# Interface to MATLAB#

According to their website, MATLAB is “a high-level language and interactive environment that enables you to perform computationally intensive tasks faster than with traditional programming languages such as C, C++, and Fortran.”

The commands in this section only work if you have the “matlab” interpreter installed and available in your PATH. It’s not necessary to install any special Sage packages.

EXAMPLES:

```sage: matlab.eval('2+2')                 # optional - matlab
'\nans =\n\n     4\n'
```
```>>> from sage.all import *
>>> matlab.eval('2+2')                 # optional - matlab
'\nans =\n\n     4\n'
```
```sage: a = matlab(10)                     # optional - matlab
sage: a**10                              # optional - matlab
1.0000e+10
```
```>>> from sage.all import *
>>> a = matlab(Integer(10))                     # optional - matlab
>>> a**Integer(10)                              # optional - matlab
1.0000e+10
```

AUTHORS:

• William Stein (2006-10-11)

## Tutorial#

EXAMPLES:

```sage: # optional - matlab
sage: matlab('4+10')
14
sage: matlab('date')
18-Oct-2006
sage: matlab('5*10 + 6')
56
sage: matlab('(6+6)/3')
4
sage: matlab('9')^2
81
sage: a = matlab(10); b = matlab(20); c = matlab(30)
sage: avg = (a+b+c)/3 ; avg
20
sage: parent(avg)
Matlab
```
```>>> from sage.all import *
>>> # optional - matlab
>>> matlab('4+10')
14
>>> matlab('date')
18-Oct-2006
>>> matlab('5*10 + 6')
56
>>> matlab('(6+6)/3')
4
>>> matlab('9')**Integer(2)
81
>>> a = matlab(Integer(10)); b = matlab(Integer(20)); c = matlab(Integer(30))
>>> avg = (a+b+c)/Integer(3) ; avg
20
>>> parent(avg)
Matlab
```
```sage: # optional - matlab
sage: my_scalar = matlab('3.1415')
sage: my_scalar
3.1415
sage: my_vector1 = matlab('[1,5,7]')
sage: my_vector1
1     5     7
sage: my_vector2 = matlab('[1;5;7]')
sage: my_vector2
1
5
7
sage: my_vector1 * my_vector2
75
```
```>>> from sage.all import *
>>> # optional - matlab
>>> my_scalar = matlab('3.1415')
>>> my_scalar
3.1415
>>> my_vector1 = matlab('[1,5,7]')
>>> my_vector1
1     5     7
>>> my_vector2 = matlab('[1;5;7]')
>>> my_vector2
1
5
7
>>> my_vector1 * my_vector2
75
```
```sage: # optional - matlab
sage: row_vector1 = matlab('[1 2 3]')
sage: row_vector2 = matlab('[3 2 1]')
sage: matrix_from_row_vec = matlab('[%s; %s]'%(row_vector1.name(), row_vector2.name()))
sage: matrix_from_row_vec
1     2     3
3     2     1
```
```>>> from sage.all import *
>>> # optional - matlab
>>> row_vector1 = matlab('[1 2 3]')
>>> row_vector2 = matlab('[3 2 1]')
>>> matrix_from_row_vec = matlab('[%s; %s]'%(row_vector1.name(), row_vector2.name()))
>>> matrix_from_row_vec
1     2     3
3     2     1
```
```sage: # optional - matlab
sage: column_vector1 = matlab('[1;3]')
sage: column_vector2 = matlab('[2;8]')
sage: matrix_from_col_vec = matlab('[%s %s]'%(column_vector1.name(), column_vector2.name()))
sage: matrix_from_col_vec
1     2
3     8
```
```>>> from sage.all import *
>>> # optional - matlab
>>> column_vector1 = matlab('[1;3]')
>>> column_vector2 = matlab('[2;8]')
>>> matrix_from_col_vec = matlab('[%s %s]'%(column_vector1.name(), column_vector2.name()))
>>> matrix_from_col_vec
1     2
3     8
```
```sage: my_matrix = matlab('[8, 12, 19; 7, 3, 2; 12, 4, 23; 8, 1, 1]')    # optional - matlab
sage: my_matrix                                      # optional - matlab
8    12    19
7     3     2
12     4    23
8     1     1
```
```>>> from sage.all import *
>>> my_matrix = matlab('[8, 12, 19; 7, 3, 2; 12, 4, 23; 8, 1, 1]')    # optional - matlab
>>> my_matrix                                      # optional - matlab
8    12    19
7     3     2
12     4    23
8     1     1
```
```sage: combined_matrix = matlab('[%s, %s]'%(my_matrix.name(), my_matrix.name()))                                        # optional - matlab
sage: combined_matrix                               # optional - matlab
8    12    19     8    12    19
7     3     2     7     3     2
12     4    23    12     4    23
8     1     1     8     1     1
```
```>>> from sage.all import *
>>> combined_matrix = matlab('[%s, %s]'%(my_matrix.name(), my_matrix.name()))                                        # optional - matlab
>>> combined_matrix                               # optional - matlab
8    12    19     8    12    19
7     3     2     7     3     2
12     4    23    12     4    23
8     1     1     8     1     1
```
```sage: tm = matlab('0.5:2:10')                       # optional - matlab
sage: tm                                            # optional - matlab
0.5000    2.5000    4.5000    6.5000    8.5000
```
```>>> from sage.all import *
>>> tm = matlab('0.5:2:10')                       # optional - matlab
>>> tm                                            # optional - matlab
0.5000    2.5000    4.5000    6.5000    8.5000
```
```sage: # optional - matlab
sage: my_vector1 = matlab('[1,5,7]')
sage: my_vector1(1)
1
sage: my_vector1(2)
5
sage: my_vector1(3)
7
```
```>>> from sage.all import *
>>> # optional - matlab
>>> my_vector1 = matlab('[1,5,7]')
>>> my_vector1(Integer(1))
1
>>> my_vector1(Integer(2))
5
>>> my_vector1(Integer(3))
7
```

