Chapter 2

f_02_03.jl



In [1]:

    
using NMfE



In [2]:

    
A=Float64[16 4 8;4 5 -4;8 -4 22];



In [3]:

    
b=Float64[4, 2, 5];



In [4]:

    
n = size(A, 1)
d = zeros(n);



In [5]:

    
ldlt!(A, d)



In [6]:

    
lower = zeros(3, 3)
for i in 1:n
  for j in 1:i
    lower[i, j] = A[i, j] / d[j]
  end
end



In [7]:

    
# Lower Triangular Factors:
lower









    Out[7]:





3x3 Array{Float64,2}:
 1.0    0.0  0.0
 0.25   1.0  0.0
 0.5   -1.5  1.0



In [8]:

    
# Diagonal Terms
d









    Out[8]:





3-element Array{Float64,1}:
 16.0
  4.0
  9.0



In [9]:

    
# Forward substitution
ldlfor!(A, b)
for i in 1:n
  A[i, :] = A[i, :] / d[i]
end



In [10]:

    
# Backward substitution
subbac!(A, b)
# Solution Vector
b









    Out[10]:





3-element Array{Float64,1}:
 -0.25
  1.0 
  0.5



In [11]:

    
d = copy(b)   # Copy b to d, reset both A and b
A=Float64[16 4 8;4 5 -4;8 -4 22]
b=Float64[4, 2, 5]
c = A\b









    Out[11]:





3-element Array{Float64,1}:
 -0.25
  1.0 
  0.5



In [12]:

    
round(A * c, 14) == b









    Out[12]:





true



In [13]:

    
round(c, 14) == d









    Out[13]:





true