| MABM_16M_MAM_November-06-2014_a November 6, 2014 |
| Obs | animal | sire | dam | afa | afb | sex | wwt |
|---|---|---|---|---|---|---|---|
| 1 | 1 | 0 | 0 | 1.00 | 0.00 | 1 | 289 |
| 2 | 2 | 0 | 0 | 0.00 | 1.00 | 2 | 245 |
| 3 | 3 | 0 | 2 | 0.50 | 0.50 | 2 | 256 |
| 4 | 4 | 1 | 0 | 0.50 | 0.50 | 2 | 261 |
| 5 | 5 | 1 | 2 | 0.50 | 0.50 | 1 | 292 |
| 6 | 6 | 1 | 3 | 0.75 | 0.25 | 1 | 286 |
| MABM_16M_MAM_November-06-2014_a November 6, 2014 |
| Model_2_Animal multibreed_eqvar_res_uneqvar_add_nadd_November-06-2014_a November 6, 2014 |
| ANIMAL BREEDING NOTES |
| CHAPTER 16M ALL MODELS |
| MULTIBREED ANIMAL MODELS WITH: |
| 1) UNEQUAL RESIDUAL, ADDITIVE, AND NONADDITIVE GENETIC VARIANCES |
| 2) EQUAL RESIDUAL VARIANCES, UNEQUAL ADDITIVE AND NONADDITIVE GENETIC VARIANCES |
| 3) EQUAL RESIDUAL AND ADDITIVE GENETIC VARIANCES, UNEQUAL NONADDITIVE GENETIC VARIANCES |
| 4) EQUAL RESIDUAL AND ADDITIVE GENETIC VARIANCES, NO RANDOM NONADDITIVE GENETIC EFFECTS |
| Mauricio A. Elzo, University of Florida, elzo@animal.ufl.edu |
| Read input dataset (SAS file) |
OBS animal sire dam afa afb sex wwt
------ --------- --------- --------- --------- --------- --------- ---------
1 1.0000 0 0 1.0000 0 1.0000 289.0000
2 2.0000 0 0 0 1.0000 2.0000 245.0000
3 3.0000 0 2.0000 0.5000 0.5000 2.0000 256.0000
4 4.0000 1.0000 0 0.5000 0.5000 2.0000 261.0000
5 5.0000 1.0000 2.0000 0.5000 0.5000 1.0000 292.0000
6 6.0000 1.0000 3.0000 0.7500 0.2500 1.0000 286.0000
|
| datmat = matrix of input data |
| datmat | ||||||
|---|---|---|---|---|---|---|
| 1 | 0 | 0 | 1 | 0 | 1 | 289 |
| 2 | 0 | 0 | 0 | 1 | 2 | 245 |
| 3 | 0 | 2 | 0.5 | 0.5 | 2 | 256 |
| 4 | 1 | 0 | 0.5 | 0.5 | 2 | 261 |
| 5 | 1 | 2 | 0.5 | 0.5 | 1 | 292 |
| 6 | 1 | 3 | 0.75 | 0.25 | 1 | 286 |
| Enter Parameters for Current Run |
| Enter restronsol = 1 to impose restrictions on solutions to solve the MME, else = 0 if not |
| restronsol |
|---|
| 0 |
| No restrictions imposed on solutions to solve MME |
| Define number of traits = nt = 1 (DO NOT CHANGE; This program is for single traits ONLY !! |
| nt |
|---|
| 1 |
| Enter nanim = Number of animals |
| nanim |
|---|
| 6 |
| Enter nrec = Number of records |
| nrec |
|---|
| 6 |
| Enter nf = Number of fixed effects in the MME |
| nf |
|---|
| 6 |
| Enter nga = Number of random additive genetic effects in the MME |
| nga |
|---|
| 6 |
| ngn = Number of random nonadditive genetic effects in the MME |
| ngn |
|---|
| 6 |
| Enter uneqresvar = 1 if unequal residual variances else uneqresvar = 0 |
| uneqresvar |
|---|
| 0 |
| Enter uneqaddvar = 1 if unequal residual variances else uneqaddvar = 0 |
| uneqaddvar |
|---|
| 1 |
| Compute neq = nf+nga+ngn = total number of MME |
| neq |
|---|
| 18 |
| Define pedigf = pedigree file with breed composition of animals, sires, and dams |
| pedigf | ||||||||
|---|---|---|---|---|---|---|---|---|
| 1 | 0 | 0 | 1 | 0 | 1 | 0 | 1 | 0 |
| 2 | 0 | 0 | 0 | 1 | 0 | 1 | 0 | 1 |
| 3 | 0 | 2 | 0.5 | 0.5 | 1 | 0 | 0 | 1 |
| 4 | 1 | 0 | 0.5 | 0.5 | 1 | 0 | 0 | 1 |
| 5 | 1 | 2 | 0.5 | 0.5 | 1 | 0 | 0 | 1 |
| 6 | 1 | 3 | 0.75 | 0.25 | 1 | 0 | 0.5 | 0.5 |
| Construct xf = matrix of fixed and random effects |
| Construct fixed effects in matrix xf |
| xf | ||||||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| COL1 | COL2 | COL3 | COL4 | COL5 | COL6 | COL7 | COL8 | COL9 | COL10 | COL11 | COL12 | COL13 | COL14 | COL15 | COL16 | COL17 | COL18 | |
| ROW1 | 1 | 1 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| ROW2 | 1 | 0 | 1 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| ROW3 | 1 | 0.5 | 0.5 | 1 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| ROW4 | 1 | 0.5 | 0.5 | 1 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| ROW5 | 1 | 0.5 | 0.5 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| ROW6 | 1 | 0.75 | 0.25 | 0.5 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| Construct random additive genetic effects in matrix xf |
| xf | ||||||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| COL1 | COL2 | COL3 | COL4 | COL5 | COL6 | COL7 | COL8 | COL9 | COL10 | COL11 | COL12 | COL13 | COL14 | COL15 | COL16 | COL17 | COL18 | |
