An F (fisher) random variate
    
    Parameters
    ----------
    d1 : int
        Numerator degrees of freedom
    d2 : int
        Denominator degrees of freedom
5478
def Fisher(d1, d2, tag=None):
    
    assert (
        int(d1) == d1 and d1 >= 1
    ), 'Fisher (F) "d1" must be an integer greater than 0'
    assert (
        int(d2) == d2 and d2 >= 1
    ), 'Fisher (F) "d2" must be an integer greater than 0'
    return uv(ss.f(d1, d2), tag=tag)
751650
private RandomVariable[] getBasisFunctions(RandomVariable underlying) {
		double min = underlying.getMin();
		double max = underlying.getMax();

		ArrayList<RandomVariable> basisFunctionList = new ArrayList<>();
		double[] discretization = (new TimeDiscretizationFromArray(min, numberOfBins, (max-min)/numberOfBins)).getAsDoubleArray();
		for(double discretizationStep : discretization) {
			RandomVariable indicator = underlying.sub(discretizationStep).choose(new RandomVariableFromDoubleArray(1.0), new RandomVariableFromDoubleArray(0.0));
			basisFunctionList.add(indicator);
		}

		return basisFunctionList.toArray(new RandomVariable[0]);
	}
1093504
def dichotomy(self, f, kmin=2, kmax=12, raise_no_convergence=True,):
        

        for k in range(kmin, kmax):
            N = pow(2, k)

            sampled = self.sample_function(f, N)
            coeffs = self.polyfit(sampled)

            # 3) Check for negligible coefficients
            #    If within bound: get negligible coeffs and bread
            bnd = self._threshold(np.max(np.abs(coeffs)))

            last = abs(coeffs[-2:])
            if np.all(last <= bnd):
                break
        else:
            if raise_no_convergence:
                raise self.NoConvergence(last, bnd)
        return coeffs
108202
def obfn_dfd(self):
        
        """

        Ef = sl.inner(self.Zf, self.obfn_fvarf(), axis=self.cri.axisM) \
          - self.Sf
        return (np.linalg.norm(self.W * sl.irfftn(Ef, self.cri.Nv,
                                                  self.cri.axisN))**2) / 2.0
1030642
public double[] getLinearRegressionParameters(RandomVariable dependents) {

		RandomVariable localizerWeights = dependents.squared().sub(Math.pow(dependents.getStandardDeviation()*standardDeviations,2.0)).choose(new Scalar(0.0), new Scalar(1.0));

		// Localize basis functions
		RandomVariable[] basisFunctionsNonLocalized = getBasisFunctionsEstimator().getBasisFunctions();
		RandomVariable[] basisFunctions = new RandomVariable[basisFunctionsNonLocalized.length];
		for(int i=0; i<basisFunctions.length; i++) {
			basisFunctions[i] = basisFunctionsNonLocalized[i].mult(localizerWeights);
		}

		// Localize dependents
		dependents = dependents.mult(localizerWeights);

		// Build XTX - the symmetric matrix consisting of the scalar products of the basis functions.
		double[][] XTX = new double[basisFunctions.length][basisFunctions.length];
		for(int i=0; i<basisFunctions.length; i++) {
			for(int j=i; j<basisFunctions.length; j++) {
				XTX[i][j] = basisFunctions[i].mult(basisFunctions[j]).getAverage();	// Scalar product
				XTX[j][i] = XTX[i][j];												// Symmetric matrix
			}
		}

		DecompositionSolver solver = new SingularValueDecomposition(new Array2DRowRealMatrix(XTX, false)).getSolver();

		// Build XTy - the projection of the dependents random variable on the basis functions.
		double[] XTy = new double[basisFunctions.length];
		for(int i=0; i<basisFunctions.length; i++) {
			XTy[i] = dependents.mult(basisFunctions[i]).getAverage();				// Scalar product
		}

		// Solve X^T X x = X^T y - which gives us the regression coefficients x = linearRegressionParameters
		double[] linearRegressionParameters = solver.solve(new ArrayRealVector(XTy)).toArray();

		return linearRegressionParameters;
	}
1191340
public static double fCdf(double x, int f1, int f2) {
        if(x<0 || f1<=0 || f2<=0) {
            throw new IllegalArgumentException("All the parameters must be positive.");
        }
        
        double Z = x/(x + (double)f2/f1);
        double FCdf = betaCdf(Z,f1/2.0,f2/2.0);
        
        return FCdf;
    }
578972
def _F(self, X, tau):
        
        t2 = tau ** 2
        #Fx = self.F(X)

