octave: Matrices
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 (1 != 2) 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
parse error:
syntax error
>>> [ 1 a ' ]
^
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.
The maximum number of elements in a matrix is fixed when Octave is
compiled. The allowable number can be queried with the function
‘sizemax’. Note that other factors, such as the amount of memory
available on your machine, may limit the maximum size of matrices to
something smaller.
-- : sizemax ()
Return the largest value allowed for the size of an array.
If Octave is compiled with 64-bit indexing, the result is of class
int64, otherwise it is of class int32. The maximum array size is
slightly smaller than the maximum value allowable for the relevant
class as reported by ‘intmax’.
See also: 
intmax XREFintmax.
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.
-- : VAL = output_max_field_width ()
-- : OLD_VAL = output_max_field_width (NEW_VAL)
-- : output_max_field_width (NEW_VAL, "local")
Query or set the internal variable that specifies the maximum width
of a numeric output field.
When called from inside a function with the "local" option, the
variable is changed locally for the function and any subroutines it
calls. The original variable value is restored when exiting the
function.
DONTPRINTYET See also: format XREFformat, *notefixed_point_format:
DONTPRINTYET DONTPRINTYET See also: format XREFformat, fixed_point_format
XREFfixed_point_format, *noteoutput_precision:
DONTPRINTYET DONTPRINTYET See also: format XREFformat, fixed_point_format
XREFfixed_point_format, output_precision
XREFoutput_precision.
-- : VAL = output_precision ()
-- : OLD_VAL = output_precision (NEW_VAL)
-- : output_precision (NEW_VAL, "local")
Query or set the internal variable that specifies the minimum
number of significant figures to display for numeric output.
When called from inside a function with the "local" option, the
variable is changed locally for the function and any subroutines it
calls. The original variable value is restored when exiting the
function.
DONTPRINTYET See also: format XREFformat, *notefixed_point_format:
DONTPRINTYET DONTPRINTYET See also: format XREFformat, fixed_point_format
XREFfixed_point_format, *noteoutput_max_field_width:
DONTPRINTYET DONTPRINTYET See also: format XREFformat, fixed_point_format
XREFfixed_point_format, output_max_field_width
XREFoutput_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.
Basic Input and Output.
-- : VAL = split_long_rows ()
-- : OLD_VAL = split_long_rows (NEW_VAL)
-- : split_long_rows (NEW_VAL, "local")
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
When called from inside a function with the "local" option, the
variable is changed locally for the function and any subroutines it
calls. The original variable value is restored when exiting the
function.
See also: format XREFformat.
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.
-- : VAL = fixed_point_format ()
-- : OLD_VAL = fixed_point_format (NEW_VAL)
-- : fixed_point_format (NEW_VAL, "local")
Query or set the internal variable that controls whether Octave
will use a scaled format to print matrix values.
The scaled format prints a scaling factor on the first line of
output chosen such that the largest matrix element can be written
with a single leading digit. For example:
logspace (1, 7, 5)'
ans =
1.0e+07 *
0.00000
0.00003
0.00100
0.03162
1.00000
Notice that the first value appears to be 0 when it is actually 1.
Because of the possibility for confusion you should be careful
about enabling ‘fixed_point_format’.
When called from inside a function with the "local" option, the
variable is changed locally for the function and any subroutines it
calls. The original variable value is restored when exiting the
function.
DONTPRINTYET See also: format XREFformat, *noteoutput_max_field_width:
DONTPRINTYET DONTPRINTYET See also: format XREFformat, output_max_field_width
XREFoutput_max_field_width, *noteoutput_precision:
DONTPRINTYET DONTPRINTYET See also: format XREFformat, output_max_field_width
XREFoutput_max_field_width, output_precision
XREFoutput_precision.
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