xref: /petsc/src/mat/tests/ex94.c (revision bbea24aa56d87d3065f0603396f6e854e33a88f9)

static char help[] = "Tests sequential and parallel MatMatMult() and MatPtAP(), MatTransposeMatMult(), sequential MatMatTransposeMult(), MatRARt()\n\
Input arguments are:\n\
  -f0 <input_file> -f1 <input_file> -f2 <input_file> -f3 <input_file> : file to load\n\n";
/* Example of usage:
   ./ex94 -f0 <A_binary> -f1 <B_binary> -matmatmult_mat_view ascii::ascii_info -matmatmulttr_mat_view
   mpiexec -n 3 ./ex94 -f0 medium -f1 medium -f2 arco1 -f3 arco1 -matmatmult_mat_view
*/

#include <petscmat.h>

/*
     B = A - B
     norm = norm(B)
*/
PetscErrorCode MatNormDifference(Mat A, Mat B, PetscReal *norm)
{
  PetscFunctionBegin;
  PetscCall(MatAXPY(B, -1.0, A, DIFFERENT_NONZERO_PATTERN));
  PetscCall(MatNorm(B, NORM_FROBENIUS, norm));
  PetscFunctionReturn(PETSC_SUCCESS);
}

int main(int argc, char **args)
{
  Mat          A, A_save, B, AT, ATT, BT, BTT, P, R, C, C1;
  Vec          x, v1, v2, v3, v4;
  PetscViewer  viewer;
  PetscMPIInt  size, rank;
  PetscInt     i, m, n, j, *idxn, M, N, nzp, rstart, rend;
  PetscReal    norm, norm_abs, norm_tmp, fill = 4.0;
  PetscRandom  rdm;
  char         file[4][128];
  PetscBool    flg, preload = PETSC_TRUE;
  PetscScalar *a, rval, alpha, none = -1.0;
  PetscBool    Test_MatMatMult = PETSC_TRUE, Test_MatMatTr = PETSC_TRUE, Test_MatPtAP = PETSC_TRUE, Test_MatRARt = PETSC_TRUE, Test_MatMatMatMult = PETSC_TRUE;
  PetscBool    Test_MatAXPY = PETSC_FALSE, view = PETSC_FALSE;
  PetscInt     pm, pn, pM, pN;
  MatInfo      info;
  PetscBool    seqaij;
  MatType      mattype;
  Mat          Cdensetest, Pdense, Cdense, Adense;

  PetscFunctionBeginUser;
  PetscCall(PetscInitialize(&argc, &args, (char *)0, help));
  PetscCallMPI(MPI_Comm_size(PETSC_COMM_WORLD, &size));
  PetscCallMPI(MPI_Comm_rank(PETSC_COMM_WORLD, &rank));

  PetscCall(PetscOptionsGetReal(NULL, NULL, "-fill", &fill, NULL));
  PetscCall(PetscOptionsGetBool(NULL, NULL, "-matops_view", &view, NULL));
  if (view) PetscCall(PetscViewerPushFormat(PETSC_VIEWER_STDOUT_WORLD, PETSC_VIEWER_ASCII_INFO));

  /*  Load the matrices A_save and B */
  PetscCall(PetscOptionsGetString(NULL, NULL, "-f0", file[0], sizeof(file[0]), &flg));
  PetscCheck(flg, PETSC_COMM_WORLD, PETSC_ERR_USER, "Must indicate a file name for small matrix A with the -f0 option.");
  PetscCall(PetscOptionsGetString(NULL, NULL, "-f1", file[1], sizeof(file[1]), &flg));
  PetscCheck(flg, PETSC_COMM_WORLD, PETSC_ERR_USER, "Must indicate a file name for small matrix B with the -f1 option.");
  PetscCall(PetscOptionsGetString(NULL, NULL, "-f2", file[2], sizeof(file[2]), &flg));
  if (!flg) {
    preload = PETSC_FALSE;
  } else {
    PetscCall(PetscOptionsGetString(NULL, NULL, "-f3", file[3], sizeof(file[3]), &flg));
    PetscCheck(flg, PETSC_COMM_WORLD, PETSC_ERR_USER, "Must indicate a file name for test matrix B with the -f3 option.");
  }

