xref: /petsc/src/mat/tests/ex120.c (revision d0e6bf2ad94dcc89b258ce16c7987200a4714786)

static char help[] = "Test LAPACK routine ZHEEV, ZHEEVX, ZHEGV and ZHEGVX. \n\
ZHEEV computes all eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix A. \n\n";

#include <petscmat.h>
#include <petscblaslapack.h>

extern PetscErrorCode CkEigenSolutions(PetscInt, Mat, PetscInt, PetscInt, PetscReal *, Vec *, PetscReal *);

int main(int argc, char **args)
{
  Mat          A, A_dense, B;
  Vec         *evecs;
  PetscBool    flg, TestZHEEV = PETSC_TRUE, TestZHEEVX = PETSC_FALSE, TestZHEGV = PETSC_FALSE, TestZHEGVX = PETSC_FALSE;
  PetscBool    isSymmetric;
  PetscScalar *arrayA, *arrayB, *evecs_array = NULL, *work;
  PetscReal   *evals, *rwork;
  PetscMPIInt  size;
  PetscInt     m, i, j, cklvl = 2;
  PetscReal    vl, vu, abstol = 1.e-8;
  PetscBLASInt nn, nevs, il, iu, *iwork, *ifail, lwork, lierr, bn, one = 1;
  PetscReal    tols[2];
  PetscScalar  v, sigma2;
  PetscRandom  rctx;
  PetscReal    h2, sigma1 = 100.0;
  PetscInt     dim, Ii, J, n = 6, use_random;

  PetscFunctionBeginUser;
  PetscCall(PetscInitialize(&argc, &args, NULL, 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(PetscOptionsHasName(NULL, NULL, "-test_zheevx", &flg));
  if (flg) {
    TestZHEEV  = PETSC_FALSE;
    TestZHEEVX = PETSC_TRUE;
  }
  PetscCall(PetscOptionsHasName(NULL, NULL, "-test_zhegv", &flg));
  if (flg) {
    TestZHEEV = PETSC_FALSE;
    TestZHEGV = PETSC_TRUE;
  }
  PetscCall(PetscOptionsHasName(NULL, NULL, "-test_zhegvx", &flg));
  if (flg) {
    TestZHEEV  = PETSC_FALSE;
    TestZHEGVX = PETSC_TRUE;
  }

  PetscCall(PetscOptionsGetReal(NULL, NULL, "-sigma1", &sigma1, NULL));
  PetscCall(PetscOptionsGetInt(NULL, NULL, "-n", &n, NULL));
  dim = n * n;

  PetscCall(MatCreate(PETSC_COMM_SELF, &A));
  PetscCall(MatSetSizes(A, PETSC_DECIDE, PETSC_DECIDE, dim, dim));
  PetscCall(MatSetType(A, MATSEQDENSE));
  PetscCall(MatSetFromOptions(A));
  PetscCall(MatSetUp(A));

  PetscCall(PetscOptionsHasName(NULL, NULL, "-norandom", &flg));
  if (flg) use_random = 0;
  else use_random = 1;
  if (use_random) {
    PetscCall(PetscRandomCreate(PETSC_COMM_SELF, &rctx));
    PetscCall(PetscRandomSetFromOptions(rctx));
    PetscCall(PetscRandomSetInterval(rctx, 0.0, PETSC_i));
  } else {
    sigma2 = 10.0 * PETSC_i;
  }
  h2 = 1.0 / ((n + 1) * (n + 1));
  for (Ii = 0; Ii < dim; Ii++) {
    v = -1.0;
    i = Ii / n;
    j = Ii - i * n;
    if (i > 0) {
      J = Ii - n;
      PetscCall(MatSetValues(A, 1, &Ii, 1, &J, &v, ADD_VALUES));
    }
    if (i < n - 1) {
      J = Ii + n;
      PetscCall(MatSetValues(A, 1, &Ii, 1, &J, &v, ADD_VALUES));
    }
    if (j > 0) {
      J = Ii - 1;
      PetscCall(MatSetValues(A, 1, &Ii, 1, &J, &v, ADD_VALUES));
    }
    if (j < n - 1) {
      J = Ii + 1;
      PetscCall(MatSetValues(A, 1, &Ii, 1, &J, &v, ADD_VALUES));
    }
    if (use_random) PetscCall(PetscRandomGetValue(rctx, &sigma2));
    v = 4.0 - sigma1 * h2;
    PetscCall(MatSetValues(A, 1, &Ii, 1, &Ii, &v, ADD_VALUES));
  }
  /* make A complex Hermitian */
  v  = sigma2 * h2;
  Ii = 0;
  J  = 1;
  PetscCall(MatSetValues(A, 1, &Ii, 1, &J, &v, ADD_VALUES));
  v = -sigma2 * h2;
  PetscCall(MatSetValues(A, 1, &J, 1, &Ii, &v, ADD_VALUES));
  if (use_random) PetscCall(PetscRandomDestroy(&rctx));
  PetscCall(MatAssemblyBegin(A, MAT_FINAL_ASSEMBLY));
  PetscCall(MatAssemblyEnd(A, MAT_FINAL_ASSEMBLY));
  m = n = dim;

