def gt21_02(x):
''' ground truth for 2nd taylor of fexpr2_01. '''
fexpr2_01 = make_prod(make_pwr('x', 1.0), make_e_expr(make_pwr('x', 1.0)))
f0 = tof(fexpr2_01)
f1 = tof(deriv(fexpr2_01))
f2 = tof(deriv(deriv(fexpr2_01)))
return f0(2.0) + f1(2.0) * (x - 2.0) + (f2(2.0) / 2) * (x - 2.0)**2
def problem_2_deriv():
fexpr = make_prod(make_pwr('t', 2.0), make_ln(make_pwr('t', 1.0)))
print(fexpr)
dv = deriv(fexpr)
print(dv)
second_dv = deriv(dv)
tof_second = tof(second_dv)
print(tof_second(1.0))
def problem_1_deriv(): # still has problems
# f(x) =(x+1)(2x+1)(3x+1) /(4x+1)^.5
fex1 = make_plus(make_pwr('x', 1.0), const(1.0))
fex2 = make_plus(make_prod(const(2.0), make_pwr('x', 1.0)), const(1.0))
fex3 = make_plus(make_prod(const(3.0), make_pwr('x', 1.0)), const(1.0))
fex4 = make_prod(fex1, fex2)
fex5 = make_prod(fex4, fex3)
fex6 = make_pwr_expr(
make_plus(make_prod(const(4.0), make_pwr('x', 1.0)), const(1.0)), 0.5)
fex = make_quot(fex5, fex6)
print(fex)
drv = deriv(fex)
print('drv: ', drv)
drvf = tof(drv)
def gt_drvf(x):
n = (60.0 * x**3) + (84 * x**2) + 34 * x + 4
d = (4 * x + 1)**(3 / 2)
return n / d
for i in range(1, 10):
print(drvf(i), gt_drvf(i))
assert abs(gt_drvf(i) - drvf(i)) <= 0.001
assert drv is not None
print(drv)
# zeros = find_poly_2_zeros(drv)
# print(zeros)
f1 = tof(fex)
f2 = tof(deriv(fex))
xvals = np.linspace(1, 5, 10000)
yvals1 = np.array([f1(x) for x in xvals])
yvals2 = np.array([f2(x) for x in xvals])
fig1 = plt.figure(1)
fig1.suptitle('Graph')
plt.xlabel('x')
plt.ylabel('y')
plt.ylim()
plt.xlim()
plt.grid()
plt.plot(xvals, yvals1, label=fex.__str__(), c='r')
plt.plot(xvals, yvals2, label=deriv(fex).__str__(), c='g')
plt.legend(loc='best')
plt.show()
def get_zeros(self, rms2, interp):
n_elements = len(
self.velocity
) * interp #number of elements of the interpolated profile
velocity_min = min(self.velocity)
velocity_max = max(self.velocity)
velocity_fino = (velocity_min + (velocity_max - velocity_min) *
numpy.arange(n_elements) / n_elements)
ind = []
perfil_fino = numpy.interp(velocity_fino, self.velocity,
self.intensity)
deriv1 = deriv.deriv(self.intensity)
deriv2_nointerpol = deriv.deriv(self.velocity, deriv1)
deriv2 = numpy.interp(velocity_fino, self.velocity, deriv2_nointerpol)
self.cont = 0
for i in range(n_elements - 1):
signo = deriv2[i] * deriv2[i + 1]
if signo < 0:
if not ((self.cont == 0) and (deriv2[i] < deriv2[i + 1])):
#we keep the zero only if it goes from negative to positive, as otherwise it corresponds to a different, undetected peak
if ((((self.cont + 1) % 2) == 0) and (self.cont != 0)):
velant = self.zero[
-1] #busca la velocidad del anterior cero
ind_antvel = numpy.where(
numpy.array(velocity_fino) == velant)[
0] #busca el indice del perfil correspondiente
flux_max = max(
perfil_fino[ind_antvel:i]
) #we estimate the intensity as the highest point between the zeros
if (max(perfil_fino[ind[self.cont - 1]:i]) >= rms2):
#we accept the peak if it is higher thatn twice the rms
