dsyevr_2stage function

Implementation

void dsyevr_2stage(
  final String JOBZ,
  final String RANGE,
  final String UPLO,
  final int N,
  final Matrix<double> A_,
  final int LDA,
  final double VL,
  final double VU,
  final int IL,
  final int IU,
  final double ABSTOL,
  final Box<int> M,
  final Array<double> W_,
  final Matrix<double> Z_,
  final int LDZ,
  final Array<int> ISUPPZ_,
  final Array<double> WORK_,
  final int LWORK,
  final Array<int> IWORK_,
  final int LIWORK,
  final Box<int> INFO,
) {
  final A = A_.having(ld: LDA);
  final W = W_.having();
  final Z = Z_.having(ld: LDZ);
  final ISUPPZ = ISUPPZ_.having();
  final WORK = WORK_.having();
  final IWORK = IWORK_.having();
  const ZERO = 0.0, ONE = 1.0, TWO = 2.0;
  bool ALLEIG, INDEIG, LOWER, LQUERY, VALEIG, WANTZ;
  String ORDER;
  int I,
      IEEEOK,
      IMAX,
      INDD,
      INDDD,
      INDE,
      INDEE,
      INDIBL,
      INDIFL,
      INDISP,
      INDIWO,
      INDTAU,
      INDWK,
      INDWKN,
      ISCALE,
      J,
      JJ,
      LIWMIN,
      LLWORK,
      LLWRKN,
      LWMIN,
      LHTRD,
      LWTRD,
      KD,
      IB,
      INDHOUS;
  double ABSTLL,
      ANRM,
      BIGNUM,
      EPS,
      RMAX,
      RMIN,
      SAFMIN,
      SIGMA = 0,
      SMLNUM,
      TMP1,
      VLL = 0,
      VUU = 0;
  final IINFO = Box(0), NSPLIT = Box(0);
  final TRYRAC = Box(false);

  // Test the input parameters.

  IEEEOK = ilaenv(10, 'DSYEVR', 'N', 1, 2, 3, 4);

  LOWER = lsame(UPLO, 'L');
  WANTZ = lsame(JOBZ, 'V');
  ALLEIG = lsame(RANGE, 'A');
  VALEIG = lsame(RANGE, 'V');
  INDEIG = lsame(RANGE, 'I');

  LQUERY = ((LWORK == -1) || (LIWORK == -1));

  KD = ilaenv2stage(1, 'DSYTRD_2STAGE', JOBZ, N, -1, -1, -1);
  IB = ilaenv2stage(2, 'DSYTRD_2STAGE', JOBZ, N, KD, -1, -1);
  LHTRD = ilaenv2stage(3, 'DSYTRD_2STAGE', JOBZ, N, KD, IB, -1);
  LWTRD = ilaenv2stage(4, 'DSYTRD_2STAGE', JOBZ, N, KD, IB, -1);

  if (N <= 1) {
    LWMIN = 1;
    LIWMIN = 1;
  } else {
    LWMIN = max(26 * N, 5 * N + LHTRD + LWTRD);
    LIWMIN = 10 * N;
  }

  INFO.value = 0;
  if (!(lsame(JOBZ, 'N'))) {
    INFO.value = -1;
  } else if (!(ALLEIG || VALEIG || INDEIG)) {
    INFO.value = -2;
  } else if (!(LOWER || lsame(UPLO, 'U'))) {
    INFO.value = -3;
  } else if (N < 0) {
    INFO.value = -4;
  } else if (LDA < max(1, N)) {
    INFO.value = -6;
  } else {
    if (VALEIG) {
      if (N > 0 && VU <= VL) INFO.value = -8;
    } else if (INDEIG) {
      if (IL < 1 || IL > max(1, N)) {
        INFO.value = -9;
      } else if (IU < min(N, IL) || IU > N) {
        INFO.value = -10;
      }
    }
  }
  if (INFO.value == 0) {
    if (LDZ < 1 || (WANTZ && LDZ < N)) {
      INFO.value = -15;
    } else if (LWORK < LWMIN && !LQUERY) {
      INFO.value = -18;
    } else if (LIWORK < LIWMIN && !LQUERY) {
      INFO.value = -20;
    }
  }

  if (INFO.value == 0) {
    // NB = ilaenv( 1, 'DSYTRD', UPLO, N, -1, -1, -1 )
    // NB = max( NB, ilaenv( 1, 'DORMTR', UPLO, N, -1, -1, -1 ) )
    // LWKOPT = max( ( NB+1 )*N, LWMIN )
    WORK[1] = LWMIN.toDouble();
    IWORK[1] = LIWMIN;
  }

  if (INFO.value != 0) {
    xerbla('DSYEVR_2STAGE', -INFO.value);
    return;
  } else if (LQUERY) {
    return;
  }

