ls));
  PetscCall(VecCopy(r, rs));
  PetscCall(VecCopy(l, ls));
  if (testproj) {
    PetscCall(MatDiagonalScale(A, r, r));
    PetscCall(MatDiagonalScale(T2, rs, rs));
  } else {
    PetscCall(MatDiagonalScale(A, l, r));
    PetscCall(MatDiagonalScale(T2, ls, rs));
  }
  PetscCall(MatDuplicate(A, MAT_COPY_VALUES, &T));
  PetscCall(MatAXPY(A, 4.5, T, SAME_NONZERO_PATTERN));
  PetscCall(MatAXPY(T2, 4.5, T, DIFFERENT_NONZERO_PATTERN));
  PetscCall(MatMultEqual(T2, A, 10, &flg));
  if (!flg) PetscCall(PetscPrintf(PETSC_COMM_WORLD, "Error with MATSHELL (MatMult)\n"));
  PetscCall(MatMultTransposeEqual(T2, A, 10, &flg));
  if (!flg) PetscCall(PetscPrintf(PETSC_COMM_WORLD, "Error with MATSHELL (MatMultTranspose)\n"));
  PetscCall(MatDestroy(&T));
  PetscCall(VecDestroy(&ls));
  PetscCall(VecDestroy(&rs));
  PetscCall(VecDestroy(&l));
  PetscCall(VecDestroy(&r));

  /* recompute projections, test reusage */
  if (PtAP) PetscCall(MatPtAP(A, B, MAT_REUSE_MATRIX, PETSC_DEFAULT, &PtAP));
  if (RARt) PetscCall(MatRARt(A, R, MAT_REUSE_MATRIX, PETSC_DEFAULT, &RARt));
  if (testshellops) { /* test callbacks for user defined MatProducts */
    PetscCall(MatShellSetMatProductOperation(T2, MATPRODUCT_AB, NULL, MyMatShellMatMultNumeric, NULL, MATDENSE, MATDENSE));
    PetscCall(MatShellSetMatProductOperation(T2, MATPRODUCT_AB, NULL, MyMatShellMatMultNumeric, NULL, MATDENSECUDA, MATDENSECUDA));
    PetscCall(MatShellSetMatProductOperation(T2, MATPRODUCT_AtB, NULL, MyMatTransposeShellMatMultNumeric, NULL, MATDENSE, MATDENSE));
    PetscCall(MatShellSetMatProductOperation(T2, MATPRODUCT_AtB, NULL, MyMatTransposeShellMatMultNumeric, NULL, MATDENSECUDA, MATDENSECUDA));
    PetscCall(MatShellSetMatProductOperation(T2, MATPRODUCT_ABt, NULL, MyMatShellMatTransposeMultNumeric, NULL, MATDENSE, MATDENSE));
    PetscCall(MatShellSetMatProductOperation(T2, MATPRODUCT_ABt, NULL, MyMatShellMatTransposeMultNumeric, NULL, MATDENSECUDA, MATDENSECUDA));
    if (testproj) {
      PetscCall(MatShellSetMatProductOperation(T2, MATPRODUCT_PtAP, MyPtShellPMultSymbolic, MyPtShellPMultNumeric, proj_destroy, MATDENSE, MATSHELL));
      PetscCall(MatShellSetMatProductOperation(T2, MATPRODUCT_PtAP, MyPtShellPMultSymbolic, MyPtShellPMultNumeric, proj_destroy, MATDENSECUDA, MATSHELL));
      PetscCall(MatShellSetMatProductOperation(T2, MATPRODUCT_RARt, MyRShellRtMultSymbolic, MyRShellRtMultNumeric, proj_destroy, MATDENSE, MATSHELL));
      PetscCall(MatShellSetMatProductOperation(T2, MATPRODUCT_RARt, MyRShellRtMultSymbolic, MyRShellRtMultNumeric, proj_destroy, MATDENSECUDA, MATSHELL));
    }
  }
  PetscCall(CheckLocal(B, X, aB, aX));
  /* we either use the shell operations or the loop over columns code, applying the operator */
  PetscCall(MatMatMult(T2, B, MAT_REUSE_MATRIX, PETSC_DEFAULT, &X));
  PetscCall(CheckLocal(B, X, aB, aX));
  PetscCall(MatMatMultEqual(T2, B, X, 10, &flg));
  if (!flg) {
    PetscCall(PetscPrintf(PETSC_COMM_WORLD, "Error with reusage (MATSHELL)\n"));
    PetscCall(MatMatMult(A, B, MAT_INITIAL_MATRIX, PETSC_DEFAULT, &T));
    PetscCall(MatAXPY(T, -1.0, X, SAME_NONZERO_PATTERN));
    PetscCall(MatView(T, NULL));
    PetscCall(MatDestroy(&T));
  }
  if (testproj) {
    PetscCall(MatPtAPMultEqual(T2, B, PtAP, 10, &flg));
    if (!flg) PetscCall(PetscPrintf(PETSC_COMM_WORLD, "Error with PtAP (MATSHELL)\n"));
    if (testshellops) { /* projections fail if the product operations are not specified */
      PetscCall(MatPtAP(T2, B, MAT_INITIAL_MATRIX, PETSC_DEFAULT, &T));
      PetscCall(MatPtAP(T2, B, MAT_REUSE_MATRIX, PETSC_DEFAULT, &T));
      PetscCall(MatPtAPMultEqual(T2, B, T, 10, &flg));
      if (!flg) {
        Mat TE;

