W6Q1: Replicate an array

Description ----------------------------------------------------------

*Identify the function by which you can replicate or* _tile_ *an array
 of numbers, and then use it to beat Andy Warhol at his own game. You
 are given a _specific_ image, and asked to tile it, i.e., repeat it,
 into a canvas that is 11 times the width of the original, and 17
 times the original height. Save the result in a vector* |Y|. 

*Note that we are not being very explicit here! You'll have to find
 where the image is on your own. Learn to use* |whos|! *If you don't
 know what the function is that performs the required tiling, learn to
 use* |lookfor|!

Solution Template ----------------------------------------------------

% Don't change this line, but look at what it does!
load('clown');
% Don't change, but use this line!
m=17;
n=11;
% Now you have an image. Find it! Tile it! Assign the output
Y=

Reference Solution ---------------------------------------------------

% Don't change this line
load(clown);
% Don't change, but use this line!
m=17;
n=11;
% Now you have an image. Find it! Tile it! Assign the output
Y=repmat(X,m,n);

Visible Tests --------------------------------------------------------


Hidden Tests ---------------------------------------------------------

%% 
run('solution')
assert(isequal(Y,repmat(X,m,n)));


W6Q2: Find an occurrence

Description ----------------------------------------------------------

*A very useful function,* |find|. *Let's put it to good use.*

*You are given a character array, a variable* |a|, *containing a
 name. Replace all occurrences of the letter O in the original string
 by the character string representing the number that is the sum of
 the indices at which the letter O occurred in the original string.

* Make your solution as short and sweet as possible!*

Solution Template ----------------------------------------------------

% Here is the given name
a='MALOOF';
% Use "find" to find the positions of all O's 
v=find
% In a, replace all O's with the requested symbols, keep the variable
% name, make it short! 
a

Reference Solution ---------------------------------------------------

a='MALOOF';
v=find(a=='O');
a(v)=sprintf('%i',sum(v));


Visible Tests --------------------------------------------------------


Hidden Tests ---------------------------------------------------------

%%
run('solution');
assert(isequal(a,'MAL99F'))


W6Q3: Make a difference

Description ----------------------------------------------------------

*The functions* |max| *and* |diff| *can operate along a _dimension_ of
 choice, i.e. along a _row_, the _first_, or _column_, the _second_
 dimension*.

*You are given a certain matrix*, |X|. *Find the _lowest column
 number_ and, for that column, the corresponding _row_ number at which
 the largest _absolute_ jump occurs in this matrix* |X|, *measured
 along the _row_ dimension, as well as the _value_ of that
 jump. Assign your results to the variables* |cr|, |rr|, *and* |jr|.

*Next, find the _lowest row number_ and, for that row, the
 _corresponding column_ number at which the largest _absolute_ jump
 occurs in this matrix* |X|, *measured across the _column_ dimension,
 as well as the _value_ of that jump. Assign those results to the
 variables* |rc|, |cc|, *and* |jc|.


Solution Template ----------------------------------------------------

% This produces the matrix X in your workspace
load clown
% Now determine the required values jr, cr, and rr, in that order
[jr,cr]=max(max(abs(diff(X,[],?)),[],?));
% Check that the next time you determine jr, you get the same!
[jr2,rr]=max(abs(diff(X(:,?),[],?)));

% These should be zero
jr-jr2;

% Now determine the values jc, rc, and cc, in that order
[jc,rc]=max(max(abs(diff(X,[],?)),[],?));
% Check that the next time you determine jc, you get the same!
[jc2,cc]=max(abs(diff(X(?,:),[],?)));

% These should be zero
jc-jc2;

% Verify your answer! These should be zero!
abs(X(rr+1,cr  )-X(rr,cr))-jr
abs(X(rc  ,cc+1)-X(rc,cc))-jc


Reference Solution ---------------------------------------------------

load clown
[jr,cr]=max(max(abs(diff(X,[],1)),[],1));
[jr2,rr]=max(abs(diff(X(:,cr),[],1)));
[jc,rc]=max(max(abs(diff(X,[],2)),[],2));
[jc2,cc]=max(abs(diff(X(rc,:),[],2)));

% Could clearly leave out the dimensions of the second pass
% But you could not get them wrong!!

jr-jr2
jc-jc2
abs(X(rr+1,cr  )-X(rr,cr))-jr
abs(X(rc  ,cc+1)-X(rc,cc))-jc

Visible Tests --------------------------------------------------------

%% 
run('solution')
assert(isequal(jr,jr2))
assert(isequal(jc,jc2))
assert(isequal(abs(X(rr+1,cr)-X(rr,cr)),jr))
assert(isequal(abs(X(rc,cc+1)-X(rc,cc)),jc))


Hidden Tests ---------------------------------------------------------

%%
run('solution');
assert(isequal(jr,79))
assert(isequal(cr,80))
assert(isequal(rr,1))
assert(isequal(jc,75))
assert(isequal(rc,45))
assert(isequal(cc,101))


W6Q4: Set a colorbar

Description ----------------------------------------------------------

*The function* |imagesc| *assigns colors to a matrix of values, and
 displays the matrix as an image. The colors used derive from a*
 |colormap|, *and* |imagesc| *makes sure that the lowest and highest
 values of the matrix take on the extremes of the colors defined in
 the* |colormap|, *scaling everything else in-between _linearly_. The
 function* |colorbar| *produces a color legend as a little add-on
 image, either below or beside the main image*.

