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DD_QD (MuPAT) >> DD_QD (MuPAT) > DD: 16 bytes decimal arithmetics > lu

lu

LU factorization of a square DD matrix

Syntax

[L,U] = lu(A)

Parameters

A

square matrix of DD real numbers, of size [n,n].

U

Upper triangular square matrix of DD real numbers, of size [n,n].

L

square matrix of DD real numbers, of size [m,n], Lower triangular after some rows permutations.

Description

[L,U]= lu(A) computes the matrices LL and U such that A = L*U, with U Upper triangular, and L Lower triangular after some rows permutations.

The implementation for matrices of DD numbers is restricted to square matrices.

Examples

:

A = ddrand(4,4)
[L,U] = lu(A)
L*U - A
--> A = ddrand(4,4)
 A  = 
[d1]
   0.2113249   0.6653811   0.8782165   0.7263507
   0.7560439   0.6283918   0.068374    0.1985144
   0.0002211   0.8497452   0.5608486   0.5442573
   0.3303271   0.685731    0.6623569   0.2320748

[d2] 10^-17 *
   0.6832332  -4.191495   -1.7567766  -1.762794 
  -2.5063366   1.3547731   0.0425332   0.6182611
  -0.0005011   2.2655615   1.9664026  -2.098293 
  -1.039939   -1.3751321  -0.5817424  -1.2407185


--> [L,U] = lu(A)
 U  = 
[d1]
   0.2113249   0.6653811   0.8782165   0.7263507
   0.         -1.7521009  -3.0735666  -2.4001053
   0.          0.         -0.9294872  -0.6195676
   0.          0.          0.         -0.3587091

[d2] 10^-17 *
   0.6832332  -4.191495   -1.7567766  -1.762794 
   0.          9.5531966  -15.971936  -10.783318
   0.          0.         -0.1814096  -0.9867343
   0.          0.          0.          0.3761884

 L  = 
[d1]
   1.          0.          0.          0.
   3.5776379   1.          0.          0.
   0.0010464  -0.4845891   1.          0.
   1.5631246   0.2022387   0.0955482   1.
[d2] 10^-17 *
   0.          0.          0.          0.
   11.073338   0.          0.          0.
  -0.008786    1.16019     0.          0.
   0.3666115  -0.8467752  -0.3476148   0.
   

--> L*U - A
 ans  =
[d1] 10^-32 *
   0.          0.          0.   0.       
  -1.2325952   2.4651903   0.   0.       
   0.          0.          0.   0.       
   0.          0.          0.   0.3081488
[d2] zeros(4,4)

See Also

Authors

Copyright (C) 2011 - Tsubasa Saito

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