  PetscPreLoadBegin(preload, "Load system");
  PetscCall(PetscViewerBinaryOpen(PETSC_COMM_WORLD, file[2 * PetscPreLoadIt], FILE_MODE_READ, &viewer));
  PetscCall(MatCreate(PETSC_COMM_WORLD, &A_save));
  PetscCall(MatSetFromOptions(A_save));
  PetscCall(MatLoad(A_save, viewer));
  PetscCall(PetscViewerDestroy(&viewer));

  PetscCall(PetscViewerBinaryOpen(PETSC_COMM_WORLD, file[2 * PetscPreLoadIt + 1], FILE_MODE_READ, &viewer));
  PetscCall(MatCreate(PETSC_COMM_WORLD, &B));
  PetscCall(MatSetFromOptions(B));
  PetscCall(MatLoad(B, viewer));
  PetscCall(PetscViewerDestroy(&viewer));

  PetscCall(MatGetType(B, &mattype));

  PetscCall(MatGetSize(B, &M, &N));
  nzp = PetscMax((PetscInt)(0.1 * M), 5);
  PetscCall(PetscMalloc((nzp + 1) * (sizeof(PetscInt) + sizeof(PetscScalar)), &idxn));
  a = (PetscScalar *)(idxn + nzp);

  /* Create vectors v1 and v2 that are compatible with A_save */
  PetscCall(VecCreate(PETSC_COMM_WORLD, &v1));
  PetscCall(MatGetLocalSize(A_save, &m, NULL));
  PetscCall(VecSetSizes(v1, m, PETSC_DECIDE));
  PetscCall(VecSetFromOptions(v1));
  PetscCall(VecDuplicate(v1, &v2));

  PetscCall(PetscRandomCreate(PETSC_COMM_WORLD, &rdm));
  PetscCall(PetscRandomSetFromOptions(rdm));
  PetscCall(PetscOptionsGetReal(NULL, NULL, "-fill", &fill, NULL));

  /* Test MatAXPY()    */
  /*-------------------*/
  PetscCall(PetscOptionsHasName(NULL, NULL, "-test_MatAXPY", &Test_MatAXPY));
  if (Test_MatAXPY) {
    Mat Btmp;
    PetscCall(MatDuplicate(A_save, MAT_COPY_VALUES, &A));
    PetscCall(MatDuplicate(B, MAT_COPY_VALUES, &Btmp));
    PetscCall(MatAXPY(A, -1.0, B, DIFFERENT_NONZERO_PATTERN)); /* A = -B + A_save */

    PetscCall(MatScale(A, -1.0));                                 /* A = -A = B - A_save */
    PetscCall(MatAXPY(Btmp, -1.0, A, DIFFERENT_NONZERO_PATTERN)); /* Btmp = -A + B = A_save */
    PetscCall(MatMultEqual(A_save, Btmp, 10, &flg));
    PetscCheck(flg, PETSC_COMM_SELF, PETSC_ERR_PLIB, "MatAXPY() is incorrect");
    PetscCall(MatDestroy(&A));
    PetscCall(MatDestroy(&Btmp));

    Test_MatMatMult    = PETSC_FALSE;
    Test_MatMatTr      = PETSC_FALSE;
    Test_MatPtAP       = PETSC_FALSE;
    Test_MatRARt       = PETSC_FALSE;
    Test_MatMatMatMult = PETSC_FALSE;
  }

