def plot_ADnum(x, 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
'''
vals = np.linspace(xmin, xmax, 100)
evals = [x(ADnum(value, der=1)).val for value in vals]
ders = [x(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
def confirm():
global function_expression
global function_output
# function_output = lambda x: eval(function_expression)
# graph_window(master)
try:
function_output = lambda x: eval(function_expression)
# graph_window(master)
except:
# error_window(master)
# raise exception("expression error")
messagebox.showinfo(
"Error", "Syntax error in your expression, please try again.")
try:
textVal = function_output(ADnum(5, der=1)).val
textDer = function_output(ADnum(5, der=1)).der
messagebox.showinfo(
"Continue",
"Your input is a function. Please continue to draw graphs.")
graph_window(master)
except AttributeError:
messagebox.showinfo("Constant result:",
"The value is {}".format(function_output(1)))
except SyntaxError:
messagebox.showerror(
"Error",
"Syntax error in your expression. Please use \'Clear All\', and try again."
)
def arctan(X):
try:
y = ADnum(np.arctan(X.val), der=1 / (1 + X.val**2) * X.der)
y.graph = X.graph
if X not in y.graph:
y.graph[X] = []
y.graph[X].append((y, 'arctan'))
return y
except AttributeError:
return np.arctan(X)
def arccos(X):
try:
y = ADnum(np.arccos(X.val), der=-1 / np.sqrt(1 - X.val**2) * X.der)
y.graph = X.graph
if X not in y.graph:
y.graph[X] = []
y.graph[X].append((y, 'arccos'))
return y
except AttributeError:
return np.arccos(X)
def cot(X):
try:
y = ADnum(1 / np.tan(X.val), der=-1 / (np.sin(X.val)**2) * X.der)
y.graph = X.graph
if X not in y.graph:
y.graph[X] = []
y.graph[X].append((y, 'cot'))
return y
except AttributeError:
return 1 / np.tan(X)
def sin(X):
try:
y = ADnum(np.sin(X.val), der=np.cos(X.val) * X.der)
y.graph = X.graph
if X not in y.graph:
y.graph[X] = []
y.graph[X].append((y, 'sin'))
return y
except AttributeError:
return np.sin(X)
def sqrt(X):
try:
y = ADnum(np.sqrt(X.val), der=X.der / (2 * np.sqrt(X.val)))
y.graph = X.graph
if X not in y.graph:
y.graph[X] = []
y.graph[X].append((y, 'sqrt'))
return y
except AttributeError:
return np.sqrt(X)
def sec(X):
try:
y = ADnum(1 / np.cos(X.val), der=np.tan(X.val) / np.cos(X.val) * X.der)
y.graph = X.graph
if X not in y.graph:
y.graph[X] = []
y.graph[X].append((y, 'sec'))
return y
except AttributeError:
return 1 / np.cos(X)
def log(X):
try:
y = ADnum(np.log(X.val), der=1 / X.val * X.der)
y.graph = X.graph
if X not in y.graph:
y.graph[X] = []
y.graph[X].append((y, 'log'))
return y
except AttributeError:
return np.log(X)
def tanh(X):
try:
y = ADnum(np.tanh(X.val), der=1 / (np.cosh(X.val)**2) * X.der)
y.graph = X.graph
if X not in y.graph:
y.graph[X] = []
y.graph[X].append((y, 'tanh'))
return y
except AttributeError:
return np.tanh(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)
y.graph = X.graph
if X not in y.graph:
y.graph[X] = []
y.graph[X].append((y, 'csc'))
return y
except:
return 1 / np.sin(X)
def display():
if not (type(value.get()) == float):
messagebox.showerror('Error',
'Please enter a numeric value for x.')
show_value = tk.Label(graph_window,
text=str(
function_output(ADnum(value.get(),
der=1)).val),
height=3,
width=20).grid(row=4, column=1, columnspan=2)
show_derivatice = tk.Label(
graph_window,
text=str(function_output(ADnum(value.get(), der=1)).der),
height=3,
width=20).grid(row=5, column=1, columnspan=2)
def test_get_labels():
X = ADnum(1, der=1)
Y = ADmath.sin(X) + 3
labs = ADgraph.get_labels(Y)
assert labs[X] == 'X0'
assert labs[Y] == 'X2'
assert len(labs) == 4
def test_plot_ADnum():
X = ADnum(1, der=1)
def Y(x):
return ADmath.sin(x)
fig = ADgraph.plot_ADnum(Y)
assert type(fig) == matplotlib.figure.Figure
def test_gen_graph():
d = {'y': [('x', 'test')]}
Y = ADnum(1, der=1, graph=d)
G = ADgraph.gen_graph(Y)
assert 'y' in G
assert 'x' in G
assert type(G) == nx.classes.digraph.DiGraph
assert G.number_of_nodes() == 2
assert G.number_of_edges() == 1
def test_get_colorsandsizes():
X = ADnum(1, der=1)
Y = ADmath.sin(X) + 3
labs = ADgraph.get_labels(Y)
G = ADgraph.gen_graph(Y)
cols = ADgraph.get_colors(G, Y)
sizes = ADgraph.get_sizes(G, Y, labs)
assert len(cols) == 4
assert len(sizes) == 4
def draw_graph():
plot_graph = tk.Toplevel(graph_window)
plot_graph.title("Computational Graph")
plot_graph.geometry("600x600")
fig = ADgraph.draw_graph(function_output(ADnum(value.get(),
der=1)))
canvas = FigureCanvasTkAgg(fig,
master=plot_graph) # A tk.DrawingArea.