self.zero.append(velocity_fino[i])
self.peak.append(flux_max)
ind.append(i)
self.cont = self.cont + 1
else:
#if not, we do not consider it and we must erase the previous zero
self.cont = self.cont - 1
self.zero.remove(self.zero[self.cont])
ind.remove(ind[self.cont])
else:
self.zero.append(velocity_fino[i])
ind.append(i)
self.cont = self.cont + 1
return self.cont
def find_infl_pnts(expr):
drv = deriv(expr)
drv_2 = deriv(drv)
# print 'f`(x) = ', drv
# print 'f``(x) = ', drv_2
zeros = None
try:
zeros = find_poly_1_zeros(drv_2)
# print '1st degree poly'
except Exception:
# print 'not a 1st degree poly'
pass
try:
zeros = find_poly_2_zeros(drv_2)
# print '2nd degree poly'
except Exception:
# print 'not a 2nd degree poly'
pass
if isinstance(zeros, const):
zeros = [zeros]
# print 'zeros:'
# for z in zeros:
# print ':',z.get_val()
f = tof(expr)
f_dp = tof(drv_2)
delta = 0.1
points = [] #will store array of points and if they are max/min
#zeros may be None if no inflection points
if not zeros == None:
for z in zeros:
z_val = f(z.get_val())
z_minus = f_dp(z.get_val() - delta)
z_plus = f_dp(z.get_val() + delta)
if z_minus < 0 and z_plus > 0:
points.append(point2d(z, const(z_val)))
if z_minus > 0 and z_plus < 0:
points.append(point2d(z, const(z_val)))
else:
return None
if points == []:
return None
else:
# print points
return points
def find_infl_pnts(expr):
deriv1 = deriv(expr)
deriv2 = deriv(deriv1)
zero = find_poly_1_zeros(deriv2)
func = tof(expr)
answers = abs(func(zero.get_val()) - 0.0)
# add answers to iflection points
inflpoints = [answers]
return inflpoints
def plot_spread_of_disease(p, t0, p0, t1, p1, tl, tu):
assert isinstance(p, const) and isinstance(t0, const)
assert isinstance(p0, const) and isinstance(t1, const)
rt = spread_of_disease_model(p, t0, p0, t1, p1)
rt_tof = tof(rt)
derv_rt = deriv(rt)
derv_tof = tof(derv_rt)
xvals = np.linspace(tl.get_val(), tu.get_val(), 10000)
yvals1 = np.array([rt_tof(x) for x in xvals])
xvals2 = np.linspace(tl.get_val(), tu.get_val(), 10000)
yvals2 = np.array([derv_tof(x) for x in xvals])
fig1 = plt.figure(1)
fig1.suptitle('Spread of Disease')
plt.xlabel('t')
plt.ylabel('sdf and dsdf')
plt.ylim([0, 100000])
plt.xlim([tl.get_val(), tu.get_val()])
plt.grid()
plt.plot(xvals, yvals1, label='sdf', c='r')
plt.plot(xvals2, yvals2, label='dsdf', c='b')
plt.legend(loc='best')
plt.show()
def plot_retention(lmbda, a, t0, t1):
assert isinstance(lmbda, const)
assert isinstance(a, const)
assert isinstance(t0, const)
assert isinstance(t1, const)
rt = percent_retention_model(lmbda, a)
rt_fn = tof(rt)
derv_rt = deriv(rt)
derv_tof = tof(derv_rt)
xvals = np.linspace(t0.get_val(), t1.get_val(), 10000)
yvals1 = np.array([rt_fn(x) for x in xvals])
xvals2 = np.linspace(t0.get_val(), t1.get_val(), 10000)
yvals2 = np.array([derv_tof(x) for x in xvals])
fig1 = plt.figure(1)
fig1.suptitle('Ebbinghaus Model of Forgetting')
plt.xlabel('t')
plt.ylabel('prf and dprf')
plt.ylim([-20, 100])
plt.xlim([t0.get_val(), t1.get_val()])