  /* 1) Test MatMatMult() */
  /* ---------------------*/
  if (Test_MatMatMult) {
    PetscCall(MatDuplicate(A_save, MAT_COPY_VALUES, &A));
    PetscCall(MatCreateTranspose(A, &AT));
    PetscCall(MatCreateTranspose(AT, &ATT));
    PetscCall(MatCreateTranspose(B, &BT));
    PetscCall(MatCreateTranspose(BT, &BTT));

    PetscCall(MatMatMult(AT, B, MAT_INITIAL_MATRIX, fill, &C));
    PetscCall(MatMatMultEqual(AT, B, C, 10, &flg));
    PetscCheck(flg, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Error: MatMatMult() for C=AT*B");
    PetscCall(MatDestroy(&C));

    PetscCall(MatMatMult(ATT, B, MAT_INITIAL_MATRIX, fill, &C));
    PetscCall(MatMatMultEqual(ATT, B, C, 10, &flg));
    PetscCheck(flg, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Error: MatMatMult() for C=ATT*B");
    PetscCall(MatDestroy(&C));

    PetscCall(MatMatMult(A, B, MAT_INITIAL_MATRIX, fill, &C));
    PetscCall(MatMatMultEqual(A, B, C, 10, &flg));
    PetscCheck(flg, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Error: MatMatMult() for reuse C=A*B");
    /* ATT has different matrix type as A (although they have same internal data structure),
       we cannot call MatProductReplaceMats(ATT,NULL,NULL,C) and MatMatMult(ATT,B,MAT_REUSE_MATRIX,fill,&C) */
    PetscCall(MatDestroy(&C));

    PetscCall(MatMatMult(A, BTT, MAT_INITIAL_MATRIX, fill, &C));
    PetscCall(MatMatMultEqual(A, BTT, C, 10, &flg));
    PetscCheck(flg, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Error: MatMatMult() for C=A*BTT");
    PetscCall(MatDestroy(&C));

    PetscCall(MatMatMult(ATT, BTT, MAT_INITIAL_MATRIX, fill, &C));
    PetscCall(MatMatMultEqual(A, B, C, 10, &flg));
    PetscCheck(flg, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Error: MatMatMult()");
    PetscCall(MatDestroy(&C));

    PetscCall(MatDestroy(&BTT));
    PetscCall(MatDestroy(&BT));
    PetscCall(MatDestroy(&ATT));
    PetscCall(MatDestroy(&AT));

    PetscCall(MatMatMult(A, B, MAT_INITIAL_MATRIX, fill, &C));
    PetscCall(MatSetOptionsPrefix(C, "matmatmult_")); /* enable option '-matmatmult_' for matrix C */
    PetscCall(MatGetInfo(C, MAT_GLOBAL_SUM, &info));

    /* Test MAT_REUSE_MATRIX - reuse symbolic C */
    alpha = 1.0;
    for (i = 0; i < 2; i++) {
      alpha -= 0.1;
      PetscCall(MatScale(A, alpha));
      PetscCall(MatMatMult(A, B, MAT_REUSE_MATRIX, fill, &C));
    }
    PetscCall(MatMatMultEqual(A, B, C, 10, &flg));
    PetscCheck(flg, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Error: MatMatMult()");
    PetscCall(MatDestroy(&A));

    /* Test MatDuplicate() of C=A*B */
    PetscCall(MatDuplicate(C, MAT_COPY_VALUES, &C1));
    PetscCall(MatDestroy(&C1));
    PetscCall(MatDestroy(&C));
  } /* if (Test_MatMatMult) */

