Merge pull request scipy#9377 from BH4/add-examples-integrate

DOC: Add examples integrate: fixed_quad and quadrature

scipy/integrate/quadrature.py

@@ -77,6 +77,24 @@ def fixed_quad(func, a, b, args=(), n=5):
     ode : ODE integrator
     odeint : ODE integrator
 
+    Examples
+    --------
+    >>> from scipy import integrate
+    >>> f = lambda x: x**8
+    >>> integrate.fixed_quad(f, 0.0, 1.0, n=4)
+    (0.1110884353741496, None)
+    >>> integrate.fixed_quad(f, 0.0, 1.0, n=5)
+    (0.11111111111111102, None)
+    >>> print(1/9.0)  # analytical result
+    0.1111111111111111
+
+    >>> integrate.fixed_quad(np.cos, 0.0, np.pi/2, n=4)
+    (0.9999999771971152, None)
+    >>> integrate.fixed_quad(np.cos, 0.0, np.pi/2, n=5)
+    (1.000000000039565, None)
+    >>> np.sin(np.pi/2)-np.sin(0)  # analytical result
+    1.0
+
     """
     x, w = _cached_roots_legendre(n)
     x = np.real(x)
@@ -181,6 +199,20 @@ def quadrature(func, a, b, args=(), tol=1.49e-8, rtol=1.49e-8, maxiter=50,
     ode: ODE integrator
     odeint: ODE integrator
 
+    Examples
+    --------
+    >>> from scipy import integrate
+    >>> f = lambda x: x**8
+    >>> integrate.quadrature(f, 0.0, 1.0)
+    (0.11111111111111106, 4.163336342344337e-17)
+    >>> print(1/9.0)  # analytical result
+    0.1111111111111111
+
+    >>> integrate.quadrature(np.cos, 0.0, np.pi/2)
+    (0.9999999999999536, 3.9611425250996035e-11)
+    >>> np.sin(np.pi/2)-np.sin(0)  # analytical result
+    1.0
+
     """
     if not isinstance(args, tuple):
         args = (args,)