| ROW1 | 1 | 1 | 0 | 0 | 1 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| ROW2 | 1 | 0 | 1 | 0 | 0 | 1 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| ROW3 | 1 | 0.5 | 0.5 | 1 | 0 | 1 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| ROW4 | 1 | 0.5 | 0.5 | 1 | 0 | 1 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| ROW5 | 1 | 0.5 | 0.5 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| ROW6 | 1 | 0.75 | 0.25 | 0.5 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 |
| Construct random nonadditive genetic effects in matrix xf |
| xf | ||||||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| COL1 | COL2 | COL3 | COL4 | COL5 | COL6 | COL7 | COL8 | COL9 | COL10 | COL11 | COL12 | COL13 | COL14 | COL15 | COL16 | COL17 | COL18 | |
| ROW1 | 1 | 1 | 0 | 0 | 1 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| ROW2 | 1 | 0 | 1 | 0 | 0 | 1 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| ROW3 | 1 | 0.5 | 0.5 | 1 | 0 | 1 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 |
| ROW4 | 1 | 0.5 | 0.5 | 1 | 0 | 1 | 0 | 0 | 0 | 1 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 |
| ROW5 | 1 | 0.5 | 0.5 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 1 | 1 | 0 | 0 | 0 | 0 |
| ROW6 | 1 | 0.75 | 0.25 | 0.5 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0.5 | 0 | 0.5 | 0 | 0 | 0 |
| Make x = xf, i.e., use computed xf |
| x | ||||||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| COL1 | COL2 | COL3 | COL4 | COL5 | COL6 | COL7 | COL8 | COL9 | COL10 | COL11 | COL12 | COL13 | COL14 | COL15 | COL16 | COL17 | COL18 | |
| ROW1 | 1 | 1 | 0 | 0 | 1 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| ROW2 | 1 | 0 | 1 | 0 | 0 | 1 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| ROW3 | 1 | 0.5 | 0.5 | 1 | 0 | 1 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 |
| ROW4 | 1 | 0.5 | 0.5 | 1 | 0 | 1 | 0 | 0 | 0 | 1 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 |
| ROW5 | 1 | 0.5 | 0.5 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 1 | 1 | 0 | 0 | 0 | 0 |
| ROW6 | 1 | 0.75 | 0.25 | 0.5 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0.5 | 0 | 0.5 | 0 | 0 | 0 |
| veaa | vebb | veab |
|---|---|---|
| 49 | 49 | 0 |
| TRICK: make r=diag(ve=1) for models with common residual variance |
| r = matrix of residual covariances |
| r | |||||
|---|---|---|---|---|---|
| 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 0 | 0 | 1 |
| invr = inverse of matrix of residual covariances |
| invr | |||||
|---|---|---|---|---|---|
| 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 0 | 0 | 1 |
| Read yf = vector of records |
| yf |
|---|
| 289 |
| 245 |
| 256 |
| 261 |
| 292 |
| 286 |
| Make y = yf, i.e., use read yf |
| y |
|---|
| 289 |
| 245 |
| 256 |
| 261 |
| 292 |
| 286 |
| Compute xtinvr = x transpose times r |
| xtinvr | |||||
|---|---|---|---|---|---|
| 1 | 1 | 1 | 1 | 1 | 1 |
| 1 | 0 | 0.5 | 0.5 | 0.5 | 0.75 |
| 0 | 1 | 0.5 | 0.5 | 0.5 | 0.25 |
| 0 | 0 | 1 | 1 | 1 | 0.5 |
| 1 | 0 | 0 | 0 | 1 | 1 |
| 0 | 1 | 1 | 1 | 0 | 0 |
| 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 0 | 0 | 1 |
| 0 | 0 | 0 | 1 | 1 | 0.5 |
| 0 | 0 | 1 | 0 | 1 | 0 |
| 0 | 0 | 0 | 0 | 0 | 0.5 |
| 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 0 |
| Compute xtinvr = x transpose times r times x |
| xtinvrx | ||||||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| COL1 | COL2 | COL3 | COL4 | COL5 | COL6 | COL7 | COL8 | COL9 | COL10 | COL11 | COL12 | COL13 | COL14 | COL15 | COL16 | COL17 | COL18 | |
| ROW1 | 6 | 3.25 | 2.75 | 3.5 | 3 | 3 | 1 | 1 | 1 | 1 | 1 | 1 | 2.5 | 2 | 0.5 | 0 | 0 | 0 |
| ROW2 | 3.25 | 2.3125 | 0.9375 | 1.875 | 2.25 | 1 | 1 | 0 | 0.5 | 0.5 | 0.5 | 0.75 | 1.375 | 1 | 0.375 | 0 | 0 | 0 |
| ROW3 | 2.75 | 0.9375 | 1.8125 | 1.625 | 0.75 | 2 | 0 | 1 | 0.5 | 0.5 | 0.5 | 0.25 | 1.125 | 1 | 0.125 | 0 | 0 | 0 |
| ROW4 | 3.5 | 1.875 | 1.625 | 3.25 | 1.5 | 2 | 0 | 0 | 1 | 1 | 1 | 0.5 | 2.25 | 2 | 0.25 | 0 | 0 | 0 |
| ROW5 | 3 | 2.25 | 0.75 | 1.5 | 3 | 0 | 1 | 0 | 0 | 0 | 1 | 1 | 1.5 | 1 | 0.5 | 0 | 0 | 0 |