  /* 2) Test MatTransposeMatMult() and MatMatTransposeMult() */
  /* ------------------------------------------------------- */
  if (Test_MatMatTr) {
    /* Create P */
    PetscInt PN, rstart, rend;
    PN  = M / 2;
    nzp = 5; /* num of nonzeros in each row of P */
    PetscCall(MatCreate(PETSC_COMM_WORLD, &P));
    PetscCall(MatSetSizes(P, PETSC_DECIDE, PETSC_DECIDE, M, PN));
    PetscCall(MatSetType(P, mattype));
    PetscCall(MatSeqAIJSetPreallocation(P, nzp, NULL));
    PetscCall(MatMPIAIJSetPreallocation(P, nzp, NULL, nzp, NULL));
    PetscCall(MatGetOwnershipRange(P, &rstart, &rend));
    for (i = 0; i < nzp; i++) PetscCall(PetscRandomGetValue(rdm, &a[i]));
    for (i = rstart; i < rend; i++) {
      for (j = 0; j < nzp; j++) {
        PetscCall(PetscRandomGetValue(rdm, &rval));
        idxn[j] = (PetscInt)(PetscRealPart(rval) * PN);
      }
      PetscCall(MatSetValues(P, 1, &i, nzp, idxn, a, ADD_VALUES));
    }
    PetscCall(MatAssemblyBegin(P, MAT_FINAL_ASSEMBLY));
    PetscCall(MatAssemblyEnd(P, MAT_FINAL_ASSEMBLY));

    /* Create R = P^T */
    PetscCall(MatTranspose(P, MAT_INITIAL_MATRIX, &R));

    { /* Test R = P^T, C1 = R*B */
      PetscCall(MatMatMult(R, B, MAT_INITIAL_MATRIX, fill, &C1));
      PetscCall(MatTranspose(P, MAT_REUSE_MATRIX, &R));
      PetscCall(MatMatMult(R, B, MAT_REUSE_MATRIX, fill, &C1));
      PetscCall(MatDestroy(&C1));
    }

    /* C = P^T*B */
    PetscCall(MatTransposeMatMult(P, B, MAT_INITIAL_MATRIX, fill, &C));
    PetscCall(MatGetInfo(C, MAT_GLOBAL_SUM, &info));

    /* Test MAT_REUSE_MATRIX - reuse symbolic C */
    PetscCall(MatTransposeMatMult(P, B, MAT_REUSE_MATRIX, fill, &C));
    if (view) {
      PetscCall(PetscPrintf(PETSC_COMM_WORLD, "C = P^T * B:\n"));
      PetscCall(MatView(C, PETSC_VIEWER_STDOUT_WORLD));
    }
    PetscCall(MatProductClear(C));
    if (view) {
      PetscCall(PetscPrintf(PETSC_COMM_WORLD, "\nC = P^T * B after MatProductClear():\n"));
      PetscCall(MatView(C, PETSC_VIEWER_STDOUT_WORLD));
    }

    /* Compare P^T*B and R*B */
    PetscCall(MatMatMult(R, B, MAT_INITIAL_MATRIX, fill, &C1));
    PetscCall(MatNormDifference(C, C1, &norm));
    PetscCheck(norm <= PETSC_SMALL, PETSC_COMM_WORLD, PETSC_ERR_PLIB, "Error in MatTransposeMatMult(): %g", (double)norm);
    PetscCall(MatDestroy(&C1));

    /* Test MatDuplicate() of C=P^T*B */
    PetscCall(MatDuplicate(C, MAT_COPY_VALUES, &C1));
    PetscCall(MatDestroy(&C1));
    PetscCall(MatDestroy(&C));

    /* C = B*R^T */
    PetscCall(PetscObjectTypeCompare((PetscObject)B, MATSEQAIJ, &seqaij));
    if (size == 1 && seqaij) {
      PetscCall(MatMatTransposeMult(B, R, MAT_INITIAL_MATRIX, fill, &C));
      PetscCall(MatSetOptionsPrefix(C, "matmatmulttr_")); /* enable '-matmatmulttr_' for matrix C */
      PetscCall(MatGetInfo(C, MAT_GLOBAL_SUM, &info));

      /* Test MAT_REUSE_MATRIX - reuse symbolic C */
      PetscCall(MatMatTransposeMult(B, R, MAT_REUSE_MATRIX, fill, &C));

