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As a general rule, functions should already be written with matrix arguments in mind and should consider whole matrix operations in a vectorized manner. Sometimes, writing functions in this way appears difficult or impossible for various reasons. For those situations, Octave provides facilities for applying a function to each element of an array, cell, or struct.
Execute a function on each element of an array.
This is useful for functions that do not accept array arguments. If the function does accept array arguments it is better to call the function directly.
The first input argument fcn can be a string, a function handle, an
inline function, or an anonymous function. The input argument A can be a
logical array, a numeric array, a string array, a structure array, or a cell
array. arrayfun passes all elements of A individually to the
function fcn and collects the results. The equivalent pseudo-code is
cls = class (fcn (A(1)); B = zeros (size (A), cls); for i = 1:numel (A) B(i) = fcn (A(i)) endfor
The named function can also take more than two input arguments, with the input arguments given as third input argument A2, fourth input argument A2, ... If given more than one array input argument then all input arguments must have the same sizes. For example:
arrayfun (@atan2, [1, 0], [0, 1])
⇒ [ 1.57080 0.00000 ]
If the parameter val after a further string input argument
"UniformOutput" is set true (the default), then the named
function fcn must return a single element which then will be concatenated
into the return value and is of type matrix. Otherwise, if that parameter is
set to false, then the outputs are concatenated in a cell array. For
example:
arrayfun (@(x,y) x:y, "abc", "def", "UniformOutput", false)
⇒
{
[1,1] = abcd
[1,2] = bcde
[1,3] = cdef
}
If more than one output arguments are given then the named function must return the number of return values that also are expected, for example:
[A, B, C] = arrayfun (@find, [10; 0], "UniformOutput", false)
⇒
A =
{
[1,1] = 1
[2,1] = [](0x0)
}
B =
{
[1,1] = 1
[2,1] = [](0x0)
}
C =
{
[1,1] = 10
[2,1] = [](0x0)
}
If the parameter errfcn after a further string input argument
"ErrorHandler" is another string, a function handle, an inline
function, or an anonymous function, then errfcn defines a function to
call in the case that fcn generates an error. The definition of the
function must be of the form
function […] = errfcn (s, …)
where there is an additional input argument to errfcn relative to
fcn, given by s. This is a structure with the elements
"identifier", "message", and "index" giving,
respectively, the error identifier, the error message, and the index of the
array elements that caused the error. The size of the output argument of
errfcn must have the same size as the output argument of fcn,
otherwise a real error is thrown. For example:
function y = ferr (s, x), y = "MyString"; endfunction
arrayfun (@str2num, [1234],
"UniformOutput", false, "ErrorHandler", @ferr)
⇒
{
[1,1] = MyString
}
Compute f (S) for the nonzero elements of S.
The input function f is applied only to the nonzero elements of the input matrix S which is typically sparse. The function f can be passed as a string, function handle, or inline function.
The output y is a sparse matrix with the same sparsity structure as
the input S. spfun preserves sparsity structure which is
different than simply applying the function f to the sparse matrix
S when f (0) != 0.
Example
Sparsity preserving spfun versus normal function application
S = pi * speye (2,2) S = Compressed Column Sparse (rows = 2, cols = 2, nnz = 2 [50%]) (1, 1) -> 3.1416 (2, 2) -> 3.1416 y = spfun (@cos, S) y = Compressed Column Sparse (rows = 2, cols = 2, nnz = 2 [50%]) (1, 1) -> -1 (2, 2) -> -1
y = cos (S) y = Compressed Column Sparse (rows = 2, cols = 2, nnz = 4 [100%]) (1, 1) -> -1 (2, 1) -> 1 (1, 2) -> 1 (2, 2) -> -1
Evaluate the function fcn on the elements of the cell array C.
cellfun accepts an arbitrary function fcn given as a name in a
character string, as a function handle, or as an inline function. Specifying
fcn with a character string is preferred as the performance is ~3X better
for builtin functions and equivalent for m-files.
cellfun has a limited number of functions which have been
specially-coded for high-performance (~8X faster than a function handle).
These functions are only used if the function is specified by name as a string,
and only the simplest calling form—cellfun ('fcn'), C)—without options is supported. If you need access to an
overloaded version of a function, such as numel for a particular
classdef file, then you cannot use the accelerated function name and
must use a function handle instead, e.g., @numel.
