def testMethod2():
_fn = lib.getFunction("simulate_apple2", _fileName)
try:
_t = apply_function(_fn, (0.01, ), (float, ))
except InvalidFunctionApplication as e:
return False, e.message
if assertlib.between(_t, 2.82, 2.86):
return True, ""
return False, f"Did not expect output {_t} (with input: 0.01)"
def testMethod():
try:
_input = 1000.0, 200.0, 72.0, 0, 0.01
_fn = lib.getFunction("simulate_free_fall", _fileName)
_xl, _tl = apply_function(_fn, _input, (list, list))
except InvalidFunctionApplication as e:
return False, e.message
except Exception as e:
return False, f"An error occured while running the function: \n {type(e).__name__}: {str(e)}"
if len(_xl) != len(_tl):
return False, "Function is expected to return two lists of the same length."
return validate_sim(_input, 12.77, _xl, _tl)
def testMethod():
try:
_input = 3474, 0.01
_fn = lib.getFunction("simulate_ultimate_free_fall", _fileName)
_rl, _vl, _tl = apply_function(_fn, _input, (list, list, list))
except InvalidFunctionApplication as e:
return False, e.message
except Exception as e:
return False, f"An error occured while running the function: \n {type(e).__name__}: {str(e)}"
if len(_rl) != len(_tl) or len(_vl) != len(_tl):
return False, "Function is expected to return three lists of the same length."
return validate_sim1(_input, (-3474, 3474, -4.315, 4.315), _rl, _vl)
def testMethod():
try:
_input = 6.38e6, 0.01
_fn = lib.getFunction("simulate_ultimate_free_fall", _fileName)
_rl, _vl, _tl = apply_function(_fn, _input, (list, list, list))
except InvalidFunctionApplication as e:
return False, e.message
except Exception as e:
return False, f"An error occured while running the function: \n {type(e).__name__}: {str(e)}"
if len(_rl) != len(_tl) or len(_vl) != len(_tl):
return False, "Function is expected to return three lists of the same length."
if not similar(_tl[-1], 5058.3, 4):
return False, f"Did not expected the time of the simulated free fall to be {_tl[-1]} seconds."
return True, ""
def testMethod():
try:
_input = 100, 0.01
_fn = lib.getFunction("simulate_apple1", _fileName)
_t, _v = apply_function(_fn, _input, (float, float))
except InvalidFunctionApplication as e:
return False, e.message
except Exception as e:
return False, f"An error occured while running the function: \n {type(e).__name__}: {str(e)}"
if similar(_v, 4.52, atol=0.1) or similar(_t, 159.47, atol=1):
return False, "Did you mix up the order of the return values?"
if similar(_v, 44.3, atol=0.3):
return False, "Did you forget to convert to km/h?"
if similar(_t, 4.52, atol=0.1) and similar(_v, 159.47, atol=1):
return True, ""
return False, f"Did not expect output {_t, _v} (with input {_input})"
def show_welcome_page():
st.title("Welcome.")
st.markdown("You will find the following in this section:")
st.markdown("1. The History of Monte Carlo Method \n "
"2. A High Level Montel Carlo Process \n"
"3. An Interactive Example")
st.markdown(
"If you are familiar with the basics, use the panel on the left to see some real-life examples."
)
# HISTORY
st.markdown("***")
st.markdown("** The Short History **")
st.video("https://youtu.be/ioVccVC_Smg")
# SIMULATION ARCHITECTURE
st.markdown("***")
st.markdown("** The Monte Carlo Process**")
st.markdown(
"The goal of Monte Carlo Method is to **approximate an expected outcome** that is difficult to "
"calculate precisely. In real life, it's often impossible to come up with a single equation to "
"describe a system from inputs to outputs; even we can, it will be time consuming to "
"calculate and analyze all possible outcome scenarios. "
"As a practical alternative, Monte Carlo method allows us to take a **probability approach**."
)
image = Image.open('./asset/monte-carlo-process.png')
st.image(image, format='PNG', use_column_width=True)
st.markdown("A more technical explanation ...")
st.video("https://youtu.be/7TybpwBlcMk")
# ILLUSTRATION OF PROBABILITY DISTRIBUTION
st.markdown("***")
st.markdown("**Step 1: Define input(s) with uncertainty ... **")
value_range = st.slider("Pick the range of value that represent the input",
min_value=20,
max_value=100,
value=(45, 60),
step=1)
shape = st.selectbox("Pick a distribution that represent the uncertainty",
("Normal", "Triangle", "Uniform"))
N = st.slider("Choose how many samples (N): ",
min_value=100,
max_value=10000,
value=500,
step=100)
st.markdown(
f"We drew {N} samples "
f"with an **uncertainty** represented by a **{shape}** distribution.")
input_items = helpers.get_items(value_range, N, shape)
hist_data = [input_items]
group_label = ['Input']
fig = ff.create_distplot(hist_data, group_label, bin_size=[0.5])
st.plotly_chart(fig, use_container_width=True)
st.markdown("**Step 2: Apply Some Transformation ...**")
distribution = st.selectbox(
"Pick a transformation",
("Secret Formula 1", "Secret Formula 2", "Secret Formula 3"))
st.markdown(
f"We apply **{distribution}** (some non-linear functions and randomness) to each of the input samples ..."
)
output_items = helpers.apply_function(input_items, distribution)
hist_data = [output_items]
group_label = ['Output']
fig = ff.create_distplot(hist_data, group_label, bin_size=[0.1])
st.plotly_chart(fig, use_container_width=True)
# ANALYZE RESULTS
st.markdown("**Step 3: Analyze the Outcome ...**")
st.markdown(
"In this case, the results are not very sensible since it's a dummy example. "
"Typically, we should ask the following quesitons: ")
st.markdown(
"1. what is the probability of achieving the acceptable outcomes? Is it good enough to proceed? \n"
"2. what is the probability of achieving sub-optimal outcomes? And how do we hedge against that? \n"
"3. what factor has the largest impact on the outcome? How can we influence it? \n"
)
st.markdown("***")
st.markdown(
"**Next Step:** Use the panel on the left to learn key techniques of designing and analyzing simulations "
"with three real-world business problems.")
st.markdown("Each example focuses on a technique: ")
st.markdown("1. CMO Lab: Influence Diagram \n"
"2. COO Lab: Sensitivity Analysis \n"
"3. CFO Lab: Optimization in Simulation \n"
"4. CPO Lab: Machine Learning in Simulation")
show_footer()