R

"R is a language and environment for statistical computing and graphics." -- http://www.r-project.org/

Sage includes R and is able to invoke it. It is possible to send lines of code, invoke commands in a standardized fashion, work with results of calculations as objects and convert those objects back into python data structures. The last point is essential to write native Sage commands that use R as backend.

Examples

sequence

sage: r.seq(1,9)    

[1] 1 2 3 4 5 6 7 8 9

Matrix

Matrix m as Sage object and R printout - then a translation to a Sage matrix.

sage: m = r.matrix(r.seq(1,12),3)

sage: type(m)
<class 'sage.interfaces.r.RElement'>

sage: m

     [,1] [,2] [,3] [,4]
[1,]    1    4    7   10
[2,]    2    5    8   11
[3,]    3    6    9   12

argument byrow=True

sage: m = r.matrix(r.seq(1,12),3, byrow=True)
sage: m

     [,1] [,2] [,3] [,4]
[1,]    1    2    3    4
[2,]    5    6    7    8
[3,]    9   10   11   12

t-Test

sage: r.t_test(r.c(1,2,3,5),r.c(1,2,4,5))

or just

sage: r.t_test([1,2,3],[1,2,4])


        Welch Two Sample t-test

data:  sage6 and sage7
t = -0.2, df = 5.973, p-value = 0.8481
alternative hypothesis: true difference in means is not equal to 0
95 percent confidence interval:
 -3.311938  2.811938
sample estimates:
mean of x mean of y
     2.75      3.00

and native

sage: t = ttest([1,2,3,4,5],[1,2,3,3.5,5.121])
sage: t

(0.941026372027427,
 {'DATA': {'alternative': 'two.sided',
           'conf_int': {'DATA': [-2.2140805547522402, 2.3656805547522399],
                        'conf_level': 0.94999999999999996},
           'data_name': 'sage5 and sage11',
           'estimate': {'DATA': [3, 2.9241999999999999],
                        '_Names': ['mean of x', 'mean of y']},
           'method': 'Welch Two Sample t-test',
           'null_value': {'DATA': 0, '_Names': 'difference in means'},
           'p_value': 0.941026372027427,
           'parameter': {'DATA': 7.9983864630024701, '_Names': 'df'},
           'statistic': {'DATA': 0.076336405881313296, '_Names': 't'}},
  '_Names': ['statistic',
             'parameter',
             'p.value',
             'conf.int',
             'estimate',
             'null.value',
             'alternative',
             'method',
             'data.name'],
  '_r_class': 'htest'})
sage: t[0]
0.941026372027427

sage: ttest([1,2,3,4,5],[1,2,3,3.5,5.121])[0] 
0.941026372027427