        _F = self.F(X)
        a = t2*(t2+1)**-2
        if isinstance(X, np.ndarray):
            #b = (t2 + 1) * (X ** 2 - 1) ** -1 * (1 - _F)
            b = np.ones_like(X)
            b[X == 1] = (t2+1) * 1./3
            b[X != 1] = (t2 + 1) * (X[X != 1] ** 2 - 1) ** -1 * (1 - _F[X != 1])

        elif isinstance(X, float) or isinstance(X, int):
            if X == 1:
                b = (t2+1)* 1./3
            else:
                b = (t2+1)*(X**2-1)**-1*(1-_F)
        else:
            raise ValueError("The variable type is not compatible with the function, please use float, int or ndarray's.")

        c = 2*_F
        d = -np.pi*(t2+X**2)**-0.5
        e = (t2-1)*(tau*(t2+X**2)**0.5)**-1*self.L(X,tau)
        result = a * (b + c + d + e)

        return result
1321484
def rand_student_t(df, mu=0, std=1):
    

    x = random.gauss(0, std)
    y = 2.0*random.gammavariate(0.5 * df, 2.0)
    return x / (math.sqrt(y / df)) + mu
125823
def MultivariateGaussian(mu: vertex_constructor_param_types, covariance: vertex_constructor_param_types, label: Optional[str]=None) -> Vertex:
    
    return Double(context.jvm_view().MultivariateGaussianVertex, label, cast_to_double_vertex(mu), cast_to_double_vertex(covariance))
1355879
def sin_fisher(y,k):
    
    return 1/np.sqrt(1-y**2) * (k/(np.sinh(k)) * y * (np.cosh(k*np.sqrt(1-y**2))))
738702
def sde(self):
        
        variance = float(self.variance.values)
        lengthscale = float(self.lengthscale)

        F  = np.array(((-1.0/lengthscale,),))
        L  = np.array(((1.0,),))
        Qc = np.array( ((2.0*variance/lengthscale,),) )
        H = np.array(((1.0,),))
        Pinf = np.array(((variance,),))
        P0 = Pinf.copy()

        dF = np.zeros((1,1,2));
        dQc = np.zeros((1,1,2));
        dPinf = np.zeros((1,1,2));

        dF[:,:,0] = 0.0
        dF[:,:,1] = 1.0/lengthscale**2

        dQc[:,:,0] = 2.0/lengthscale
        dQc[:,:,1] = -2.0*variance/lengthscale**2

        dPinf[:,:,0] = 1.0
        dPinf[:,:,1] = 0.0

        dP0 = dPinf.copy()

        return (F, L, Qc, H, Pinf, P0, dF, dQc, dPinf, dP0)
411808
def obfn_dfd(self):
        
        """

        return 0.5*np.linalg.norm((self.D.dot(self.obfn_fvar()) - self.S))**2
365773
def R_r(self, r):
        
        phi = np.random.uniform(0, 2*np.pi)
        theta = np.random.uniform(0, np.pi)
        x = r * np.sin(theta) * np.cos(phi)
        y = r * np.sin(theta) * np.sin(phi)
        R = np.sqrt(x**2 + y**2)
        return R, x, y
571925
function randomAxis(v) {
    v = v || new Vector3();

    v.x = Math$1.randFloatSpread(2.0);
    v.y = Math$1.randFloatSpread(2.0);
    v.z = Math$1.randFloatSpread(2.0);
    v.normalize();

    return v;
  }
1343334
private RandomVariableInterface[] getBasisFunctions(RandomVariableInterface underlying) {
		double min = underlying.getMin();
		double max = underlying.getMax();

		ArrayList<RandomVariableInterface> basisFunctionList = new ArrayList<RandomVariableInterface>();
		double[] discretization = (new TimeDiscretization(min, numberOfBins, (max-min)/numberOfBins)).getAsDoubleArray();
		for(double discretizationStep : discretization) {
			RandomVariableInterface indicator = underlying.barrier(underlying.sub(discretizationStep), new RandomVariable(1.0), 0.0);
			basisFunctionList.add(indicator);
		}

		return basisFunctionList.toArray(new RandomVariableInterface[0]);
	}
109209
def posterior_covariance_between_points(self, X1, X2):
        
        return self.posterior.covariance_between_points(self.kern, self.X, X1, X2)
742488
def rand(n, d=None, r=2, samplefunc=_np.random.randn):
    
    n0 = _np.asanyarray(n, dtype=_np.int32)
    r0 = _np.asanyarray(r, dtype=_np.int32)
    if d is None:
        d = n.size
    if n0.size is 1:
        n0 = _np.ones((d,), dtype=_np.int32) * n0
    if r0.size is 1:
        r0 = _np.ones((d + 1,), dtype=_np.int32) * r0
        r0[0] = 1
        r0[d] = 1
    c = _vector.vector()
    c.d = d
    c.n = n0
    c.r = r0
    c.get_ps()
    c.core = samplefunc(c.ps[d] - 1)
    return c