  /* Check whether A is symmetric */
  PetscCall(PetscOptionsHasName(NULL, NULL, "-check_symmetry", &flg));
  if (flg) {
    Mat Trans;
    PetscCall(MatTranspose(A, MAT_INITIAL_MATRIX, &Trans));
    PetscCall(MatEqual(A, Trans, &isSymmetric));
    PetscCheck(isSymmetric, PETSC_COMM_SELF, PETSC_ERR_USER, "A must be symmetric");
    PetscCall(MatDestroy(&Trans));
  }

  /* Convert aij matrix to MatSeqDense for LAPACK */
  PetscCall(PetscObjectTypeCompare((PetscObject)A, MATSEQDENSE, &flg));
  if (flg) {
    PetscCall(MatDuplicate(A, MAT_COPY_VALUES, &A_dense));
  } else {
    PetscCall(MatConvert(A, MATSEQDENSE, MAT_INITIAL_MATRIX, &A_dense));
  }

  PetscCall(MatCreate(PETSC_COMM_SELF, &B));
  PetscCall(MatSetSizes(B, PETSC_DECIDE, PETSC_DECIDE, dim, dim));
  PetscCall(MatSetType(B, MATSEQDENSE));
  PetscCall(MatSetFromOptions(B));
  PetscCall(MatSetUp(B));
  v = 1.0;
  for (Ii = 0; Ii < dim; Ii++) PetscCall(MatSetValues(B, 1, &Ii, 1, &Ii, &v, ADD_VALUES));

  /* Solve standard eigenvalue problem: A*x = lambda*x */
  /*===================================================*/
  PetscCall(PetscBLASIntCast(2 * n, &lwork));
  PetscCall(PetscBLASIntCast(n, &bn));
  PetscCall(PetscMalloc1(n, &evals));
  PetscCall(PetscMalloc1(lwork, &work));
  PetscCall(MatDenseGetArray(A_dense, &arrayA));

  if (TestZHEEV) { /* test zheev() */
    PetscCall(PetscPrintf(PETSC_COMM_WORLD, " LAPACKsyev: compute all %" PetscInt_FMT " eigensolutions...\n", m));
    PetscCall(PetscMalloc1(3 * n - 2, &rwork));
    LAPACKsyev_("V", "U", &bn, arrayA, &bn, evals, work, &lwork, rwork, &lierr);
    PetscCall(PetscFree(rwork));

    evecs_array = arrayA;
    nevs        = m;
    il          = 1;
    iu          = m;
  }
  if (TestZHEEVX) {
    il = 1;
    PetscCall(PetscBLASIntCast(0.2 * m, &iu));
    PetscCall(PetscPrintf(PETSC_COMM_WORLD, " LAPACKsyevx: compute %d to %d-th eigensolutions...\n", il, iu));
    PetscCall(PetscMalloc1(m * n + 1, &evecs_array));
    PetscCall(PetscMalloc1(7 * n + 1, &rwork));
    PetscCall(PetscMalloc1(5 * n + 1, &iwork));
    PetscCall(PetscMalloc1(n + 1, &ifail));