| ROW6 | 3 | 1 | 2 | 2 | 0 | 3 | 0 | 1 | 1 | 1 | 0 | 0 | 1 | 1 | 0 | 0 | 0 | 0 |
| ROW7 | 1 | 1 | 0 | 0 | 1 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| ROW8 | 1 | 0 | 1 | 0 | 0 | 1 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| ROW9 | 1 | 0.5 | 0.5 | 1 | 0 | 1 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 |
| ROW10 | 1 | 0.5 | 0.5 | 1 | 0 | 1 | 0 | 0 | 0 | 1 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 |
| ROW11 | 1 | 0.5 | 0.5 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 1 | 1 | 0 | 0 | 0 | 0 |
| ROW12 | 1 | 0.75 | 0.25 | 0.5 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0.5 | 0 | 0.5 | 0 | 0 | 0 |
| ROW13 | 2.5 | 1.375 | 1.125 | 2.25 | 1.5 | 1 | 0 | 0 | 0 | 1 | 1 | 0.5 | 2.25 | 1 | 0.25 | 0 | 0 | 0 |
| ROW14 | 2 | 1 | 1 | 2 | 1 | 1 | 0 | 0 | 1 | 0 | 1 | 0 | 1 | 2 | 0 | 0 | 0 | 0 |
| ROW15 | 0.5 | 0.375 | 0.125 | 0.25 | 0.5 | 0 | 0 | 0 | 0 | 0 | 0 | 0.5 | 0.25 | 0 | 0.25 | 0 | 0 | 0 |
| ROW16 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| ROW17 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| ROW18 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| Enter intrabreed and interbreed additive genetic variances |
| vaaa | vabb | vaab |
|---|---|---|
| 36 | 9 | 4 |
| Compute vaf = vector of multibreed additive genetic variances |
| pedigf | ||||||||
|---|---|---|---|---|---|---|---|---|
| 1 | 0 | 0 | 1 | 0 | 1 | 0 | 1 | 0 |
| 2 | 0 | 0 | 0 | 1 | 0 | 1 | 0 | 1 |
| 3 | 0 | 2 | 0.5 | 0.5 | 1 | 0 | 0 | 1 |
| 4 | 1 | 0 | 0.5 | 0.5 | 1 | 0 | 0 | 1 |
| 5 | 1 | 2 | 0.5 | 0.5 | 1 | 0 | 0 | 1 |
| 6 | 1 | 3 | 0.75 | 0.25 | 1 | 0 | 0.5 | 0.5 |
| vaf |
|---|
| 36 |
| 9 |
| 22.5 |
| 22.5 |
| 22.5 |
| 30.25 |
| Compute daf = vector of computed residual additive genetic variances |
| Recall: (Ga)-1 = (I - 1/2 P') (Da)-1 (I - 1/2 P) |
| daf |
|---|
| 36 |
| 9 |
| 20.25 |
| 13.5 |
| 11.25 |
| 15.625 |
| Make da = daf, i.e., use computed da |
| Compute dainv = inverse of da |
| dainv = inverse of matrix of residual additive genetic variances |
| dainv |
|---|
| 0.0277778 |
| 0.1111111 |
| 0.0493827 |
| 0.0740741 |
| 0.0888889 |
| 0.064 |
| Enter intrabreed and interbreed nonadditive genetic variances |
| vnab |
|---|
| 16 |
| Compute vnf = vector of multibreed additive genetic variances |
| vnf |
|---|
| 16 |
| 16 |
| 16 |
| 16 |
| 16 |
| 16 |
| Compute dnf = vector of computed residual nonadditive genetic variances |
| Recall: (Gn)-1 = (I - 1/2 P') (Dn)-1 (I - 1/2 P) |
| dnf |
|---|
| 16 |
| 16 |
| 12 |
| 12 |
| 8 |
| 8 |
| Make dn = dnf, i.e., use computed dn |
| Compute dninv = inverse of dn |
| dninv = inverse of matrix of residual nonadditive genetic variances |
| dninv |
|---|
| 0.0625 |
| 0.0625 |
| 0.0833333 |
| 0.0833333 |
| 0.125 |
| 0.125 |
| Compute gainv = inverse of the matrix of multibreed additive genetic covariances |
| Using algorithm to compute gainv directly; Elzo (1990a),JAS 68:1215-1228 |
| gainv | |||||
|---|---|---|---|---|---|
| 0.0845185 | 0.0222222 | 0.016 | -0.037037 | -0.044444 | -0.032 |
| 0.0222222 | 0.145679 | -0.024691 | 0 | -0.044444 | 0 |
| 0.016 | -0.024691 | 0.0653827 | 0 | 0 | -0.032 |
| -0.037037 | 0 | 0 | 0.0740741 | 0 | 0 |
| -0.044444 | -0.044444 | 0 | 0 | 0.0888889 | 0 |
| -0.032 | 0 | -0.032 | 0 | 0 | 0.064 |
| gainv | |||||
|---|---|---|---|---|---|
| 0.085 | 0.022 | 0.016 | -0.037 | -0.044 | -0.032 |
| 0.022 | 0.146 | -0.025 | 0.000 | -0.044 | 0.000 |
| 0.016 | -0.025 | 0.065 | 0.000 | 0.000 | -0.032 |
| -0.037 | 0.000 | 0.000 | 0.074 | 0.000 | 0.000 |
| -0.044 | -0.044 | 0.000 | 0.000 | 0.089 | 0.000 |
| -0.032 | 0.000 | -0.032 | 0.000 | 0.000 | 0.064 |
| Compute gninv = inverse of the matrix of regression nonadditive genetic covariances |
| Using algorithm to compute gninv directly; Elzo (1990b),JAS 68:4079-4099 |
| gninv | |||||
|---|---|---|---|---|---|
| 0.1458333 | 0.03125 | 0.03125 | -0.041667 | -0.0625 | -0.0625 |
| 0.03125 | 0.1145833 | -0.041667 | 0 | -0.0625 | 0 |
| 0.03125 | -0.041667 | 0.1145833 | 0 | 0 | -0.0625 |
| -0.041667 | 0 | 0 | 0.0833333 | 0 | 0 |
| -0.0625 | -0.0625 | 0 | 0 | 0.125 | 0 |
| -0.0625 | 0 | -0.0625 | 0 | 0 | 0.125 |
| gninv | |||||
