First Semester in Numerical Analysis with Julia, 2020a

CHAPTER 5. APPROXIMATION THEORY 193
A[1,4]=sum(t->cos(2*pi*t/365),time)
A[2,2]=sum(t->t^2,time)
A[2,3]=sum(t->t*sin(2*pi*t/365),time)
A[2,4]=sum(t->t*cos(2*pi*t/365),time)
A[3,3]=sum(t->(sin(2*pi*t/365))^2,time)
A[3,4]=sum(t->(sin(2*pi*t/365)*cos(2*pi*t/365)),time)
A[4,4]=sum(t->(cos(2*pi*t/365))^2,time)
for i=2:4
for j=1:i
A[i,j]=A[j,i]
end
end
In [10]: A
Out[10]: 4×4 Array{Float64,2}:
1056.0 558096.0 12.2957 -36.2433
558096.0 3.93086e8 -50458.1 -38477.3
12.2957 -50458.1 542.339 10.9944
-36.2433 -38477.3 10.9944 513.661
Now we define the vector r. The function dot(x,y) takes the dot product of the
arrays x, y. For example, dot([1, 2, 3], [4, 5, 6]) = 1 × 4+2× 5+3× 6=32.
In [11]: r=zeros(4,1)
r[1]=sum(temp)
r[2]=dot(temp,time)
r[3]=dot(temp,map(t->sin(2*pi*t/365),time))
r[4]=dot(temp,map(t->cos(2*pi*t/365),time));
In [12]: r
Out[12]: 4×1 Array{Float64,2}:
21861.499999999996
1.1380310200000009e7
1742.0770653857649
2787.7612743690415