      /* Check */
      PetscCall(MatMatMult(B, P, MAT_INITIAL_MATRIX, fill, &C1));
      PetscCall(MatNormDifference(C, C1, &norm));
      PetscCheck(norm <= PETSC_SMALL, PETSC_COMM_WORLD, PETSC_ERR_PLIB, "Error in MatMatTransposeMult() %g", (double)norm);
      PetscCall(MatDestroy(&C1));
      PetscCall(MatDestroy(&C));
    }
    PetscCall(MatDestroy(&P));
    PetscCall(MatDestroy(&R));
  }

  /* 3) Test MatPtAP() */
  /*-------------------*/
  if (Test_MatPtAP) {
    PetscInt PN;
    Mat      Cdup;

    PetscCall(MatDuplicate(A_save, MAT_COPY_VALUES, &A));
    PetscCall(MatGetSize(A, &M, &N));
    PetscCall(MatGetLocalSize(A, &m, &n));

    PN  = M / 2;
    nzp = (PetscInt)(0.1 * PN + 1); /* num of nonzeros in each row of P */
    PetscCall(MatCreate(PETSC_COMM_WORLD, &P));
    PetscCall(MatSetSizes(P, PETSC_DECIDE, PETSC_DECIDE, N, PN));
    PetscCall(MatSetType(P, mattype));
    PetscCall(MatSeqAIJSetPreallocation(P, nzp, NULL));
    PetscCall(MatMPIAIJSetPreallocation(P, nzp, NULL, nzp, NULL));
    for (i = 0; i < nzp; i++) PetscCall(PetscRandomGetValue(rdm, &a[i]));
    PetscCall(MatGetOwnershipRange(P, &rstart, &rend));
    for (i = rstart; i < rend; i++) {
      for (j = 0; j < nzp; j++) {
        PetscCall(PetscRandomGetValue(rdm, &rval));
        idxn[j] = (PetscInt)(PetscRealPart(rval) * PN);
      }
      PetscCall(MatSetValues(P, 1, &i, nzp, idxn, a, ADD_VALUES));
    }
    PetscCall(MatAssemblyBegin(P, MAT_FINAL_ASSEMBLY));
    PetscCall(MatAssemblyEnd(P, MAT_FINAL_ASSEMBLY));

    /* PetscCall(MatView(P,PETSC_VIEWER_STDOUT_WORLD)); */
    PetscCall(MatGetSize(P, &pM, &pN));
    PetscCall(MatGetLocalSize(P, &pm, &pn));
    PetscCall(MatPtAP(A, P, MAT_INITIAL_MATRIX, fill, &C));

    /* Test MAT_REUSE_MATRIX - reuse symbolic C */
    alpha = 1.0;
    for (i = 0; i < 2; i++) {
      alpha -= 0.1;
      PetscCall(MatScale(A, alpha));
      PetscCall(MatPtAP(A, P, MAT_REUSE_MATRIX, fill, &C));
    }

    /* Test PtAP ops with P Dense and A either AIJ or SeqDense (it assumes MatPtAP_XAIJ_XAIJ is fine) */
    PetscCall(PetscObjectTypeCompare((PetscObject)A, MATSEQAIJ, &seqaij));
    if (seqaij) {
      PetscCall(MatConvert(C, MATSEQDENSE, MAT_INITIAL_MATRIX, &Cdensetest));
      PetscCall(MatConvert(P, MATSEQDENSE, MAT_INITIAL_MATRIX, &Pdense));
    } else {
      PetscCall(MatConvert(C, MATMPIDENSE, MAT_INITIAL_MATRIX, &Cdensetest));
      PetscCall(MatConvert(P, MATMPIDENSE, MAT_INITIAL_MATRIX, &Pdense));
    }