plt.grid()
plt.plot(xvals, yvals1, label='prf', c='r')
plt.plot(xvals2, yvals2, label='dprf', c='b')
plt.legend(loc='best')
plt.show()
def plot_spread_of_news(p, k, tl, tu):
assert isinstance(p, const) and isinstance(k, const)
assert isinstance(tl, const) and isinstance(tu, const)
nm = spread_of_news_model(p, k)
nm_tof = tof(nm)
deriv_nm = deriv(nm)
deriv_nm_tof = tof(deriv_nm)
xvals = np.linspace(tl.get_val(), tu.get_val(), 10000)
yvals1 = np.array([nm_tof(x) for x in xvals])
xvals2 = np.linspace(tl.get_val(), tu.get_val(), 10000)
yvals2 = np.array([deriv_nm_tof(x) for x in xvals])
fig1 = plt.figure(1)
fig1.suptitle('Spread of News')
plt.xlabel('t')
plt.ylabel('snf and dsnf')
plt.ylim([-2000, 52000])
plt.xlim([tl.get_val(), tu.get_val()])
plt.grid()
plt.plot(xvals, yvals1, label='snf', c='r')
plt.plot(xvals2, yvals2, label='dsnf', c='b')
plt.legend(loc='best')
plt.show()
def plot_plant_growth(m, t0, h0, t1, h1, tl, tu):
assert isinstance(m, const) and isinstance(t1, const)
assert isinstance(t0, const) and isinstance(h0, const)
assert isinstance(h1, const) and isinstance(tl, const)
assert isinstance(tu, const)
pg = plant_growth_model(m, t0, h0, t1, h1)
pg_tof = tof(pg)
derv_pg = deriv(pg)
derv_tof = tof(derv_pg)
xvals = np.linspace(tl.get_val() - t0.get_val(), tu.get_val(), 10000)
yvals1 = np.array([pg_tof(x) for x in xvals])
xvals2 = np.linspace(tl.get_val() - t0.get_val(), tu.get_val(), 10000)
yvals2 = np.array([derv_tof(x) for x in xvals2])
fig1 = plt.figure(1)
fig1.suptitle('Plant Growth')
plt.xlabel('t')
plt.ylabel('pgf and dpgf')
plt.ylim([-2, 58])
plt.xlim([tl.get_val() - t0.get_val(), tu.get_val()])
plt.grid()
plt.plot(xvals, yvals1, label='pgf', c='r')
plt.plot(xvals2, yvals2, label='dpgf', c='b')
plt.legend(loc='best')
plt.show()
def test_10(self):
#(3x+2)^4
print("****Unit Test 10********")
fex0 = make_prod(make_const(3.0), make_pwr('x', 1.0))
fex1 = make_plus(fex0, make_const(2.0))
fex = make_pwr_expr(fex1, 4.0)
print(fex)
afex = antideriv(fex)
assert not afex is None
print(afex)
afexf = tof(afex)
err = 0.0001
def gt(x):
return (1.0 / 15) * ((3 * x + 2.0)**5)
for i in range(1, 10):
assert abs(afexf(i) - gt(i)) <= err
fexf = tof(fex)
assert not fexf is None
fex2 = deriv(afex)
assert not fex2 is None
print(fex2)
fex2f = tof(fex2)
assert not fex2f is None
for i in range(1, 1000):
assert abs(fexf(i) - fex2f(i)) <= err
print('Test 10:pass')
def plot_plant_growth(m, t1, x1, t2, x2, tl, tu):
assert isinstance(m, const) and isinstance(t1, const)
assert isinstance(x1, const) and isinstance(t2, const)
assert isinstance(x2, const) and isinstance(tl, const)
assert isinstance(tu, const)
expr = plant_growth_model(m, t1, x1, t2, x2)
growth = tof(expr)
growth_deriv = tof(deriv(expr))
min = tl.get_val()
max = tu.get_val()
xvals = np.linspace(min, max, 10000)
yvals1 = np.array([growth(x) for x in xvals])
yvals2 = np.array([growth_deriv(x) for x in xvals])
fig1 = plt.figure(1)
fig1.suptitle("Plant Growth")
