-
Notifications
You must be signed in to change notification settings - Fork 15
/
assignment2.jl
78 lines (64 loc) · 1.52 KB
/
assignment2.jl
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
using PyPlot
##########
# Task 2 #
##########
"""
hermite_interpolate(f,x)
Evaluate `p(x)` where `p` is the unique polynomial specified by the
interpolation problem on the assignment sheet.
"""
function hermite_interpolate(f,x)
# TODO: Your code here
return NaN
end
function draw_heart()
f = [
0.0 0.0
0.2 2.0
1.0 0.0
0.0 -1.8
0.0 -1.2
-1.0 -1.5
]
t = LinRange(0,1,1000)
clf()
for s in (+1,-1)
plot(
s .* hermite_interpolate.(Ref(f[1:4,1]),t),
hermite_interpolate.(Ref(f[1:4,2]),t),
)
plot(
s .* hermite_interpolate.(Ref(f[3:6,1]),t),
hermite_interpolate.(Ref(f[3:6,2]),t),
)
end
axis("equal")
display(gcf())
end
##########
# Task 3 #
##########
using FastGaussQuadrature
function composite_gauss(f,a,b,m,n)
# TODO: Your code here
return NaN
end
function composite_gauss_convergence()
f = sin
a,b = 0,π
Iref = 2
clf()
for (i,n) = enumerate(1:3)
d = 2n
m = round.(Int, 10.0.^LinRange(0.5,3,20))
errors = abs.(composite_gauss.(f,a,b,m,n) .- Iref)
loglog(m, errors, "C$(i-1)", label=latexstring("n = $n"))
s = 2*errors[1]*m[1]^d
loglog(m, s.*float.(m).^(-d), "C$(i-1)--", label=latexstring("O(m^{-$d})"))
end
ylim([1e-16,1])
legend(frameon=false, loc="center left", bbox_to_anchor=(1,0.5))
xlabel(L"m")
ylabel(L"\mathrm{error}(m)")
display(gcf())
end