    /* in the case "I", vl and vu are not referenced */
    vl = 0.0;
    vu = 8.0;
    PetscCall(PetscBLASIntCast(n, &nn));
    LAPACKsyevx_("V", "I", "U", &bn, arrayA, &bn, &vl, &vu, &il, &iu, &abstol, &nevs, evals, evecs_array, &nn, work, &lwork, rwork, iwork, ifail, &lierr);
    PetscCall(PetscFree(iwork));
    PetscCall(PetscFree(ifail));
    PetscCall(PetscFree(rwork));
  }
  if (TestZHEGV) {
    PetscCall(PetscPrintf(PETSC_COMM_WORLD, " LAPACKsygv: compute all %" PetscInt_FMT " eigensolutions...\n", m));
    PetscCall(PetscMalloc1(3 * n + 1, &rwork));
    PetscCall(MatDenseGetArray(B, &arrayB));
    LAPACKsygv_(&one, "V", "U", &bn, arrayA, &bn, arrayB, &bn, evals, work, &lwork, rwork, &lierr);
    evecs_array = arrayA;
    nevs        = m;
    il          = 1;
    iu          = m;
    PetscCall(MatDenseRestoreArray(B, &arrayB));
    PetscCall(PetscFree(rwork));
  }
  if (TestZHEGVX) {
    il = 1;
    PetscCall(PetscBLASIntCast(0.2 * m, &iu));
    PetscCall(PetscPrintf(PETSC_COMM_WORLD, " LAPACKsygv: compute %d to %d-th eigensolutions...\n", il, iu));
    PetscCall(PetscMalloc1(m * n + 1, &evecs_array));
    PetscCall(PetscMalloc1(6 * n + 1, &iwork));
    ifail = iwork + 5 * n;
    PetscCall(PetscMalloc1(7 * n + 1, &rwork));
    PetscCall(MatDenseGetArray(B, &arrayB));
    vl = 0.0;
    vu = 8.0;
    PetscCall(PetscBLASIntCast(n, &nn));
    LAPACKsygvx_(&one, "V", "I", "U", &bn, arrayA, &bn, arrayB, &bn, &vl, &vu, &il, &iu, &abstol, &nevs, evals, evecs_array, &nn, work, &lwork, rwork, iwork, ifail, &lierr);
    PetscCall(MatDenseRestoreArray(B, &arrayB));
    PetscCall(PetscFree(iwork));
    PetscCall(PetscFree(rwork));
  }
  PetscCall(MatDenseRestoreArray(A_dense, &arrayA));
  PetscCheck(nevs > 0, PETSC_COMM_SELF, PETSC_ERR_CONV_FAILED, "nev=%d, no eigensolution has found", nevs);

  /* View evals */
  PetscCall(PetscOptionsHasName(NULL, NULL, "-eig_view", &flg));
  if (flg) {
    PetscCall(PetscPrintf(PETSC_COMM_WORLD, " %d evals: \n", nevs));
    for (i = 0; i < nevs; i++) PetscCall(PetscPrintf(PETSC_COMM_WORLD, "%" PetscInt_FMT "  %g\n", i + il, (double)evals[i]));
  }

  /* Check residuals and orthogonality */
  PetscCall(PetscMalloc1(nevs + 1, &evecs));
  for (i = 0; i < nevs; i++) {
    PetscCall(VecCreate(PETSC_COMM_SELF, &evecs[i]));
    PetscCall(VecSetSizes(evecs[i], PETSC_DECIDE, n));
    PetscCall(VecSetFromOptions(evecs[i]));
    PetscCall(VecPlaceArray(evecs[i], evecs_array + i * n));
  }

  tols[0] = PETSC_SQRT_MACHINE_EPSILON;
  tols[1] = PETSC_SQRT_MACHINE_EPSILON;
  PetscCall(CkEigenSolutions(cklvl, A, il - 1, iu - 1, evals, evecs, tols));
  for (i = 0; i < nevs; i++) PetscCall(VecDestroy(&evecs[i]));
  PetscCall(PetscFree(evecs));

