[CMSC 455] |
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CS455 Details of homework assignments and Quiz
The most important item on all homework is YOUR NAME!
Print. No readable name, no credit.
Staple or clip pages together.
Homework must be submitted when due. You loose 10%, one grade,
the first day homework is late. Then 10% each week thereafter.
Max 50% off. A zero really hurts your average!
Paper or EMail to squire@umbc.edu ONLY PLAIN TEXT.
I can NOT accept OCTET/STREAM. .doc .gif .jpg .rtf ...
If I can not read or understand your homework, you do
not get credit. Type or print if your handwriting is bad.
Homework is always due on a scheduled class day before midnight.
If class is canceled then homework is due the next time the
class meets. EMailed or submitted homework has until midnight
of the day it is due, or under my office door before I get in.
EMail only plain text! No word processor formats.
You may use a word processor or other software tools and
print the results and turn in paper.
Submit Homework
The "submit" facility only works on the "gl" machines.
The student commands are:
submit cs455 hw1 some_file
submitrm cs455 hw1
submitls cs455 hw1
Do your own homework!
You can discuss homework with other class members but DO NOT COPY!
All parties involved in copying get zero or negative on that assignment.
Homework 1
Homework 2
Quiz 1
Homework 3
Homework 4
Quiz 2
Homework 5
Homework 6
Quiz 3
Other Links
In a language of your choice, write the program defined in
lecture 2. Test your program and
produce an output file, then submit both files on a GL machine:
submit cs455 hw1 your-source your-output
In a language of your choice, write a program that
does a least square fit of the thrust data used in Homework 1.
Use your data x = 0.0 0.1 0.2 ... 1.9
y = 0.0 6.0 14.1 ... 0.0
Be sure time 0.0 has value 0.0, time 1.9 has value 0.0
Do the least square fit with 3, 4, ... , 17 degree polynomials.
Compute the maximum error, the average error and RMS error
for each fit. If convenient, look at the plots of your fit
and compare to the input.
Print out your data. Remove excess printout, print:
Print out your polynomial coefficients for each degree 3..17
Print out maximum, average and RMS error for each.
Lecture 1 shows how to compute error
copy whatever you need from Lecture 4, Least square fit
Submit your source code file(s) and your output file
submit cs455 hw2 your-source your-output
My MatLab errors looked like:hw2_m.out
(with a lot of complaints from MatLab!)
My "C" errors did not improve as much:hw2_c.out
Plotting three points between each starting point in MatLab, n=19, gave:
The steps are typically:
Have the thrust data in X array, time values.
Have the thrust data in Y array, newton values.
Build the least square simultaneous equations, n=3 first
Given a value of Y for each value of X,
Y_approximate = C0 + C1 * X + C2 * X^2 + C3 * X^3
Then the linear equations would be:
| SUM(1 *1) SUM(1 *X) SUM(1 *X^2) SUM(1 *X^3) | | C0 | | SUM(1 *Y) |
| SUM(X *1) SUM(X *X) SUM(X *X^2) SUM(X *X^3) | | C1 | | SUM(X *Y) |
| SUM(X^2*1) SUM(X^2*X) SUM(X^2*X^2) SUM(X^2*X^3) |x| C2 | = | SUM(X^2*Y) |
| SUM(X^3*1) SUM(X^3*X) SUM(X^3*X^2) SUM(X^3*X^3) | | C3 | | SUM(X^3*Y) |
Note that index [i][j] of the matric has SUM(X^(i+j))
Solve the simultaneous equations for C0, C1, C2, C3
using some version of "simeq".
Compute errors by using "peval" with the coefficients
for each X and subtract the corresponding Y.
Save maximum error, compute average and RMS error.
Print.
Repeat, advancing n to 4, 5, ..., 17
If you use least_square_fit.c or least_square_fit.java
make changes in function data_set
put in time and thrust data from homework 1
k=20
xx=time[i] in java, i is idata
yy=thrust[i] in java, i is idata
See Lecture 9
1. Compare two methods of integrating sin(x) from 0 to 1
Take as the exact solution -cos(1.0)+cos(0.0) = 1.0-cos(1.0)
Print out number of points, your integration value, and
error your_value-exact
1.a) Use the trapezoidal method with 8, 16, 32, 64 and 128 points.
Put this in a loop e.g. in C for(n=8; n<=128; n=n*2)
Note how the error decreases as n increases.
h = 1/n
your_value = h * ((sin(0)+sin(1.0))/2 + sum i=1..n-1 sin(i*h))
1.b) Use the Gauss Legendre method with 8 and 16 points.
