Test sheet

This is where we compute something important $a_i=1$

x = [1,2,3,4,5,6]
print x[2:]
plot(sin,(-1,1))

[3, 4, 5, 6]

var('x y')
density_plot(sin(x^2 + y^2) * cos(x+y^2) * sin(y), (x,-4, 4), (y,-4, 4), cmap='jet', plot_points=100).show(figsize=(6,6), frame=True)

stnc = 'I am a cool multiedge graph with loops'
g = DiGraph({}, loops=True, multiedges=True)
for a,b in [(stnc[i], stnc[i+1]) for i in xrange(len(stnc)-1)]:
    g.add_edge(a, b, b)
g.plot(color_by_label=True, edge_style='solid').show(figsize=(8,8))

x0  = 0
f   = sin(x)*e^(-x)
p   = plot(f,-1,5, thickness=2)
dot = point((x0,f(x=x0)),pointsize=80,rgbcolor=(1,0,0))
ft = f.taylor(x,x0,5)
pt = plot(ft,-1, 5, color='green', thickness=2)
html('$f(x)\;=\;%s$'%latex(f))
html('$\hat{f}(x;%s)\;=\;%s+\mathcal{O}(x^{%s})$'%(x0,latex(ft),5+1))
show(dot + p + pt, ymin = -.5, ymax = 1)

f(x)\;=\;e^{\left(-x\right)} \sin\left(x\right)

\hat{f}(x;0)\;=\;-\frac{1}{30} \, x^{5} + \frac{1}{3} \, x^{3} - x^{2} + x+\mathcal{O}(x^{6})

var('x1 x2 w1 w2 b')
model(x1, x2) = w1*x1 + w2*x2 + b
data = [[1, 2, -1], [1, 4, -1], [2, 4, -1], [2, 1, 1], [5, 1, 1], [4, 2,
1]]
fit = find_fit(data, model, solution_dict=True); 
print fit
f(x1, x2) = model.subs(fit);
pl6 = implicit_plot(f(x1, x2) == 0, (x1, 0, 5), (x2, 0, 5))
pl1 = list_plot([(x,y) for (x,y,z) in data if z == -1], rgbcolor='red')
pl2 = list_plot([(x,y) for (x,y,z) in data if z == 1], rgbcolor ='blue') 
(pl1 + pl2 +pl6).show(xmin=0, xmax=5, ymin=0)
pl3 = plot3d(f(x1, x2), (x1, 0, 5), (x2, 0, 5))
pl4 = list_plot([(x,y) for (x,y,z) in data if z == -1], rgbcolor='red')
pl5 = list_plot([(x,y) for (x,y,z) in data if z == 1], rgbcolor='blue')
(pl3+pl4+pl5).show(xmin=0, xmax=5)

sv = plot(lambda x : x, (x, 0, 5))
cl1 = plot(lambda x : x + 1, (x, 0, 5), linestyle='dashed')
cl2 = plot(lambda x : x - 1, (x, 0, 5), linestyle='dashed')
(sv+cl1+cl2+pl1+pl2).show(xmin=0, xmax=5)

from libsvm import *
prob = svm_problem([1,-1],[[1,0,1],[-1,0,-1]])
param = svm_parameter(kernel_type = LINEAR, C=float(10))
m = svm_model(prob, param)

Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
  File "_sage_input_36.py", line 9, in <module>
    exec compile(ur'open("___code___.py","w").write("# -*- coding: utf-8 -*-\n" + _support_.preparse_worksheet_cell(base64.b64decode("ZnJvbSBsaWJzdm0gaW1wb3J0ICoKcHJvYiA9IHN2bV9wcm9ibGVtKFsxLC0xXSxbWzEsMCwxXSxbLTEsMCwtMV1dKQpwYXJhbSA9IHN2bV9wYXJhbWV0ZXIoa2VybmVsX3R5cGUgPSBMSU5FQVIsIEM9ZmxvYXQoMTApKQptID0gc3ZtX21vZGVsKHByb2IsIHBhcmFtKQ=="),globals())+"\n"); execfile(os.path.abspath("___code___.py"))' + '\n', '', 'single')
  File "", line 1, in <module>
    
  File "/tmp/tmpokA7PK/___code___.py", line 3, in <module>
    from libsvm import *
ImportError: No module named libsvm

from rpy2.robjects import *
r('''

  data = data.frame(x = c(1,1,2,2,5,4), y = c(2,4,4,1,1,2), cls = c(-1,-1,-1,1,1,1))
  model = lm(cls ~ x + y, data=data)
  print(summary(model))
  
''')

Call:
lm(formula = cls ~ x + y, data = data)

Residuals:
      1       2       3       4       5       6 
-0.6556  0.2111 -0.1148  0.5852 -0.3926  0.3667 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)
(Intercept)   0.1963     0.9478   0.207    0.849
x             0.3259     0.1966   1.658    0.196
y            -0.4333     0.2365  -1.832    0.164

Residual standard error: 0.6106 on 3 degrees of freedom
Multiple R-squared: 0.8136,	Adjusted R-squared: 0.6893 
F-statistic: 6.546 on 2 and 3 DF,  p-value: 0.08049