Sudoku Solver, check each 3x3 box - matlab

To sum my problem up in a nutshell, I am checking each 3x3 box if there is one missing value, if there is, it computes what that number is, and then fills that number in. However, it only does the upper left 3x3 box, and stops there. Here is the snippet of my code that relates to my issue. If you'd like to see the rest of the code just ask and I'll post the rest.
EDIT: The user inputs the board. For test purposes I tried inputting a completed Sudoku puzzle, and then take out the top right value in each box. It only filled in the first 3x3, it still output the board at the end, but had 8 other blanks to fill in (from the other 8 3x3 boxes)
% Check each 3x3 box for one through nine, fill in
for i = 0:2
for j = 0:2
if sum(sum(board([1:3]+i*3,[1:3]+j*3)~=0))==8
[row,col] = find(board([1:3]+i*3,[1:3]+j*3)==0);
answer = 45 - sum(sum(board([1:3]+i*3,[1:3]+j*3)));
board(row,col) = answer;
end
end
end
disp(board);

You are very close. The problem is that for each block you are getting the row and column index of the 3x3 block. So, for each block the following is true: row <= 3 and col <= 3.
You can easily solve this by adding these two lines after the line where you use find:
row = row + (3*i);
col = col + (3*j);
This way you convert the block-relative index back to the board-relative index.

Related

Indexing issue in MATLAB (image processing)

I'm dealing with a predictive block-matching motion estimation algorithm. This means, the values of motion vectors are found using the previously found values and I am stuck with a really trivial thing.
I'm dealing with images divided into blocks, so I should have a motion vector for each block. I created a 2xN matrix motion_vectors, where N is the number of all blocks (blocks_in_the_first_row*blocks_in_the_first_column). The first row is the x coordinate and second row the y coordinate of the motion vector.
I have 2 predictors to help to estimate the motion vector of the current block.
If my current block is at position (i,j) then the positions of the predictors are (i, j-1) (the block "on top)" and (i-1, j) (the block on the left).
My problem is, that I can't figure out a way how to adress the predictor blocks (in for loops) in motion_vectors since the dimensions are different (one is a 2xN matrix, the other blocks_in_row x blocks_in_column). I also wouldn't like to change the dimensions of motion_vectors, since then I would need a two-"layer" array. One for the x coordinates and one for y, but that doesn't fit to the further design.
I hope I made myself understandable, if not, please let me know.
Thanks for any clues!
If you're accessing an element of motion_vectors, you're getting data about a corresponding block. That means that there's a system of translating between an index 1 through N, where N is blocks_in_row*blocks_in_column, and a specific block. If index 1 is the top-left block, index 2 is the block to its right, and you increment as reading a book (left-to-right and wrap to the next row), then you would translate as follows:
row_of_block = floor((index_in_motion_vector-1)/number_of_columns) + 1
col_of_block = mod((index_in_motion_vector-1), number_of_columns) + 1
(This is called row-major ordering.)
If instead index 1 is the top-left block and index 2 is the block below it, and you wrap to the top of the next column when done with one, then the conversion would be
row_of_block = mod((index_in_motion_vector-1), number_of_rows) + 1
col_of_block = floor((index_in_motion_vector-1)/number_of_rows) + 1
(This is called column-major ordering, and is what MATLAB uses by default.)
So, if you're iterating 1 to N, you can just use those conversions. If you'd like to iterate 1 through number_of_rows, and 1 through number_of_columns you would do the opposite.
If you're using the book-like indexing of blocks (row-major ordering), the conversion to index of the motion vector would be
col_in_motion_vector = (row_of_block-1)*number_of_columns + column_of_block
If you're using the second, top-to-bottom-and-wrap method of indexing blocks (column-major ordering), the conversion would instead be
col_in_motion_vector = (column_of_block-1)*number_of_rows + row_of_block

How to highlight or identify a column with a specific value in matrix?

