zgbmv function

Implementation

void zgbmv(
  final String TRANS,
  final int M,
  final int N,
  final int KL,
  final int KU,
  final Complex ALPHA,
  final Matrix<Complex> A_,
  final int LDA,
  final Array<Complex> X_,
  final int INCX,
  final Complex BETA,
  final Array<Complex> Y_,
  final int INCY,
) {
  final A = A_.having(ld: LDA);
  final X = X_.having();
  final Y = Y_.having();

  // Test the input parameters.

  var INFO = 0;
  if (!lsame(TRANS, 'N') && !lsame(TRANS, 'T') && !lsame(TRANS, 'C')) {
    INFO = 1;
  } else if (M < 0) {
    INFO = 2;
  } else if (N < 0) {
    INFO = 3;
  } else if (KL < 0) {
    INFO = 4;
  } else if (KU < 0) {
    INFO = 5;
  } else if (LDA < (KL + KU + 1)) {
    INFO = 8;
  } else if (INCX == 0) {
    INFO = 10;
  } else if (INCY == 0) {
    INFO = 13;
  }
  if (INFO != 0) {
    xerbla('ZGBMV', INFO);
    return;
  }

  // Quick return if possible.

  if ((M == 0) ||
      (N == 0) ||
      ((ALPHA == Complex.zero) && (BETA == Complex.one))) return;

  final NOCONJ = lsame(TRANS, 'T');

  // Set  LENX  and  LENY, the lengths of the vectors x and y, and set
  // up the start points in  X  and  Y.

  final (LENX, LENY) = lsame(TRANS, 'N') ? (N, M) : (M, N);
  var KX = INCX > 0 ? 1 : 1 - (LENX - 1) * INCX;
  var KY = INCY > 0 ? 1 : 1 - (LENY - 1) * INCY;

  // Start the operations. In this version the elements of A are
  // accessed sequentially with one pass through the band part of A.

  // First form  y := beta*y.

  if (BETA != Complex.one) {
    if (INCY == 1) {
      if (BETA == Complex.zero) {
        for (var I = 1; I <= LENY; I++) {
          Y[I] = Complex.zero;
        }
      } else {
        for (var I = 1; I <= LENY; I++) {
          Y[I] *= BETA;
        }
      }
    } else {
      var IY = KY;
      if (BETA == Complex.zero) {
        for (var I = 1; I <= LENY; I++) {
          Y[IY] = Complex.zero;
          IY += INCY;
        }
      } else {
        for (var I = 1; I <= LENY; I++) {
          Y[IY] *= BETA;
          IY += INCY;
        }
      }
    }
  }
  if (ALPHA == Complex.zero) return;

  final KUP1 = KU + 1;
  if (lsame(TRANS, 'N')) {
    // Form  y := alpha*A*x + y.

    var JX = KX;
    if (INCY == 1) {
      for (var J = 1; J <= N; J++) {
        final TEMP = ALPHA * X[JX];
        final K = KUP1 - J;
        for (var I = max(1, J - KU); I <= min(M, J + KL); I++) {
          Y[I] += TEMP * A[K + I][J];
        }
        JX += INCX;
      }
    } else {
      for (var J = 1; J <= N; J++) {
        final TEMP = ALPHA * X[JX];
        var IY = KY;
        final K = KUP1 - J;
        for (var I = max(1, J - KU); I <= min(M, J + KL); I++) {
          Y[IY] += TEMP * A[K + I][J];
          IY += INCY;
        }
        JX += INCX;
        if (J > KU) KY += INCY;
      }
    }
  } else {
    // Form  y := alpha*A**T*x + y  or  y := alpha*A**H*x + y.

    var JY = KY;
    if (INCX == 1) {
      for (var J = 1; J <= N; J++) {
        var TEMP = Complex.zero;
        final K = KUP1 - J;
        if (NOCONJ) {
          for (var I = max(1, J - KU); I <= min(M, J + KL); I++) {
            TEMP += A[K + I][J] * X[I];
          }
        } else {
          for (var I = max(1, J - KU); I <= min(M, J + KL); I++) {
            TEMP += A[K + I][J].conjugate() * X[I];
          }
        }
        Y[JY] += ALPHA * TEMP;
        JY += INCY;
      }
    } else {
      for (var J = 1; J <= N; J++) {
        var TEMP = Complex.zero;
        var IX = KX;
        final K = KUP1 - J;
        if (NOCONJ) {
          for (var I = max(1, J - KU); I <= min(M, J + KL); I++) {
            TEMP += A[K + I][J] * X[IX];
            IX += INCX;
          }
        } else {
          for (var I = max(1, J - KU); I <= min(M, J + KL); I++) {
            TEMP += A[K + I][J].conjugate() * X[IX];
            IX += INCX;
          }
        }
        Y[JY] += ALPHA * TEMP;
        JY += INCY;
        if (J > KU) KX += INCX;
      }
    }
  }
}