Copy the function gaulegf from your choice of language
or convert to your choice of language. Be sure to keep
the #undef abs and #define abs in "C" code.
double x[17], w[17]
n=8 then again for n=16
gaulegf(0.0, 1.0, x, w, n)
your_value = 0.0
for(j=1; j<=n; j++)
your_value = your_value + w[j]*sin(x[j])
Note the significantly smaller error than for trapezoid.
2. Write a small program in the language of your choice to
numerically compute, to at least 3 significant digits,
the area that is outside Circle 1 and inside both Circle 2
and Circle 3.
Circle 1 center at (2,2) radius 1 (x-2)^2+(y-2)^2=1^2
Circle 2 center at (0,2) radius 2 x^2+(y-2)^2=2^2
Circle 3 center at (0,0) radius 3 x^2+y^2=3^2
Hint: count the dots in the area and multiply by the
area of a square. Run with a grid 0.1, 0.01, 0.001, 0.0001
to see if your computation is converging. Obviously, if the
left hand side of the equation is larger than the right
hand side of the equation, the point is outside the circle.
submit cs455 hw3 your-source your-output for 1a, 1b and 2
(Note: in problem 2, if you were given a function z=F(x,y) and
needed to compute the volume over the area, you would
probably combine part of problem 1 with problem 2.)
Use a language and big numbers package of your choice to
compute the exact integer value of the following:
How many ways can you lay out a deck of cards in a line?
52 cards in a deck, all permutations is 52!.
Thus, just compute 52 factorial.
How many seven card hands from a deck of 52 cards?
This is an n choose m problem. n! / ((n-m)! m!).
n is 52, m is 7. Direct computation, no math reductions.
print all digits as an integer, big number,
no scientific notation E+xx.
Submit your source code and your output.
(Clean out unused source code, it should be small.)
See Lecture 19
Take a .wav file. Listen to it.
Extract the amplitude data from the .wav file.
Use a FFT to get the frequency spectrum.
Modify the frequency spectrum
Use inverse FFT to get amplitude data.
Insert the modified amplitude data into the .wav file.
Listen to the new .wav file.
Just do one of, a) b) c)
a) delete high and low frequencies from the spectrum or
perform some other modification. Comment on how the
sound changed.
b) Move all of the spectrum from i to n down into 1 to n-i,
zero spectrum from n to top. You should be able to
understand the modified .wav yet it will be a much
deeper voice. You have lowered the frequency.
c) Mess up the sound with some other change to the spectrum.
Look at the spectrum plots. It depends on what code you use:
Possibly leave the zeroth frequency alone or zero it.
For N=2^n, leave the N/2 as it is, this is the Nyquist frequency.
Moving the top half down and the bottom half up, raises the pitch.
It also introduces noise.
Sample code for FFT and IFFT provided.
copy whatever you need from Lecture 18, FFT
Sample code to read and write a .wav is provided for a few languages.
waveplay.m reads a .wav file, plays the file
at three speeds, then writes a .dat file with just the sound.
The .dat file can be read with %f format. soundplay.m
Will play a .dat file, that may be read, modified, and rewritten.
In Matlab, if it works for you, use fft_wav.m
In Python, hack sound.py and use Python's fft and ifft.
In Java, hack ClipPlayerTest.java and use
my Cxfft.java for fft and ifft functions.
There is read_wav.java to read
and write .wav files.
Or, if it works for you, use fft_wav.java
With a plot, use fft_frame.java
In Ubuntu using plain "C", hack pcm_dat.c and use any of the FFT and
IFFT written in "C".
The program read_wav.c reads and writes a .wav file.
You can put a FFT in between the read and write for your homework.
Use common existing software to play the .wav file(s).
You may need to convert complex values to magnitude.
Given a+bi amplitude = sqrt(a*a+b*b)
Submit your source code, input .wav files and output .wav files.
(option: use just ascii files of numbers, read and write with %f
MatLab code soundplay.m plays file.
short_count.dat is one two three.)
See Lecture 18 for more information
Compile and run the program time_matmul.c
on some computer. You may use other languages and MatLab.
Time the matrix multiply for 100 by 100, 200 by 200, 400 by 400 etc
and record the actual time and a normalized time. It is OK to stop
when a single size takes over 10 minutes.
The normalized time is some constant time actual time divided by N^3.
Matrix multiply is order N cubed, thus the time goes up by a factor
of 8 each time N doubles. Note that the small 100 by 100 runs very fast.
As the matrix gets larger, the time increases by more than a factor of 8.
This is because of cache performance verses memory bandwidth.
If you can not run "C", a Java version, much slower, is:
time_matmul.java
If you want a really slow version, run the Python:
time_matmul.py
Actually, you should be using numpy for numerical computation.
Comment on any large variation in normalized time on the
language and operating system and machine you run this homework.
Submit your code (or my code) and your output.
See Lecture 29
Last updated 6/11/11