  /* Free work space. */
  if (TestZHEEVX || TestZHEGVX) PetscCall(PetscFree(evecs_array));
  PetscCall(PetscFree(evals));
  PetscCall(PetscFree(work));
  PetscCall(MatDestroy(&A_dense));
  PetscCall(MatDestroy(&A));
  PetscCall(MatDestroy(&B));
  PetscCall(PetscFinalize());
  return 0;
}
/*------------------------------------------------
  Check the accuracy of the eigen solution
  ----------------------------------------------- */
/*
  input:
     cklvl      - check level:
                    1: check residual
                    2: 1 and check B-orthogonality locally
     A          - matrix
     il,iu      - lower and upper index bound of eigenvalues
     eval, evec - eigenvalues and eigenvectors stored in this process
     tols[0]    - reporting tol_res: || A * evec[i] - eval[i]*evec[i] ||
     tols[1]    - reporting tol_orth: evec[i]^T*evec[j] - delta_ij
*/
PetscErrorCode CkEigenSolutions(PetscInt cklvl, Mat A, PetscInt il, PetscInt iu, PetscReal *eval, Vec *evec, PetscReal *tols)
{
  PetscInt    i, j, nev;
  Vec         vt1, vt2; /* tmp vectors */
  PetscReal   norm, tmp, norm_max, dot_max, rdot;
  PetscScalar dot;

  PetscFunctionBegin;
  nev = iu - il;
  if (nev <= 0) PetscFunctionReturn(PETSC_SUCCESS);

  PetscCall(VecDuplicate(evec[0], &vt1));
  PetscCall(VecDuplicate(evec[0], &vt2));

  switch (cklvl) {
  case 2:
    dot_max = 0.0;
    for (i = il; i < iu; i++) {
      PetscCall(VecCopy(evec[i], vt1));
      for (j = il; j < iu; j++) {
        PetscCall(VecDot(evec[j], vt1, &dot));
        if (j == i) {
          rdot = PetscAbsScalar(dot - (PetscScalar)1.0);
        } else {
          rdot = PetscAbsScalar(dot);
        }
        if (rdot > dot_max) dot_max = rdot;
        if (rdot > tols[1]) {
          PetscCall(VecNorm(evec[i], NORM_INFINITY, &norm));
          PetscCall(PetscPrintf(PETSC_COMM_SELF, "|delta(%" PetscInt_FMT ",%" PetscInt_FMT ")|: %g, norm: %g\n", i, j, (double)rdot, (double)norm));
        }
      }
    }
    PetscCall(PetscPrintf(PETSC_COMM_SELF, "    max|(x_j^T*x_i) - delta_ji|: %g\n", (double)dot_max));

  case 1:
    norm_max = 0.0;
    for (i = il; i < iu; i++) {
      PetscCall(MatMult(A, evec[i], vt1));
      PetscCall(VecCopy(evec[i], vt2));
      tmp = -eval[i];
      PetscCall(VecAXPY(vt1, tmp, vt2));
      PetscCall(VecNorm(vt1, NORM_INFINITY, &norm));
      norm = PetscAbs(norm);
      if (norm > norm_max) norm_max = norm;
      /* sniff, and bark if necessary */
      if (norm > tols[0]) PetscCall(PetscPrintf(PETSC_COMM_WORLD, "  residual violation: %" PetscInt_FMT ", resi: %g\n", i, (double)norm));
    }
    PetscCall(PetscPrintf(PETSC_COMM_SELF, "    max_resi:                    %g\n", (double)norm_max));
    break;
  default:
    PetscCall(PetscPrintf(PETSC_COMM_SELF, "Error: cklvl=%" PetscInt_FMT " is not supported \n", cklvl));
  }
  PetscCall(VecDestroy(&vt2));
  PetscCall(VecDestroy(&vt1));
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*TEST

   build:
      requires: complex

   test:

   test:
      suffix: 2
      args: -test_zheevx

   test:
      suffix: 3
      args: -test_zhegv

   test:
      suffix: 4
      args: -test_zhegvx

TEST*/