I would like to highlight or identify a column in a matrix with a specific value in MATLAB. Suppose I have a matrix A = [1 0 1 1 0 1; 1 1 0 0 0 1; 1 0 1 1 0 1; 0 1 1 0 0 1].
The result of the above matrix is a 5th column, as it contains all zeroes. I am also wondering if I could highlight the resulting column for identification. Please help me. I have a very large matrix to work on applying this principle.
How about combining find and all to get the column index of the all-zero column like this?
A = [1 0 1 1 0 1; 1 1 0 0 0 1; 1 0 1 1 0 1; 0 1 1 0 0 1];
ind = find(all(A==0,1))
ind =
5
The second input argument to all is to specify that it's along the first dimension, i.e. rows. It's not really necessary here, but I find that it's a good practice as you're always sure it's the right dimension. This is especially important if there are scenarios where you might get a 1xn vector instead of mxn.
Create a colored matrix:
This is a hack, and I don't necessarily recommend it, but if you really want to do this in MATLAB, this is an alternative. Also, I think you might learn quite a lot about MATLAB when doing this, so it might be worth the time.
You can create a colored plot with all values 1 except those in column 5 that will be 0 (or the other way around, doesn't matter) using imagesc. This will give a plot with only two colors, one for those values that are 1, and one for those that are 0. You can select which colors you want with colormap. Then you create a mesh to determine the location of all the values you want to show, convert the matrix to strings using num2str, and combine it all. You need to experiment some to get the correct locations, as you probably want less padding between the rows than the columns. You can use this answer as a guide. In the end, remove the axes. It should be fairly simple to adapt if you read and try to understand each line of the referenced answer.
The simple approach:
I have a very large matrix...". Such matrices are often not a good idea to include in a report. However, if you really want to, I actually suggest you copy paste it from the variable explorer and into MS Excel (or use xlswrite if you're doing this more than once). Since you know which column you want to color, it should be fairly simple to click the "color button".
The following displays the matrix in the command window with the matching columns in boldface. There may be several matching columns, and arbitrary column values can be matched.
A = [1 0 1 0 0 1; 1 1 0 1 0 1; 1 0 1 0 0 1; 0 1 1 1 0 1]; %// matrix
c = [0;1;0;1]; %// column to be matched
nn = find(all(bsxfun(#eq, A, c),1)); %// indices of matching columns
s = cellstr(num2str(A)); %// cell array of strings, one for each row; all same length
for n = nn %// for each matching column, with index n
s = regexprep(s, '\S+', '<strong>$0</strong>', n); %// make bold n-th value of each cell
end
s = vertcat(s{:}); %// convert back into a char array; all strings have the same length
disp(s); %// display
The result in this example is
Highlighting with red (stderr)
Just for proof of concept, you could highlight some of your data in the command window, although I wouldn't suggest actually doing this. Consider the following code:
A=randi(10,8);
%ind = find(all(A==0,1),1) %for actual data
ind = 5; %manual choice for demonstration
for k=1:size(A,1)
fprintf('%5d ',A(k,1:ind-1));
fprintf(2,'%5d ',A(k,ind));
fprintf('%5d ',A(k,ind+1:end));
fprintf('\n');
end
First we create a dummy matrix for demonstration purposes, and select column ind to highlight. Then we go along from line to line in A, we use fprintf(...) to write the non-highlighted values with a given format, then use fprintf(2,...) to write to stderr in red, then write the rest of the line, then newline. Note that for some reason fprintf(2,...) will not highlight the final character, I guess because usually this is \n and nobody noticed that highlighting is missing there.
Also, you can play around with the formats inside fprintf to suit your needs. If you need to print floating points, something like '%10.8f' might work. Or '%g'. The main point is to have a fixed width+precision for your print in order to get pretty columns.
For the sake of completeness, you can make it even a bit more messy to treat multiple highlightable columns:
A=randi(10,8);
%ind = find(all(A==0,1)) %for actual data
ind=[5 2];
fprintf('A = \n\n');
for k1=1:size(A,1)
for k2=1:size(A,2)
if ismember(k2,ind)
fprintf(2,'%5d ',A(k1,k2));
else
fprintf('%5d ',A(k1,k2));
end
end
fprintf('\n');
end
fprintf('\n');
I also added some extra printouts to make it prettier. Result:
Highlighting with blue (links)
As an afterthought, after some discussion with Luis Mendo, I decided that it's worth overdoing a bit while we're at it. You can turn your numbers into blue-and-underlined hyperlinks, making use of the built-in parsing of the link HTML tag implemented both in disp and in fprintf. Here's the corresponding code:
A=randi(10,8);
ind=[5 2];
fieldlen=5; %width of output fields, i.e. 5 in '%5d'
fprintf('A = \n\n');
for k1=1:size(A,1)
for k2=1:size(A,2)
if ismember(k2,ind)
fprintf([repmat(' ',1,fieldlen-length(num2str(A(k1,k2)))) '%d '],A(k1,k2));
else
fprintf('%5d ',A(k1,k2));
end
end
fprintf('\n');
end
fprintf('\n');
This will turn the elements of the highlighted column(s) into strings of the form '3' for an example value of 3.
Another trick here is that hyperlinks starting with matlab: are parsed as proper matlab commands, which are activated when you click the link. You can try it by typing disp('link') in your command window. By setting ... we make sure that nothing happens when someone clicks on the now-link-valued highlighted numbers.
And on a technical note: we only want to include the actual number in the links (and not the preceding spaces), so we have to manually check the length of the string we are about to print (using length(num2str(A(k1,k2)))) and manually include the rest of the spaces before the number. This is done via the parameter fieldlen which I set at the beginning: this specifies the total width of each printing field, i.e. if we originally had fprintf('%5d',...) then we need to set fieldlen=5; for the same effect. Result:

