xref: /petsc/src/mat/tests/ex30.c (revision d71ae5a4db6382e7f06317b8d368875286fe9008)

static char help[] = "Tests ILU and ICC factorization with and without matrix ordering on seqaij format, and illustrates drawing of matrix sparsity structure with MatView().\n\
  Input parameters are:\n\
  -lf <level> : level of fill for ILU (default is 0)\n\
  -lu : use full LU or Cholesky factorization\n\
  -m <value>,-n <value> : grid dimensions\n\
Note that most users should employ the KSP interface to the\n\
linear solvers instead of using the factorization routines\n\
directly.\n\n";

#include <petscmat.h>

int main(int argc, char **args)
{
  Mat           C, A;
  PetscInt      i, j, m = 5, n = 5, Ii, J, lf = 0;
  PetscBool     LU = PETSC_FALSE, CHOLESKY, TRIANGULAR = PETSC_FALSE, MATDSPL = PETSC_FALSE, flg, matordering;
  PetscScalar   v;
  IS            row, col;
  PetscViewer   viewer1, viewer2;
  MatFactorInfo info;
  Vec           x, y, b, ytmp;
  PetscReal     norm2, norm2_inplace, tol = 100. * PETSC_MACHINE_EPSILON;
  PetscRandom   rdm;
  PetscMPIInt   size;

  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, "-m", &m, NULL));
  PetscCall(PetscOptionsGetInt(NULL, NULL, "-n", &n, NULL));
  PetscCall(PetscOptionsGetInt(NULL, NULL, "-lf", &lf, NULL));

  PetscCall(PetscViewerDrawOpen(PETSC_COMM_SELF, 0, 0, 0, 0, 400, 400, &viewer1));
  PetscCall(PetscViewerDrawOpen(PETSC_COMM_SELF, 0, 0, 400, 0, 400, 400, &viewer2));

  PetscCall(MatCreate(PETSC_COMM_SELF, &C));
  PetscCall(MatSetSizes(C, m * n, m * n, m * n, m * n));
  PetscCall(MatSetFromOptions(C));
  PetscCall(MatSetUp(C));

  /* Create matrix C in seqaij format and sC in seqsbaij. (This is five-point stencil with some extra elements) */
  for (i = 0; i < m; i++) {
    for (j = 0; j < n; j++) {
      v  = -1.0;
      Ii = j + n * i;
      J  = Ii - n;
      if (J >= 0) PetscCall(MatSetValues(C, 1, &Ii, 1, &J, &v, INSERT_VALUES));
      J = Ii + n;
      if (J < m * n) PetscCall(MatSetValues(C, 1, &Ii, 1, &J, &v, INSERT_VALUES));
      J = Ii - 1;
      if (J >= 0) PetscCall(MatSetValues(C, 1, &Ii, 1, &J, &v, INSERT_VALUES));
      J = Ii + 1;
      if (J < m * n) PetscCall(MatSetValues(C, 1, &Ii, 1, &J, &v, INSERT_VALUES));
      v = 4.0;
      PetscCall(MatSetValues(C, 1, &Ii, 1, &Ii, &v, INSERT_VALUES));
    }
  }
  PetscCall(MatAssemblyBegin(C, MAT_FINAL_ASSEMBLY));
  PetscCall(MatAssemblyEnd(C, MAT_FINAL_ASSEMBLY));

  PetscCall(MatIsSymmetric(C, 0.0, &flg));
  PetscCheck(flg, PETSC_COMM_SELF, PETSC_ERR_SUP, "C is non-symmetric");

  /* Create vectors for error checking */
  PetscCall(MatCreateVecs(C, &x, &b));
  PetscCall(VecDuplicate(x, &y));
  PetscCall(VecDuplicate(x, &ytmp));
  PetscCall(PetscRandomCreate(PETSC_COMM_SELF, &rdm));
  PetscCall(PetscRandomSetFromOptions(rdm));
  PetscCall(VecSetRandom(x, rdm));
  PetscCall(MatMult(C, x, b));

  PetscCall(PetscOptionsHasName(NULL, NULL, "-mat_ordering", &matordering));
  if (matordering) {
    PetscCall(MatGetOrdering(C, MATORDERINGRCM, &row, &col));
  } else {
    PetscCall(MatGetOrdering(C, MATORDERINGNATURAL, &row, &col));
  }

  PetscCall(PetscOptionsHasName(NULL, NULL, "-display_matrices", &MATDSPL));
  if (MATDSPL) {
    printf("original matrix:\n");
    PetscCall(PetscViewerPushFormat(PETSC_VIEWER_STDOUT_SELF, PETSC_VIEWER_ASCII_INFO));
    PetscCall(MatView(C, PETSC_VIEWER_STDOUT_SELF));
    PetscCall(PetscViewerPopFormat(PETSC_VIEWER_STDOUT_SELF));
    PetscCall(MatView(C, PETSC_VIEWER_STDOUT_SELF));
    PetscCall(MatView(C, viewer1));
  }

  /* Compute LU or ILU factor A */
  PetscCall(MatFactorInfoInitialize(&info));

  info.fill          = 1.0;
  info.diagonal_fill = 0;
  info.zeropivot     = 0.0;

  PetscCall(PetscOptionsHasName(NULL, NULL, "-lu", &LU));
  if (LU) {
    printf("Test LU...\n");
    PetscCall(MatGetFactor(C, MATSOLVERPETSC, MAT_FACTOR_LU, &A));
    PetscCall(MatLUFactorSymbolic(A, C, row, col, &info));
  } else {
    printf("Test ILU...\n");
    info.levels = lf;