|---|---|---|---|---|---|
| 0.146 | 0.031 | 0.031 | -0.042 | -0.063 | -0.063 |
| 0.031 | 0.115 | -0.042 | 0.000 | -0.063 | 0.000 |
| 0.031 | -0.042 | 0.115 | 0.000 | 0.000 | -0.063 |
| -0.042 | 0.000 | 0.000 | 0.083 | 0.000 | 0.000 |
| -0.063 | -0.063 | 0.000 | 0.000 | 0.125 | 0.000 |
| -0.063 | 0.000 | -0.063 | 0.000 | 0.000 | 0.125 |
| Compute lhs = left hand side of the MME |
| Add gainv to lhs |
| Add gninv to lhs |
| lhs | ||||||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| COL1 | COL2 | COL3 | COL4 | COL5 | COL6 | COL7 | COL8 | COL9 | COL10 | COL11 | COL12 | COL13 | COL14 | COL15 | COL16 | COL17 | COL18 | |
| ROW1 | 6 | 3.25 | 2.75 | 3.5 | 3 | 3 | 1 | 1 | 1 | 1 | 1 | 1 | 2.5 | 2 | 0.5 | 0 | 0 | 0 |
| ROW2 | 3.25 | 2.3125 | 0.9375 | 1.875 | 2.25 | 1 | 1 | 0 | 0.5 | 0.5 | 0.5 | 0.75 | 1.375 | 1 | 0.375 | 0 | 0 | 0 |
| ROW3 | 2.75 | 0.9375 | 1.8125 | 1.625 | 0.75 | 2 | 0 | 1 | 0.5 | 0.5 | 0.5 | 0.25 | 1.125 | 1 | 0.125 | 0 | 0 | 0 |
| ROW4 | 3.5 | 1.875 | 1.625 | 3.25 | 1.5 | 2 | 0 | 0 | 1 | 1 | 1 | 0.5 | 2.25 | 2 | 0.25 | 0 | 0 | 0 |
| ROW5 | 3 | 2.25 | 0.75 | 1.5 | 3 | 0 | 1 | 0 | 0 | 0 | 1 | 1 | 1.5 | 1 | 0.5 | 0 | 0 | 0 |
| ROW6 | 3 | 1 | 2 | 2 | 0 | 3 | 0 | 1 | 1 | 1 | 0 | 0 | 1 | 1 | 0 | 0 | 0 | 0 |
| ROW7 | 1 | 1 | 0 | 0 | 1 | 0 | 5.1414074 | 1.0888889 | 0.784 | -1.814815 | -2.177778 | -1.568 | 0 | 0 | 0 | 0 | 0 | 0 |
| ROW8 | 1 | 0 | 1 | 0 | 0 | 1 | 1.0888889 | 8.1382716 | -1.209877 | 0 | -2.177778 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| ROW9 | 1 | 0.5 | 0.5 | 1 | 0 | 1 | 0.784 | -1.209877 | 4.2037531 | 0 | 0 | -1.568 | 0 | 1 | 0 | 0 | 0 | 0 |
| ROW10 | 1 | 0.5 | 0.5 | 1 | 0 | 1 | -1.814815 | 0 | 0 | 4.6296296 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 |
| ROW11 | 1 | 0.5 | 0.5 | 1 | 1 | 0 | -2.177778 | -2.177778 | 0 | 0 | 5.3555556 | 0 | 1 | 1 | 0 | 0 | 0 | 0 |
| ROW12 | 1 | 0.75 | 0.25 | 0.5 | 1 | 0 | -1.568 | 0 | -1.568 | 0 | 0 | 4.136 | 0.5 | 0 | 0.5 | 0 | 0 | 0 |
| ROW13 | 2.5 | 1.375 | 1.125 | 2.25 | 1.5 | 1 | 0 | 0 | 0 | 1 | 1 | 0.5 | 9.3958333 | 2.53125 | 1.78125 | -2.041667 | -3.0625 | -3.0625 |
| ROW14 | 2 | 1 | 1 | 2 | 1 | 1 | 0 | 0 | 1 | 0 | 1 | 0 | 2.53125 | 7.6145833 | -2.041667 | 0 | -3.0625 | 0 |
| ROW15 | 0.5 | 0.375 | 0.125 | 0.25 | 0.5 | 0 | 0 | 0 | 0 | 0 | 0 | 0.5 | 1.78125 | -2.041667 | 5.8645833 | 0 | 0 | -3.0625 |
| ROW16 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -2.041667 | 0 | 0 | 4.0833333 | 0 | 0 |
| ROW17 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -3.0625 | -3.0625 | 0 | 0 | 6.125 | 0 |
| ROW18 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -3.0625 | 0 | -3.0625 | 0 | 0 | 6.125 |
| lhs | |||||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 6.000 | 3.250 | 2.750 | 3.500 | 3.000 | 3.000 | 1.000 | 1.000 | 1.000 | 1.000 | 1.000 | 1.000 | 2.500 | 2.000 | 0.500 | 0.000 | 0.000 | 0.000 |
| 3.250 | 2.313 | 0.938 | 1.875 | 2.250 | 1.000 | 1.000 | 0.000 | 0.500 | 0.500 | 0.500 | 0.750 | 1.375 | 1.000 | 0.375 | 0.000 | 0.000 | 0.000 |
| 2.750 | 0.938 | 1.813 | 1.625 | 0.750 | 2.000 | 0.000 | 1.000 | 0.500 | 0.500 | 0.500 | 0.250 | 1.125 | 1.000 | 0.125 | 0.000 | 0.000 | 0.000 |
| 3.500 | 1.875 | 1.625 | 3.250 | 1.500 | 2.000 | 0.000 | 0.000 | 1.000 | 1.000 | 1.000 | 0.500 | 2.250 | 2.000 | 0.250 | 0.000 | 0.000 | 0.000 |
| 3.000 | 2.250 | 0.750 | 1.500 | 3.000 | 0.000 | 1.000 | 0.000 | 0.000 | 0.000 | 1.000 | 1.000 | 1.500 | 1.000 | 0.500 | 0.000 | 0.000 | 0.000 |
| 3.000 | 1.000 | 2.000 | 2.000 | 0.000 | 3.000 | 0.000 | 1.000 | 1.000 | 1.000 | 0.000 | 0.000 | 1.000 | 1.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| 1.000 | 1.000 | 0.000 | 0.000 | 1.000 | 0.000 | 5.141 | 1.089 | 0.784 | -1.815 | -2.178 | -1.568 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| 1.000 | 0.000 | 1.000 | 0.000 | 0.000 | 1.000 | 1.089 | 8.138 | -1.210 | 0.000 | -2.178 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| 1.000 | 0.500 | 0.500 | 1.000 | 0.000 | 1.000 | 0.784 | -1.210 | 4.204 | 0.000 | 0.000 | -1.568 | 0.000 | 1.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| 1.000 | 0.500 | 0.500 | 1.000 | 0.000 | 1.000 | -1.815 | 0.000 | 0.000 | 4.630 | 0.000 | 0.000 | 1.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| 1.000 | 0.500 | 0.500 | 1.000 | 1.000 | 0.000 | -2.178 | -2.178 | 0.000 | 0.000 | 5.356 | 0.000 | 1.000 | 1.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| 1.000 | 0.750 | 0.250 | 0.500 | 1.000 | 0.000 | -1.568 | 0.000 | -1.568 | 0.000 | 0.000 | 4.136 | 0.500 | 0.000 | 0.500 | 0.000 | 0.000 | 0.000 |
