### 4.1 Matrices

It is easy to define a matrix of values in Octave. The size of the matrix is determined automatically, so it is not necessary to explicitly state the dimensions. The expression

         a = [1, 2; 3, 4]

results in the matrix

                 /      \
                 | 1  2 |
           a  =  |      |
                 | 3  4 |
                 \      /

Elements of a matrix may be arbitrary expressions, provided that the dimensions all make sense when combining the various pieces. For example, given the above matrix, the expression

         [ a, a ]

produces the matrix

         ans =

           1  2  1  2
           3  4  3  4

but the expression

         [ a, 1 ]

produces the error

         error: number of rows must match near line 13, column 6

(assuming that this expression was entered as the first thing on line 13, of course).

Inside the square brackets that delimit a matrix expression, Octave looks at the surrounding context to determine whether spaces and newline characters should be converted into element and row separators, or simply ignored, so an expression like

         a = [ 1 2
               3 4 ]

will work. However, some possible sources of confusion remain. For example, in the expression

         [ 1 - 1 ]

the ‘`-`’ is treated as a binary operator and the result is the scalar 0, but in the expression

         [ 1 -1 ]

the ‘`-`’ is treated as a unary operator and the result is the vector `[ 1, -1 ]`. Similarly, the expression

         [ sin (pi) ]

will be parsed as

         [ sin, (pi) ]

and will result in an error since the `sin` function will be called with no arguments. To get around this, you must omit the space between `sin` and the opening parenthesis, or enclose the expression in a set of parentheses:

         [ (sin (pi)) ]

Whitespace surrounding the single quote character (‘`'`’, used as a transpose operator and for delimiting character strings) can also cause confusion. Given `a = 1`, the expression

         [ 1 a' ]

results in the single quote character being treated as a transpose operator and the result is the vector `[ 1, 1 ]`, but the expression

         [ 1 a ' ]

produces the error message

         error: unterminated string constant

because not doing so would cause trouble when parsing the valid expression

         [ a 'foo' ]

For clarity, it is probably best to always use commas and semicolons to separate matrix elements and rows.

When you type a matrix or the name of a variable whose value is a matrix, Octave responds by printing the matrix in with neatly aligned rows and columns. If the rows of the matrix are too large to fit on the screen, Octave splits the matrix and displays a header before each section to indicate which columns are being displayed. You can use the following variables to control the format of the output.

— Built-in Function: val = output_max_field_width ()
— Built-in Function: old_val = output_max_field_width (new_val)

> Query or set the internal variable that specifies the maximum width of a numeric output field.

> See also: format, output_precision.

— Built-in Function: val = output_precision ()
— Built-in Function: old_val = output_precision (new_val)

> Query or set the internal variable that specifies the minimum number of significant figures to display for numeric output.

> See also: format, output_max_field_width.

It is possible to achieve a wide range of output styles by using different values of `output_precision` and `output_max_field_width`. Reasonable combinations can be set using the `format` function. See Basic Input and Output.

— Built-in Function: val = split_long_rows ()
— Built-in Function: old_val = split_long_rows (new_val)

> Query or set the internal variable that controls whether rows of a matrix may be split when displayed to a terminal window. If the rows are split, Octave will display the matrix in a series of smaller pieces, each of which can fit within the limits of your terminal width and each set of rows is labeled so that you can easily see which columns are currently being displayed. For example:

>               octave:13> rand (2,10)
>               ans =

>                Columns 1 through 6:

>                 0.75883  0.93290  0.40064  0.43818  0.94958  0.16467
>                 0.75697  0.51942  0.40031  0.61784  0.92309  0.40201

>                Columns 7 through 10:

>                 0.90174  0.11854  0.72313  0.73326
>                 0.44672  0.94303  0.56564  0.82150

Octave automatically switches to scientific notation when values become very large or very small. This guarantees that you will see several significant figures for every value in a matrix. If you would prefer to see all values in a matrix printed in a fixed point format, you can set the built-in variable `fixed_point_format` to a nonzero value. But doing so is not recommended, because it can produce output that can easily be misinterpreted.

— Built-in Function: val = fixed_point_format ()
— Built-in Function: old_val = fixed_point_format (new_val)

> Query or set the internal variable that controls whether Octave will use a scaled format to print matrix values such that the largest element may be written with a single leading digit with the scaling factor is printed on the first line of output. For example,

>               octave:1> logspace (1, 7, 5)'
>               ans =

>                 1.0e+07  *

>                 0.00000
>                 0.00003
>                 0.00100
>                 0.03162
>                 1.00000

> Notice that first value appears to be zero when it is actually 1. For this reason, you should be careful when setting `fixed_point_format` to a nonzero value.