    PetscCall(MatGetFactor(C, MATSOLVERPETSC, MAT_FACTOR_ILU, &A));
    PetscCall(MatILUFactorSymbolic(A, C, row, col, &info));
  }
  PetscCall(MatLUFactorNumeric(A, C, &info));

  /* Solve A*y = b, then check the error */
  PetscCall(MatSolve(A, b, y));
  PetscCall(VecAXPY(y, -1.0, x));
  PetscCall(VecNorm(y, NORM_2, &norm2));
  PetscCall(MatDestroy(&A));

  /* Test in-place ILU(0) and compare it with the out-place ILU(0) */
  if (!LU && lf == 0) {
    PetscCall(MatDuplicate(C, MAT_COPY_VALUES, &A));
    PetscCall(MatILUFactor(A, row, col, &info));
    /*
    printf("In-place factored matrix:\n");
    PetscCall(MatView(C,PETSC_VIEWER_STDOUT_SELF));
    */
    PetscCall(MatSolve(A, b, y));
    PetscCall(VecAXPY(y, -1.0, x));
    PetscCall(VecNorm(y, NORM_2, &norm2_inplace));
    PetscCheck(PetscAbs(norm2 - norm2_inplace) <= tol, PETSC_COMM_SELF, PETSC_ERR_PLIB, "ILU(0) %g and in-place ILU(0) %g give different residuals", (double)norm2, (double)norm2_inplace);
    PetscCall(MatDestroy(&A));
  }

  /* Test Cholesky and ICC on seqaij matrix with matrix reordering on aij matrix C */
  CHOLESKY = LU;
  if (CHOLESKY) {
    printf("Test Cholesky...\n");
    lf = -1;
    PetscCall(MatGetFactor(C, MATSOLVERPETSC, MAT_FACTOR_CHOLESKY, &A));
    PetscCall(MatCholeskyFactorSymbolic(A, C, row, &info));
  } else {
    printf("Test ICC...\n");
    info.levels        = lf;
    info.fill          = 1.0;
    info.diagonal_fill = 0;
    info.zeropivot     = 0.0;

    PetscCall(MatGetFactor(C, MATSOLVERPETSC, MAT_FACTOR_ICC, &A));
    PetscCall(MatICCFactorSymbolic(A, C, row, &info));
  }
  PetscCall(MatCholeskyFactorNumeric(A, C, &info));

  /* test MatForwardSolve() and MatBackwardSolve() with matrix reordering on aij matrix C */
  if (lf == -1) {
    PetscCall(PetscOptionsHasName(NULL, NULL, "-triangular_solve", &TRIANGULAR));
    if (TRIANGULAR) {
      printf("Test MatForwardSolve...\n");
      PetscCall(MatForwardSolve(A, b, ytmp));
      printf("Test MatBackwardSolve...\n");
      PetscCall(MatBackwardSolve(A, ytmp, y));
      PetscCall(VecAXPY(y, -1.0, x));
      PetscCall(VecNorm(y, NORM_2, &norm2));
      if (norm2 > tol) PetscCall(PetscPrintf(PETSC_COMM_SELF, "MatForwardSolve and BackwardSolve: Norm of error=%g\n", (double)norm2));
    }
  }

  PetscCall(MatSolve(A, b, y));
  PetscCall(MatDestroy(&A));
  PetscCall(VecAXPY(y, -1.0, x));
  PetscCall(VecNorm(y, NORM_2, &norm2));
  if (lf == -1 && norm2 > tol) PetscCall(PetscPrintf(PETSC_COMM_SELF, " reordered SEQAIJ:   Cholesky/ICC levels %" PetscInt_FMT ", residual %g\n", lf, (double)norm2));

  /* Test in-place ICC(0) and compare it with the out-place ICC(0) */
  if (!CHOLESKY && lf == 0 && !matordering) {
    PetscCall(MatConvert(C, MATSBAIJ, MAT_INITIAL_MATRIX, &A));
    PetscCall(MatICCFactor(A, row, &info));
    /*
    printf("In-place factored matrix:\n");
    PetscCall(MatView(A,PETSC_VIEWER_STDOUT_SELF));
    */
    PetscCall(MatSolve(A, b, y));
    PetscCall(VecAXPY(y, -1.0, x));
    PetscCall(VecNorm(y, NORM_2, &norm2_inplace));
    PetscCheck(PetscAbs(norm2 - norm2_inplace) <= tol, PETSC_COMM_SELF, PETSC_ERR_PLIB, "ICC(0) %g and in-place ICC(0) %g give different residuals", (double)norm2, (double)norm2_inplace);
    PetscCall(MatDestroy(&A));
  }

  /* Free data structures */
  PetscCall(ISDestroy(&row));
  PetscCall(ISDestroy(&col));
  PetscCall(MatDestroy(&C));
  PetscCall(PetscViewerDestroy(&viewer1));
  PetscCall(PetscViewerDestroy(&viewer2));
  PetscCall(PetscRandomDestroy(&rdm));
  PetscCall(VecDestroy(&x));
  PetscCall(VecDestroy(&y));
  PetscCall(VecDestroy(&ytmp));
  PetscCall(VecDestroy(&b));
  PetscCall(PetscFinalize());
  return 0;
}

/*TEST

   test:
      args: -mat_ordering -display_matrices -nox
      filter: grep -v " MPI process"

   test:
      suffix: 2
      args: -mat_ordering -display_matrices -nox -lu

   test:
      suffix: 3
      args: -mat_ordering -lu -triangular_solve

   test:
      suffix: 4

   test:
      suffix: 5
      args: -lu

   test:
      suffix: 6
      args: -lu -triangular_solve
      output_file: output/ex30_3.out

TEST*/