C.2 Tips for Making Code Run Faster.

Here are some ways of improving the execution speed of Octave programs.

• Vectorize loops. For instance, rather than

  for i = 1:n-1 a(i) = b(i+1) - b(i); endfor

  write

  a = b(2:n) - b(1:n-1);

  This is especially important for loops with "cheap" bodies. Often it suffices to vectorize just the innermost loop to get acceptable performance. A general rule of thumb is that the "order" of the vectorized body should be greater or equal to the "order" of the enclosing loop.

• Use built-in and library functions if possible. Built-in and compiled functions are very fast. Even with a m-file library function, chances are good that it is already optimized, or will be optimized more in a future release.
• Avoid computing costly intermediate results multiple times. Octave currently does not eliminate common subexpressions.
• Be aware of lazy copies (copy-on-write). When a copy of an object is created, the data is not immediately copied, but rather shared. The actual copying is postponed until the copied data needs to be modified. For example:

  a = zeros (1000); # create a 1000x1000 matrix b = a; # no copying done here b(1) = 1; # copying done here

  Lazy copying applies to whole Octave objects such as matrices, cells, struct, and also individual cell or struct elements (not array elements).

  Additionally, index expressions also use lazy copying when Octave can determine that the indexed portion is contiguous in memory. For example:

  a = zeros (1000); # create a 1000x1000 matrix b = a(:,10:100); # no copying done here b = a(10:100,:); # copying done here

  This applies to arrays (matrices), cell arrays, and structs indexed using (). Index expressions generating cs-lists can also benefit of shallow copying in some cases. In particular, when a is a struct array, expressions like {a.x}, {a(:,2).x} will use lazy copying, so that data can be shared between a struct array and a cell array.

  Most indexing expressions do not live longer than their `parent' objects. In rare cases, however, a lazily copied slice outlasts its parent, in which case it becomes orphaned, still occupying unnecessarily more memory than needed. To provide a remedy working in most real cases, Octave checks for orphaned lazy slices at certain situations, when a value is stored into a "permanent" location, such as a named variable or cell or struct element, and possibly economizes them. For example

  a = zeros (1000); # create a 1000x1000 matrix b = a(:,10:100); # lazy slice a = []; # the original a array is still allocated c{1} = b; # b is reallocated at this point

• Avoid deep recursion. Function calls to m-file functions carry a relatively significant overhead, so rewriting a recursion as a loop often helps. Also, note that the maximum level of recursion is limited.
• Avoid resizing matrices unnecessarily. When building a single result matrix from a series of calculations, set the size of the result matrix first, then insert values into it. Write

  result = zeros (big_n, big_m) for i = over:and_over r1 = … r2 = … result (r1, r2) = new_value (); endfor

  instead of

  result = []; for i = ever:and_ever result = [ result, new_value() ]; endfor

  Sometimes the number of items can't be computed in advance, and stack-like operations are needed. When elements are being repeatedly inserted at/removed from the end of an array, Octave detects it as stack usage and attempts to use a smarter memory management strategy preallocating the array in bigger chunks. Likewise works for cell and struct arrays.

  a = []; while (condition) … a(end+1) = value; # "push" operation … a(end) = []; # "pop" operation … endwhile

• Use cellfun intelligently. The cellfun function is a useful tool for avoiding loops. See section Processing Data in Cell Arrays. cellfun is often use with anonymous function handles; however, calling an anonymous function involves an overhead quite comparable to the overhead of an m-file function. Passing a handle to a built-in function is faster, because the interpreter is not involved in the internal loop. For example:

  a = {…} v = cellfun (@(x) det(x), a); # compute determinants v = cellfun (@det, a); # faster

• Avoid calling eval or feval excessively, because they require Octave to parse input or look up the name of a function in the symbol table.

  If you are using eval as an exception handling mechanism and not because you need to execute some arbitrary text, use the try statement instead. See section The try Statement.

• If you are calling lots of functions but none of them will need to change during your run, set the variable ignore_function_time_stamp to "all" so that Octave doesn't waste a lot of time checking to see if you have updated your function files.