zggesx function

Implementation

void zggesx(
  final String JOBVSL,
  final String JOBVSR,
  final String SORT,
  final bool Function(Complex, Complex) SELCTG,
  final String SENSE,
  final int N,
  final Matrix<Complex> A_,
  final int LDA,
  final Matrix<Complex> B_,
  final int LDB,
  final Box<int> SDIM,
  final Array<Complex> ALPHA_,
  final Array<Complex> BETA_,
  final Matrix<Complex> VSL_,
  final int LDVSL,
  final Matrix<Complex> VSR_,
  final int LDVSR,
  final Array<double> RCONDE_,
  final Array<double> RCONDV_,
  final Array<Complex> WORK_,
  final int LWORK,
  final Array<double> RWORK_,
  final Array<int> IWORK_,
  final int LIWORK,
  final Array<bool> BWORK_,
  final Box<int> INFO,
) {
  final A = A_.having(ld: LDA);
  final B = B_.having(ld: LDB);
  final VSL = VSL_.having(ld: LDVSL);
  final VSR = VSR_.having(ld: LDVSR);
  final WORK = WORK_.having();
  final RWORK = RWORK_.having();
  final IWORK = IWORK_.having();
  final BWORK = BWORK_.having();
  final ALPHA = ALPHA_.having();
  final BETA = BETA_.having();
  final RCONDE = RCONDE_.having(length: 2);
  final RCONDV = RCONDV_.having(length: 2);
  const ZERO = 0.0, ONE = 1.0;
  bool CURSL,
      ILASCL,
      ILBSCL,
      ILVSL,
      ILVSR,
      LASTSL,
      LQUERY,
      WANTSB,
      WANTSE,
      WANTSN,
      WANTST,
      WANTSV;
  int I,
      ICOLS,
      IJOB = 0,
      IJOBVL,
      IJOBVR,
      ILEFT,
      IRIGHT,
      IROWS,
      IRWRK,
      ITAU,
      IWRK,
      LIWMIN = 0,
      LWRK,
      MAXWRK = 0,
      MINWRK;
  double ANRM, ANRMTO = 0, BIGNUM, BNRM, BNRMTO = 0, EPS, SMLNUM;
  final DIF = Array<double>(2);
  final IERR = Box(0), IHI = Box(0), ILO = Box(0);
  final PL = Box(0.0), PR = Box(0.0);

  // Decode the input arguments

  if (lsame(JOBVSL, 'N')) {
    IJOBVL = 1;
    ILVSL = false;
  } else if (lsame(JOBVSL, 'V')) {
    IJOBVL = 2;
    ILVSL = true;
  } else {
    IJOBVL = -1;
    ILVSL = false;
  }

  if (lsame(JOBVSR, 'N')) {
    IJOBVR = 1;
    ILVSR = false;
  } else if (lsame(JOBVSR, 'V')) {
    IJOBVR = 2;
    ILVSR = true;
  } else {
    IJOBVR = -1;
    ILVSR = false;
  }

  WANTST = lsame(SORT, 'S');
  WANTSN = lsame(SENSE, 'N');
  WANTSE = lsame(SENSE, 'E');
  WANTSV = lsame(SENSE, 'V');
  WANTSB = lsame(SENSE, 'B');
  LQUERY = (LWORK == -1 || LIWORK == -1);
  if (WANTSN) {
    IJOB = 0;
  } else if (WANTSE) {
    IJOB = 1;
  } else if (WANTSV) {
    IJOB = 2;
  } else if (WANTSB) {
    IJOB = 4;
  }

  // Test the input arguments

  INFO.value = 0;
  if (IJOBVL <= 0) {
    INFO.value = -1;
  } else if (IJOBVR <= 0) {
    INFO.value = -2;
  } else if (!WANTST && !lsame(SORT, 'N')) {
    INFO.value = -3;
  } else if (!(WANTSN || WANTSE || WANTSV || WANTSB) || (!WANTST && !WANTSN)) {
    INFO.value = -5;
  } else if (N < 0) {
    INFO.value = -6;
  } else if (LDA < max(1, N)) {
    INFO.value = -8;
  } else if (LDB < max(1, N)) {
    INFO.value = -10;
  } else if (LDVSL < 1 || (ILVSL && LDVSL < N)) {
    INFO.value = -15;
  } else if (LDVSR < 1 || (ILVSR && LDVSR < N)) {
    INFO.value = -17;
  }

  // Compute workspace
  //  (Note: Comments in the code beginning "Workspace:" describe the
  //   minimal amount of workspace needed at that point in the code,
  //   as well as the preferred amount for good performance.
  //   NB refers to the optimal block size for the immediately
  //   following subroutine, as returned by ILAENV.)

