def compare(hbar=1, k0=1, m=1, r0=1, V0=-1, deg=40, c=10, maxl=10):
an.setparams(hbar, k0, m)
sc.setparams(hbar, k0, m)
sc.setquadparams(deg, c)
print(len(sc.KK))
b = an.box(r0, V0)
V = b.V
f = sc.amplitude_f(V, maxl, isbox=False, r0=0)
fan = b.amplitude_f(maxl)
theta = np.linspace(0, np.pi, 10000)
plt.plot(theta, sc.modsq(f(theta)), theta, sc.modsq(fan(theta)))
print('sc: {}'.format(sc.stot(f) - np.pi * 4 / k0 * np.imag(f(0))))
print('an: {}'.format(sc.stot(fan) - np.pi * 4 / k0 * np.imag(fan(0))))
print('----fl----')
for l in range(maxl + 1):
print('l={}'.format(l))
print('sc: {}'.format(sc.tmp_fl[l]))
print('an: {}'.format(b.f[l]))
print()
plt.xlabel(
'hbar={}, k0={}, m={}, r0={}, V0={}, maxl={}, deg_legendre={}'.format(
hbar, k0, m, r0, V0, maxl, deg))
plt.show()
def degdeg():
r = np.linspace(0, 10, 10000)
th = np.linspace(0, np.pi, 10000)
V = col.shell(2, 1, 5)
plt.plot(r, V(r))
plt.show()
g = an.general(1, 1, 1, V, 10)
fg = g.amplitude_f(10)
sigg = sc.modsq(fg(th))
#b = an.box(1, -1)
#fan = b.amplitude_f(10)
plt.plot(th, sigg, label='pwa')
#plt.plot(th, sc.modsq(fan(th)), label='pwa2')
for deg1 in [20, 30, 40, 60, 80, 100]:
sc.setquadparams(deg=deg1)
f = sc.amplitude_f(V, 10)
sig = sc.modsq(f(th))
err = utils.error(th, sig, sigg)
print('deg: {}, error: {}'.format(deg1, err))
plt.plot(th, sig, label=str(deg1))
plt.legend()
plt.xlabel('theta')
plt.ylabel('differential cross section')
plt.show()
def kkk():
r = np.linspace(0, 10, 10000)
th = np.linspace(0, np.pi, 10000)
V = col.box(-1, 5)
plt.plot(r, V(r))
plt.show()
K_SAMPLE = [0.01, 0.1, 0.5, 1, 10, 20, 50, 100]
for k0 in K_SAMPLE:
g = an.general(1, k0, 1, V, 5)
fg = g.amplitude_f(10)
an.k0 = k0
b = an.box(5, -1)
fan = b.amplitude_f(10)
sc.setquadparams(deg=40)
sc.setparams(k01=k0)
f = sc.amplitude_f(V, 10, isbox=True, r0=5)
q = utils.maxerror(th, fg, f)
#print('maxereror: {}'.format(q))
plt.plot(th, fg(th), th, f(th), th, fan(th))
plt.xlabel(sc.summary())
plt.show()
def a2():
sc.setquadrature(quad='leg')
f = lambda r: np.exp(-r**2)
I = np.sqrt(np.pi) / 2
S = sum(sc.W * f(sc.K))
print(S)
print((S - I) / I)
sc.setquadrature(quad='lag')
S = sum(sc.W * f(sc.K))
print((S - I) / I)
sc.setquadrature(quad='mixed')
sc.setquadparams(c=2, r0=0.2)
S = sum(sc.W * f(sc.K))
print((S - I) / I)
def maxlmaxl():
r = np.linspace(0, 10, 10000)
th = np.linspace(0, np.pi, 10000)
V = col.ring(2, 1, 5)
plt.plot(r, V(r))
plt.show()
g = an.general(1, 1, 1, V, 10)
fg = g.amplitude_f(10)
plt.plot(th, fg(th), label='pwa')
sc.setquadparams(deg=40)
for maxl1 in [5, 10, 15, 20, 40, 60]:
f = sc.amplitude_f(V, maxl1)
plt.plot(th, f(th), label=str(maxl1))
plt.legend()
plt.xlabel('V=ring(2, 1, 5), k=1, deg=40')
plt.show()
def a1():
r = np.linspace(0, 10, 10000)
th = np.linspace(0, np.pi, 10000)
V = col.box(-1, 5)
plt.plot(r, V(r))
plt.show()
g = an.general(1, 50, 1, V, 5)
fg = g.amplitude_f(10)
an.k0 = 50
b = an.box(5, -1)
fan = b.amplitude_f(10)
sc.setquadparams(deg=80)
sc.setparams(k01=50)
f = sc.amplitude_f(V, 10)
plt.plot(th, fg(th), th, f(th), th, fan(th))
plt.xlabel(sc.summary())
plt.show()
def sc_l_deg(hbar=1,
k0=1,
m=1,
V=V_sample,
degs=[30, 40, 50, 60, 70],
c=10,
maxl=10):
an.setparams(hbar, k0, m)
sc.setparams(hbar, k0, m)
theta = np.linspace(0, np.pi, 10000)
b = an.box(5, -1)
for deg in degs:
sc.setquadparams(deg, c)
f = sc.amplitude_f(V, maxl, isbox=True, r0=5)
plt.plot(theta, sc.modsq(f(theta)), label=str(deg))
fan = b.amplitude_f(maxl)
plt.plot(theta, sc.modsq(fan(theta)), label='partial wave')
plt.legend()
plt.xlabel('hbar={}, k0={}, m={}, V={}, maxl={}, degs={}'.format(
hbar, k0, m, 'box(5, -1)', maxl, degs))
plt.show()