(octave.info)The for Statement

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10.5 The for Statement
======================

The ‘for’ statement makes it more convenient to count iterations of a
loop.  The general form of the ‘for’ statement looks like this:

     for VAR = EXPRESSION
       BODY
     endfor

where BODY stands for any statement or list of statements, EXPRESSION is
any valid expression, and VAR may take several forms.  Usually it is a
simple variable name or an indexed variable.  If the value of EXPRESSION
is a structure, VAR may also be a vector with two elements.  Note:
Looping Over Structure Elements, below.

   The assignment expression in the ‘for’ statement works a bit
differently than Octave’s normal assignment statement.  Instead of
assigning the complete result of the expression, it assigns each column
of the expression to VAR in turn.  If EXPRESSION is a range, a row
vector, or a scalar, the value of VAR will be a scalar each time the
loop body is executed.  If VAR is a column vector or a matrix, VAR will
be a column vector each time the loop body is executed.

   The following example shows another way to create a vector containing
the first ten elements of the Fibonacci sequence, this time using the
‘for’ statement:

     fib = ones (1, 10);
     for i = 3:10
       fib(i) = fib(i-1) + fib(i-2);
     endfor

This code works by first evaluating the expression ‘3:10’, to produce a
range of values from 3 to 10 inclusive.  Then the variable ‘i’ is
assigned the first element of the range and the body of the loop is
executed once.  When the end of the loop body is reached, the next value
in the range is assigned to the variable ‘i’, and the loop body is
executed again.  This process continues until there are no more elements
to assign.

   Within Octave is it also possible to iterate over matrices or cell
arrays using the ‘for’ statement.  For example consider

     disp ("Loop over a matrix")
     for i = [1,3;2,4]
       i
     endfor
     disp ("Loop over a cell array")
     for i = {1,"two";"three",4}
       i
     endfor

In this case the variable ‘i’ takes on the value of the columns of the
matrix or cell matrix.  So the first loop iterates twice, producing two
column vectors ‘[1;2]’, followed by ‘[3;4]’, and likewise for the loop
over the cell array.  This can be extended to loops over
multi-dimensional arrays.  For example:

     a = [1,3;2,4]; c = cat (3, a, 2*a);
     for i = c
       i
     endfor

In the above case, the multi-dimensional matrix C is reshaped to a
two-dimensional matrix as ‘reshape (c, rows (c), prod (size
(c)(2:end)))’ and then the same behavior as a loop over a
two-dimensional matrix is produced.

   Although it is possible to rewrite all ‘for’ loops as ‘while’ loops,
the Octave language has both statements because often a ‘for’ loop is
both less work to type and more natural to think of.  Counting the
number of iterations is very common in loops and it can be easier to
think of this counting as part of looping rather than as something to do
inside the loop.

Looping Over Structure Elements