| 2.500 | 1.375 | 1.125 | 2.250 | 1.500 | 1.000 | 0.000 | 0.000 | 0.000 | 1.000 | 1.000 | 0.500 | 9.396 | 2.531 | 1.781 | -2.042 | -3.063 | -3.063 |
| 2.000 | 1.000 | 1.000 | 2.000 | 1.000 | 1.000 | 0.000 | 0.000 | 1.000 | 0.000 | 1.000 | 0.000 | 2.531 | 7.615 | -2.042 | 0.000 | -3.063 | 0.000 |
| 0.500 | 0.375 | 0.125 | 0.250 | 0.500 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.500 | 1.781 | -2.042 | 5.865 | 0.000 | 0.000 | -3.063 |
| 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | -2.042 | 0.000 | 0.000 | 4.083 | 0.000 | 0.000 |
| 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | -3.063 | -3.063 | 0.000 | 0.000 | 6.125 | 0.000 |
| 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | -3.063 | 0.000 | -3.063 | 0.000 | 0.000 | 6.125 |
| Compute rhs = right hand side of the MME |
| rhs |
|---|
| 1629 |
| 908 |
| 721 |
| 952 |
| 867 |
| 762 |
| 289 |
| 245 |
| 256 |
| 261 |
| 292 |
| 286 |
| 696 |
| 548 |
| 143 |
| 0 |
| 0 |
| 0 |
| rhs |
|---|
| 1629.0 |
| 908.00 |
| 721.00 |
| 952.00 |
| 867.00 |
| 762.00 |
| 289.00 |
| 245.00 |
| 256.00 |
| 261.00 |
| 292.00 |
| 286.00 |
| 696.00 |
| 548.00 |
| 143.00 |
| 0.00 |
| 0.00 |
| 0.00 |
| Compute ginvlhs = generalized inverse of the left hand side of the MME |
| ginvlhs | ||||||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| COL1 | COL2 | COL3 | COL4 | COL5 | COL6 | COL7 | COL8 | COL9 | COL10 | COL11 | COL12 | COL13 | COL14 | COL15 | COL16 | COL17 | COL18 | |
| ROW1 | 0.167793 | 0.126577 | 0.041216 | -0.281208 | 0.079556 | 0.088236 | -0.163740 | -0.047246 | -0.046048 | -0.077888 | -0.096352 | -0.130285 | 0.004719 | 0.001781 | -0.008860 | 0.002359 | 0.003250 | -0.002070 |
| ROW2 | 0.126577 | 1.266360 | -1.139783 | -0.417773 | -0.424776 | 0.551353 | -0.346270 | 0.086853 | -0.083601 | -0.227062 | -0.014199 | -0.216919 | 0.099352 | 0.064421 | 0.031449 | 0.049676 | 0.081887 | 0.065400 |
| ROW3 | 0.041216 | -1.139783 | 1.180999 | 0.136566 | 0.504333 | -0.463117 | 0.182531 | -0.134099 | 0.037552 | 0.149174 | -0.082153 | 0.086634 | -0.094633 | -0.062640 | -0.040308 | -0.047317 | -0.078636 | -0.067471 |
| ROW4 | -0.281208 | -0.417773 | 0.136566 | 1.354706 | 0.099009 | -0.380217 | 0.088466 | 0.024859 | -0.087095 | -0.030343 | -0.055492 | -0.006653 | -0.251652 | -0.236266 | -0.120951 | -0.125826 | -0.243959 | -0.186301 |
| ROW5 | 0.079556 | -0.424776 | 0.504333 | 0.099009 | 0.491153 | -0.411596 | -0.135932 | -0.047293 | 0.025961 | 0.005034 | -0.180005 | -0.128327 | -0.076746 | -0.067744 | -0.062035 | -0.038373 | -0.072245 | -0.069391 |
| ROW6 | 0.088236 | 0.551353 | -0.463117 | -0.380217 | -0.411596 | 0.499833 | -0.027808 | 0.000047 | -0.072009 | -0.082923 | 0.083654 | -0.001958 | 0.081465 | 0.069525 | 0.053175 | 0.040733 | 0.075495 | 0.067320 |
| ROW7 | -0.163740 | -0.346270 | 0.182531 | 0.088466 | -0.135932 | -0.027808 | 0.684474 | 0.009016 | 0.061006 | 0.315188 | 0.337898 | 0.397314 | -0.032058 | 0.025767 | 0.022320 | -0.016029 | -0.003145 | -0.004869 |
| ROW8 | -0.047246 | 0.086853 | -0.134099 | 0.024859 | -0.047293 | 0.000047 | 0.009016 | 0.181297 | 0.080505 | 0.011637 | 0.094851 | 0.045610 | 0.008449 | -0.008667 | -0.004007 | 0.004225 | -0.000109 | 0.002221 |
| ROW9 | -0.046048 | -0.083601 | 0.037552 | -0.087095 | 0.025961 | -0.072009 | 0.061006 | 0.080505 | 0.384886 | 0.064498 | 0.080555 | 0.195725 | 0.040290 | -0.033322 | -0.027114 | 0.020145 | 0.003484 | 0.006588 |
| ROW10 | -0.077888 | -0.227062 | 0.149174 | -0.030343 | 0.005034 | -0.082923 | 0.315188 | 0.011637 | 0.064498 | 0.398192 | 0.159906 | 0.199582 | -0.041377 | 0.038884 | 0.023182 | -0.020688 | -0.001247 | -0.009098 |
