Chapter 2

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