zpstf2 function

Implementation

void zpstf2(
  final String UPLO,
  final int N,
  final Matrix<Complex> A_,
  final int LDA,
  final Array<int> PIV_,
  final Box<int> RANK,
  final double TOL,
  final Array<double> WORK_,
  final Box<int> INFO,
) {
  final A = A_.having(ld: LDA);
  final PIV = PIV_.having(length: N);
  final WORK = WORK_.having(length: 2 * N);
  const ONE = 1.0, ZERO = 0.0;
  Complex ZTEMP;
  double AJJ, DSTOP, DTEMP;
  int I, ITEMP, J, PVT;
  bool UPPER;

  // Test the input parameters

  INFO.value = 0;
  UPPER = lsame(UPLO, 'U');
  if (!UPPER && !lsame(UPLO, 'L')) {
    INFO.value = -1;
  } else if (N < 0) {
    INFO.value = -2;
  } else if (LDA < max(1, N)) {
    INFO.value = -4;
  }
  if (INFO.value != 0) {
    xerbla('ZPSTF2', -INFO.value);
    return;
  }

  // Quick return if possible

  if (N == 0) return;

  // Initialize PIV

  for (I = 1; I <= N; I++) {
    PIV[I] = I;
  }

  // Compute stopping value

  for (I = 1; I <= N; I++) {
    WORK[I] = A[I][I].real;
  }
  PVT = WORK.maxloc(1, N);
  AJJ = A[PVT][PVT].real;
  if (AJJ <= ZERO || disnan(AJJ)) {
    RANK.value = 0;
    INFO.value = 1;
    return;
  }

  // Compute stopping value if not supplied

  if (TOL < ZERO) {
    DSTOP = N * dlamch('Epsilon') * AJJ;
  } else {
    DSTOP = TOL;
  }

  // Set first half of WORK to zero, holds dot products

  for (I = 1; I <= N; I++) {
    WORK[I] = 0;
  }

  if (UPPER) {
    // Compute the Cholesky factorization P**T * A * P = U**H* U

    for (J = 1; J <= N; J++) {
      // Find pivot, test for exit, else swap rows and columns
      // Update dot products, compute possible pivots which are
      // stored in the second half of WORK

      for (I = J; I <= N; I++) {
        if (J > 1) {
          WORK[I] = WORK[I] + (A[J - 1][I].conjugate() * A[J - 1][I]).real;
        }
        WORK[N + I] = A[I][I].real - WORK[I];
      }

      if (J > 1) {
        ITEMP = WORK.maxloc(N + J, 2 * N);
        PVT = ITEMP + J - 1;
        AJJ = WORK[N + PVT];
        if (AJJ <= DSTOP || disnan(AJJ)) {
          A[J][J] = AJJ.toComplex();
          // Rank is number of steps completed.  Set INFO = 1 to signal
          // that the factorization cannot be used to solve a system.

          RANK.value = J - 1;
          INFO.value = 1;
          return;
        }
      }

      if (J != PVT) {
        // Pivot OK, so can now swap pivot rows and columns

        A[PVT][PVT] = A[J][J];
        zswap(J - 1, A(1, J).asArray(), 1, A(1, PVT).asArray(), 1);
        if (PVT < N) {
          zswap(N - PVT, A(J, PVT + 1).asArray(), LDA,
              A(PVT, PVT + 1).asArray(), LDA);
        }
        for (I = J + 1; I <= PVT - 1; I++) {
          ZTEMP = A[J][I].conjugate();
          A[J][I] = A[I][PVT].conjugate();
          A[I][PVT] = ZTEMP;
        }
        A[J][PVT] = A[J][PVT].conjugate();

        // Swap dot products and PIV

        DTEMP = WORK[J];
        WORK[J] = WORK[PVT];
        WORK[PVT] = DTEMP;
        ITEMP = PIV[PVT];
        PIV[PVT] = PIV[J];
        PIV[J] = ITEMP;
      }

      AJJ = sqrt(AJJ);
      A[J][J] = AJJ.toComplex();

      // Compute elements J+1:N of row J

      if (J < N) {
        zlacgv(J - 1, A(1, J).asArray(), 1);
        zgemv('Trans', J - 1, N - J, -Complex.one, A(1, J + 1), LDA,
            A(1, J).asArray(), 1, Complex.one, A(J, J + 1).asArray(), LDA);
        zlacgv(J - 1, A(1, J).asArray(), 1);
        zdscal(N - J, ONE / AJJ, A(J, J + 1).asArray(), LDA);
      }
    }
  } else {
    // Compute the Cholesky factorization P**T * A * P = L * L**H

    for (J = 1; J <= N; J++) {
      // Find pivot, test for exit, else swap rows and columns
      // Update dot products, compute possible pivots which are
      // stored in the second half of WORK

      for (I = J; I <= N; I++) {
        if (J > 1) {
          WORK[I] = WORK[I] + (A[I][J - 1].conjugate() * A[I][J - 1]).real;
        }
        WORK[N + I] = A[I][I].real - WORK[I];
      }

      if (J > 1) {
        ITEMP = WORK.maxloc(N + J, 2 * N);
        PVT = ITEMP + J - 1;
        AJJ = WORK[N + PVT];
        if (AJJ <= DSTOP || disnan(AJJ)) {
          A[J][J] = AJJ.toComplex();
          // Rank is number of steps completed.  Set INFO = 1 to signal
          // that the factorization cannot be used to solve a system.

          RANK.value = J - 1;
          INFO.value = 1;
          return;
        }
      }

      if (J != PVT) {
        // Pivot OK, so can now swap pivot rows and columns

        A[PVT][PVT] = A[J][J];
        zswap(J - 1, A(J, 1).asArray(), LDA, A(PVT, 1).asArray(), LDA);
        if (PVT < N) {
          zswap(N - PVT, A(PVT + 1, J).asArray(), 1, A(PVT + 1, PVT).asArray(),
              1);
        }
        for (I = J + 1; I <= PVT - 1; I++) {
          ZTEMP = A[I][J].conjugate();
          A[I][J] = A[PVT][I].conjugate();
          A[PVT][I] = ZTEMP;
        }
        A[PVT][J] = A[PVT][J].conjugate();

        // Swap dot products and PIV

        DTEMP = WORK[J];
        WORK[J] = WORK[PVT];
        WORK[PVT] = DTEMP;
        ITEMP = PIV[PVT];
        PIV[PVT] = PIV[J];
        PIV[J] = ITEMP;
      }

      AJJ = sqrt(AJJ);
      A[J][J] = AJJ.toComplex();

      // Compute elements J+1:N of column J

      if (J < N) {
        zlacgv(J - 1, A(J, 1).asArray(), LDA);
        zgemv('No Trans', N - J, J - 1, -Complex.one, A(J + 1, 1), LDA,
            A(J, 1).asArray(), LDA, Complex.one, A(J + 1, J).asArray(), 1);
        zlacgv(J - 1, A(J, 1).asArray(), LDA);
        zdscal(N - J, ONE / AJJ, A(J + 1, J).asArray(), 1);
      }
    }
  }

  // Ran to completion, A has full rank

  RANK.value = N;
}