The high-performance functions are
'isempty'Return true for empty elements.
'islogical'Return true for logical elements.
'isnumeric'Return true for numeric elements.
'isreal'Return true for real elements.
'length'Return a vector of the lengths of cell elements.
'ndims'Return the number of dimensions of each element.
'numel''prodofsize'Return the number of elements contained within each cell element. The number is the product of the dimensions of the object of each cell element.
'size'Return the size along dimension dim.
'isclass'Return true for elements which are of type class.
Elements in C are passed to the function individually and the result of each function invocation is collected in the output. The function can take more than one argument with the inputs arguments given by C1, C2, etc. Input arguments that are singleton (1x1) cells will be automatically expanded to the size of the other arguments. For example:
cellfun ("atan2", {1, 0}, {0, 1})
⇒ [ 1.57080 0.00000 ]
The number of output arguments of cellfun matches the number of output
arguments of the function and can be greater than one. When there are multiple
outputs of the function they will be collected into the output arguments of
cellfun like this:
function [a, b] = twoouts (x)
a = x;
b = x*x;
endfunction
[aa, bb] = cellfun (@twoouts, {1, 2, 3})
⇒
aa =
1 2 3
bb =
1 4 9
Note that, by default, the output argument(s) are arrays of the same size as the input arguments.
If the parameter "UniformOutput" is set to true (the default), then the
function must return scalars which will be concatenated into the return
array(s). If "UniformOutput" is false, the outputs are concatenated
into a cell array (or cell arrays). For example:
cellfun ("lower", {"Foo", "Bar", "FooBar"},
"UniformOutput", false)
⇒ {"foo", "bar", "foobar"}
The parameter "ErrorHandler" specifies a function errfcn to call
if fcn generates an error. The form of the function is
function […] = errfcn (s, …)
where there is an additional input argument to errfcn relative to
fcn, given by s. This is a structure with the elements
"identifier", "message", and "index" giving
respectively the error identifier, the error message, and the index into the
input arguments of the element that caused the error. For example:
function y = foo (s, x), y = NaN; endfunction
cellfun ("factorial", {-1,2}, "ErrorHandler", @foo)
⇒ [NaN 2]
Programming Note: Use cellfun intelligently. The cellfun
function is a useful tool for avoiding loops. It is often used 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:
C = {…}
v = cellfun (@(x) det (x), C); # compute determinants
v = cellfun (@det, C); # 40% faster
Evaluate the function named name on the fields of the structure S. The fields of S are passed to the function fcn individually.
structfun accepts an arbitrary function fcn in the form of an
inline function, function handle, or the name of a function (in a character
string). In the case of a character string argument, the function must
accept a single argument named x, and it must return a string value.
If the function returns more than one argument, they are returned as
separate output variables.
If the parameter "UniformOutput" is set to true (the default), then
the function must return a single element which will be concatenated into
the return value. If "UniformOutput" is false, the outputs are
placed into a structure with the same fieldnames as the input structure.
s.name1 = "John Smith";
s.name2 = "Jill Jones";
structfun (@(x) regexp (x, '(\w+)$', "matches"){1}, s,
"UniformOutput", false)
⇒ scalar structure containing the fields:
name1 = Smith
name2 = Jones
Given the parameter "ErrorHandler", errfcn defines a function
to call in case fcn generates an error. The form of the function is
function […] = errfcn (se, …)
where there is an additional input argument to errfcn relative to
fcn, given by se. This is a structure with the
elements "identifier", "message" and "index",
giving respectively the error identifier, the error message, and the index
into the input arguments of the element that caused the error. For an
example on how to use an error handler, see cellfun.
Consistent with earlier advice, seek to use Octave built-in functions whenever
possible for the best performance. This advice applies especially to the four
functions above. For example, when adding two arrays together
element-by-element one could use a handle to the built-in addition function
@plus or define an anonymous function @(x,y) x + y. But, the
anonymous function is 60% slower than the first method.
See Operator Overloading, for a list of basic functions which might be used
in place of anonymous ones.
Next: Accumulation, Previous: Broadcasting, Up: Vectorization and Faster Code Execution [Contents][Index]