1-D Gaussian function.

@param x value.
@return Function's value at point x.
184228
public double Function1D(double x) {
        return Math.exp(x * x / (-2 * sqrSigma)) / (Math.sqrt(2 * Math.PI) * sigma);
    }
827222
private static double logSumExp(double[] x) {
    double max = x[0];
    for(int i = 1; i < x.length; i++) {
      final double v = x[i];
      max = v > max ? v : max;
    }
    final double cutoff = max - 35.350506209; // log_e(2**51)
    double acc = 0.;
    for(int i = 0; i < x.length; i++) {
      final double v = x[i];
      if(v > cutoff) {
        acc += v < max ? FastMath.exp(v - max) : 1.;
      }
    }
    return acc > 1. ? (max + FastMath.log(acc)) : max;
  }
908967
def evaluate(x, amplitude, mean, stddev):
        
        return 1.0 - Gaussian1D.evaluate(x, amplitude, mean, stddev)
758350
public static float max(float[] x) {
        float m = Float.NEGATIVE_INFINITY;

        for (float n : x) {
            if (n > m) {
                m = n;
            }
        }

        return m;
    }
640461
public static BigFloat acoth(BigFloat x) {
		return x.context.valueOf(BigDecimalMath.acoth(x.value, x.context.mathContext));
	}
76466
public static double standardDeviation(double[] x, double mean) {
        if (x.length == 0) {
            return Double.NaN;
        }
        if (x.length == 1) {
            return 0.0;
        }
        return Math.sqrt(variance(x, mean));
    }
992713
def gaussian(x,  a, b, c, d=0):
    '''
    
    '''
    return a * np.exp(  -(((x-b)**2 )/ (2*(c**2)))  ) + d
1084462
def funcGauss1D(x, mu, sig):
    
    arrOut = np.exp(-np.power((x - mu)/sig, 2.)/2)
    # normalize
    arrOut = arrOut/(np.sqrt(2.*np.pi)*sig)

    return arrOut
1096009
def F(self, x):
        
        if isinstance(x, np.ndarray):
            nfwvals = np.ones_like(x)
            inds1 = np.where(x < 1)
            inds2 = np.where(x > 1)
            nfwvals[inds1] = (1 - x[inds1] ** 2) ** -.5 * np.arctanh((1 - x[inds1] ** 2) ** .5)
            nfwvals[inds2] = (x[inds2] ** 2 - 1) ** -.5 * np.arctan((x[inds2] ** 2 - 1) ** .5)
            return nfwvals

        elif isinstance(x, float) or isinstance(x, int):
            if x == 1:
                return 1
            if x < 1:
                return (1 - x ** 2) ** -.5 * np.arctanh((1 - x ** 2) ** .5)
            else:
                return (x ** 2 - 1) ** -.5 * np.arctan((x ** 2 - 1) ** .5)
1185682
def gaussian(x, y, xsigma, ysigma):
    
    if xsigma==0.0 or ysigma==0.0:
        return x*0.0

    with float_error_ignore():
        x_w = np.divide(x,xsigma)
        y_h = np.divide(y,ysigma)
        return np.exp(-0.5*x_w*x_w + -0.5*y_h*y_h)
1269159
public double[] solveLInplace(double[] X) {
    final int n = L.length;
    X[0] /= L[0][0]; // First iteration, simplified.
    for(int k = 1; k < n; k++) {
      final double[] Lk = L[k];
      for(int i = 0; i < k; i++) {
        X[k] -= X[i] * Lk[i];
      }
      X[k] /= Lk[k];
    }
    return X;
  }
711313
public double get(double x, double epsilon)
    {
        Point nearest = getNearest(x, epsilon);
        return nearest.getY();
    }
383796
public double inverseCumulativeDistribution(double x) {
		double p = Math.exp(-lambda);
		double dp = p;
		int k = 0;
		while(x > p) {
			k++;
			dp *= lambda / k;
			p += dp;
		}
		return k;
	}
28801
public static float min(float[] x) {
        float m = Float.POSITIVE_INFINITY;

        for (float n : x) {
            if (n < m) {
                m = n;
            }
        }

        return m;
    }
882826
def _call(self, x):
        """"""
        if isinstance(self.domain, ProductSpace):
            norm = PointwiseNorm(self.domain, 2)(x)
        else:
            norm = x.ufuncs.absolute()

        if self.gamma > 0:
            tmp = norm.ufuncs.square()
            tmp *= 1 / (2 * self.gamma)

            index = norm.ufuncs.greater_equal(self.gamma)
            tmp[index] = norm[index] - self.gamma / 2
        else:
            tmp = norm

        return tmp.inner(tmp.space.one())
1347903
public static double Function1D(double x, double mean, double amplitude, double position, double width, double phase, double frequency) {
        double envelope = mean + amplitude * Math.exp(-Math.pow((x - position), 2) / Math.pow((2 * width), 2));
        double carry = Math.cos(2 * Math.PI * frequency * (x - position) + phase);
        return envelope * carry;
    }
564499
public float linear(float[] x, int m) {
    float result = (float) 1.0;
    int M = x.length;

    for (int i = 1; i <= M - m; i++) {
      result *= x[i - 1];
    }

    if (m != 1) {
      result *= (1 - x[M - m]);
    }

    return result;
  }