  // Quick return if possible

  M.value = 0;
  if (N == 0) {
    WORK[1] = 1;
    return;
  }

  if (N == 1) {
    WORK[1] = 1;
    if (ALLEIG || INDEIG) {
      M.value = 1;
      W[1] = A[1][1];
    } else {
      if (VL < A[1][1] && VU >= A[1][1]) {
        M.value = 1;
        W[1] = A[1][1];
      }
    }
    if (WANTZ) {
      Z[1][1] = ONE;
      ISUPPZ[1] = 1;
      ISUPPZ[2] = 1;
    }
    return;
  }

  // Get machine constants.

  SAFMIN = dlamch('Safe minimum');
  EPS = dlamch('Precision');
  SMLNUM = SAFMIN / EPS;
  BIGNUM = ONE / SMLNUM;
  RMIN = sqrt(SMLNUM);
  RMAX = min(sqrt(BIGNUM), ONE / sqrt(sqrt(SAFMIN)));

  // Scale matrix to allowable range, if necessary.

  ISCALE = 0;
  ABSTLL = ABSTOL;
  if (VALEIG) {
    VLL = VL;
    VUU = VU;
  }
  ANRM = dlansy('M', UPLO, N, A, LDA, WORK);
  if (ANRM > ZERO && ANRM < RMIN) {
    ISCALE = 1;
    SIGMA = RMIN / ANRM;
  } else if (ANRM > RMAX) {
    ISCALE = 1;
    SIGMA = RMAX / ANRM;
  }
  if (ISCALE == 1) {
    if (LOWER) {
      for (J = 1; J <= N; J++) {
        dscal(N - J + 1, SIGMA, A(J, J).asArray(), 1);
      }
    } else {
      for (J = 1; J <= N; J++) {
        dscal(J, SIGMA, A(1, J).asArray(), 1);
      }
    }
    if (ABSTOL > 0) ABSTLL = ABSTOL * SIGMA;
    if (VALEIG) {
      VLL = VL * SIGMA;
      VUU = VU * SIGMA;
    }
  }

  // Initialize indices into workspaces.  Note: The IWORK indices are
  // used only if DSTERF or DSTEMR fail.

  // WORK[INDTAU:INDTAU+N-1] stores the scalar factors of the
  // elementary reflectors used in DSYTRD.
  INDTAU = 1;
  // WORK[INDD:INDD+N-1] stores the tridiagonal's diagonal entries.
  INDD = INDTAU + N;
  // WORK[INDE:INDE+N-1] stores the off-diagonal entries of the
  // tridiagonal matrix from DSYTRD.
  INDE = INDD + N;
  // WORK[INDDD:INDDD+N-1] is a copy of the diagonal entries over
  // -written by DSTEMR (the DSTERF path copies the diagonal to W).
  INDDD = INDE + N;
  // WORK[INDEE:INDEE+N-1] is a copy of the off-diagonal entries over
  // -written while computing the eigenvalues in DSTERF and DSTEMR.
  INDEE = INDDD + N;
  // INDHOUS is the starting offset Householder storage of stage 2
  INDHOUS = INDEE + N;
  // INDWK is the starting offset of the left-over workspace, and
  // LLWORK is the remaining workspace size.
  INDWK = INDHOUS + LHTRD;
  LLWORK = LWORK - INDWK + 1;

  // IWORK[INDIBL:INDIBL+M-1] corresponds to IBLOCK in DSTEBZ and
  // stores the block indices of each of the M<=N eigenvalues.
  INDIBL = 1;
  // IWORK[INDISP:INDISP+NSPLIT-1] corresponds to ISPLIT in DSTEBZ and
  // stores the starting and finishing indices of each block.
  INDISP = INDIBL + N;
  // IWORK[INDIFL:INDIFL+N-1] stores the indices of eigenvectors
  // that corresponding to eigenvectors that fail to converge in
  // DSTEIN.  This information is discarded; if any fail, the driver
  // returns INFO > 0.
  INDIFL = INDISP + N;
  // INDIWO is the offset of the remaining integer workspace.
  INDIWO = INDIFL + N;

  // Call DSYTRD_2STAGE to reduce symmetric matrix to tridiagonal form.