    /* test with A(AIJ), Pdense -- call MatPtAP_Basic() when np>1 */
    PetscCall(MatPtAP(A, Pdense, MAT_INITIAL_MATRIX, fill, &Cdense));
    PetscCall(MatPtAP(A, Pdense, MAT_REUSE_MATRIX, fill, &Cdense));
    PetscCall(MatPtAPMultEqual(A, Pdense, Cdense, 10, &flg));
    PetscCheck(flg, PETSC_COMM_WORLD, PETSC_ERR_PLIB, "Error in MatPtAP with A AIJ and P Dense");
    PetscCall(MatDestroy(&Cdense));

    /* test with A SeqDense */
    if (seqaij) {
      PetscCall(MatConvert(A, MATSEQDENSE, MAT_INITIAL_MATRIX, &Adense));
      PetscCall(MatPtAP(Adense, Pdense, MAT_INITIAL_MATRIX, fill, &Cdense));
      PetscCall(MatPtAP(Adense, Pdense, MAT_REUSE_MATRIX, fill, &Cdense));
      PetscCall(MatPtAPMultEqual(Adense, Pdense, Cdense, 10, &flg));
      PetscCheck(flg, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Error in MatPtAP with A SeqDense and P SeqDense");
      PetscCall(MatDestroy(&Cdense));
      PetscCall(MatDestroy(&Adense));
    }
    PetscCall(MatDestroy(&Cdensetest));
    PetscCall(MatDestroy(&Pdense));

    /* Test MatDuplicate() of C=PtAP and MatView(Cdup,...) */
    PetscCall(MatDuplicate(C, MAT_COPY_VALUES, &Cdup));
    if (view) {
      PetscCall(PetscPrintf(PETSC_COMM_WORLD, "\nC = P^T * A * P:\n"));
      PetscCall(MatView(C, PETSC_VIEWER_STDOUT_WORLD));

      PetscCall(MatProductClear(C));
      PetscCall(PetscPrintf(PETSC_COMM_WORLD, "\nC = P^T * A * P after MatProductClear():\n"));
      PetscCall(MatView(C, PETSC_VIEWER_STDOUT_WORLD));

      PetscCall(PetscPrintf(PETSC_COMM_WORLD, "\nCdup:\n"));
      PetscCall(MatView(Cdup, PETSC_VIEWER_STDOUT_WORLD));
    }
    PetscCall(MatDestroy(&Cdup));

    if (size > 1 || !seqaij) Test_MatRARt = PETSC_FALSE;
    /* 4) Test MatRARt() */
    /* ----------------- */
    if (Test_MatRARt) {
      Mat R, RARt, Rdense, RARtdense;
      PetscCall(MatTranspose(P, MAT_INITIAL_MATRIX, &R));

      /* Test MatRARt_Basic(), MatMatMatMult_Basic() */
      PetscCall(MatConvert(R, MATDENSE, MAT_INITIAL_MATRIX, &Rdense));
      PetscCall(MatRARt(A, Rdense, MAT_INITIAL_MATRIX, 2.0, &RARtdense));
      PetscCall(MatRARt(A, Rdense, MAT_REUSE_MATRIX, 2.0, &RARtdense));

      PetscCall(MatConvert(RARtdense, MATAIJ, MAT_INITIAL_MATRIX, &RARt));
      PetscCall(MatNormDifference(C, RARt, &norm));
      PetscCheck(norm <= PETSC_SMALL, PETSC_COMM_SELF, PETSC_ERR_PLIB, "|PtAP - RARtdense| = %g", (double)norm);
      PetscCall(MatDestroy(&Rdense));
      PetscCall(MatDestroy(&RARtdense));
      PetscCall(MatDestroy(&RARt));