  if (INFO.value == 0) {
    if (N > 0) {
      MINWRK = 2 * N;
      MAXWRK = N * (1 + ilaenv(1, 'ZGEQRF', ' ', N, 1, N, 0));
      MAXWRK = max(MAXWRK, N * (1 + ilaenv(1, 'ZUNMQR', ' ', N, 1, N, -1)));
      if (ILVSL) {
        MAXWRK = max(MAXWRK, N * (1 + ilaenv(1, 'ZUNGQR', ' ', N, 1, N, -1)));
      }
      LWRK = MAXWRK;
      if (IJOB >= 1) LWRK = max(LWRK, N * N ~/ 2);
    } else {
      MINWRK = 1;
      MAXWRK = 1;
      LWRK = 1;
    }
    WORK[1] = LWRK.toComplex();
    if (WANTSN || N == 0) {
      LIWMIN = 1;
    } else {
      LIWMIN = N + 2;
    }
    IWORK[1] = LIWMIN;

    if (LWORK < MINWRK && !LQUERY) {
      INFO.value = -21;
    } else if (LIWORK < LIWMIN && !LQUERY) {
      INFO.value = -24;
    }
  }

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

  // Quick return if possible

  if (N == 0) {
    SDIM.value = 0;
    return;
  }

  // Get machine constants

  EPS = dlamch('P');
  SMLNUM = dlamch('S');
  BIGNUM = ONE / SMLNUM;
  SMLNUM = sqrt(SMLNUM) / EPS;
  BIGNUM = ONE / SMLNUM;

  // Scale A if max element outside range [SMLNUM,BIGNUM]

  ANRM = zlange('M', N, N, A, LDA, RWORK);
  ILASCL = false;
  if (ANRM > ZERO && ANRM < SMLNUM) {
    ANRMTO = SMLNUM;
    ILASCL = true;
  } else if (ANRM > BIGNUM) {
    ANRMTO = BIGNUM;
    ILASCL = true;
  }
  if (ILASCL) zlascl('G', 0, 0, ANRM, ANRMTO, N, N, A, LDA, IERR);

  // Scale B if max element outside range [SMLNUM,BIGNUM]

  BNRM = zlange('M', N, N, B, LDB, RWORK);
  ILBSCL = false;
  if (BNRM > ZERO && BNRM < SMLNUM) {
    BNRMTO = SMLNUM;
    ILBSCL = true;
  } else if (BNRM > BIGNUM) {
    BNRMTO = BIGNUM;
    ILBSCL = true;
  }
  if (ILBSCL) zlascl('G', 0, 0, BNRM, BNRMTO, N, N, B, LDB, IERR);

  // Permute the matrix to make it more nearly triangular
  // (Real Workspace: need 6*N)

  ILEFT = 1;
  IRIGHT = N + 1;
  IRWRK = IRIGHT + N;
  zggbal('P', N, A, LDA, B, LDB, ILO, IHI, RWORK(ILEFT), RWORK(IRIGHT),
      RWORK(IRWRK), IERR);

  // Reduce B to triangular form (QR decomposition of B)
  // (Complex Workspace: need N, prefer N*NB)

  IROWS = IHI.value + 1 - ILO.value;
  ICOLS = N + 1 - ILO.value;
  ITAU = 1;
  IWRK = ITAU + IROWS;
  zgeqrf(IROWS, ICOLS, B(ILO.value, ILO.value), LDB, WORK(ITAU), WORK(IWRK),
      LWORK + 1 - IWRK, IERR);

  // Apply the unitary transformation to matrix A
  // (Complex Workspace: need N, prefer N*NB)

  zunmqr(
      'L',
      'C',
      IROWS,
      ICOLS,
      IROWS,
      B(ILO.value, ILO.value),
      LDB,
      WORK(ITAU),
      A(ILO.value, ILO.value),
      LDA,
      WORK(IWRK),
      LWORK + 1 - IWRK,
      IERR);

  // Initialize VSL
  // (Complex Workspace: need N, prefer N*NB)

  if (ILVSL) {
    zlaset('Full', N, N, Complex.zero, Complex.one, VSL, LDVSL);
    if (IROWS > 1) {
      zlacpy('L', IROWS - 1, IROWS - 1, B(ILO.value + 1, ILO.value), LDB,
          VSL(ILO.value + 1, ILO.value), LDVSL);
    }
    zungqr(IROWS, IROWS, IROWS, VSL(ILO.value, ILO.value), LDVSL, WORK(ITAU),
        WORK(IWRK), LWORK + 1 - IWRK, IERR);
  }

  // Initialize VSR

  if (ILVSR) zlaset('Full', N, N, Complex.zero, Complex.one, VSR, LDVSR);

