xref: /petsc/src/mat/tests/ex76.c (revision 48a46eb9bd028bec07ec0f396b1a3abb43f14558)

static char help[] = "Tests cholesky, icc factorization and solve on sequential aij, baij and sbaij matrices. \n";

#include <petscmat.h>

int main(int argc, char **args) {
  Vec           x, y, b;
  Mat           A;      /* linear system matrix */
  Mat           sA, sC; /* symmetric part of the matrices */
  PetscInt      n, mbs = 16, bs = 1, nz = 3, prob = 1, i, j, col[3], block, row, Ii, J, n1, lvl;
  PetscMPIInt   size;
  PetscReal     norm2;
  PetscScalar   neg_one = -1.0, four = 4.0, value[3];
  IS            perm, cperm;
  PetscRandom   rdm;
  PetscBool     reorder = PETSC_FALSE, displ = PETSC_FALSE;
  MatFactorInfo factinfo;
  PetscBool     equal;
  PetscBool     TestAIJ = PETSC_FALSE, TestBAIJ = PETSC_TRUE;
  PetscInt      TestShift = 0;

  PetscFunctionBeginUser;
  PetscCall(PetscInitialize(&argc, &args, (char *)0, help));
  PetscCallMPI(MPI_Comm_size(PETSC_COMM_WORLD, &size));
  PetscCheck(size == 1, PETSC_COMM_WORLD, PETSC_ERR_WRONG_MPI_SIZE, "This is a uniprocessor example only!");
  PetscCall(PetscOptionsGetInt(NULL, NULL, "-bs", &bs, NULL));
  PetscCall(PetscOptionsGetInt(NULL, NULL, "-mbs", &mbs, NULL));
  PetscCall(PetscOptionsGetBool(NULL, NULL, "-reorder", &reorder, NULL));
  PetscCall(PetscOptionsGetBool(NULL, NULL, "-testaij", &TestAIJ, NULL));
  PetscCall(PetscOptionsGetInt(NULL, NULL, "-testShift", &TestShift, NULL));
  PetscCall(PetscOptionsGetBool(NULL, NULL, "-displ", &displ, NULL));

  n = mbs * bs;
  if (TestAIJ) { /* A is in aij format */
    PetscCall(MatCreateSeqAIJ(PETSC_COMM_WORLD, n, n, nz, NULL, &A));
    TestBAIJ = PETSC_FALSE;
  } else { /* A is in baij format */
    PetscCall(MatCreateSeqBAIJ(PETSC_COMM_WORLD, bs, n, n, nz, NULL, &A));
    TestAIJ = PETSC_FALSE;
  }

  /* Assemble matrix */
  if (bs == 1) {
    PetscCall(PetscOptionsGetInt(NULL, NULL, "-test_problem", &prob, NULL));
    if (prob == 1) { /* tridiagonal matrix */
      value[0] = -1.0;
      value[1] = 2.0;
      value[2] = -1.0;
      for (i = 1; i < n - 1; i++) {
        col[0] = i - 1;
        col[1] = i;
        col[2] = i + 1;
        PetscCall(MatSetValues(A, 1, &i, 3, col, value, INSERT_VALUES));
      }
      i      = n - 1;
      col[0] = 0;
      col[1] = n - 2;
      col[2] = n - 1;

      value[0] = 0.1;
      value[1] = -1;
      value[2] = 2;
      PetscCall(MatSetValues(A, 1, &i, 3, col, value, INSERT_VALUES));

      i      = 0;
      col[0] = 0;
      col[1] = 1;
      col[2] = n - 1;

      value[0] = 2.0;
      value[1] = -1.0;
      value[2] = 0.1;
      PetscCall(MatSetValues(A, 1, &i, 3, col, value, INSERT_VALUES));
    } else if (prob == 2) { /* matrix for the five point stencil */
      n1 = (PetscInt)(PetscSqrtReal((PetscReal)n) + 0.001);
      PetscCheck(n1 * n1 == n, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "sqrt(n) must be a positive integer!");
      for (i = 0; i < n1; i++) {
        for (j = 0; j < n1; j++) {
          Ii = j + n1 * i;
          if (i > 0) {
            J = Ii - n1;
            PetscCall(MatSetValues(A, 1, &Ii, 1, &J, &neg_one, INSERT_VALUES));
          }
          if (i < n1 - 1) {
            J = Ii + n1;
            PetscCall(MatSetValues(A, 1, &Ii, 1, &J, &neg_one, INSERT_VALUES));
          }
          if (j > 0) {
            J = Ii - 1;
            PetscCall(MatSetValues(A, 1, &Ii, 1, &J, &neg_one, INSERT_VALUES));
          }
          if (j < n1 - 1) {
            J = Ii + 1;
            PetscCall(MatSetValues(A, 1, &Ii, 1, &J, &neg_one, INSERT_VALUES));
          }
          PetscCall(MatSetValues(A, 1, &Ii, 1, &Ii, &four, INSERT_VALUES));
        }
      }
    }
  } else { /* bs > 1 */
    for (block = 0; block < n / bs; block++) {
      /* diagonal blocks */
      value[0] = -1.0;
      value[1] = 4.0;
      value[2] = -1.0;
      for (i = 1 + block * bs; i < bs - 1 + block * bs; i++) {
        col[0] = i - 1;
        col[1] = i;
        col[2] = i + 1;
        PetscCall(MatSetValues(A, 1, &i, 3, col, value, INSERT_VALUES));
      }
      i      = bs - 1 + block * bs;
      col[0] = bs - 2 + block * bs;
      col[1] = bs - 1 + block * bs;