plt.xlabel('t')
plt.ylabel('pgf and dgdf')
ymax = max(np.max(yvals1), np.max(yvals2))
ymin = min(np.min(yvals1), np.min(yvals2))
plt.ylim([ymin, ymax])
plt.xlim([min, max])
plt.grid()
plt.plot(xvals, yvals1, label='pgf', c='r')
plt.plot(xvals, yvals2, label='dgdf', c='b')
plt.legend(loc='best')
plt.show()
def test_08(self):
#(5x-7)^-2 => -1/5 * (5x-7)^-1
print("****Unit Test 08********")
fex1 = make_plus(make_prod(make_const(5.0), make_pwr('x', 1.0)),
make_const(-7.0))
fex = make_pwr_expr(fex1, -2.0)
print(fex)
afex = antideriv(fex)
assert not afex is None
print("antideriv: ", afex)
afexf = tof(afex)
err = 0.0001
def gt(x):
return (-1.0 / 5.0) * ((5 * x - 7.0)**-1)
for i in range(1, 100):
assert abs(afexf(i) - gt(i)) <= err
fexf = tof(fex)
assert not fexf is None
fex2 = deriv(afex)
assert not fex2 is None
print("deriv fex2: ", fex2)
fex2f = tof(fex2)
assert not fex2f is None
for i in range(1, 100):
print(fexf(i), " ", fex2f(i))
assert abs(fexf(i) - fex2f(i)) <= err
print('Test 08:pass')
def test_assign_03_prob_01_ut_06(self):
print('\n***** Assign 03: Problem 01: Unit Test 06 *****')
e1 = make_prod(make_const(2.0), make_pwr('x', 4.0))
e2 = make_prod(make_const(-1.0), make_pwr('x', 1.0))
e3 = make_plus(e1, e2)
e4 = make_plus(e3, make_const(1.0))
e5 = make_prod(make_const(-1.0), make_pwr('x', 5.0))
e6 = make_prod(make_const(0.0), make_pwr('x', 4.0))
e7 = make_plus(e5, e6)
e8 = make_prod(make_const(0.0), make_pwr('x', 3.0))
e9 = make_plus(e7, e8)
e10 = make_prod(make_const(0.0), make_pwr('x', 2.0))
e11 = make_plus(e9, e10)
e12 = make_prod(make_const(0.0), make_pwr('x', 1.0))
e13 = make_plus(e11, e12)
e14 = make_plus(e13, make_const(1.0))
e15 = make_prod(e4, e14)
print('-- function expression is:\n')
print(e15)
drv = deriv(e15)
assert not drv is None
print('\n-- derivative is:\n')
print(drv)
e15f = tof(drv)
assert not e15f is None
gt = lambda x: -18.0 * (x**8) + 6.0 * (x**5) - 5.0 * (x**4) + 8.0 * (
x**3) - 1.0
err = 0.00001
print('\n--comparison with ground truth:\n')
for i in range(10):
#print(e15f(i), gt(i))
assert abs(e15f(i) - gt(i)) <= err
print('Assign 03: Problem 01: Unit Test 06: pass')
def problem_3_tangent():
fex = make_e_expr(make_pwr('x', 1.0))
print("f(x)= ", fex)
drv = deriv(fex)
print("f'(x)= ", drv)
drvf = tof(drv)
print("f'(-1)= ", drvf(-1))
def test_assign_03_prob_01_ut_05(self):
print('\n***** Assign 03: Problem 01: Unit Test 05 *****')
e1 = make_plus(make_pwr('x', 1.0), make_const(1.0))
e2 = make_pwr('x', 3.0)
e3 = make_prod(make_const(0.0), make_pwr('x', 2.0))
e4 = make_plus(e2, e3)
e5 = make_prod(make_const(5.0), make_pwr('x', 1.0))
e6 = make_plus(e4, e5)
e7 = make_plus(e6, make_const(2.0))
e8 = make_prod(e1, e7)
# 1) print the expression we just constructed
print('-- function expression is:\n')
print(e8)
# 2) differentiate and make sure that it not None
drv = deriv(e8)
assert not drv is None
print('\n-- derivative is:\n')
print(e8)
# 3) convert drv into a function
e8f = tof(drv)
