parameters: (func, a, b, args=(), tol=1.49e-8, rtol=1.49e-8, maxiter=50,
                 vec_func=True, miniter=1)
return_statement: return val, err
docstring: Compute a definite integral using fixed-tolerance Gaussian quadrature.
  
      Integrate `func` from `a` to `b` using Gaussian quadrature
      with absolute tolerance `tol`.
  
      Parameters
      ----------
      func : function
          A Python function or method to integrate.
      a : float
          Lower limit of integration.
      b : float
          Upper limit of integration.
      args : tuple, optional
          Extra arguments to pass to function.
      tol, rtol : float, optional
          Iteration stops when error between last two iterates is less than
          `tol` OR the relative change is less than `rtol`.
      maxiter : int, optional
          Maximum order of Gaussian quadrature.
      vec_func : bool, optional
          True or False if func handles arrays as arguments (is
          a "vector" function). Default is True.
      miniter : int, optional
          Minimum order of Gaussian quadrature.
  
      Returns
      -------
      val : float
          Gaussian quadrature approximation (within tolerance) to integral.
      err : float
          Difference between last two estimates of the integral.
  
      See also
      --------
      romberg: adaptive Romberg quadrature
      fixed_quad: fixed-order Gaussian quadrature
      quad: adaptive quadrature using QUADPACK
      dblquad: double integrals
      tplquad: triple integrals
      romb: integrator for sampled data
      simps: integrator for sampled data
      cumtrapz: cumulative integration for sampled data
      ode: ODE integrator
      odeint: ODE integrator
docstring_summary: Compute a definite integral using fixed-tolerance Gaussian quadrature.
docstring_tokens: Compute a definite integral using fixed - tolerance Gaussian quadrature .
function: def quadrature(func, a, b, args=(), tol=1.49e-8, rtol=1.49e-8, maxiter=50,
                 vec_func=True, miniter=1):
      """
      Compute a definite integral using fixed-tolerance Gaussian quadrature.
  
      Integrate `func` from `a` to `b` using Gaussian quadrature
      with absolute tolerance `tol`.
  
      Parameters
      ----------
      func : function
          A Python function or method to integrate.
      a : float
          Lower limit of integration.
      b : float
          Upper limit of integration.
      args : tuple, optional
          Extra arguments to pass to function.
      tol, rtol : float, optional
          Iteration stops when error between last two iterates is less than
          `tol` OR the relative change is less than `rtol`.
      maxiter : int, optional
          Maximum order of Gaussian quadrature.
      vec_func : bool, optional
          True or False if func handles arrays as arguments (is
          a "vector" function). Default is True.
      miniter : int, optional
          Minimum order of Gaussian quadrature.
  
      Returns
      -------
      val : float
          Gaussian quadrature approximation (within tolerance) to integral.
      err : float
          Difference between last two estimates of the integral.
  
      See also
      --------
      romberg: adaptive Romberg quadrature
      fixed_quad: fixed-order Gaussian quadrature
      quad: adaptive quadrature using QUADPACK
      dblquad: double integrals
      tplquad: triple integrals
      romb: integrator for sampled data
      simps: integrator for sampled data
      cumtrapz: cumulative integration for sampled data
      ode: ODE integrator
      odeint: ODE integrator
  
      """
      if not isinstance(args, tuple):
          args = (args,)
      vfunc = vectorize1(func, args, vec_func=vec_func)
      val = np.inf
      err = np.inf
      maxiter = max(miniter+1, maxiter)
      for n in xrange(miniter, maxiter+1):
          newval = fixed_quad(vfunc, a, b, (), n)[0]
          err = abs(newval-val)
          val = newval
  
          if err < tol or err < rtol*abs(val):
              break
      else:
          warnings.warn(
              "maxiter (%d) exceeded. Latest difference = %e" % (maxiter, err),
              AccuracyWarning)
      return val, err
function_tokens: def quadrature ( func , a , b , args = ( ) , tol = 1.49e-8 , rtol = 1.49e-8 , maxiter = 50 , vec_func = True , miniter = 1 ) : if not isinstance ( args , tuple ) : args = ( args , ) vfunc = vectorize1 ( func , args , vec_func = vec_func ) val = np . inf err = np . inf maxiter = max ( miniter + 1 , maxiter ) for n in xrange ( miniter , maxiter + 1 ) : newval = fixed_quad ( vfunc , a , b , ( ) , n ) [ 0 ] err = abs ( newval - val ) val = newval if err < tol or err < rtol * abs ( val ) : break else : warnings . warn ( "maxiter (%d) exceeded. Latest difference = %e" % ( maxiter , err ) , AccuracyWarning ) return val , err