14.13.2 Tutorial

sage: octave('4+10')                     # optional
14
sage: octave('date')                    # optional; random output
18-Oct-2007
sage: octave('5*10 + 6')                 # optional
56
sage: octave('(6+6)/3')                  # optional
4
sage: octave('9')^2                      # optional
81
sage: a = octave(10); b = octave(20); c = octave(30)    # optional
sage: avg = (a+b+c)/3                    # optional
sage: avg                                # optional
20
sage: parent(avg)                        # optional
Octave

sage: my_scalar = octave('3.1415')       # optional
sage: my_scalar                          # optional
3.1415
sage: my_vector1 = octave('[1,5,7]')     # optional
sage: my_vector1                         # optional
1     5     7
sage: my_vector2 = octave('[1;5;7]')     # optional
sage: my_vector2                         # optional
1
5
7
sage: my_vector1 * my_vector2            # optional
75

Module-level Functions

octave_console( )

Spawn a new Octave command-line session.

This requires that the optional octave program be installed and in your PATH, but no optional Sage packages need be installed.

sage: octave_console()         # not tested
GNU Octave, version 2.1.73 (i386-apple-darwin8.5.3).
Copyright (C) 2006 John W. Eaton.
...
octave:1> 2+3
ans = 5
octave:2> [ctl-d]

Pressing ctrl-d exits the octave console and returns you to SAGE. octave, like SAGE, remembers its history from one session to another.

octave_version( )

Return the version of Octave installed.

sage: octave_version()    # optional -- requires octave; and output is random
'2.9.12'

reduce_load_Octave( )

sage: from sage.interfaces.octave import reduce_load_Octave
sage: reduce_load_Octave()
Octave

Class: Octave

class Octave

Interface to the Octave interpreter.

sage: octave.eval("a = [ 1, 1, 2; 3, 5, 8; 13, 21, 33 ]")    # optional
'a =

1 1 2 3 5 8 13 21 33

sage: octave.eval("b = [ 1; 3; 13]")                         # optional
'b =

1 3 13

sage: octave.eval("c=a \ b") # solves linear equation: a*c = b  # optional random output
'c =

1 7.21645e-16 -7.21645e-16

sage: octave.eval("c")                                 # optional random output
'c =

1 7.21645e-16 -7.21645e-16

Octave( self, [maxread=100], [script_subdirectory=], [logfile=None], [server=None], [server_tmpdir=None])

sage: octave == loads(dumps(octave))
True

Functions: clear, $\,$ console, $\,$ de_system_plot, $\,$ get, $\,$ quit, $\,$ sage2octave_matrix_string, $\,$ set, $\,$ solve_linear_system, $\,$ version

clear( self, var)

Clear the variable named var.

sage: octave.set('x', '2') #optional -- requires Octave
sage: octave.clear('x') #optional
sage: octave.get('x') #optional
"error: `x' undefined near line ... column 1"

console( self)

Spawn a new Octave command-line session.

This requires that the optional octave program be installed and in your PATH, but no optional Sage packages need be installed.

sage: octave_console()         # not tested
GNU Octave, version 2.1.73 (i386-apple-darwin8.5.3).
Copyright (C) 2006 John W. Eaton.
...
octave:1> 2+3
ans = 5
octave:2> [ctl-d]

Pressing ctrl-d exits the octave console and returns you to SAGE. octave, like SAGE, remembers its history from one session to another.

de_system_plot( self, f, ics, trange)

Plots (using octave's interface to gnuplot) the solution to a $2\times 2$ system of differential equations.

Input:

f: - a pair of strings representing the differential equations; The independent variable must be called x and the dependent variable must be called y.
ics: - a pair [x0,y0] such that x(t0) = x0, y(t0) = y0
trange: - a pair [t0,t1]

Output: a gnuplot window appears

sage: octave.de_system_plot(['x+y','x-y'], [1,-1], [0,2])  # not tested -- does this actually work (on OS X it fails for me -- William Stein, 2007-10)

This should yield the two plots on the same graph (the -axis is the horizonal axis) of the system of ODEs

$\displaystyle x' = x+y, x(0) = 1;\qquad y' = x-y, y(0) = -1,$ for $\displaystyle \quad 0 < t < 2.$

get( self, var)

Get the value of the variable var.

sage: octave.set('x', '2') #optional -- requires Octave
sage: octave.get('x') #optional
' 2'

quit( self, [verbose=False])

sage: o = Octave()
sage: o._start()    #optional -- requires Octave
sage: o.quit(True)  #optional
Exiting spawned Octave process.

sage2octave_matrix_string( self, A)

Return an octave matrix from a SAGE matrix.

Input: A SAGE matrix with entries in the rationals or reals.

Output: A string that evaluates to an Octave matrix.

sage: M33 = MatrixSpace(QQ,3,3)
sage: A = M33([1,2,3,4,5,6,7,8,0])
sage: octave.sage2octave_matrix_string(A)   # requires optional octave
'[1, 2, 3; 4, 5, 6; 7, 8, 0]'

Author: David Joyner and William Stein

set( self, var, value)

Set the variable var to the given value.

sage: octave.set('x', '2') #optional -- requires Octave
sage: octave.get('x') #optional
' 2'

solve_linear_system( self, A, b)

Use octave to compute a solution x to A*x = b, as a list.

Input:

A: - mxn matrix A with entries in QQ or RR
b: - m-vector b entries in QQ or RR (resp)

Output: An list x (if it exists) which solves M*x = b

sage: M33 = MatrixSpace(QQ,3,3)
sage: A   = M33([1,2,3,4,5,6,7,8,0])
sage: V3  = VectorSpace(QQ,3)
sage: b   = V3([1,2,3])
sage: octave.solve_linear_system(A,b)    # requires optional octave (and output is slightly random in low order bits)
[-0.33333299999999999, 0.66666700000000001, -3.5236600000000002e-18]

Author: David Joyner and William Stein

version( self)

Return the version of Octave.

Output: string

sage: octave.version()   # optional and random output depending on version
'2.1.73'

Special Functions: __init__, $\,$ __reduce__, $\,$ _install_hints, $\,$ _object_class, $\,$ _quit_string, $\,$ _read_in_file_command, $\,$ _start

__reduce__( self)

sage: octave.__reduce__()
(<function reduce_load_Octave at 0x...>, ())

_install_hints( self)

Returns hints on how to install Octave.

sage: print octave._install_hints()
You must get ...

_object_class( self)

sage: octave._object_class()
<class 'sage.interfaces.octave.OctaveElement'>

_quit_string( self)

sage: octave._quit_string()
'quit;'

_read_in_file_command( self, filename)

sage: filename = tmp_filename()
sage: octave._read_in_file_command(filename)
'source("...");'

_start( self)

Starts the Octave process.

sage: o = Octave()    #optioanl -- requires Octave
sage: o.is_running()  #optional
False
sage: o._start()      #optional
sage: o.is_running()  #optional
True

Class: OctaveElement

class OctaveElement

Special Functions: _matrix_

_matrix_( self, R)

Return Sage matrix from this octave element.

sage: A = octave('[1,2;3,4]')       # optional octave package
sage: matrix(ZZ, A)
[1 2]
[3 4]
sage: A = octave('[1,2;3,4.5]')     # optional octave package
sage: matrix(RR, A)
[1.00000000000000 2.00000000000000]
[3.00000000000000 4.50000000000000]

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