assert not e8f is None
# steps 2) and 3) can be combined into tof(deriv(e6)).
# 4) construct the ground truth function
gt = lambda x: 4.0 * (x**3) + 3 * (x**2) + 10.0 * x + 7.0
# 5) compare the ground gruth with what we got in
# step 3) on an appropriate number range.
print('\n--comparison with ground truth:\n')
err = 0.00001
for i in range(15):
#print(e8f(i), gt(i))
assert abs(e8f(i) - gt(i)) <= err
print('Assign 03: Problem 01: Unit Test 05: pass')
def loc_xtrm_1st_drv_test(expr):
#step 1 take derivative
myderiv = deriv(expr)
#step2 solve for x
zeros = find_poly_2_zeros(myderiv)
# for c in zeros:
# print c
pf = tof(expr)
extremas = []
for c in zeros:
yval = abs(pf(c.get_val()) - 0.0)
if (pf(c.get_val()) - 1 > 0 & pf(c.get_val()) + 1 < 0):
extremas.append("min", point2d(c.get_val(), yval))
else:
extremas.append("max", point2d(c.get_val(), yval))
return extremas
def maximize_revenue(
dmnd_eq,
constraint=lambda x: x >= 0): #only works on linear demand eqs
rev = incrementPolyPwrs(dmnd_eq, 1)
rev_drv = deriv(rev)
# print 'eq:',dmnd_eq
# print 'rev',rev
# print 'rev deriv',rev_drv
rev_drv_f = tof(rev_drv)
dmnd_f = tof(dmnd_eq)
rev_f = tof(rev)
# print 'f(20)',dmnd_f(20)
# print 'R(20)',rev_f(20)
# print 'R`(20)',rev_drv_f(20)
xtrm = loc_xtrm_2nd_drv_test(rev)
for val in xtrm:
# print val[0]
# print val[1]
x = val[1].get_x().get_val()
y = val[1].get_y().get_val()
if (val[0] == 'max' and constraint(x)):
num_units = const(x)
revenue = const(y)
price = const(dmnd_f(x))
return (num_units, revenue, price)
def plot_spread_of_news(p, k, tl, tu):
assert isinstance(p, const) and isinstance(k, const)
assert isinstance(tl, const) and isinstance(tu, const)
expr = spread_of_news_model(p, k)
news = tof(expr)
expr_deriv = deriv(expr)
news_deriv = tof(expr_deriv)
min = tl.get_val()
max = tu.get_val()
xvals = np.linspace(min, max, 10000)
yvals1 = np.array([news(x) for x in xvals])
yvals2 = np.array([news_deriv(x) for x in xvals])
fig1 = plt.figure(1)
fig1.suptitle("Spread of News")
plt.xlabel('t')
plt.ylabel('snf and dsnf')
ymax = max(np.max(yvals1), np.max(yvals2))
ymin = min(np.min(yvals1), np.min(yvals2))
plt.ylim([ymin, ymax])
plt.xlim([min, max])
plt.grid()
plt.plot(xvals, yvals1, label='snf', c='r')
plt.plot(xvals, yvals2, label='dnsf', c='b')
plt.legend(loc='best')
plt.show()
if __name__ == '__main__':
print("test 1: ")
fex = percent_retention_model(make_const(1.0), make_const(1.0))
def plot_spread_of_disease(p, t0, p0, t1, p1, tl, tu):
assert isinstance(p, const) and isinstance(t0, const)
assert isinstance(p0, const) and isinstance(t1, const)
expr = spread_of_disease_model(p, t0, p0, t1, p1)
disease = tof(expr)
disease_derive = tof(deriv(expr))
min = tl.get_val()
