LRdecomposition -- LR decomposition

Synopsis

• Usage:

  LRdecomposition(A,pivotfunction)

• Inputs:
  • A, a matrix, square and invertible.
  • pivotfunction, a function, used for pivoting.
• Outputs:
  • a sequence, of a list with a permutation of the rows of A corresponding to P, and a matrix containing L and R.

Description

i1 : A=random(QQ^3,QQ^3)

o1 = | 9/2 1/2 3/2 |
     | 1/2 1   3/4 |
     | 9/4 3/4 7/4 |

              3        3
o1 : Matrix QQ  <--- QQ

i2 : (perm,LR)=LRdecomposition(A,j->-j);

i3 : perm

o3 = {0, 1, 2}

o3 : List

i4 : P=transpose (id_(QQ^3))_perm

o4 = | 1 0 0 |
     | 0 1 0 |
     | 0 0 1 |

              3        3
o4 : Matrix QQ  <--- QQ

i5 : R=extractRightUpper(LR)

o5 = | 9/2 1/2   3/2   |
     | 0   17/18 7/12  |
     | 0   0     47/68 |

              3        3
o5 : Matrix QQ  <--- QQ

i6 : L=extractLeftLower(LR)

o6 = | 1   0    0 |
     | 1/9 1    0 |
     | 1/2 9/17 1 |

              3        3
o6 : Matrix QQ  <--- QQ

i7 : L*R==P*A

o7 = true

See also

• extractRightUpper -- Extract R from the LR decomposition result.
• extractLeftLower -- Extract L from the LR decomposition result.