  dsytrd_2stage(JOBZ, UPLO, N, A, LDA, WORK(INDD), WORK(INDE), WORK(INDTAU),
      WORK(INDHOUS), LHTRD, WORK(INDWK), LLWORK, IINFO);

  // If all eigenvalues are desired
  // then call DSTERF or DSTEMR and DORMTR.
  while (true) {
    if ((ALLEIG || (INDEIG && IL == 1 && IU == N)) && IEEEOK == 1) {
      if (!WANTZ) {
        dcopy(N, WORK(INDD), 1, W, 1);
        dcopy(N - 1, WORK(INDE), 1, WORK(INDEE), 1);
        dsterf(N, W, WORK(INDEE), INFO);
      } else {
        dcopy(N - 1, WORK(INDE), 1, WORK(INDEE), 1);
        dcopy(N, WORK(INDD), 1, WORK(INDDD), 1);

        if (ABSTOL <= TWO * N * EPS) {
          TRYRAC.value = true;
        } else {
          TRYRAC.value = false;
        }
        dstemr(JOBZ, 'A', N, WORK(INDDD), WORK(INDEE), VL, VU, IL, IU, M, W, Z,
            LDZ, N, ISUPPZ, TRYRAC, WORK(INDWK), LWORK, IWORK, LIWORK, INFO);

        // Apply orthogonal matrix used in reduction to tridiagonal
        // form to eigenvectors returned by DSTEMR.

        if (WANTZ && INFO.value == 0) {
          INDWKN = INDE;
          LLWRKN = LWORK - INDWKN + 1;
          dormtr('L', UPLO, 'N', N, M.value, A, LDA, WORK(INDTAU), Z, LDZ,
              WORK(INDWKN), LLWRKN, IINFO);
        }
      }

      if (INFO.value == 0) {
        // Everything worked.  Skip DSTEBZ/DSTEIN.  IWORK[:] are
        // undefined.
        M.value = N;
        break;
      }
      INFO.value = 0;
    }

    // Otherwise, call DSTEBZ and, if eigenvectors are desired, DSTEIN.
    // Also call DSTEBZ and DSTEIN if DSTEMR fails.

    if (WANTZ) {
      ORDER = 'B';
    } else {
      ORDER = 'E';
    }
    dstebz(
        RANGE,
        ORDER,
        N,
        VLL,
        VUU,
        IL,
        IU,
        ABSTLL,
        WORK(INDD),
        WORK(INDE),
        M,
        NSPLIT,
        W,
        IWORK(INDIBL),
        IWORK(INDISP),
        WORK(INDWK),
        IWORK(INDIWO),
        INFO);

    if (WANTZ) {
      dstein(
          N,
          WORK(INDD),
          WORK(INDE),
          M.value,
          W,
          IWORK(INDIBL),
          IWORK(INDISP),
          Z,
          LDZ,
          WORK(INDWK),
          IWORK(INDIWO),
          IWORK(INDIFL),
          INFO);

      // Apply orthogonal matrix used in reduction to tridiagonal
      // form to eigenvectors returned by DSTEIN.

      INDWKN = INDE;
      LLWRKN = LWORK - INDWKN + 1;
      dormtr('L', UPLO, 'N', N, M.value, A, LDA, WORK(INDTAU), Z, LDZ,
          WORK(INDWKN), LLWRKN, IINFO);
    }
    break;
  }

  // If matrix was scaled, then rescale eigenvalues appropriately.

  // Jump here if DSTEMR/DSTEIN succeeded.
  if (ISCALE == 1) {
    if (INFO.value == 0) {
      IMAX = M.value;
    } else {
      IMAX = INFO.value - 1;
    }
    dscal(IMAX, ONE / SIGMA, W, 1);
  }

  // If eigenvalues are not in order, then sort them, along with
  // eigenvectors.  Note: We do not sort the IFAIL portion of IWORK.
  // It may not be initialized (if DSTEMR/DSTEIN succeeded), and we do
  // not return this detailed information to the user.

  if (WANTZ) {
    for (J = 1; J <= M.value - 1; J++) {
      I = 0;
      TMP1 = W[J];
      for (JJ = J + 1; JJ <= M.value; JJ++) {
        if (W[JJ] < TMP1) {
          I = JJ;
          TMP1 = W[JJ];
        }
      }

      if (I != 0) {
        W[I] = W[J];
        W[J] = TMP1;
        dswap(N, Z(1, I).asArray(), 1, Z(1, J).asArray(), 1);
      }
    }
  }

  // Set WORK[1] to optimal workspace size.

  WORK[1] = LWMIN.toDouble();
  IWORK[1] = LIWMIN;
}