max = tu.get_val()
xvals = np.linspace(min, max, 10000)
yvals1 = np.array([disease(x) for x in xvals])
yvals2 = np.array([disease_derive(x) for x in xvals])
fig1 = plt.figure(1)
fig1.suptitle("Spread of Disease")
plt.xlabel('t')
plt.ylabel('sdf and dsdf')
ymax = max(np.max(yvals1), np.max(yvals2))
ymin = min(np.min(yvals1), np.min(yvals2))
plt.ylim([ymin, ymax])
plt.xlim([min, max])
plt.grid()
plt.plot(xvals, yvals1, label='sdf', c='r')
plt.plot(xvals, yvals2, label='dsdf', c='b')
plt.legend(loc='best')
plt.show()
def test_09(self):
#3*(x+2)^-1 => 3*ln|x+2|
print("****Unit Test 09********")
fex0 = make_plus(make_pwr('x', 1.0), make_const(2.0))
fex1 = make_pwr_expr(fex0, -1.0)
fex = make_prod(make_const(3.0), fex1)
print(fex)
afex = antideriv(fex)
print("antideriv: ", afex)
err = 0.0001
afexf = tof(afex)
def gt(x):
return 3.0 * math.log(abs(2.0 + x), math.e)
for i in range(1, 101):
assert abs(afexf(i) - gt(i)) <= err
assert not afex is None
print(afex)
fexf = tof(fex)
assert not fexf is None
fex2 = deriv(afex)
assert not fex2 is None
print(fex2)
fex2f = tof(fex2)
assert not fex2f is None
for i in range(1, 1000):
assert abs(fexf(i) - fex2f(i)) <= err
print('Test 09:pass')
def test_03(self):
#(x+11)/(x-3) ^3
print('\n***** Test 03 ***********')
q = make_quot(make_plus(make_pwr('x', 1.0), make_const(11.0)),
make_plus(make_pwr('x', 1.0), make_const(-3.0)))
pex = make_pwr_expr(q, 3.0)
print('-- function expression is:\n')
print(pex)
pexdrv = deriv(pex)
assert not pexdrv is None
print('\n - - derivative is:\n')
print(pexdrv)
pexdrvf = tof(pexdrv)
assert not pexdrvf is None
gt = lambda x: -42.0 * (((x + 11.0)**2) / ((x - 3.0)**4))
err = 0.00001
print('\n - -comparison with ground truth:\n')
for i in range(10):
if i != 3.0:
print(pexdrvf(i), gt(i))
#print("gt: ",gt(0))
assert abs(pexdrvf(i) - gt(i)) <= err
#print("pexdrvf(0): ",pexdrvf(0),"gt(i): ", gt(0))
print('Test 03:pass')
def test_assign_03_prob_01_ut_04(self):
print('\n***** Assign 03: Problem 01: Unit Test 04 *****')
e1 = make_pwr('x', 2.0)
e2 = make_plus(e1, make_prod(make_const(0.0), make_pwr('x', 1.0)))
e3 = make_plus(e2, make_const(-1.0))
e4 = make_pwr_expr(e3, 4.0)
e5 = make_pwr('x', 2.0)
e6 = make_plus(e5, make_prod(make_const(0.0), make_pwr('x', 1.0)))
e7 = make_plus(e6, make_const(1.0))
e8 = make_pwr_expr(e7, 5.0)
e9 = make_prod(e4, e8)
print(e9)
e9f = tof(deriv(e9))
assert not e9f is None
err = 0.000001
def drvf(x):
return 2 * x * ((x**2 - 1.0)**3) * (
(x**2 + 1.0)**4) * (9 * x**2 - 1.0)
for i in range(10):
#print(e9f(i), drvf(i))
assert abs(e9f(i) - drvf(i)) <= err
print('Assign 03: Problem 01: Unit Test 04: pass')
def find_infl_pnts(expr):
#find the second derivative