| ROW11 | -0.096352 | -0.014199 | -0.082153 | -0.055492 | -0.180005 | 0.083654 | 0.337898 | 0.094851 | 0.080555 | 0.159906 | 0.435097 | 0.239420 | -0.010718 | 0.002988 | 0.013088 | -0.005359 | -0.003865 | 0.001185 |
| ROW12 | -0.130285 | -0.216919 | 0.086634 | -0.006653 | -0.128327 | -0.001958 | 0.397314 | 0.045610 | 0.195725 | 0.199582 | 0.239420 | 0.565514 | 0.001097 | 0.011673 | -0.013319 | 0.000548 | 0.006385 | -0.006111 |
| ROW13 | 0.004719 | 0.099352 | -0.094633 | -0.251652 | -0.076746 | 0.081465 | -0.032058 | 0.008449 | 0.040290 | -0.041377 | -0.010718 | 0.001097 | 0.296489 | 0.030815 | 0.014248 | 0.148244 | 0.163652 | 0.155368 |
| ROW14 | 0.001781 | 0.064421 | -0.062640 | -0.236266 | -0.067744 | 0.069525 | 0.025767 | -0.008667 | -0.033322 | 0.038884 | 0.002988 | 0.011673 | 0.030815 | 0.291761 | 0.151813 | 0.015407 | 0.161288 | 0.091314 |
| ROW15 | -0.008860 | 0.031449 | -0.040308 | -0.120951 | -0.062035 | 0.053175 | 0.022320 | -0.004007 | -0.027114 | 0.023182 | 0.013088 | -0.013319 | 0.014248 | 0.151813 | 0.316611 | 0.007124 | 0.083031 | 0.165429 |
| ROW16 | 0.002359 | 0.049676 | -0.047317 | -0.125826 | -0.038373 | 0.040733 | -0.016029 | 0.004225 | 0.020145 | -0.020688 | -0.005359 | 0.000548 | 0.148244 | 0.015407 | 0.007124 | 0.319020 | 0.081826 | 0.077684 |
| ROW17 | 0.003250 | 0.081887 | -0.078636 | -0.243959 | -0.072245 | 0.075495 | -0.003145 | -0.000109 | 0.003484 | -0.001247 | -0.003865 | 0.006385 | 0.163652 | 0.161288 | 0.083031 | 0.081826 | 0.325735 | 0.123341 |
| ROW18 | -0.002070 | 0.065400 | -0.067471 | -0.186301 | -0.069391 | 0.067320 | -0.004869 | 0.002221 | 0.006588 | -0.009098 | 0.001185 | -0.006111 | 0.155368 | 0.091314 | 0.165429 | 0.077684 | 0.123341 | 0.323664 |
| ginvlhs | |||||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 0.168 | 0.127 | 0.041 | -0.281 | 0.080 | 0.088 | -0.164 | -0.047 | -0.046 | -0.078 | -0.096 | -0.130 | 0.005 | 0.002 | -0.009 | 0.002 | 0.003 | -0.002 |
| 0.127 | 1.266 | -1.140 | -0.418 | -0.425 | 0.551 | -0.346 | 0.087 | -0.084 | -0.227 | -0.014 | -0.217 | 0.099 | 0.064 | 0.031 | 0.050 | 0.082 | 0.065 |
| 0.041 | -1.140 | 1.181 | 0.137 | 0.504 | -0.463 | 0.183 | -0.134 | 0.038 | 0.149 | -0.082 | 0.087 | -0.095 | -0.063 | -0.040 | -0.047 | -0.079 | -0.067 |
| -0.281 | -0.418 | 0.137 | 1.355 | 0.099 | -0.380 | 0.088 | 0.025 | -0.087 | -0.030 | -0.055 | -0.007 | -0.252 | -0.236 | -0.121 | -0.126 | -0.244 | -0.186 |
| 0.080 | -0.425 | 0.504 | 0.099 | 0.491 | -0.412 | -0.136 | -0.047 | 0.026 | 0.005 | -0.180 | -0.128 | -0.077 | -0.068 | -0.062 | -0.038 | -0.072 | -0.069 |
| 0.088 | 0.551 | -0.463 | -0.380 | -0.412 | 0.500 | -0.028 | 0.000 | -0.072 | -0.083 | 0.084 | -0.002 | 0.081 | 0.070 | 0.053 | 0.041 | 0.075 | 0.067 |
| -0.164 | -0.346 | 0.183 | 0.088 | -0.136 | -0.028 | 0.684 | 0.009 | 0.061 | 0.315 | 0.338 | 0.397 | -0.032 | 0.026 | 0.022 | -0.016 | -0.003 | -0.005 |
| -0.047 | 0.087 | -0.134 | 0.025 | -0.047 | 0.000 | 0.009 | 0.181 | 0.081 | 0.012 | 0.095 | 0.046 | 0.008 | -0.009 | -0.004 | 0.004 | -0.000 | 0.002 |
| -0.046 | -0.084 | 0.038 | -0.087 | 0.026 | -0.072 | 0.061 | 0.081 | 0.385 | 0.064 | 0.081 | 0.196 | 0.040 | -0.033 | -0.027 | 0.020 | 0.003 | 0.007 |
| -0.078 | -0.227 | 0.149 | -0.030 | 0.005 | -0.083 | 0.315 | 0.012 | 0.064 | 0.398 | 0.160 | 0.200 | -0.041 | 0.039 | 0.023 | -0.021 | -0.001 | -0.009 |
| -0.096 | -0.014 | -0.082 | -0.055 | -0.180 | 0.084 | 0.338 | 0.095 | 0.081 | 0.160 | 0.435 | 0.239 | -0.011 | 0.003 | 0.013 | -0.005 | -0.004 | 0.001 |
| -0.130 | -0.217 | 0.087 | -0.007 | -0.128 | -0.002 | 0.397 | 0.046 | 0.196 | 0.200 | 0.239 | 0.566 | 0.001 | 0.012 | -0.013 | 0.001 | 0.006 | -0.006 |
| 0.005 | 0.099 | -0.095 | -0.252 | -0.077 | 0.081 | -0.032 | 0.008 | 0.040 | -0.041 | -0.011 | 0.001 | 0.296 | 0.031 | 0.014 | 0.148 | 0.164 | 0.155 |
| 0.002 | 0.064 | -0.063 | -0.236 | -0.068 | 0.070 | 0.026 | -0.009 | -0.033 | 0.039 | 0.003 | 0.012 | 0.031 | 0.292 | 0.152 | 0.015 | 0.161 | 0.091 |
| -0.009 | 0.031 | -0.040 | -0.121 | -0.062 | 0.053 | 0.022 | -0.004 | -0.027 | 0.023 | 0.013 | -0.013 | 0.014 | 0.152 | 0.317 | 0.007 | 0.083 | 0.165 |
| 0.002 | 0.050 | -0.047 | -0.126 | -0.038 | 0.041 | -0.016 | 0.004 | 0.020 | -0.021 | -0.005 | 0.001 | 0.148 | 0.015 | 0.007 | 0.319 | 0.082 | 0.078 |
