.. highlightlang:: us

.. _functions-for-vectors-and-matrices:

Functions for Vectors and Matrices
==================================

This chapter introduces some important vector and matrix functions. More
information about these functions is available through the online help system.

The :ref:`zeros` and :ref:`ones` functions create a vector or a matrix where all
elements have the value 0 or 1. The function call ``zeros(nr, nc)`` returns a
zero matrix with nr rows and nc columns. ``zeros(1, 10) + 1.0`` is equivalent to
the expression ``ones(1, 10)``. The :ref:`rand` function (``rand(nr, nc)``)
function returns a matrix with random numbers in the range 0 to 1.

The ``size(x)`` function returns the size of the variable
``x``. The size is a 1 * 2 vector. The first element is the
number of  rows and the second is the number of columns. Example:

::

   * size(rand(3, 4))
       3  4

The function :ref:`nr` returns the number of rows of a matrix
or a vector. The function :ref:`nc` returns the number of columns of
a matrix or a vector. The function :ref:`len` returns the number of
elements of a matrix or vector. The expression 
``len(x) == nr(x) * nc(x)`` is true. Some examples:

::

   v[len(v):1] = v[1:len(v)]

changes the element order of a vector. In the same way, the
statement

::

   m[1:nr(m);] = m[nr(m):1;]

changes the row order of a matrix and

::

   m[;1:nc(m)] = m[;nc(m):1]

changes the column order.

The statement

::

   m = m[; 2:nc(m), 1]

"rotates" the matrix columns, i.e. moves the first 
column behind the last column of the matrix ``m``.

::

   v = v[1:3-1, 3+1:len(v)]

removes the 3rd element from a vector. The following statement 
removes the first element of a vector

::

   v = v[2:len(v)]

and

::

   v = v[1:len(v)-1]

removes the last element.

The matrix data type can be retrieved with the function :ref:`type`. The 
function returns one of the following strings: ``"real"``, ``"complex"``, 
``"string"``, ``"undef"``, or ``"function"``.

The :ref:`min` function returns the minimum of its argument vector. If the 
argrument is a matrix, :ref:`min` returns a row vector with the minimum of 
the matrix columns. The :ref:`max` function returns the maximum of a vector 
or matrix:

::

   * m = rand(2,2)
   * m
       0.3237   0.2887
       0.3244   0.3530
   * min(m)
       0.3237   0.1540
   * max(m)
       0.4934   0.3530

Double use of the function returns the smallest or largest of 
all matrix elements: ``min(min(m))`` or ``max(max(m))``.

The :ref:`sort` function can sort the elements of a vector or a matrix. If the
function argument is a matrix, all rows  will be sorted by the first column.

::

   * srand() // Sets the seed to the standard value
       1.0000
   * m = rand(3,4)
   * m
       0.7744   0.2484  0.1606  0.6082
       0.3925   0.7937  0.4888  0.1344
       0.6235   0.9313  0.6486  0.8489
   * sort(m)
       0.3925   0.7937  0.4888  0.1344
       0.6235   0.9313  0.6486  0.8489
       0.7744   0.2484  0.1606  0.6082

The :ref:`find` function returns the indices of all values which are not equal
to 0. :ref:`find` is mainly used in conjunction with comparison operators::

   * a = [1,7,5,22]
   * a <= 5
       1.0000   0.0000  1.0000  0.0000
   * find(a <= 5)
       1.0000   3.0000

The next statement will set all elements of the vector 
``a`` which are less than 5 to the value 9::

   a[find(a < 5)] = 9;

:sub:`id-1594549`