second_drv = deriv(deriv(expr))
degree = findDegree(second_drv)
expr_tof = tof(expr)
inflection_points = []
if degree == 2:
zeros = find_poly_2_zeros(second_drv)
for x in zeros:
y = expr_tof(x.get_val())
inflection_points.append(make_point2d(x.get_val() , y))
else:
x = find_poly_1_zeros(second_drv)
y = expr_tof(x.get_val())
inflection_points.append(make_point2d(x.get_val(), y))
return inflection_points
def max_profit(cost_fun, rev_fun):
profit = plus(cost_fun, prod(rev_fun,-1))
profit_deriv = deriv(profit)
zeroes = find_poly_2_zeros(profit_deriv)
return max(zeroes)
def newton_raphson(poly_fexpr, g, n):
tof_expr = tof(poly_fexpr)
deriv_expr = tof(deriv(poly_fexpr))
for i in range(n.get_val()):
x = g.get_val() - (tof_expr(g.get_val()) / deriv_expr(g.get_val()))
g = const(x)
return g
def demand_elasticity(demand_eq, price):
assert isinstance(price, const)
# E(p) = (-p*f`(p))/f(p)
f = tof(demand_eq)
drv = deriv(demand_eq)
fprime = tof(drv)
p = price.get_val()
return const((-p * fprime(p)) / f(p))
def getCarleman(f, size):
#Gets the carlemanmatrix of a function
result = []
for m in range(0, size):
result.append([])
for n in range(0, size):
result[m].append(
deriv.deriv(lambda x: pow(f(x), m), 0, n) / fac(n))
return np.matrix(result)
def graph_drv(fexpr, xlim, ylim):
f1 = tof(fexpr)
f2 = tof(deriv(fexpr))
xvals = np.linspace(-2, 2, 10000)
yvals1 = np.array([f1(x) for x in xvals])
yvals2 = np.array([f2(x) for x in xvals])
fig1 = plt.figure(1)
fig1.suptitle('Graph')
plt.xlabel('x')
plt.ylabel('y')
plt.ylim()
plt.xlim()
plt.grid()
plt.plot(xvals, yvals1, label=fexpr.__str__(), c='r')
plt.plot(xvals, yvals2, label=deriv(fexpr).__str__(), c='g')
plt.legend(loc='best')
plt.show()
def demand_elasticity(demand_eq, price):
assert isinstance(price, const)
fx_drv = tof(deriv(demand_eq))
fx = tof(demand_eq)
p = price.get_val()
n = (-1.0 * p) * fx_drv(p)
d = fx(p)
return n / d
def get_zeros(self,rms2,interp):
n_elements=len(self.velocity)*interp#number of elements of the interpolated profile
velocity_min=min(self.velocity)
velocity_max=max(self.velocity)
velocity_fino=(velocity_min+(velocity_max-velocity_min)*numpy.arange(n_elements)/n_elements)
ind=[]
perfil_fino=numpy.interp(velocity_fino,self.velocity,self.intensity)
deriv1=deriv.deriv(self.intensity)
deriv2_nointerpol=deriv.deriv(self.velocity,deriv1)
deriv2=numpy.interp(velocity_fino,self.velocity,deriv2_nointerpol)
self.cont=0
for i in range(n_elements-1):
signo=deriv2[i]*deriv2[i+1]
if signo < 0:
if not((self.cont== 0) and (deriv2[i] < deriv2[i+1])):
#we keep the zero only if it goes from negative to positive, as otherwise it corresponds to a different, undetected peak
if ((((self.cont+1)%2) == 0) and (self.cont != 0)):