| 0.003 | 0.082 | -0.079 | -0.244 | -0.072 | 0.075 | -0.003 | -0.000 | 0.003 | -0.001 | -0.004 | 0.006 | 0.164 | 0.161 | 0.083 | 0.082 | 0.326 | 0.123 |
| -0.002 | 0.065 | -0.067 | -0.186 | -0.069 | 0.067 | -0.005 | 0.002 | 0.007 | -0.009 | 0.001 | -0.006 | 0.155 | 0.091 | 0.165 | 0.078 | 0.123 | 0.324 |
| Compute gl = ginvlhs*lhs = matrix of expectations of solutions |
| gl | |||||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 0.500 | 0.250 | 0.250 | 0.000 | 0.250 | 0.250 | 0.000 | -0.000 | -0.000 | -0.000 | 0.000 | -0.000 | 0.000 | -0.000 | 0.000 | -0.000 | -0.000 | -0.000 |
| 0.250 | 0.625 | -0.375 | -0.000 | 0.125 | 0.125 | 0.000 | -0.000 | 0.000 | -0.000 | -0.000 | 0.000 | 0.000 | -0.000 | 0.000 | -0.000 | -0.000 | -0.000 |
| 0.250 | -0.375 | 0.625 | 0.000 | 0.125 | 0.125 | -0.000 | 0.000 | -0.000 | 0.000 | 0.000 | 0.000 | -0.000 | 0.000 | -0.000 | 0.000 | 0.000 | 0.000 |
| 0.000 | 0.000 | -0.000 | 1.000 | 0.000 | 0.000 | -0.000 | 0.000 | -0.000 | 0.000 | 0.000 | -0.000 | -0.000 | 0.000 | -0.000 | 0.000 | 0.000 | 0.000 |
| 0.250 | 0.125 | 0.125 | 0.000 | 0.625 | -0.375 | -0.000 | 0.000 | -0.000 | -0.000 | 0.000 | 0.000 | 0.000 | 0.000 | -0.000 | 0.000 | -0.000 | 0.000 |
| 0.250 | 0.125 | 0.125 | 0.000 | -0.375 | 0.625 | 0.000 | -0.000 | 0.000 | -0.000 | -0.000 | 0.000 | 0.000 | -0.000 | 0.000 | -0.000 | -0.000 | -0.000 |
| -0.000 | -0.000 | -0.000 | 0.000 | -0.000 | 0.000 | 1.000 | 0.000 | -0.000 | -0.000 | -0.000 | 0.000 | -0.000 | 0.000 | -0.000 | -0.000 | 0.000 | 0.000 |
| -0.000 | -0.000 | 0.000 | -0.000 | -0.000 | 0.000 | -0.000 | 1.000 | 0.000 | 0.000 | -0.000 | 0.000 | -0.000 | -0.000 | 0.000 | -0.000 | 0.000 | -0.000 |
| -0.000 | -0.000 | 0.000 | 0.000 | -0.000 | 0.000 | -0.000 | 0.000 | 1.000 | 0.000 | -0.000 | 0.000 | -0.000 | 0.000 | -0.000 | -0.000 | 0.000 | 0.000 |
| 0.000 | -0.000 | 0.000 | 0.000 | -0.000 | 0.000 | -0.000 | -0.000 | -0.000 | 1.000 | -0.000 | 0.000 | -0.000 | 0.000 | -0.000 | -0.000 | -0.000 | -0.000 |
| -0.000 | -0.000 | 0.000 | 0.000 | -0.000 | 0.000 | -0.000 | -0.000 | -0.000 | -0.000 | 1.000 | 0.000 | -0.000 | 0.000 | -0.000 | -0.000 | 0.000 | 0.000 |
| -0.000 | -0.000 | -0.000 | 0.000 | -0.000 | -0.000 | -0.000 | -0.000 | -0.000 | -0.000 | 0.000 | 1.000 | -0.000 | 0.000 | -0.000 | -0.000 | -0.000 | 0.000 |
| -0.000 | -0.000 | 0.000 | 0.000 | -0.000 | -0.000 | 0.000 | -0.000 | 0.000 | -0.000 | -0.000 | 0.000 | 1.000 | -0.000 | 0.000 | -0.000 | 0.000 | 0.000 |
| -0.000 | -0.000 | 0.000 | 0.000 | -0.000 | 0.000 | -0.000 | -0.000 | 0.000 | -0.000 | -0.000 | -0.000 | 0.000 | 1.000 | -0.000 | -0.000 | -0.000 | -0.000 |
| -0.000 | -0.000 | 0.000 | 0.000 | -0.000 | 0.000 | 0.000 | 0.000 | -0.000 | -0.000 | -0.000 | -0.000 | 0.000 | -0.000 | 1.000 | -0.000 | -0.000 | 0.000 |
| -0.000 | -0.000 | -0.000 | -0.000 | -0.000 | -0.000 | 0.000 | 0.000 | 0.000 | -0.000 | -0.000 | 0.000 | -0.000 | -0.000 | 0.000 | 1.000 | -0.000 | -0.000 |
| -0.000 | -0.000 | 0.000 | 0.000 | -0.000 | 0.000 | 0.000 | 0.000 | 0.000 | -0.000 | -0.000 | -0.000 | 0.000 | 0.000 | -0.000 | -0.000 | 1.000 | -0.000 |
| -0.000 | -0.000 | -0.000 | 0.000 | -0.000 | -0.000 | 0.000 | -0.000 | 0.000 | -0.000 | -0.000 | 0.000 | -0.000 | -0.000 | 0.000 | 0.000 | -0.000 | 1.000 |
| Notice that lg = gl (i.e., lhs*ginvlhs = lhs*ginvlhs) |
| lg | |||||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 0.500 | 0.250 | 0.250 | 0.000 | 0.250 | 0.250 | 0.000 | 0.000 | -0.000 | 0.000 | 0.000 | 0.000 | 0.000 | -0.000 | -0.000 | -0.000 | -0.000 | -0.000 |
| 0.250 | 0.625 | -0.375 | 0.000 | 0.125 | 0.125 | 0.000 | -0.000 | 0.000 | -0.000 | 0.000 | 0.000 | 0.000 | -0.000 | -0.000 | -0.000 | -0.000 | -0.000 |
| 0.250 | -0.375 | 0.625 | 0.000 | 0.125 | 0.125 | 0.000 | 0.000 | -0.000 | 0.000 | 0.000 | 0.000 | 0.000 | -0.000 | -0.000 | -0.000 | -0.000 | -0.000 |
| -0.000 | 0.000 | -0.000 | 1.000 | -0.000 | 0.000 | -0.000 | 0.000 | -0.000 | 0.000 | 0.000 | -0.000 | 0.000 | 0.000 | -0.000 | 0.000 | -0.000 | -0.000 |
