Cookbook

An Octave cookbook. Each entry should go in a separate section and have the following subsection: problem, solution, discussion and maybe a see also.

Programs, Libraries, and Packages

Recipes for developers of Octave programs and libraries. The type of stuff an Octave programmer should be aware when writing code for others.

Find Octave configuration

Octave can be built with many configurations so programs may end up running in a machine without features they need. Developers should never expect an Octave installation to have all features. And programs should identify if the required features are available.

This is a list of possible tests to check for features:

   ## support for 64 bit indexing
   sizemax () > intmax ("int32")

   ## built with support for java
   usejava ("jvm")

   ## Image IO with support for tif files
   any (cellfun (@(x) ismember ("tif", x), {imformats.ext}))
   ## Image IO with support for png files
   any (cellfun (@(x) ismember ("png", x), {imformats.ext}))

Find if a package is installed

Problem

You have a program that uses different functions or behaves different depending on the availability of specific packages.

Solution

Use pkg ("describe", pkg-name) like so:

if (! isempty (pkg ("describe", "foo")))
  ## use functions from package foo, the prefered way
elseif (! isempty (pkg ("describe", "bar")))
  ## use functions from package bar, not so optimal
else
  ## default case
endif

Discussion

It's not recommended to use this if the only purpose is to then fail in the absence of the package. In such case, simply try to load the package and Octave will already give a error message that is informative enough.

There is only purpose to check this, if there is something different to do if a package is missing. The same is true for catching an error from pkg load. If you only catch an error to then throw it again then you might as well not catch it in the first place.

## This contraption doesn't add anything.  If 'pkg load' fails, it
## will already give an error message to the user.
try
  pkg load foo;
catch
  error ("failed to load foo: %s", lasterr ());
end_try_catch

## Again, doesn't add anything.  The failure of 'pkg load' is enough
if (isempty (pkg ("describe", "foo")))
  error ("program: package foo is not installed");
endif

Beware that an installed package is not always a guarantee that a function will be available. Some packages may disable functions at build time, or specific functions may have specific runtime requirements.

Structures

Retrieve a field value from all entries in a struct array

Problem

You have a struct array with multiple fields, and you want to access the value from a specific field from all elements. For example, you want to return the age from all patients in the following case:

 samples = struct ("patient", {"Bob", "Kevin", "Bob" , "Andrew"},
                   "age",     { 45  ,  52    ,  45   ,  23     },
                   "protein", {"H2B", "CDK2" , "CDK2", "Tip60" },
                   "tube"   , { 3   ,  5     ,  2    ,  18     }
                   );

Solution

Indexing the struct returns a comma separated list so use them to create a matrix.

 [samples(:).age]

This however does not keep the original structure of the data, instead returning all values in a single column. To fix this, use reshape().

 reshape ([samples(:).age], size (samples))

Discussion

Returning all values in a comma separated lists allows you to make anything out of them. If numbers are expected, create a matrix by enclosing them in square brackets. But if strings are to be expected, a cell array can also be easily generated with curly brackets

 {samples(:).patient}

You are also not limited to return all elements, you may use logical indexing from other fields to get values from the others:

 [samples([samples(:).age] > 34).tube]                 ## return tube numbers from all samples from patients older than 34
 [samples(strcmp({samples(:).protein}, "CDK2")).tube]  ## return all tube numbers for protein CDK2

Array manipulation

Select a slice from an n-D array

Problem

For an array A with arbitrary number of dimensions, select, for example, the first column. This would be A(:, 1) if A was 2-D, A(:, 1, :) if A was 3-D, and so on.

Solution

One possibility is to use subsref with the input idx created dynamically with repelems to have the right number of dimensions. This can be written as a function:

function [B]= array_slice (A,k,d) #return the k-th slice (row, column...) of A, with d specifying the dimension to slice on idx.type = "()"; idx.subs = repelems ({':'}, [1;ndims(A)]); idx.subs(d) = k; B = subsref (A,idx); endfunction #test cases %!shared A %! A=rand(2, 3); %!assert (array_slice (A,1,2), A(:, 1)) %! A=rand(2, 3, 4); %!assert (array_slice (A,2,1), A(2, :, :)) %! A=rand(2, 3, 4, 5); %!assert (array_slice (A,1,2), A(:, 1, :, :)) %! A=rand(2, 3, 4, 5, 6); %!assert (array_slice (A,2,3), A(:, :, 2, :, :))

To remove the singleton dimension d from the result B, use

B = reshape(B, [size(B)([1:d-1 d+1:end])]);

Input/output

Display matched elements from different arrays

Problem

You have two, or more, arrays with paired elements and want to print out a string about them. For example:

   keys   = {"human",  "mouse", "chicken"};
   values = [ 64        72       70      ];

and you want to display:

   Calculated human genome GC content is 64%
   Calculated mouse genome GC content is 72%
   Calculated chicken genome GC content is 70%

Solution

Make a two rows cell array, with each paired data in a column and supply a cs-list to printf

   values = num2cell (values);
   new    = {keys{:}; values{:}};
   printf ("Calculated %s genome GC content is %i%%\n", new{:})

or in a single line:

   printf ("Calculated %s genome GC content is %i%%\n", {keys{:}; num2cell(values){:}}{:})
   

Discussion

printf and family do not accept cell arrays as values. However, they keep repeating the template given as long as it has enough arguments to keep going. As such, the trick is on supplying a cs-list of elements which can be done by using a cell array and index it with {}.