Matrix indexing works as follows:

```sage: my_matrix = matlab('[8, 12, 19; 7, 3, 2; 12, 4, 23; 8, 1, 1]')     # optional - matlab
sage: my_matrix(3,2)                                # optional - matlab
4
```
```>>> from sage.all import *
>>> my_matrix = matlab('[8, 12, 19; 7, 3, 2; 12, 4, 23; 8, 1, 1]')     # optional - matlab
>>> my_matrix(Integer(3),Integer(2))                                # optional - matlab
4
```

Setting using parenthesis cannot work (because of how the Python language works). Use square brackets or the set function:

```sage: my_matrix = matlab('[8, 12, 19; 7, 3, 2; 12, 4, 23; 8, 1, 1]')    # optional - matlab
sage: my_matrix.set(2,3, 1999)                          # optional - matlab
sage: my_matrix                                         # optional - matlab
8          12          19
7           3        1999
12           4          23
8           1           1
```
```>>> from sage.all import *
>>> my_matrix = matlab('[8, 12, 19; 7, 3, 2; 12, 4, 23; 8, 1, 1]')    # optional - matlab
>>> my_matrix.set(Integer(2),Integer(3), Integer(1999))                          # optional - matlab
>>> my_matrix                                         # optional - matlab
8          12          19
7           3        1999
12           4          23
8           1           1
```
class sage.interfaces.matlab.Matlab(maxread=None, script_subdirectory=None, logfile=None, server=None, server_tmpdir=None)[source]#

Bases: `Expect`

Interface to the Matlab interpreter.

EXAMPLES:

```sage: # optional - matlab
sage: a = matlab('[ 1, 1, 2; 3, 5, 8; 13, 21, 33 ]')
sage: b = matlab('[ 1; 3; 13]')
sage: c = a * b
sage: print(c)
30
122
505
```
```>>> from sage.all import *
>>> # optional - matlab
>>> a = matlab('[ 1, 1, 2; 3, 5, 8; 13, 21, 33 ]')
>>> b = matlab('[ 1; 3; 13]')
>>> c = a * b
>>> print(c)
30
122
505
```
chdir(directory)[source]#

Change MATLAB’s current working directory.

EXAMPLES:

```sage: matlab.chdir('/')          # optional - matlab
sage: matlab.pwd()               # optional - matlab
/
```
```>>> from sage.all import *
>>> matlab.chdir('/')          # optional - matlab
>>> matlab.pwd()               # optional - matlab
/
```
console()[source]#
get(var)[source]#

Get the value of the variable var.

EXAMPLES:

```sage: s = matlab.eval('a = 2') # optional - matlab
sage: matlab.get('a')               # optional - matlab
'     2'
```
```>>> from sage.all import *
>>> s = matlab.eval('a = 2') # optional - matlab
>>> matlab.get('a')               # optional - matlab
'     2'
```
sage2matlab_matrix_string(A)[source]#

Return a matlab matrix from a Sage matrix.

INPUT: A Sage matrix with entries in the rationals or reals.

OUTPUT: A string that evaluates to a Matlab matrix.

EXAMPLES:

```sage: M33 = MatrixSpace(QQ,3,3)
sage: A = M33([1,2,3,4,5,6,7,8,0])
sage: matlab.sage2matlab_matrix_string(A)   # optional - matlab
'[1, 2, 3; 4, 5, 6; 7, 8, 0]'
```
```>>> from sage.all import *
>>> M33 = MatrixSpace(QQ,Integer(3),Integer(3))
>>> A = M33([Integer(1),Integer(2),Integer(3),Integer(4),Integer(5),Integer(6),Integer(7),Integer(8),Integer(0)])
>>> matlab.sage2matlab_matrix_string(A)   # optional - matlab
'[1, 2, 3; 4, 5, 6; 7, 8, 0]'
```

AUTHOR:

• David Joyner and William Stein

set(var, value)[source]#

Set the variable var to the given value.

Returns the string s with Matlab’s answer prompt removed.

EXAMPLES:

```sage: s = '\nans =\n\n     2\n'
'     2'
```
```>>> from sage.all import *
>>> s = '\nans =\n\n     2\n'
'     2'
```
version()[source]#
whos()[source]#
class sage.interfaces.matlab.MatlabElement(parent, value, is_name=False, name=None)[source]#

Bases: `ExpectElement`

set(i, j, x)[source]#
sage.interfaces.matlab.matlab_console()[source]#

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

EXAMPLES:

```sage: matlab_console()                # optional - matlab; not tested
< M A T L A B >
...
>> 2+3
```
```>>> from sage.all import *
>>> matlab_console()                # optional - matlab; not tested
< M A T L A B >
...
>> 2+3
```

ans =

5

quit

Typing quit exits the matlab console and returns you to Sage. matlab, like Sage, remembers its history from one session to another.

sage.interfaces.matlab.matlab_version()[source]#

Return the version of Matlab installed.

EXAMPLES:

```sage: matlab_version()    # random; optional - matlab
'7.2.0.283 (R2006a)'
```
```>>> from sage.all import *
>>> matlab_version()    # random; optional - matlab
'7.2.0.283 (R2006a)'
```