        PetscCall(PetscPrintf(PETSC_COMM_WORLD, "Error with PtAP (MATSHELL user defined)\n"));
        PetscCall(MatComputeOperator(T, MATDENSE, &TE));
        PetscCall(MatView(TE, NULL));
        PetscCall(MatView(PtAP, NULL));
        PetscCall(MatAXPY(TE, -1.0, PtAP, SAME_NONZERO_PATTERN));
        PetscCall(MatView(TE, NULL));
        PetscCall(MatDestroy(&TE));
      }
      PetscCall(MatDestroy(&T));
    }
    if (RARt) {
      PetscCall(MatRARtMultEqual(T2, R, RARt, 10, &flg));
      if (!flg) PetscCall(PetscPrintf(PETSC_COMM_WORLD, "Error with RARt (MATSHELL)\n"));
    }
    if (testshellops) {
      PetscCall(MatRARt(T2, R, MAT_INITIAL_MATRIX, PETSC_DEFAULT, &T));
      PetscCall(MatRARt(T2, R, MAT_REUSE_MATRIX, PETSC_DEFAULT, &T));
      PetscCall(MatRARtMultEqual(T2, R, T, 10, &flg));
      if (!flg) {
        Mat TE;

        PetscCall(PetscPrintf(PETSC_COMM_WORLD, "Error with RARt (MATSHELL user defined)\n"));
        PetscCall(MatComputeOperator(T, MATDENSE, &TE));
        PetscCall(MatView(TE, NULL));
        if (RARt) {
          PetscCall(MatView(RARt, NULL));
          PetscCall(MatAXPY(TE, -1.0, RARt, SAME_NONZERO_PATTERN));
          PetscCall(MatView(TE, NULL));
        }
        PetscCall(MatDestroy(&TE));
      }
      PetscCall(MatDestroy(&T));
    }
  }