      value[0] = -1.0;
      value[1] = 4.0;
      PetscCall(MatSetValues(A, 1, &i, 2, col, value, INSERT_VALUES));

      i      = 0 + block * bs;
      col[0] = 0 + block * bs;
      col[1] = 1 + block * bs;

      value[0] = 4.0;
      value[1] = -1.0;
      PetscCall(MatSetValues(A, 1, &i, 2, col, value, INSERT_VALUES));
    }
    /* off-diagonal blocks */
    value[0] = -1.0;
    for (i = 0; i < (n / bs - 1) * bs; i++) {
      col[0] = i + bs;
      PetscCall(MatSetValues(A, 1, &i, 1, col, value, INSERT_VALUES));
      col[0] = i;
      row    = i + bs;
      PetscCall(MatSetValues(A, 1, &row, 1, col, value, INSERT_VALUES));
    }
  }

  if (TestShift) {
    /* set diagonals in the 0-th block as 0 for testing shift numerical factor */
    for (i = 0; i < bs; i++) {
      row      = i;
      col[0]   = i;
      value[0] = 0.0;
      PetscCall(MatSetValues(A, 1, &row, 1, col, value, INSERT_VALUES));
    }
  }

  PetscCall(MatAssemblyBegin(A, MAT_FINAL_ASSEMBLY));
  PetscCall(MatAssemblyEnd(A, MAT_FINAL_ASSEMBLY));

  /* Test MatConvert */
  PetscCall(MatSetOption(A, MAT_SYMMETRIC, PETSC_TRUE));
  PetscCall(MatConvert(A, MATSEQSBAIJ, MAT_INITIAL_MATRIX, &sA));
  PetscCall(MatMultEqual(A, sA, 20, &equal));
  PetscCheck(equal, PETSC_COMM_SELF, PETSC_ERR_USER, "A != sA");

  /* Test MatGetOwnershipRange() */
  PetscCall(MatGetOwnershipRange(A, &Ii, &J));
  PetscCall(MatGetOwnershipRange(sA, &i, &j));
  PetscCheck(i == Ii && j == J, PETSC_COMM_SELF, PETSC_ERR_PLIB, "MatGetOwnershipRange() in MatSBAIJ format");

  /* Vectors */
  PetscCall(PetscRandomCreate(PETSC_COMM_SELF, &rdm));
  PetscCall(PetscRandomSetFromOptions(rdm));
  PetscCall(VecCreateSeq(PETSC_COMM_SELF, n, &x));
  PetscCall(VecDuplicate(x, &b));
  PetscCall(VecDuplicate(x, &y));
  PetscCall(VecSetRandom(x, rdm));

  /* Test MatReordering() - not work on sbaij matrix */
  if (reorder) {
    PetscCall(MatGetOrdering(A, MATORDERINGRCM, &perm, &cperm));
  } else {
    PetscCall(MatGetOrdering(A, MATORDERINGNATURAL, &perm, &cperm));
  }
  PetscCall(ISDestroy(&cperm));

  /* initialize factinfo */
  PetscCall(MatFactorInfoInitialize(&factinfo));
  if (TestShift == 1) {
    factinfo.shifttype   = (PetscReal)MAT_SHIFT_NONZERO;
    factinfo.shiftamount = 0.1;
  } else if (TestShift == 2) {
    factinfo.shifttype = (PetscReal)MAT_SHIFT_POSITIVE_DEFINITE;
  }

  /* Test MatCholeskyFactor(), MatICCFactor() */
  /*------------------------------------------*/
  /* Test aij matrix A */
  if (TestAIJ) {
    if (displ) PetscCall(PetscPrintf(PETSC_COMM_WORLD, "AIJ: \n"));
    i = 0;
    for (lvl = -1; lvl < 10; lvl++) {
      if (lvl == -1) { /* Cholesky factor */
        factinfo.fill = 5.0;

        PetscCall(MatGetFactor(A, MATSOLVERPETSC, MAT_FACTOR_CHOLESKY, &sC));
        PetscCall(MatCholeskyFactorSymbolic(sC, A, perm, &factinfo));
      } else { /* incomplete Cholesky factor */
        factinfo.fill   = 5.0;
        factinfo.levels = lvl;

        PetscCall(MatGetFactor(A, MATSOLVERPETSC, MAT_FACTOR_ICC, &sC));
        PetscCall(MatICCFactorSymbolic(sC, A, perm, &factinfo));
      }
      PetscCall(MatCholeskyFactorNumeric(sC, A, &factinfo));

