Processing math: 100%

Problem 1: Inverse Numerator Relationship Matrix

During the lecture the method of computing the inverse numerator relationship matrix A1 directly was introduced. The computation is based on the LDL-decomposition. As a result, we can write

A1=(LT)1D1L1 where L1=IP, and D1 is a diagonal matrix with (D1)iiσ2u=var(mi)1.

Tasks

Pedigree

nr_animal <- 6
tbl_pedigree <- tibble::tibble(Calf = c(1:nr_animal),
                               Sire = c(NA, NA, NA, 1 ,3, 4),
                               Dam = c(NA, NA, NA, 2, 2, 5))
tbl_pedigree
ABCDEFGHIJ0123456789
Calf
<int>
Sire
<dbl>
Dam
<dbl>
1NANA
2NANA
3NANA
412
532
645

Your Solution

  • Construct matrix P from the pedigree
  • Use matrix P to compute the matrix L1
  • Construct the matrix D1
  • Compute A1 based on L1 and D1

Problem 2: Rules

The following diagram helps to illustrate the rules for constructing A1

Tasks

Your Solution

Problem 3: Program using the Rules

Write a program in R that implements the rules found in the solution of Problem 2. Test your program with the pedigree given in Problem 1. Compare the results that you obtain with the result obtained from the function pedigreemm::getAinv().

Your Solution

  • Because the focus of this problem is the implementation of Henderson’s rules in a function, we use then function pedigreemm::Dmat() to obtain the values of the matrix D.
  • Write a function get_A_inverse which takes as input a pedigree and that returns the inverse numerator relationship matrix

Latest Changes: 2022-12-12 06:02:31 (pvr)

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