Since values are stored in column-major order, paired values need to be on the same column. A new row of data can then be added later with new(end+1,:) = {"Andrew", "Bob", "Kevin"}. Note that normal brackets are now being used for indexing.

Swap values

If you want to exchange the value between two variables without creating a dummy one, you can simply do:

Code: Swap values without dummy variable

[b,a] = deal (a,b);

Collect all output arguments of a function

If you have a function that returns several values, e.g.

function [a b c]= myfunc () [a,b,c] = deal (1,2,3); endfunction

and you want to collect them all into a single cell (similarly to Python's zip() function) you can do:

Code: Collect multiple output arguments

outargs = nthargout (1:3, @myfunc)

Create a text table with fprintf

(a.k.a. A funny formatting trick with fprintf found by chance)

Imagine that you want to create a text table with fprintf with 2 columns of 15 characters width and both right justified. How to do this thing?

That's easy:

If the variable Text is a cell array of strings (of length <15) with two columns and a certain number of rows, simply type for the kth row of Text

fprintf('%15.15s | %15.15s\n', Text{k,1}, Text{k,2});

The syntax '%<n>.<m>s' allocates '<n>' places to write chars and display the '<m>' first characters of the string to display.

Example:

Code: Example create a text table with fprintf

octave:1> Text={'Hello','World'}; octave:2> fprintf('%15.15s | %15.15s\n', Text{1,1}, Text{1,2}) Hello | World

Load comma separated values (*.csv) files

Code: Load comma separated values files

A=textread("file.csv", "%d", "delimiter", ","); B=textread("file.csv", "%s", "delimiter", ","); inds = isnan(A); B(!inds) = num2cell(A(!inds))

This gets you a 1 column cell array. You can reshape it to the original size by using the reshape function

The next version of octave (3.6) implements the CollectOutput switch as seen in example 8 here: http://www.mathworks.com/help/techdoc/ref/textscan.html

Another option is to use the function csvread, however this function can't handle non-numerical data.

The probably best option is to use the function csv2cell() from the io package. This function can read mixed-type (numerical and text) .csv files, allows to specify other field separators than a comma and other text protection characters (default: " double quote) and can skip headerlines. If you have the io package installed and loaded, type "help csv2cell" at the Octave prompt for more info.

Load XML files

Reading XML in octave can be achieved using the java library Xerces (from apache).

It seems that the matlab's xmlread is just a thin wrapper around the Xerces library. One should note however, that Java functions have the working directory set to the working directory when octave starts and the working directory is not modified by a cd in octave. Matlab has the same behavior, as Java does not provide a way to change the current working directory (http://bugs.java.com/bugdatabase/view_bug.do?bug_id=4045688). To avoid any issues, it is thus better to use the absolute path to the XML file.

You need the jar files xercesImpl.jar and xml-apis.jar from e.g. https://www.apache.org/dist/xerces/j/Xerces-J-bin.2.11.0.tar.gz (check for the latest version). Use javaaddpath to include these files:

Code: Define java path

javaaddpath('/path/to/xerces-2_11_0/xercesImpl.jar'); javaaddpath('/path/to/xerces-2_11_0/xml-apis.jar');

A sample script:

Code: Load XML file

filename = 'sample.xml'; % These 3 lines are equivalent to xDoc = xmlread(filename) in matlab parser = javaObject('org.apache.xerces.parsers.DOMParser'); parser.parse(filename); xDoc = parser.getDocument; % get first data element elem = xDoc.getElementsByTagName('data').item(0); % get text from child data = elem.getFirstChild.getTextContent % get attribute named att att = elem.getAttribute('att')

The file sample.xml:

Code: Sample XML file

<root> <data att="1">hello</data> </root>

Using variable strings in commands

For example, to plot data using a string variable as a legend:

Option 1 (simplest):

Code: Using variable strings in commands. op1

legend = "-1;My data;"; plot(x, y, legend);

Option 2 (to insert variables):

Code: Using variable strings in commands. op2

plot(x, y, sprintf("-1;%s;", dataName));

Option 3 (not as neat):

Code: Using variable strings in commands. op3

legend = 'my legend'; plot_command = ['plot(x,y,\';',legend,';\')']; eval(plot_command);

These same tricks are useful for reading and writing data files with unique names, etc.