Beginner Matrix Access in MATLAB

Now first off, I am not even sure this is called a matrix, and I am new to MATLAB. But let's say I have a "matrix" that looks like this:
for n=1:10
...
someImage = mat(:,:,n) %The "matrix"
...
end
where n could be the frames in a video, for example, and the first 2 ':' are the row and column data for the 2D image (the frame).
If I only wanted the first ':' of data (the row? column? element?), how would I access only that?
Intuitively, I think something like:
row1 = mat(:,0,0)
row2 = mat(0,:,0)
row3 = mat(0,0,:)
but that doesn't seem to be working.
P.S. I know that these aren't really rows, the terminology for all this would also be greatly appreciated
Also, it may not have anything to do with this, but I am using a MATLAB GUI as well, and the "matrix" is stored like this:
handles.mat(:,:,n)
I don't think it has anything to do with my actual question, but it might so I will put it here
-Thanks!
One point I would like to make before starting: MATLAB starts indexing at 1, and not 0. This is a common mistake that most people who have a C/Java/Python programming background make going into MATLAB.
Also, by doing:
row1 = mat(:,1,1);
This accesses all of the rows for the first column and the first frame of your video. Be aware that this will produce a M x 1 vector, where M denotes the number of rows for a frame in your video.
Also:
row2 = mat(1,:,1);
This accesses all of the columns in the first row of the first frame. Be aware that this will produce a 1 x N vector, where N denotes the number of columns for a frame in your video.
Also:
row3 = mat(1,1,:);
This accesses all of the pixels in the entire video sequence at row 1 and column 1. You can think of this as a temporal slice at the top left corner of your video sequence. Be aware that this will produce a 1 x 1 x T vector, where T is the number of frames in your video. If you access just a single pixel location in your video, the first two dimensions are superfluous, and so you can use the squeeze command to shrink all of the singleton dimensions so that it simplifies to a T x 1 vector. In other words, do this:
row3 = squeeze(mat(1,1,:));
FWIW, you do have the right terminology. Rows and columns are used in image / video processing all the time. As for the "matrix", you can call this a temporal sequence or a frame sequence in terms of video processing. It certainly is a 3D matrix, but people in this domain denote it as either one of the two as it is really a sequence of images / frames stacked on top of each other.