  if (testmattmat) { /* we either use the shell operations or the loop over columns code applying the transposed operator */
    PetscCall(MatTransposeMatMult(T2, X, MAT_REUSE_MATRIX, PETSC_DEFAULT, &B));
    PetscCall(CheckLocal(B, X, aB, aX));
    PetscCall(MatTransposeMatMultEqual(T2, X, B, 10, &flg));
    if (!flg) {
      PetscCall(PetscPrintf(PETSC_COMM_WORLD, "Error with reusage (MatTranspose, MATSHELL)\n"));
      PetscCall(MatTransposeMatMult(A, X, MAT_INITIAL_MATRIX, PETSC_DEFAULT, &T));
      PetscCall(MatAXPY(T, -1.0, B, SAME_NONZERO_PATTERN));
      PetscCall(MatView(T, NULL));
      PetscCall(MatDestroy(&T));
    }
  }
  if (testmatmatt && testshellops) { /* only when shell operations are set */
    PetscCall(MatMatTransposeMult(T2, Bt, MAT_REUSE_MATRIX, PETSC_DEFAULT, &X));
    PetscCall(CheckLocal(Bt, X, aBt, aX));
    PetscCall(MatMatTransposeMultEqual(T2, Bt, X, 10, &flg));
    if (!flg) {
      PetscCall(PetscPrintf(PETSC_COMM_WORLD, "Error with reusage (MatMatTranspose, MATSHELL)\n"));
      PetscCall(MatMatTransposeMult(A, Bt, MAT_INITIAL_MATRIX, PETSC_DEFAULT, &T));
      PetscCall(MatAXPY(T, -1.0, X, SAME_NONZERO_PATTERN));
      PetscCall(MatView(T, NULL));
      PetscCall(MatDestroy(&T));
    }
  }
  PetscCall(MatDestroy(&T2));

  if (testnest) { /* test with MatNest */
    Mat NA;

    PetscCall(MatCreateNest(PETSC_COMM_WORLD, 1, NULL, 1, NULL, &A, &NA));
    PetscCall(MatViewFromOptions(NA, NULL, "-NA_view"));
    PetscCall(MatMatMult(NA, B, MAT_REUSE_MATRIX, PETSC_DEFAULT, &X));
    PetscCall(CheckLocal(B, X, aB, aX));
    PetscCall(MatMatMultEqual(NA, B, X, 10, &flg));
    if (!flg) {
      PetscCall(PetscPrintf(PETSC_COMM_WORLD, "Error with Nest\n"));
      PetscCall(MatMatMult(NA, B, MAT_INITIAL_MATRIX, PETSC_DEFAULT, &T));
      PetscCall(MatAXPY(T, -1.0, X, SAME_NONZERO_PATTERN));
      PetscCall(MatView(T, NULL));
      PetscCall(MatDestroy(&T));
    }
    PetscCall(MatDestroy(&NA));
  }

  if (testtranspose) { /* test with Transpose */
    Mat TA;

    PetscCall(MatCreateTranspose(A, &TA));
    PetscCall(MatMatMult(TA, X, MAT_REUSE_MATRIX, PETSC_DEFAULT, &B));
    PetscCall(CheckLocal(B, X, aB, aX));
    PetscCall(MatMatMultEqual(TA, X, B, 10, &flg));
    if (!flg) {
      PetscCall(PetscPrintf(PETSC_COMM_WORLD, "Error with Transpose\n"));
      PetscCall(MatMatMult(TA, X, MAT_INITIAL_MATRIX, PETSC_DEFAULT, &T));
      PetscCall(MatAXPY(T, -1.0, B, SAME_NONZERO_PATTERN));
      PetscCall(MatView(T, NULL));
      PetscCall(MatDestroy(&T));
    }
    PetscCall(MatDestroy(&TA));
  }

  if (testhtranspose) { /* test with Hermitian Transpose */
    Mat TA;

    PetscCall(MatCreateHermitianTranspose(A, &TA));
    PetscCall(MatMatMult(TA, X, MAT_REUSE_MATRIX, PETSC_DEFAULT, &B));
    PetscCall(CheckLocal(B, X, aB, aX));
    PetscCall(MatMatMultEqual(TA, X, B, 10, &flg));
    if (!flg) {
      PetscCall(PetscPrintf(PETSC_COMM_WORLD, "Error with Transpose\n"));
      PetscCall(MatMatMult(TA, X, MAT_INITIAL_MATRIX, PETSC_DEFAULT, &T));
      PetscCall(MatAXPY(T, -1.0, B, SAME_NONZERO_PATTERN));
      PetscCall(MatView(T, NULL));
      PetscCall(MatDestroy(&T));
    }
    PetscCall(MatDestroy(&TA));
  }

  if (testtt) { /* test with Transpose(Transpose) */
    Mat TA, TTA;

