Chapter 2

In [12]:

    

using NMfE


    

In [13]:

    

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


    

In [14]:

    

b=Float64[4, 2, 5];


    

In [15]:

    

c = A\b


    

    
Out[15]:





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

In [16]:

    

?chol


    

    




search: chol cholfact cholfact! searchsortedlast chop chomp chmod Cshort







    
Out[16]:





chol(A, [LU]) -> F
Compute the Cholesky factorization of a symmetric positive definite matrix A and return the matrix F. If LU is Val{:U} (Upper), F is of type UpperTriangular and A = F'*F. If LU is Val{:L} (Lower), F is of type LowerTriangular and A = F*F'. LU defaults to Val{:U}.

In [21]:

    

chol(A, Val{:L})


    

    
Out[21]:





3x3 LowerTriangular{Float64,Array{Float64,2}}:
 4.0   0.0  0.0
 1.0   2.0  0.0
 2.0  -3.0  3.0

In [22]:

    

chol(A, Val{:U})


    

    
Out[22]:





3x3 UpperTriangular{Float64,Array{Float64,2}}:
 4.0  1.0   2.0
 0.0  2.0  -3.0
 0.0  0.0   3.0

In [18]:

    

round(A * c, 14) == b


    

    
Out[18]:





true