Chapter 2

f_02_02.jl



In [16]:

    
using NMfE



In [17]:

    
A=[10. 1. -5.;-20. 3. 20.;5. 3. 5.]









    Out[17]:





3x3 Array{Float64,2}:
  10.0  1.0  -5.0
 -20.0  3.0  20.0
   5.0  3.0   5.0



In [18]:

    
b=[1., 2., 6.]









    Out[18]:





3-element Array{Float64,1}:
 1.0
 2.0
 6.0



In [19]:

    
(lower, upper) = lufac(A)
# NMfE lufac(A) - lower
lower









    Out[19]:





3x3 Array{Float64,2}:
  1.0  0.0  0.0
 -2.0  1.0  0.0
  0.5  0.5  1.0



In [20]:

    
# NMfE lufac(A) - upper
upper









    Out[20]:





3x3 Array{Float64,2}:
 10.0  1.0  -5.0
  0.0  5.0  10.0
  0.0  0.0   2.5



In [21]:

    
# Check if we get A back
lower * upper









    Out[21]:





3x3 Array{Float64,2}:
  10.0  1.0  -5.0
 -20.0  3.0  20.0
   5.0  3.0   5.0



In [22]:

    
subfor!(lower, b)
# Updated RHS
b









    Out[22]:





3-element Array{Float64,1}:
 1.0
 4.0
 3.5



In [23]:

    
subbac!(upper, b)
# Solution vector:
b









    Out[23]:





3-element Array{Float64,1}:
  1.0
 -2.0
  1.4



In [24]:

    
d = copy(b)
# Restore b
b=[1., 2., 6.];



In [25]:

    
c = A\b









    Out[25]:





3-element Array{Float64,1}:
  1.0
 -2.0
  1.4



In [26]:

    
round(A * c, 14) == b









    Out[26]:





true



In [27]:

    
round(c, 14) == d









    Out[27]:





true



In [28]:

    
# Julia lufact(A)
f = lufact(A);



In [29]:

    
f[:L]









    Out[29]:





3x3 Array{Float64,2}:
  1.0   0.0       0.0
 -0.25  1.0       0.0
 -0.5   0.666667  1.0



In [30]:

    
f[:U]









    Out[30]:





3x3 Array{Float64,2}:
 -20.0  3.0   20.0    
   0.0  3.75  10.0    
   0.0  0.0   -1.66667