    PetscCall(MatCreateTranspose(A, &TA));
    PetscCall(MatCreateTranspose(TA, &TTA));
    PetscCall(MatMatMult(TTA, B, MAT_REUSE_MATRIX, PETSC_DEFAULT, &X));
    PetscCall(CheckLocal(B, X, aB, aX));
    PetscCall(MatMatMultEqual(TTA, B, X, 10, &flg));
    if (!flg) {
      PetscCall(PetscPrintf(PETSC_COMM_WORLD, "Error with Transpose(Transpose)\n"));
      PetscCall(MatMatMult(TTA, B, MAT_INITIAL_MATRIX, PETSC_DEFAULT, &T));
      PetscCall(MatAXPY(T, -1.0, X, SAME_NONZERO_PATTERN));
      PetscCall(MatView(T, NULL));
      PetscCall(MatDestroy(&T));
    }
    PetscCall(MatDestroy(&TA));
    PetscCall(MatDestroy(&TTA));
  }

  if (testcircular) { /* test circular */
    Mat AB;

    PetscCall(MatMatMult(A, B, MAT_INITIAL_MATRIX, PETSC_DEFAULT, &AB));
    PetscCall(MatMatMult(A, B, MAT_REUSE_MATRIX, PETSC_DEFAULT, &X));
    PetscCall(CheckLocal(B, X, aB, aX));
    if (M == N && N == K) {
      PetscCall(MatMatMult(A, X, MAT_REUSE_MATRIX, PETSC_DEFAULT, &B));
    } else {
      PetscCall(MatTransposeMatMult(A, X, MAT_REUSE_MATRIX, PETSC_DEFAULT, &B));
    }
    PetscCall(CheckLocal(B, X, aB, aX));
    PetscCall(MatDestroy(&AB));
  }

  /* Test by Pierre Jolivet */
  {
    Mat C, D, D2, AtA;
    PetscCall(MatCreateNormal(A, &AtA));
    PetscCall(MatDuplicate(X, MAT_DO_NOT_COPY_VALUES, &C));
    PetscCall(MatDuplicate(B, MAT_DO_NOT_COPY_VALUES, &D));
    PetscCall(MatDuplicate(B, MAT_DO_NOT_COPY_VALUES, &D2));
    PetscCall(MatSetRandom(B, NULL));
    PetscCall(MatSetRandom(C, NULL));
    PetscCall(MatSetRandom(D, NULL));
    PetscCall(MatSetRandom(D2, NULL));
    PetscCall(MatProductCreateWithMat(A, B, NULL, C));
    PetscCall(MatProductSetType(C, MATPRODUCT_AB));
    PetscCall(MatProductSetFromOptions(C));
    PetscCall(MatProductSymbolic(C));
    PetscCall(MatProductCreateWithMat(A, C, NULL, D));
    PetscCall(MatProductSetType(D, MATPRODUCT_AtB));
    PetscCall(MatProductSetFromOptions(D));
    PetscCall(MatProductSymbolic(D));
    PetscCall(MatProductNumeric(C));
    PetscCall(MatMatMultEqual(A, B, C, 10, &flg));
    if (!flg) {
      PetscCall(PetscPrintf(PETSC_COMM_WORLD, "Error with Normal (AB != C)\n"));
      PetscCall(MatView(A, NULL));
      PetscCall(MatView(B, NULL));
      PetscCall(MatView(C, NULL));
    }
    PetscCall(MatProductNumeric(D));
    PetscCall(MatMatMultEqual(AtA, B, D, 10, &flg));
    if (!flg) {
      PetscCall(PetscPrintf(PETSC_COMM_WORLD, "Error with Normal (2)\n"));
      PetscCall(MatMatMult(AtA, C, MAT_INITIAL_MATRIX, PETSC_DEFAULT, &T));
      PetscCall(MatView(D, NULL));
      PetscCall(MatView(T, NULL));
      PetscCall(MatAXPY(T, -1.0, D, SAME_NONZERO_PATTERN));
      PetscCall(MatView(T, NULL));
      PetscCall(MatDestroy(&T));
    }
    PetscCall(MatDestroy(&C));
    PetscCall(MatDestroy(&D));
    PetscCall(MatDestroy(&D2));
    PetscCall(MatDestroy(&AtA));
  }

