代写Python编程设计、代做data程序、Python语言编程代写

日期：2021-03-15 11:25

CR3 (Submission phase)

Submission phase

Instructions for submission

Using your preferred code editor (e.g. VSCode), in a Python script called "CR3.py", write code to answer the following problem.

Problem

Consider the following ODE, describing the displacement of an oscillator (e.g. a mass attached to a spring) at time away from its

resting position:

where is the angular frequency of the oscillator, given as a fixed parameter. The initial conditions are given as

, the initial displacement,

, the initial velocity.

We seek to solve this equation numerically, using a finite difference method. We discretise time with a step size , and denote by the

approximation to computed at time step , that is .

We approximate the second derivative in the ODE with , to obtain the difference equation:

Rearranging this equation allows us to compute using values computed at the two previous time steps, and . We can initialise

and by discretising the initial conditions:

,

Then, we can compute , followed by , etc., for as many time steps as we desire.

Note that this method provides a "valid" solution as long as . This is called the stability condition.

Your task

Write a function "oscillator(w0, u0, v0, nmax, dt)" which takes 5 input arguments:

a positive number "w0", representing the parameter ,

two numbers "u0" and "v0", representing the initial conditions and respectively,

a positive integer "nmax" greater than or equal to 2, representing the total number of time steps,

a positive number "dt", representing the step size ,

and returns a Numpy vector "U" with a total of "nmax" elements, where the th element is the value of , the approximated solution for the

oscillator displacement at the th time step, computed using the method described above.

Dashboard / My courses / www.learn.ed__81855_1 / Code reviews / CR3

Computing and Numerics (2020-2021)[SEM2]

Setup phase Submission phase

Current phase ?

Submit your work

Open for submissions from

Monday, 8 March 2021,

2:00 PM (5 days ago)

Submissions deadline:

Monday, 15 March 2021,

12:00 PM (2 days left)

Assessment phase

Open for assessment from

Monday, 15 March 2021,

4:00 PM (2 days left)

Assessment deadline:

Monday, 22 March 2021,

12:00 PM (9 days left)

Grading evaluation phase Closed

Additionally, before computing the result, the function should check the value of and display a message if necessary:

if , display a message warning the user that the stability condition has been violated. Your message should include the maximum

value of "dt" allowed for the chosen value of "w0", to help your user choose a better step size next time.

if , display a message warning the user that the chosen step size is at the stability limit.

In either case, you should still compute and return the solution.

Testing

After the function definition, write a few tests to check that your function is working. Your first test should use the following values:

You can compare the computed solution to the exact solution, which is given by:

You could plot the exact and computed solutions on the same graph over time -- for valid step sizes (such that ), the two curves should

be close, but they will never be exactly overlapping; the peak values will often be where you see the largest error. For values of and close

to the stability condition (but still valid), you should see that the computed solution oscillates slightly faster than the exact solution. As we have

seen in many other situations, decreasing the step size should generally improve accuracy.

Try different values for the initial conditions and , and check that the first two values of your computed solution are set correctly. Try different

values for the frequency , increasing it should produce a faster-oscillating solution.

Make sure you check that the warning messages appear for appropriate values. Plot the computed solution for both problematic cases -- this is

what you should see:

when (and only when) , the amplitude of the oscillations in the computed solution should grow exponentially over time, and you

should see the first warning message.

when (and only when) , the amplitude of the oscillations in the computed solution should grow linearly over time, and you should

see the second warning message.

when (and only when) , the computed solution should oscillate without growing linearly or exponentially over time, and you should

not see any message.

You should include your test code in the script CR3.py, after the function definition. Make sure you label any plots you produce appropriately

and clearly.

Scope

This is for the more experienced programmers amongst you: remember that this is peer-assessed, and that Computing & Numerics is a course

designed for beginner programmers. Please try to stick to what we've seen in the course material so far, even if you feel confident in doing

something more advanced -- keep it simple.

You should not need to -- but if you absolutely want to use something we haven't seen in the course, then please keep it to a minimum, and make

sure you explain clearly what you are doing (and why) in the code comments, so that a student with little or no previous programming

experience can assess your work with confidence. If you don't follow these guidelines, and submit code which requires much more advanced

knowledge/experience with Python to fully understand than we have seen in the course so far, then your assessors will be able to penalise you

(see marking scheme below).

Submission

Upload your file "CR3.py" here when you are finished. Make sure you upload your file before Monday 15th March, 12pm (noon), otherwise you

won't be able to participate to the peer-assessment phase, and you will get a zero for the whole CR3 task!

Marking scheme

The marking scheme which you will use when assessing next week is given in the table below. Each criterion counts equally towards the grade,

and is assessed on a scale of 0 to 3.

Criteria 0 1 2 3

Δ??

??0Δ?? > 2

??0Δ?? = 2

??0 = 5, ??0 = 0.2, ??0 = 5, ??m = 500, Δ?? = 0.03. ax

??(??) = ??0 cos(??0 ??) + sin( ??).

??0

??0 ??0

??0Δ?? < 2

Δ?? ??0

Δ??

??0 ??0

??0

??0Δ?? > 2

??0Δ?? = 2

??0Δ?? < 2

2021/3/13 CR3 (Submission phase)

https://moodle2.maths.ed.ac.uk/live2018/mod/workshop/view.php?id=3628 3/3

Was the file CR3.py submitted

correctly, and the code written as

instructed?

If you penalise here, indicate what

the problem was in the text box.

The file was in the

wrong format, which

made it difficult or

impossible to open.

The file was in the correct format,

but either didn't have the correct

name, or the code inside did not

follow the instructions (e.g. the

function was named differently, or

performed a completely different

task, or there was no function, or

there were no tests).

Everything was submitted in

the correct format and the

code followed the

specifications, but the code

was much too

complex/advanced compared

to what we have seen in the

course.

Everything was

submitted in the

correct format

and the code

followed the

specifications

(regardless of

whether it was

correct or not).

Is the code correct and without

bugs? Does the function

"oscillator()" produce the correct

results for any appropriate inputs?

If you can find any bugs or issues,

then you can indicate them in the

text box below to help the author fix

them. If you know that there is an

issue but you aren't sure why, then

indicate which test(s) look incorrect,

and give your best guess as to what

could be wrong.

(Use the test code provided in the

script by the student, as well as the

model answer and test code

provided by the instructors, to make

sure the code is fully functional.)

The code does not

work at all, there are a

lot of problems which

would take a long time

to find and fix.

There are a few bugs, so the code

works only for some input values,

but fails for many others (either

giving an error or returning the

wrong result).

There is a small number of

minor bugs or omissions, so

the code perhaps works for

most input values but fails for

a few special cases; or

perhaps the code doesn't work

but only because of a minor

issue which is trivial to fix.

The code works

correctly and

returns the

correct results for

all input values.

Was the function tested with an

appropriate range of different

inputs, to check if it worked?

(Whether or not the tests passed is

not relevant here.)

No tests were included

in the script.

Very few tests were performed,

not nearly enough to fully check

that the function worked.

A number of tests were

performed, which covered a

good number of possible

values, but perhaps some

important cases were missed.

A good number of

tests were

performed, which

covered all (or

almost all) of the

possible values

we could use with

this function.

Are the plots clear, easy to

understand, and appropriately

labelled?

The plots are extremely

messy, very hard to

read, and not clearly

The plots are perhaps too small or

squeezed, overlapping plots may

The plots are generally well

presented although a couple

The plots are very

well presented,

clearly and

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