*You are given such a matrix image, and you are using* |imagesc| *to
 plot it, and* |colorbar| *to make a color bar for it. You are given a
 special value*, |v|, *and you are setting the tick marks on the color
 bar to definitely include it.*

*What are the RGB values of the color used to represent that special
 value? Assign that RGB triad to the vector named* |hh|.

*Use* |colormap| *to obtain the* _default_ *colormap (which is the one
 you get when you ask for nothing in particular) that was used, saving
 this result in the variable* |h|. *Reassign the color used for the
 special value in the original colormap to _white_, overwriting the
 colormap into the variable* |h|.

*Return the sum of the absolute values of the new color map as a
 single number in the variable* |shabs|.

*Check that you did the right thing by inspecting your image! You
 should be rendering the interval containing your special value in
 _white_, and there should be a tick label right inside of it.*


Solution Template ----------------------------------------------------

% Special value, do not change
v=61;
% Get the image, do not change
load mandrill
% Display the image, do not change
imagesc(X)
% Make a colorbar, do not change
c=colorbar;
% Set the tick marks on the colorbar to include the special value
set(c,'Ytick',   )
% Get the color map, do not change
h=colormap;
% What is the color that is being used for the value v?
% I recommend first finding that color's row number (i.e. the row of h)
colpos=
% Now extract the special color from the color map
hh=
% Set the corresponding color to white, instead, and save the new colormap
h
% Return the sum of the absolute values of the color map as a single number
shabs=
% And then check how your picture fares, do not change
colormap(h)

Reference Solution ---------------------------------------------------

v=61;
load mandrill; imagesc(X)
c=colorbar; 
minx=min(X(:)); 
maxx=max(X(:));
mimax=[minx maxx];
set(c,'Ytick',unique([mimax v]))
colormap('default');
% FJS test colormap(gray(6));
h=colormap;
% Is this an actionable fraction? Must be a completed new interval!
colpos=min(1+floor([v-minx]/[maxx-minx]*length(h)),length(h));
% Adam colpos=round((v/c.Limits(2)*length(h)))
hh=h(colpos,:); 
h(colpos,:)=1; shabs=sum(abs(h(:)));
colormap(h)

Visible Tests --------------------------------------------------------

Hidden Tests ---------------------------------------------------------

% These numbers depend on the Cody version!!

%%
run('solution');
assessVariableEqual('hh',[0.1834 0.5074 0.9798],'AbsoluteTolerance',1e-4)
assessVariableEqual('shabs',107.7783,'AbsoluteTolerance',1e-4)

W6Q5: Cumulate a distribution

Description ----------------------------------------------------------

*A _cumulative distribution function_ is a function that, for a given
independent variable* |v|, *returns the probability, under a certain
_probability density function_, of all the numbers between negative
infinity and the given value* |v|.

*For a normal (Gaussian) distribution with an* _expectation of 2_ and*
 *_a variance of 3,_ *calculate the value of the cumulative
 *distribution function at the variable* |v|, *and quote your result
 *as an integer, a rounded percentage, assigned to the variable*
 *|p|. *You can pick the number* |v| *yourself, as long as it is
 *positive, which is for my convenience.*

*Now you are given a number*, |N|, *and you generate as many samples
 from the normal distribution with the same expectation and
 variance. Compute the* |p|*th percentile of your sample, and assign
 the result to a character string that has a length of precisely three
 with precisely one digit past the decimal point (which is included in
 the length!), which you call* |vp|. 

Solution Template ----------------------------------------------------

% Set the values, do complete with a positive number
v=
% Set the parameters, do not change, but make sure to use them below
ep=1;
vr=3;
% If you don't understand your answer, make this larger, but not lower
N=1e4;
% Answer the question, as related to the given distribution
p=
% Generate N synthetic data, as related to the given distribution
x=ep+sqrt(vr)*randn(N,1);
% The value of the rounded pth percentile of this data set, as a string
vp=

Reference Solution ---------------------------------------------------

% If they pick really high values, it will still work but we cannot
then check that v and vp are the same. That, they need to do.  
v=1;
ep=2;
vr=3;
N=1e4;
p=round(100*normcdf(v,ep,sqrt(vr)));
x=ep+sqrt(vr)*randn(N,1);
vp=sprintf('%3.1f',prctile(x,p))

Visible Tests --------------------------------------------------------

%%
run('solution');
assert(ischar(vp),'I am expecting a character string for vp')
assert(isequal(length(vp),3),'I am expecting EXACTLY 3 characters for vp')

Hidden Tests ---------------------------------------------------------

%%
run('solution');
assert(isequal(p,round(100*normcdf(v,ep,sqrt(vr)))))
assert(isequal(vp,sprintf('%3.1f',prctile(x,p))))