  PetscCall(MatDestroy(&X));
  PetscCall(MatDestroy(&Bt));
  PetscCall(MatDestroy(&B));
  PetscCall(MatDestroy(&A));
  PetscCall(MatDestroy(&R));
  PetscCall(MatDestroy(&PtAP));
  PetscCall(MatDestroy(&RARt));
  PetscCall(PetscFree(dataX));
  PetscCall(PetscFree(dataB));
  PetscCall(PetscFree(dataR));
  PetscCall(PetscFree(dataBt));
  PetscCall(PetscFinalize());
  return 0;
}

/*TEST

  test:
    suffix: 1
    args: -local {{0 1}} -testshellops

  test:
    output_file: output/ex70_1.out
    requires: cuda
    suffix: 1_cuda
    args: -local {{0 1}} -xgpu {{0 1}} -bgpu {{0 1}} -A_mat_type {{seqaijcusparse seqaij}} -testshellops {{0 1}}

  test:
    output_file: output/ex70_1.out
    nsize: 2
    suffix: 1_par
    args: -local {{0 1}} -testmatmatt 0

  test:
    output_file: output/ex70_1.out
    requires: cuda
    nsize: 2
    suffix: 1_par_cuda
    args: -local {{0 1}} -xgpu {{0 1}} -bgpu {{0 1}} -A_mat_type {{mpiaijcusparse mpiaij}} -testnest 0 -testmatmatt 0 -matmatmult_Bbn 3

  test:
    output_file: output/ex70_1.out
    suffix: 2
    nsize: 1
    args: -M {{7 11}} -N {{12 9}} -K {{1 3}} -local {{0 1}}

  testset:
    requires: cuda
    output_file: output/ex70_1.out
    nsize: 1
    args: -M 7 -N 9 -K 2 -local {{0 1}} -testnest 0 -A_mat_type {{seqdensecuda seqdense}} -xgpu {{0 1}} -bgpu {{0 1}}
    test:
      requires: !complex
      suffix: 2_cuda_real
    test:
      # complex+single gives a little bigger error in the MatDenseGetColumnVec test
      requires: complex !single
      suffix: 2_cuda_complex

  test:
    output_file: output/ex70_1.out
    suffix: 2_par
    nsize: 2
    args: -M {{7 11}} -N {{12 9}} -K {{1 3}} -local {{0 1}} -testcircular -testmatmatt 0

  test:
    requires: cuda
    output_file: output/ex70_1.out
    suffix: 2_par_cuda
    nsize: 2
    args: -M 11 -N 9 -K 1 -local {{0 1}} -testcircular 0 -A_mat_type mpiaijcusparse -xgpu -bgpu -testnest 0 -testmatmatt 0

  test:
    output_file: output/ex70_1.out
    suffix: 3
    nsize: {{1 3}}
    args: -M 13 -N 13 -K {{1 3}} -local {{0 1}} -A_mat_type sbaij -symm -testproj 0 -testmatmatt 0

  test:
    output_file: output/ex70_1.out
    suffix: 4
    nsize: 1
    args: -M 3 -N 3 -K 3 -local {{0 1}} -testcircular

  test:
    output_file: output/ex70_1.out
    suffix: 5
    nsize: {{2 4}}
    args: -M 3 -N 3 -K 3 -local {{0 1}} -testcircular -testmatmatt 0

  test:
    output_file: output/ex70_1.out
    suffix: 6
    nsize: 1
    args: -M {{1 3}} -N {{2 5}} -K {{1 2}} -local {{0 1}} -testcircular

  test:
    output_file: output/ex70_1.out
    suffix: 7
    nsize: 1
    args: -M 13 -N 13 -K {{1 3}} -local {{0 1}} -A_mat_type dense -testnest -testcircular

TEST*/