Combinatorics

Combinations with string characters

Problem

You want to get all combinations of different letters but nchoosek only accepts numeric input.

Solution

Convert your string to numbers and then back to characters.

char (nchoosek (uint8 (string), n)

Discussion

A string in Octave is just a character matrix and can easily be converted to numeric form back and forth. Each character has an associated number (the asci function of the miscellaneous package displays a nicely formatted conversion table).

Permutations with repetition

Problem

You want to generate all possible permutations of a vector with repetition.

Solution

Use ndgrid

[x y z] = ndgrid ([1 2 3 4 5]); [x(:) y(:) z(:)]

Discussion

It is possible to expand the code above and make it work for any length of permutations.

cart = nthargout ([1:n], @ndgrid, vector); combs = cell2mat (cellfun (@(c) c(:), cart, "UniformOutput", false));

Mathematics

Test if a number is a integer

There are several methods to do this. The simplest method is probably fix (x) == x

Find if a number is even/odd

Problem

You have a number, or an array or matrix of them, and want to know if any of them is an odd or even number, i.e., their parity.

Solution

Check the remainder of a division by two. If the remainder is zero, the number is odd.

 mod (value, 2) ## 1 if odd, zero if even

Since mod() acceps a matrix, the following can be done:

 any  (mod (values, 2)) ## true if at least one number in values is even
 all  (mod (values, 2)) ## true if all numbers in values are odd
 
 any (!logical (mod (values, 2))) ## true if at least one number in values is even
 all (!logical (mod (values, 2))) ## true if all numbers in values are even

Discussion

Since we are checking for the remainder of a division, the first choice would be to use rem(). However, in the case of negative numbers mod() will still return a positive number making it easier for comparisons. Another alternative is to use bitand (X, 1) or bitget (X, 1) but those are a bit slower.

Note that this solution applies to integers only. Non-integers such as 1/2 or 4.201 are neither even nor odd. If the source of the numbers are unknown, such as user input, some sort of checking should be applied for NaN, Inf, or non-integer values.

See also

Find if a number is an integer.

Parametrized Functions

Problem

One sometimes needs to define a family of functions depending on a set of parameters, e.g., $f(x,y,z;a,b,c)$ where $x,y,z$ denote a the variables on which the function operates and $a,b,c$ are the parameters used to chose one specific element of the family of functions.

For example, let's say we need to compute the time evolution of the elongation of a spring for different values of the spring constant $k$

Solution

We could solve the problem with the following code:

Code: Solve spring equation for different values of the spring constant

t = linspace (0, 10, 100); function sprime = spring (s, t, k) x = s(1); v = s(2); sprime(1) = v; sprime(2) = -k * x; endfunction k = 1; x1 = lsode (@(x, t) spring (x, t, k), [1;0], t)(:, 1); k = 2; x2 = lsode (@(x, t) spring (x, t, k), [1;0], t)(:, 2); plot (t, x1, t, x2) legend ('x1', 'x2')

Discussion

In the above example, the function "sprime" represents a family of functions of the variables $x,t$ parametrized by the parameter $k$.

The anonymous function

@(x, t) sprime (x, t, k)

is a function of only $x,t$ where the parameter $k$ is 'frozen' to the value it has at the moment in the current scope.

Distance between points

Problem

Given a set of points in space we want to calculate the distance between all of them. Each point is described by its components $(x_{i},y_{i},\ldots )$. Asusme that the points are saved in a matrix P with N rows (one for each point) and D columns, one for each component.

Solution

One way of proceeding is to use the broadcast properties of operators in GNU Octave. The square distance between the points can be calculated with the code

Code: Calculate square distance between points

[N, dim] = size (P); Dsq = zeros (N); for i = 1:dim Dsq += (P(:,i) - P(:,i)').^2; endfor

This matrix is symmetric with zero diagonal.

Similarly the vectors pointing from one point to the another is

Code: Calculate radius vector between points

R = zeros (N,N,dim); for i = 1:dim R(:,:,i) = P(:,i) - P(:,i)'; endfor

The relation between Dsq and R is

Dsq = sumsq (R,3);

Discussion

The calculation can be implemented using functions like cellfun and avoid the loop over components of the points. However in most cases we will have more points than components and the improvement, if any, will be minimal.

Another observation is that the matrix Dsq is symmetric and we could store only the lower or upper triangular part. To use this optimization in a practical way check the help of the functions vech and unvech (this one is in the Forge package general). Two functions that haven't seen the light yet are sub2ind_tril and ind2sub_tril (currently private functions in the Forge package mechanics) that are useful to index the elements of a vector constructed with the function vech. Each page (the third index) of the multidimensional array R is an anti-symmetric matrix and we could also save some memory by keeping only one of the triangular submatrices.

Check the Geometry package for many more distance functions (points, lines, polygons, etc.).