recording 'bursts' of samples at 300 samples per sec

I am recording voltage changes over a small circuit- this records mouse feeding. When the mouse is eating, the circuit voltage changes, I convert that into ones and zeroes, all is well.
BUT- I want to calculate the number and duration of 'bursts' of feeding- that is, instances of circuit closing that occur within 250 ms (75 samples) of one another. If the gap between closings is larger than 250ms I want to count it as a new 'burst'
I guess I am looking for help in asking matlab to compare the sample number of each 1 in the digital file with the sample number of the next 1 down- if the difference is more than 75, call the first 1 the end of one bout and the second one the start of another bout, classifying the difference as a gap, but if it is NOT, keep the sample number of the first 1 and compare it against the next and next and next until there is a 75-sample difference
I can compare each 1 to the next 1 down:
n=1; m=2;
for i = 1:length(bouts4)-1
if bouts4(i+1) - bouts4(i) >= 75 %250 msec gap at a sample rate of 300
boutend4(n) = bouts4(i);
boutstart4(m)= bouts4(i+1);
m = m+1;
n = n+1;
end
I don't really want to iterate through i for both variables though...
any ideas??
-DB
You can try the following code
time_diff = diff(bouts4);
new_feeding = time_diff > 75;
boutend4 = bouts4(new_feeding);
boutstart4 = [0; bouts4(find(new_feeding) + 1)];
That's actually not too bad. We can actually make this completely vectorized. First, let's start with two signals:
A version of your voltages untouched
A version of your voltages that is shifted in time by 1 step (i.e. it starts at time index = 2).
Now the basic algorithm is really:
Go through each element and see if the difference is above a threshold (in your case 75).
Enumerate the locations of each one in separate arrays
Now onto the code!
%// Make those signals
bout4a = bouts4(1:end-1);
bout4b = bouts4(2:end);
%// Ensure column vectors - you'll see why soon
bout4a = bout4a(:);
bout4b = bout4b(:);
% // Step #1
loc = find(bouts4b - bouts4a >= 75);
% // Step #2
boutend4 = [bouts4(loc); 0];
boutstart4 = [0; bouts4(loc + 1)];
Aside:
Thanks to tail.b.lo, you can also use diff. It basically performs that difference operation with the copying of those vectors like I did before. diff basically works the same way. However, I decided not to use it so you can see how exactly your code that you wrote translates over in a vectorized way. Only way to learn, right?
Back to it!
Let's step through this slowly. The first two lines of code make those signals I was talking about. An original one (up to length(bouts) - 1) and another one that is the same length but shifted over by one time index. Next, we use find to find those time slots where the time index was >= 75. After, we use these locations to access the bouts array. The ending array accesses the original array while the starting array accesses the same locations but moved over by one time index.
The reason why we need to make these two signals column vector is the way I am appending information to the starting vector. I am not sure whether your data comes in rows or columns, so to make this completely independent of orientation, I'm going to make sure that your data is in columns. This is because if I try to append a 0, if I do it to a row vector I have to use a space to denote that I'm going to the next column. If I do it for a column vector, I have to use a semi-colon to go to the next row. To completely avoid checking to see whether it's a row or column vector, I'm going to make sure that it's a column vector no matter what.
By looking at your code m=2. This means that when you start writing into this array, the first location is 0. As such, I've artificially placed a 0 at the beginning of this array and followed that up with the rest of the values.
Hope this helps!

