def sin(X):
try:
y = ADnum(np.sin(X.val),
der=np.cos(X.val) * X.der,
ops=(1 - X.counted) * X.ops + 2,
rops=1,
tfops=X.tfops + 2 + X.ins,
trops=X.trops + 2 + 2 * X.ins)
X.counted = 1
y.graph = X.graph
if X not in y.graph:
y.graph[X] = []
y.graph[X].append((y, 'sin', np.cos(X.val)))
return y
except AttributeError:
return np.sin(X)
def tan(X):
try:
y = ADnum(np.tan(X.val),
der=(1 / np.cos(X.val)**2) * X.der,
ops=(1 - X.counted) * X.ops + 4,
rops=3,
tfops=X.tfops + 2 + X.ins,
trops=X.trops + 2 + 2 * X.ins)
X.counted = 1
y.graph = X.graph
if X not in y.graph:
y.graph[X] = []
y.graph[X].append((y, 'tan', (1 / np.cos(X.val))**2))
return y
except AttributeError:
return np.tan(X)
def sqrt(X):
try:
y = ADnum(np.sqrt(X.val),
der=X.der / (2 * np.sqrt(X.val)),
ops=(1 - X.counted) * X.ops + 3,
rops=3,
tfops=X.tfops + 2 + X.ins,
trops=X.trops + 2 + 2 * X.ins)
X.counted = 1
y.graph = X.graph
if X not in y.graph:
y.graph[X] = []
y.graph[X].append((y, 'sqrt', 1 / (2 * np.sqrt(X.val))))
return y
except AttributeError:
return np.sqrt(X)
def arccos(X):
try:
y = ADnum(np.arccos(X.val),
der=-1 / np.sqrt(1 - X.val**2) * X.der,
ops=(1 - X.counted) * X.ops + 5,
rops=4,
tfops=X.tfops + 2 + X.ins,
trops=X.trops + 2 + 2 * X.ins)
X.counted = 1
y.graph = X.graph
if X not in y.graph:
y.graph[X] = []
y.graph[X].append((y, 'arccos', -1 / np.sqrt(1 - X.val**2)))
return y
except AttributeError:
return np.arccos(X)
def csc(X):
try:
y = ADnum(1 / np.sin(X.val),
der=(-1 / np.tan(X.val)) * (1 / np.sin(X.val)) * X.der,
ops=(1 - X.counted) * X.ops + 5,
rops=4,
tfops=X.tfops + 2 + X.ins,
trops=X.trops + 2 + 2 * X.ins)
X.counted = 1
y.graph = X.graph
if X not in y.graph:
y.graph[X] = []
y.graph[X].append(
(y, 'csc', (-1 / np.tan(X.val)) * (1 / np.sin(X.val))))
return y
except:
return 1 / np.sin(X)
def get_x():
xval = input(
'At what value of x would you like to evaluate the function and its derivative?\n'
)
try:
x = ADnum(float(xval), ins=2, ind=0)
except:
print('x value must be a float.')
x = get_x()
return x
def get_y():
yval = input(
'At what value of y would you like to evaluate the function and its derivative?\n'
)
try:
y = ADnum(float(yval), ins=2, ind=1)
except:
print('y value must be a float.')
y = get_y()
return y
def plot_ADnum(f, ins=1, xmin=-10, xmax=10):
'''Function to plot f and its derivative for single variable input
INPUTS
======
x : ADnum
xmin : starting value of input
xmax : ending value of input
OUTPUTS
=======
A plot of x evaluated from xmin to xmax and its derivative
'''
if ins == 1:
vals = np.linspace(xmin, xmax, 100)
evals = [f(ADnum(value, der=1)).val for value in vals]
ders = [f(ADnum(value, der=1)).der for value in vals]
fig = plt.figure()
plt.plot(vals, evals, label='f', linewidth=2)
plt.plot(vals, ders, label='df/dx', linewidth=2)
plt.legend(fontsize=20)
plt.xlabel('x', fontsize=20)
plt.ylabel('f', fontsize=20)
plt.xticks(fontsize=12)
plt.yticks(fontsize=12)
return fig
if ins == 2:
fig = plt.figure()
ax = fig.gca(projection='3d')
vals = np.linspace(xmin, xmax, 100)
z = f(vals, vals)
ax.plot_trisurf(vals, vals, z, antialiased=True)
return fig
if ins > 2:
fig = plt.figure()
return fig