      /* Test MatRARt() for aij matrices */
      PetscCall(MatRARt(A, R, MAT_INITIAL_MATRIX, 2.0, &RARt));
      PetscCall(MatRARt(A, R, MAT_REUSE_MATRIX, 2.0, &RARt));
      PetscCall(MatNormDifference(C, RARt, &norm));
      PetscCheck(norm <= PETSC_SMALL, PETSC_COMM_SELF, PETSC_ERR_PLIB, "|PtAP - RARt| = %g", (double)norm);
      PetscCall(MatDestroy(&R));
      PetscCall(MatDestroy(&RARt));
    }

    if (Test_MatMatMatMult && size == 1) {
      Mat R, RAP;
      PetscCall(MatTranspose(P, MAT_INITIAL_MATRIX, &R));
      PetscCall(MatMatMatMult(R, A, P, MAT_INITIAL_MATRIX, 2.0, &RAP));
      PetscCall(MatMatMatMult(R, A, P, MAT_REUSE_MATRIX, 2.0, &RAP));
      PetscCall(MatNormDifference(C, RAP, &norm));
      PetscCheck(norm <= PETSC_SMALL, PETSC_COMM_SELF, PETSC_ERR_PLIB, "PtAP != RAP %g", (double)norm);
      PetscCall(MatDestroy(&R));
      PetscCall(MatDestroy(&RAP));
    }

    /* Create vector x that is compatible with P */
    PetscCall(VecCreate(PETSC_COMM_WORLD, &x));
    PetscCall(MatGetLocalSize(P, &m, &n));
    PetscCall(VecSetSizes(x, n, PETSC_DECIDE));
    PetscCall(VecSetFromOptions(x));

    PetscCall(VecCreate(PETSC_COMM_WORLD, &v3));
    PetscCall(VecSetSizes(v3, n, PETSC_DECIDE));
    PetscCall(VecSetFromOptions(v3));
    PetscCall(VecDuplicate(v3, &v4));

    norm = 0.0;
    for (i = 0; i < 10; i++) {
      PetscCall(VecSetRandom(x, rdm));
      PetscCall(MatMult(P, x, v1));
      PetscCall(MatMult(A, v1, v2)); /* v2 = A*P*x */

      PetscCall(MatMultTranspose(P, v2, v3)); /* v3 = Pt*A*P*x */
      PetscCall(MatMult(C, x, v4));           /* v3 = C*x   */
      PetscCall(VecNorm(v4, NORM_2, &norm_abs));
      PetscCall(VecAXPY(v4, none, v3));
      PetscCall(VecNorm(v4, NORM_2, &norm_tmp));

      norm_tmp /= norm_abs;
      if (norm_tmp > norm) norm = norm_tmp;
    }
    PetscCheck(norm < PETSC_SMALL, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Error: MatPtAP(), |v1 - v2|: %g", (double)norm);

    PetscCall(MatDestroy(&A));
    PetscCall(MatDestroy(&P));
    PetscCall(MatDestroy(&C));
    PetscCall(VecDestroy(&v3));
    PetscCall(VecDestroy(&v4));
    PetscCall(VecDestroy(&x));
  }

  /* Destroy objects */
  PetscCall(VecDestroy(&v1));
  PetscCall(VecDestroy(&v2));
  PetscCall(PetscRandomDestroy(&rdm));
  PetscCall(PetscFree(idxn));

  PetscCall(MatDestroy(&A_save));
  PetscCall(MatDestroy(&B));

  PetscPreLoadEnd();
  PetscCall(PetscFinalize());
  return 0;
}

/*TEST

   test:
      suffix: 2_mattransposematmult_matmatmult
      nsize: 3
      requires: datafilespath !complex double !defined(PETSC_USE_64BIT_INDICES)
      args: -f0 ${DATAFILESPATH}/matrices/medium -f1 ${DATAFILESPATH}/matrices/medium -mattransposematmult_via at*b> ex94_2.tmp 2>&1

   test:
      suffix: 2_mattransposematmult_scalable
      nsize: 3
      requires: datafilespath !complex double !defined(PETSC_USE_64BIT_INDICES)
      args: -f0 ${DATAFILESPATH}/matrices/medium -f1 ${DATAFILESPATH}/matrices/medium -mattransposematmult_via scalable> ex94_2.tmp 2>&1
      output_file: output/ex94_1.out