matlab: understanding matlab behavior

Could somebody explain the following code snippet? I have no background in computer science or programming and just recently became aware of Matlab. I understand the preallocation part from data=ceil(rand(7,5)*10)... to ...N*(N-1)/2).
I need to understand every aspect of how matlab processes the code from kk=0 to the end. Also, the reasons why the code is codified in that manner. There's no need to explain the function of: bsxfun(#minus), just how it operates in the scheme of the code.
data=ceil(rand(7,5)*10);
N = size(data,2);
b=cell(N-1,1);
c=NaN(size(data,1),N*(N-1)/2);
kk=0;
for ii=1:N-1
b{ii} = bsxfun(#minus,data(:,ii),data(:,ii+1:end));
c(:,kk+(1:N-ii)) = bsxfun(#minus,data(:,ii),data(:,ii+1:end));
kk=kk+N-ii;
end
Start at zero
kk=0;
Loop with ii going from 1 up to N-1 incrementing by 1 every iteration. Type 1:10 in the command line of matlab and you'll see that it outputs 1 2 3 4 5 6 7 8 9 10. Thuis colon operator is a very important operator to understand in matlab.
for ii=1:N-1
b{ii} = ... this just stores a matrix in the next element of the cell vector b. Cell arrays can hold anything in each of their elements, this is necessary as in this case each iteration is creating a matrix with one fewer column than the previous iteration.
data(:,ii) --> just get the iith column of the matrix data (: means get all the rows)
data(:, ii + 1:end) means get a subset of the matrix data consisting of all the rows but only of columns that appear after column ii
bsxfun(#minus, data(:,ii), data(:,ii+1:end)) --> for each column in the matrix data(:, ii+1:end), subtract the single column data(:,ii)
b{ii} = bsxfun(#minus,data(:,ii),data(:,ii+1:end));
%This does the same thing as the line above but instead of storing the resulting matrix of the loop in a separate cell of a cell array, this is appending the original array with the new matrix. Note that the new matrix will have the same number of rows each time but one fewer column, so this appends as new columns.
%c(:,kk + (1:N-ii)) = .... --> So 1:(N-ii) produces the numbers 1 up to the number of columns in the result of this iteration. In matlab, you can index an array using another array. So for example try this in the command line of matlab: a = [0 0 0 0 0]; a([1 3 5]) = 1. The result you should see is a = 1 0 1 0 1. but you can also extend a matrix like this so for example now type a(6) = 2. The result: a = 1 0 1 0 1 2. So by using c(:, 1:N-ii) we are indexing all the rows of c and also the right number of columns (in order). Adding the kk is just offsetting it so that we do not overwrite our previous results.
c(:,kk+(1:N-ii)) = bsxfun(#minus,data(:,ii),data(:,ii+1:end));
Now we just increment kk by the number of new columns we added so that in the next iteration, c is appended at the end.
kk=kk+N-ii;
end;
I suggest that you put a breakpoint in this code and step through it line by line and look at how the variables change in matlab. To do this click on the little dashed line next to k=0; in the mfile, you will see a red dot appear there, and then run the code. The code will only execute as far as the dot, you are now in debug mode. If you hover over a variable in debug mode matlab will show its contents in a tool tip. For a really big variable check it out in the workspace. Now step through the code line by line and use my explanations above to make sure you understand how each line is changing each variable. For more complex lines like b{ii} = bsxfun(#minus,data(:,ii),data(:,ii+1:end)); you should highlight code snippets and ruin these in the command line to see what each part is doing so for example run data(:,ii) to see what that does and then try data(:,ii+1:end)) or even just ii+1:end (well in that case it wont work, replace end with size(data, 2)). Debugging is the best way to understand code that confuses you.
bsxfun(#minus,A,B)
is almost the same as
A-B
The difference is that the bsxfun version will handle inputs of different size: In each dimension (“direction,” if you find it easier to think about that way), if one of the inputs is scalar and the other one a vector, the scalar one will simply be repeated sufficiently often.
http://www.mathworks.com/help/techdoc/ref/bsxfun.html