  // Reduce to generalized Hessenberg form
  // (Workspace: none needed)

  zgghrd(JOBVSL, JOBVSR, N, ILO.value, IHI.value, A, LDA, B, LDB, VSL, LDVSL,
      VSR, LDVSR, IERR);

  SDIM.value = 0;

  // Perform QZ algorithm, computing Schur vectors if desired
  // (Complex Workspace: need N)
  // (Real Workspace:    need N)

  IWRK = ITAU;
  zhgeqz(
      'S',
      JOBVSL,
      JOBVSR,
      N,
      ILO.value,
      IHI.value,
      A,
      LDA,
      B,
      LDB,
      ALPHA,
      BETA,
      VSL,
      LDVSL,
      VSR,
      LDVSR,
      WORK(IWRK),
      LWORK + 1 - IWRK,
      RWORK(IRWRK),
      IERR);
  if (IERR.value != 0) {
    if (IERR.value > 0 && IERR.value <= N) {
      INFO.value = IERR.value;
    } else if (IERR.value > N && IERR.value <= 2 * N) {
      INFO.value = IERR.value - N;
    } else {
      INFO.value = N + 1;
    }
  } else {
    // Sort eigenvalues ALPHA/BETA and compute the reciprocal of
    // condition number(s)

    if (WANTST) {
      // Undo scaling on eigenvalues before SELCTGing

      if (ILASCL) {
        zlascl('G', 0, 0, ANRMTO, ANRM, N, 1, ALPHA.asMatrix(N), N, IERR);
      }
      if (ILBSCL) {
        zlascl('G', 0, 0, BNRMTO, BNRM, N, 1, BETA.asMatrix(N), N, IERR);
      }

      // Select eigenvalues

      for (I = 1; I <= N; I++) {
        BWORK[I] = SELCTG(ALPHA[I], BETA[I]);
      }

      // Reorder eigenvalues, transform Generalized Schur vectors, and
      // compute reciprocal condition numbers
      // (Complex Workspace: If IJOB >= 1, need max(1, 2*SDIM*(N-SDIM))
      //                     otherwise, need 1 )

      ztgsen(
          IJOB,
          ILVSL,
          ILVSR,
          BWORK,
          N,
          A,
          LDA,
          B,
          LDB,
          ALPHA,
          BETA,
          VSL,
          LDVSL,
          VSR,
          LDVSR,
          SDIM,
          PL,
          PR,
          DIF,
          WORK(IWRK),
          LWORK - IWRK + 1,
          IWORK,
          LIWORK,
          IERR);

      if (IJOB >= 1) MAXWRK = max(MAXWRK, 2 * SDIM.value * (N - SDIM.value));
      if (IERR.value == -21) {
        // not enough complex workspace

        INFO.value = -21;
      } else {
        if (IJOB == 1 || IJOB == 4) {
          RCONDE[1] = PL.value;
          RCONDE[2] = PR.value;
        }
        if (IJOB == 2 || IJOB == 4) {
          RCONDV[1] = DIF[1];
          RCONDV[2] = DIF[2];
        }
        if (IERR.value == 1) INFO.value = N + 3;
      }
    }

    // Apply permutation to VSL and VSR
    // (Workspace: none needed)

    if (ILVSL) {
      zggbak('P', 'L', N, ILO.value, IHI.value, RWORK(ILEFT), RWORK(IRIGHT), N,
          VSL, LDVSL, IERR);
    }

    if (ILVSR) {
      zggbak('P', 'R', N, ILO.value, IHI.value, RWORK(ILEFT), RWORK(IRIGHT), N,
          VSR, LDVSR, IERR);
    }

    // Undo scaling

    if (ILASCL) {
      zlascl('U', 0, 0, ANRMTO, ANRM, N, N, A, LDA, IERR);
      zlascl('G', 0, 0, ANRMTO, ANRM, N, 1, ALPHA.asMatrix(N), N, IERR);
    }

    if (ILBSCL) {
      zlascl('U', 0, 0, BNRMTO, BNRM, N, N, B, LDB, IERR);
      zlascl('G', 0, 0, BNRMTO, BNRM, N, 1, BETA.asMatrix(N), N, IERR);
    }

    if (WANTST) {
      // Check if reordering is correct

      LASTSL = true;
      SDIM.value = 0;
      for (I = 1; I <= N; I++) {
        CURSL = SELCTG(ALPHA[I], BETA[I]);
        if (CURSL) SDIM.value++;
        if (CURSL && !LASTSL) INFO.value = N + 2;
        LASTSL = CURSL;
      }
    }
  }

  WORK[1] = MAXWRK.toComplex();
  IWORK[1] = LIWMIN;
}