   test:
      suffix: axpy_mpiaij
      requires: datafilespath !complex double !defined(PETSC_USE_64BIT_INDICES)
      nsize: 8
      args: -f0 ${DATAFILESPATH}/matrices/poisson_2d5p -f1 ${DATAFILESPATH}/matrices/poisson_2d13p -test_MatAXPY
      output_file: output/ex94_1.out

   test:
      suffix: axpy_mpibaij
      requires: datafilespath !complex double !defined(PETSC_USE_64BIT_INDICES)
      nsize: 8
      args: -f0 ${DATAFILESPATH}/matrices/poisson_2d5p -f1 ${DATAFILESPATH}/matrices/poisson_2d13p -test_MatAXPY -mat_type baij
      output_file: output/ex94_1.out

   test:
      suffix: axpy_mpisbaij
      requires: datafilespath !complex double !defined(PETSC_USE_64BIT_INDICES)
      nsize: 8
      args: -f0 ${DATAFILESPATH}/matrices/poisson_2d5p -f1 ${DATAFILESPATH}/matrices/poisson_2d13p -test_MatAXPY -mat_type sbaij
      output_file: output/ex94_1.out

   test:
      suffix: matmatmult
      requires: datafilespath !complex double !defined(PETSC_USE_64BIT_INDICES)
      args: -f0 ${DATAFILESPATH}/matrices/arco1 -f1 ${DATAFILESPATH}/matrices/arco1 -viewer_binary_skip_info
      output_file: output/ex94_1.out

   test:
      suffix: matmatmult_2
      requires: datafilespath !complex double !defined(PETSC_USE_64BIT_INDICES)
      args: -f0 ${DATAFILESPATH}/matrices/arco1 -f1 ${DATAFILESPATH}/matrices/arco1 -mat_type mpiaij -viewer_binary_skip_info
      output_file: output/ex94_1.out

   test:
      suffix: matmatmult_scalable
      nsize: 4
      requires: datafilespath !complex double !defined(PETSC_USE_64BIT_INDICES)
      args: -f0 ${DATAFILESPATH}/matrices/arco1 -f1 ${DATAFILESPATH}/matrices/arco1 -matmatmult_via scalable
      output_file: output/ex94_1.out

   test:
      suffix: ptap
      nsize: 3
      requires: datafilespath !complex double !defined(PETSC_USE_64BIT_INDICES)
      args: -f0 ${DATAFILESPATH}/matrices/medium -f1 ${DATAFILESPATH}/matrices/medium -matptap_via scalable
      output_file: output/ex94_1.out

   test:
      suffix: rap
      nsize: 3
      requires: datafilespath !complex double !defined(PETSC_USE_64BIT_INDICES)
      args: -f0 ${DATAFILESPATH}/matrices/medium -f1 ${DATAFILESPATH}/matrices/medium
      output_file: output/ex94_1.out

   test:
      suffix: scalable0
      requires: datafilespath !complex double !defined(PETSC_USE_64BIT_INDICES)
      args: -f0 ${DATAFILESPATH}/matrices/arco1 -f1 ${DATAFILESPATH}/matrices/arco1 -viewer_binary_skip_info
      output_file: output/ex94_1.out

   test:
      suffix: scalable1
      requires: datafilespath !complex double !defined(PETSC_USE_64BIT_INDICES)
      args: -f0 ${DATAFILESPATH}/matrices/arco1 -f1 ${DATAFILESPATH}/matrices/arco1 -viewer_binary_skip_info -matptap_via scalable
      output_file: output/ex94_1.out

   test:
      suffix: view
      nsize: 2
      requires: datafilespath !complex double !defined(PETSC_USE_64BIT_INDICES)
      args: -f0 ${DATAFILESPATH}/matrices/tiny -f1 ${DATAFILESPATH}/matrices/tiny -viewer_binary_skip_info -matops_view
      output_file: output/ex94_2.out

TEST*/