In [1]:

    

from cvxopt import matrix, solvers
Q = 2*matrix([ [2, .5], [.5, 1] ])
p = matrix([1.0, 1.0])
G = matrix([[-1.0,0.0],[0.0,-1.0]])
h = matrix([0.0,0.0])
A = matrix([1.0, 1.0], (1,2))
b = matrix(1.0)
sol=solvers.qp(Q, p, G, h, A, b)


    

    




     pcost       dcost       gap    pres   dres
 0:  1.8889e+00  7.7778e-01  1e+00  3e-16  2e+00
 1:  1.8769e+00  1.8320e+00  4e-02  2e-16  6e-02
 2:  1.8750e+00  1.8739e+00  1e-03  2e-16  5e-04
 3:  1.8750e+00  1.8750e+00  1e-05  1e-16  5e-06
 4:  1.8750e+00  1.8750e+00  1e-07  1e-16  5e-08
Optimal solution found.

In [2]:

    

print(sol['x'])


    

    




[ 2.50e-01]
[ 7.50e-01]

In [3]:

    

import rpy2


    

In [4]:

    

%load_ext rmagic


    

In [5]:

    

%matplotlib inline
import numpy as np
import matplotlib.pyplot as plt


    

In [6]:

    

X = np.array([0,1,2,3,4])
Y = np.array([3,5,4,6,7])
plt.scatter(X, Y)


    

    
Out[6]:





<matplotlib.collections.PathCollection at 0x10cae5e10>






    

In [7]:

    

%Rpush X Y
%R lm(Y~X)$coef


    

    
Out[7]:





array([ 3.2,  0.9])

In [8]:

    

%R resid(lm(Y~X)); coef(lm(X~Y))


    

    
Out[8]:





array([-2.5,  0.9])

In [9]:

    

b = %R a=resid(lm(Y~X))
%Rpull a
print(a)
assert id(b.data) == id(a.data)
%R -o a


    

    




[-0.2  0.9 -1.   0.1  0.2]

In [10]:

    

from __future__ import print_function
v1 = %R plot(X,Y); print(summary(lm(Y~X))); vv=mean(X)*mean(Y)
print('v1 is:', v1)
v2 = %R mean(X)*mean(Y)
print('v2 is:', v2)


    

    






Call:
lm(formula = Y ~ X)

Residuals:
   1    2    3    4    5 
-0.2  0.9 -1.0  0.1  0.2 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)  
(Intercept)   3.2000     0.6164   5.191   0.0139 *
X             0.9000     0.2517   3.576   0.0374 *
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.7958 on 3 degrees of freedom
Multiple R-squared:   0.81,	Adjusted R-squared:  0.7467 
F-statistic: 12.79 on 1 and 3 DF,  p-value: 0.03739








    













    




v1 is: [ 10.]
v2 is: [ 10.]

In [11]:

    

%%R -i X,Y -o XYcoef
XYlm = lm(Y~X)
XYcoef = coef(XYlm)
print(summary(XYlm))
par(mfrow=c(2,2))
plot(XYlm)


    

    






Call:
lm(formula = Y ~ X)

Residuals:
   1    2    3    4    5 
-0.2  0.9 -1.0  0.1  0.2 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)  
(Intercept)   3.2000     0.6164   5.191   0.0139 *
X             0.9000     0.2517   3.576   0.0374 *
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.7958 on 3 degrees of freedom
Multiple R-squared:   0.81,	Adjusted R-squared:  0.7467 
F-statistic: 12.79 on 1 and 3 DF,  p-value: 0.03739








    

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