def c1(t):
    return np.cos(pi*t*t/2)

def s1(t):
    return np.sin(pi*t*t/2)

def e1(t):
    return np.exp(t*t*pi*1j*0.5)

def fren_cos_int(t):
    z = quadpy.line_segment.integrate(c1,[0.0, t],quadpy.line_segment.GaussPatterson(6))
    if len(np.shape(z))!=0:
        z = z[0,:]
    #z,e = integrate.quad(c1,0,t)
    return z

def fren_sin_int(t):
    z = quadpy.line_segment.integrate(s1,[0.0, t],quadpy.line_segment.GaussPatterson(6))
    if len(np.shape(z))!=0:
        z = z[0,:]
    #z,e = integrate.quad(s1,0,t)
    return z

#page 20 goodman 4th ed.
def ft_chirp(fx,wavel,z,L):
    b = 1/(wavel*z)
    b1 = np.sqrt(2*b)
    a1 = b1 * (L/2 - (fx/b))
    a2 = b1 * (-L/2 - (fx/b))
    if len(np.shape(a1))!= 0 :
        A1 = []
        for i in a1: A1.append([i])
        A1 = np.stack(A1)
    else :
        A1 = a1
    if len(np.shape(a2))!=0:
        A2 = []
        for i in a2: A2.append([i])
        A2 = np.stack(A2)
    else :
        A2 = a2
    z = (fren_cos_int(A1) - fren_cos_int(A2)) + 1j*(fren_sin_int(A1) - fren_sin_int(A2))
    #print(np.shape(A1),np.shape(A2),np.shape(z))
    p = np.exp(-1j*pi*fx*fx/b)*(1/np.sqrt(2*b))
    return z*p