Table 5 Joint constrained sparse haplotype frequency estimation algorithm with missing data

1

Set k = 0

2

Set ρ > 0

3

Set X⁰ = 0, Z⁰ = 0, ${\mathbf{U}}_1^0=0$, ${\mathbf{U}}_2^0=0$

4:

U₄ = (I−H^T(I+H H^T)⁻¹H)

5

Repeat

6

  k = k + 1

7

  For i = 1,⋯,O

8

   $u_{3,i}=\frac{1^T{\mathbf{U}}_4\left({\mathbf{H}}_i^T\left({\mathbf{u}}_{2,i}^k-{\tilde{\mathbf{a}}}_i\right)+{\mathbf{u}}_i^1-{\mathbf{z}}_i^k\right)-1}{1^T{\mathbf{U}}_{4}1}$

9

   ${\mathbf{x}}_i^{k+1}={\mathbf{U}}_4\left({\mathbf{u}}_{1,i}^k-{\mathbf{z}}_i^k+{\mathbf{H}}_i^T({\mathbf{u}}_{2,i}^k-\widetilde{{\mathbf{a}}_i})-u_{3,i}1\right)$

10

  end for;

11

   ${\mathbf{Z}}^{k+1}=max\left(\text{Shrink}\left({\mathbf{X}}^{k+1}+\frac{1}{\rho }{\mathbf{U}}_1^k,\frac{1}{\rho }\right),0\right)$

12

   ${\mathbf{U}}_1^{k+1}={\mathbf{U}}_1^k+{\mathbf{X}}^{k+1}-{\mathbf{Z}}^{k+1}$

13

  For i = 1,⋯,O

14

   ${\mathbf{u}}_{2,i}^{k+1}={\mathbf{u}}_{2,i}^k+{\mathbf{H}}_i{\mathbf{x}}_i^{k+1}-{\tilde{\mathbf{a}}}_i$

15

  end for

16

until convergence