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### 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 to not do 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.

— Built-in Variable: warn_separator_insert

Print warning if commas or semicolons might be inserted automatically in literal matrices.

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 Variable: output_max_field_width

This variable specifies the maximum width of a numeric output field. The default value is 10.

— Built-in Variable: output_precision

This variable specifies the minimum number of significant figures to display for numeric output. The default value is 5.

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 Variable: split_long_rows

For large matrices, Octave may not be able to display all the columns of a given row on one line of your screen. This can result in missing information or output that is nearly impossible to decipher, depending on whether your terminal truncates or wraps long lines.

If the value of `split_long_rows` is nonzero, Octave will display the matrix in a series of smaller pieces, each of which can fit within the limits of your terminal width. 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
```

The default value of `split_long_rows` is nonzero.

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 Variable: fixed_point_format

If the value of this variable is nonzero, Octave will scale all values in a matrix so that the largest may be written with one leading digit. 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.

The default value of `fixed_point_format` is 0.