canvas.get_tk_widget().pack(side=tk.TOP, fill=tk.BOTH, expand=1)
canvas.draw()
toolbar = NavigationToolbar2Tk(canvas, plot_graph)
toolbar.update()
canvas.get_tk_widget().pack(side=tk.TOP, fill=tk.BOTH, expand=1)
def draw_table():
plot_graph2 = tk.Toplevel(graph_window)
plot_graph2.title("Computational Table")
plot_graph2.geometry("600x600")
# fig = ADgraph.gen_table(function_output)
f = tk.Frame(plot_graph2)
f.pack(side=tk.TOP, fill=tk.BOTH, expand=1)
df = ADgraph.gen_table(function_output(ADnum(value.get(), der=1)))
table = pt = Table(f,
dataframe=df,
showtoolbar=True,
showstatusbar=True)
pt.show()
def display():
if not (type(value_x.get()) == float and type(
value_y.get()) == float and type(value_z.get()) == float
and type(value_m.get()) == float and type(value_n.get())
== float and type(value_k.get()) == float):
messagebox.showerror('Error',
'Please enter a numeric value for x.')
x = ADnum(value_x.get(), ins=master_ins, ind=0)
if master_ins > 1:
y = ADnum(value_y.get(), ins=master_ins, ind=1)
if master_ins > 2:
z = ADnum(value_z.get(), ins=master_ins, ind=2)
if master_ins > 3:
u = ADnum(value_m.get(), ins=master_ins, ind=3)
if master_ins > 4:
v = ADnum(value_n.get(), ins=master_ins, ind=4)
if master_ins > 5:
w = ADnum(value_k.get(), ins=master_ins, ind=5)
global out_num
if master_ins == 1:
out_num = function_output(x)
if master_ins == 2:
out_num = function_output(x, y)
if master_ins == 3:
out_num = function_output(x, y, z)
if master_ins == 4:
out_num = function_output(x, y, z, u)
if master_ins == 5:
out_num = function_output(x, y, z, u, v)
if master_ins == 6:
out_num = function_output(x, y, z, u, v, w)
show_value = tk.Label(graph_window,
text=str(round(out_num.val, 2)),
height=3,
width=20).grid(row=master_ins + 3,
column=1,
columnspan=2)
show_derivatice = tk.Label(graph_window,
text=str(round(out_num.der, 2)),
height=3,
width=20).grid(row=master_ins + 4,
column=1,
columnspan=2)
def test_vecinput_multi():
x = ADnum([1, 2, 3], ins=2, ind=0)
assert np.array_equal(x.der, np.array([[1., 1., 1.], [0., 0., 0.]]))
def test_ADnum_nodernothing():
with pytest.raises(Exception):
z = ADnum(3)
def test_ADnum_sub():
x = ADnum(5.0, der=1)
f = x - 2.0
assert f.val == 3.0
assert f.der == 1.0
assert len(f.graph) == 2
def test_reverse_graph():
d = {'y': [('x', 'test')]}
rd = {'x': [('y', 'test')]}
Y = ADnum(1, der=1, graph=d)
rg = ADgraph.reverse_graph(Y)
assert rd == rg
def test_ADnum_rmul():
x = ADnum(3.0, der=1)
f = 2.0 * x
assert f.val == 6.0
assert f.der == 2.0
assert len(f.graph) == 2
def test_ADnum_radd():
x = ADnum(3.0, der=1)
f = 2.0 + x
assert f.val == 5.0
assert f.der == 1.0
assert len(f.graph) == 2
def test_neg():
x = ADnum(4, der=1)
f = -x
assert f.val == -4.0
assert f.der == -1.0
assert len(f.graph) == 1
def test_graphiput():
z = ADnum(1, der=1, graph={'a': 1})
assert z.graph == {'a': 1}
def test_draw_graph():
X = ADnum(1, der=1)
Y = ADmath.sin(X) + 3
fig = ADgraph.draw_graph(Y)
assert type(fig) == matplotlib.figure.Figure
def test_ADnum_derconsistent():
with pytest.raises(ValueError):
z = ADnum(3, der=np.array([1, 3]), ins=5)
def test_gen_table():
X = ADnum(1, der=1)
Y = ADmath.sin(X) + 3
dat = ADgraph.gen_table(Y)
assert type(dat) == pandas.core.frame.DataFrame