velant=self.zero[-1]#busca la velocidad del anterior cero
ind_antvel=numpy.where(numpy.array(velocity_fino)==velant)[0]#busca el indice del perfil correspondiente
flux_max=max(perfil_fino[ind_antvel:i])#we estimate the intensity as the highest point between the zeros
if (max(perfil_fino[ind[self.cont-1]:i]) >= rms2):
#we accept the peak if it is higher thatn twice the rms
self.zero.append(velocity_fino[i])
self.peak.append(flux_max)
ind.append(i)
self.cont=self.cont+1
else:
#if not, we do not consider it and we must erase the previous zero
self.cont=self.cont-1
self.zero.remove(self.zero[self.cont])
ind.remove(ind[self.cont])
else:
self.zero.append(velocity_fino[i])
ind.append(i)
self.cont=self.cont+1
return self.cont
def lk(im1, im2, i, j, window_size):
fx, fy, ft = deriv.deriv(im1, im2)
halfWindow = np.floor(window_size / 2)
curFx = fx[i - halfWindow - 1 : i + halfWindow, j - halfWindow - 1 : j + halfWindow]
curFy = fy[i - halfWindow - 1 : i + halfWindow, j - halfWindow - 1 : j + halfWindow]
curFt = ft[i - halfWindow - 1 : i + halfWindow, j - halfWindow - 1 : j + halfWindow]
curFx = curFx.T
curFy = curFy.T
curFt = curFt.T
curFx = curFx.flatten(order="F")
curFy = curFy.flatten(order="F")
curFt = -curFt.flatten(order="F")
A = np.vstack((curFx, curFy)).T
U = np.dot(np.dot(lin.pinv(np.dot(A.T, A)), A.T), curFt)
return U[0], U[1]
def lk(g, im1, im2, i_s, j_s, window_size):
fx, fy, ft = deriv.deriv(im1, im2, g)
halfWindow = np.floor(window_size/2)
res = []
for i,j in itertools.izip(i_s,j_s):
curFx = fx[i-halfWindow-1:i+halfWindow,
j-halfWindow-1:j+halfWindow]
curFy = fy[i-halfWindow-1:i+halfWindow,
j-halfWindow-1:j+halfWindow]
curFt = ft[i-halfWindow-1:i+halfWindow,
j-halfWindow-1:j+halfWindow]
curFx = curFx.T
curFy = curFy.T
curFt = curFt.T
curFx = curFx.flatten(order='F')
curFy = curFy.flatten(order='F')
curFt = -curFt.flatten(order='F')
A = np.vstack((curFx, curFy)).T
U = np.dot(np.dot(lin.pinv(np.dot(A.T,A)),A.T),curFt)
res.append((i,j,U[0],U[1]))
return res
def lk(im1, im2, window_size) :
u = np.zeros(im1.shape)
v = np.zeros(im2.shape)
fx, fy, ft = deriv.deriv(im1, im2)
halfWindow = np.floor(window_size/2)
for i in range(int(halfWindow+1),int(fx.shape[0]-halfWindow)):
for j in range(int(halfWindow+1),int(fx.shape[1]-halfWindow)):
curFx = fx[i-halfWindow-1:i+halfWindow,
j-halfWindow-1:j+halfWindow]
curFy = fy[i-halfWindow-1:i+halfWindow,
j-halfWindow-1:j+halfWindow]
curFt = ft[i-halfWindow-1:i+halfWindow,
j-halfWindow-1:j+halfWindow]
curFx = curFx.flatten()
curFy = curFy.flatten()
curFt = -curFt.flatten()
A = np.vstack((curFx, curFy)).T
U = np.dot(np.dot(lin.pinv(np.dot(A.T,A)),A.T),curFt)
u[i,j] = U[0]
v[i,j] = U[1]
return (u,v)