      PetscCall(MatMult(A, x, b));
      PetscCall(MatSolve(sC, b, y));
      PetscCall(MatDestroy(&sC));

      /* Check the residual */
      PetscCall(VecAXPY(y, neg_one, x));
      PetscCall(VecNorm(y, NORM_2, &norm2));

      if (displ) PetscCall(PetscPrintf(PETSC_COMM_WORLD, "  lvl: %" PetscInt_FMT ", residual: %g\n", lvl, (double)norm2));
    }
  }

  /* Test baij matrix A */
  if (TestBAIJ) {
    if (displ) PetscCall(PetscPrintf(PETSC_COMM_WORLD, "BAIJ: \n"));
    i = 0;
    for (lvl = -1; lvl < 10; lvl++) {
      if (lvl == -1) { /* Cholesky factor */
        factinfo.fill = 5.0;

        PetscCall(MatGetFactor(A, MATSOLVERPETSC, MAT_FACTOR_CHOLESKY, &sC));
        PetscCall(MatCholeskyFactorSymbolic(sC, A, perm, &factinfo));
      } else { /* incomplete Cholesky factor */
        factinfo.fill   = 5.0;
        factinfo.levels = lvl;

        PetscCall(MatGetFactor(A, MATSOLVERPETSC, MAT_FACTOR_ICC, &sC));
        PetscCall(MatICCFactorSymbolic(sC, A, perm, &factinfo));
      }
      PetscCall(MatCholeskyFactorNumeric(sC, A, &factinfo));

      PetscCall(MatMult(A, x, b));
      PetscCall(MatSolve(sC, b, y));
      PetscCall(MatDestroy(&sC));

      /* Check the residual */
      PetscCall(VecAXPY(y, neg_one, x));
      PetscCall(VecNorm(y, NORM_2, &norm2));
      if (displ) PetscCall(PetscPrintf(PETSC_COMM_WORLD, "  lvl: %" PetscInt_FMT ", residual: %g\n", lvl, (double)norm2));
    }
  }

  /* Test sbaij matrix sA */
  if (displ) PetscCall(PetscPrintf(PETSC_COMM_WORLD, "SBAIJ: \n"));
  i = 0;
  for (lvl = -1; lvl < 10; lvl++) {
    if (lvl == -1) { /* Cholesky factor */
      factinfo.fill = 5.0;

      PetscCall(MatGetFactor(sA, MATSOLVERPETSC, MAT_FACTOR_CHOLESKY, &sC));
      PetscCall(MatCholeskyFactorSymbolic(sC, sA, perm, &factinfo));
    } else { /* incomplete Cholesky factor */
      factinfo.fill   = 5.0;
      factinfo.levels = lvl;

      PetscCall(MatGetFactor(sA, MATSOLVERPETSC, MAT_FACTOR_ICC, &sC));
      PetscCall(MatICCFactorSymbolic(sC, sA, perm, &factinfo));
    }
    PetscCall(MatCholeskyFactorNumeric(sC, sA, &factinfo));

    if (lvl == 0 && bs == 1) { /* Test inplace ICC(0) for sbaij sA - does not work for new datastructure */
      /*
        Mat B;
        PetscCall(MatDuplicate(sA,MAT_COPY_VALUES,&B));
        PetscCall(MatICCFactor(B,perm,&factinfo));
        PetscCall(MatEqual(sC,B,&equal));
        if (!equal) {
          SETERRQ(PETSC_COMM_SELF,PETSC_ERR_USER,"in-place Cholesky factor != out-place Cholesky factor");
        }
        PetscCall(MatDestroy(&B));
      */
    }

    PetscCall(MatMult(sA, x, b));
    PetscCall(MatSolve(sC, b, y));

    /* Test MatSolves() */
    if (bs == 1) {
      Vecs xx, bb;
      PetscCall(VecsCreateSeq(PETSC_COMM_SELF, n, 4, &xx));
      PetscCall(VecsDuplicate(xx, &bb));
      PetscCall(MatSolves(sC, bb, xx));
      PetscCall(VecsDestroy(xx));
      PetscCall(VecsDestroy(bb));
    }
    PetscCall(MatDestroy(&sC));

    /* Check the residual */
    PetscCall(VecAXPY(y, neg_one, x));
    PetscCall(VecNorm(y, NORM_2, &norm2));
    if (displ) PetscCall(PetscPrintf(PETSC_COMM_WORLD, "  lvl: %" PetscInt_FMT ", residual: %g\n", lvl, (double)norm2));
  }

  PetscCall(ISDestroy(&perm));
  PetscCall(MatDestroy(&A));
  PetscCall(MatDestroy(&sA));
  PetscCall(VecDestroy(&x));
  PetscCall(VecDestroy(&y));
  PetscCall(VecDestroy(&b));
  PetscCall(PetscRandomDestroy(&rdm));

  PetscCall(PetscFinalize());
  return 0;
}

/*TEST

   test:
      args: -bs {{1 2 3 4 5 6 7 8}}

   test:
      suffix: 3
      args: -testaij
      output_file: output/ex76_1.out

TEST*/