| 0.250 | 0.125 | 0.125 | 0.000 | 0.625 | -0.375 | 0.000 | 0.000 | 0.000 | -0.000 | 0.000 | 0.000 | 0.000 | -0.000 | -0.000 | -0.000 | -0.000 | -0.000 |
| 0.250 | 0.125 | 0.125 | 0.000 | -0.375 | 0.625 | 0.000 | 0.000 | -0.000 | 0.000 | 0.000 | 0.000 | 0.000 | -0.000 | -0.000 | -0.000 | -0.000 | -0.000 |
| -0.000 | 0.000 | -0.000 | 0.000 | 0.000 | 0.000 | 1.000 | 0.000 | -0.000 | -0.000 | -0.000 | 0.000 | -0.000 | -0.000 | 0.000 | -0.000 | 0.000 | -0.000 |
| -0.000 | -0.000 | -0.000 | -0.000 | -0.000 | 0.000 | 0.000 | 1.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | -0.000 | 0.000 | 0.000 |
| -0.000 | -0.000 | 0.000 | 0.000 | 0.000 | -0.000 | 0.000 | 0.000 | 1.000 | 0.000 | -0.000 | 0.000 | 0.000 | -0.000 | -0.000 | -0.000 | -0.000 | -0.000 |
| 0.000 | -0.000 | 0.000 | 0.000 | -0.000 | 0.000 | -0.000 | -0.000 | 0.000 | 1.000 | -0.000 | -0.000 | -0.000 | -0.000 | -0.000 | -0.000 | -0.000 | -0.000 |
| -0.000 | -0.000 | 0.000 | 0.000 | 0.000 | -0.000 | -0.000 | -0.000 | -0.000 | -0.000 | 1.000 | -0.000 | -0.000 | -0.000 | -0.000 | -0.000 | -0.000 | -0.000 |
| -0.000 | 0.000 | -0.000 | 0.000 | 0.000 | -0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 1.000 | -0.000 | 0.000 | 0.000 | -0.000 | -0.000 | -0.000 |
| -0.000 | -0.000 | 0.000 | 0.000 | 0.000 | -0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 1.000 | -0.000 | -0.000 | -0.000 | -0.000 | -0.000 |
| 0.000 | -0.000 | 0.000 | 0.000 | 0.000 | -0.000 | 0.000 | -0.000 | -0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 1.000 | -0.000 | 0.000 | 0.000 | 0.000 |
| -0.000 | -0.000 | 0.000 | 0.000 | -0.000 | -0.000 | 0.000 | 0.000 | -0.000 | -0.000 | -0.000 | 0.000 | -0.000 | -0.000 | 1.000 | -0.000 | -0.000 | -0.000 |
| 0.000 | 0.000 | -0.000 | -0.000 | -0.000 | 0.000 | -0.000 | 0.000 | 0.000 | -0.000 | -0.000 | 0.000 | -0.000 | 0.000 | 0.000 | 1.000 | 0.000 | -0.000 |
| 0.000 | 0.000 | -0.000 | 0.000 | -0.000 | 0.000 | -0.000 | 0.000 | -0.000 | -0.000 | -0.000 | -0.000 | -0.000 | 0.000 | -0.000 | -0.000 | 1.000 | -0.000 |
| 0.000 | 0.000 | -0.000 | -0.000 | -0.000 | 0.000 | 0.000 | -0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | -0.000 | 1.000 |
| Verify that lgl = lhs (i.e., lhs*ginvlhs*lhs = lhs => generalized inverse is correct) |
| lgl | |||||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 6.000 | 3.250 | 2.750 | 3.500 | 3.000 | 3.000 | 1.000 | 1.000 | 1.000 | 1.000 | 1.000 | 1.000 | 2.500 | 2.000 | 0.500 | -0.000 | -0.000 | -0.000 |
| 3.250 | 2.313 | 0.938 | 1.875 | 2.250 | 1.000 | 1.000 | 0.000 | 0.500 | 0.500 | 0.500 | 0.750 | 1.375 | 1.000 | 0.375 | -0.000 | -0.000 | -0.000 |
| 2.750 | 0.938 | 1.813 | 1.625 | 0.750 | 2.000 | 0.000 | 1.000 | 0.500 | 0.500 | 0.500 | 0.250 | 1.125 | 1.000 | 0.125 | -0.000 | -0.000 | -0.000 |
| 3.500 | 1.875 | 1.625 | 3.250 | 1.500 | 2.000 | -0.000 | 0.000 | 1.000 | 1.000 | 1.000 | 0.500 | 2.250 | 2.000 | 0.250 | -0.000 | -0.000 | -0.000 |
| 3.000 | 2.250 | 0.750 | 1.500 | 3.000 | -0.000 | 1.000 | 0.000 | -0.000 | -0.000 | 1.000 | 1.000 | 1.500 | 1.000 | 0.500 | -0.000 | -0.000 | -0.000 |
| 3.000 | 1.000 | 2.000 | 2.000 | 0.000 | 3.000 | 0.000 | 1.000 | 1.000 | 1.000 | 0.000 | -0.000 | 1.000 | 1.000 | 0.000 | -0.000 | -0.000 | -0.000 |
| 1.000 | 1.000 | -0.000 | 0.000 | 1.000 | -0.000 | 5.141 | 1.089 | 0.784 | -1.815 | -2.178 | -1.568 | -0.000 | -0.000 | 0.000 | -0.000 | 0.000 | -0.000 |
| 1.000 | 0.000 | 1.000 | 0.000 | 0.000 | 1.000 | 1.089 | 8.138 | -1.210 | 0.000 | -2.178 | 0.000 | 0.000 | -0.000 | 0.000 | -0.000 | 0.000 | -0.000 |
| 1.000 | 0.500 | 0.500 | 1.000 | -0.000 | 1.000 | 0.784 | -1.210 | 4.204 | 0.000 | -0.000 | -1.568 | 0.000 | 1.000 | -0.000 | -0.000 | -0.000 | 0.000 |
| 1.000 | 0.500 | 0.500 | 1.000 | -0.000 | 1.000 | -1.815 | 0.000 | 0.000 | 4.630 | -0.000 | -0.000 | 1.000 | 0.000 | 0.000 | -0.000 | -0.000 | -0.000 |
| 1.000 | 0.500 | 0.500 | 1.000 | 1.000 | 0.000 | -2.178 | -2.178 | -0.000 | -0.000 | 5.356 | -0.000 | 1.000 | 1.000 | -0.000 | -0.000 | -0.000 | 0.000 |
| 1.000 | 0.750 | 0.250 | 0.500 | 1.000 | -0.000 | -1.568 | -0.000 | -1.568 | -0.000 | 0.000 | 4.136 | 0.500 | 0.000 | 0.500 | -0.000 | -0.000 | -0.000 |
| 2.500 | 1.375 | 1.125 | 2.250 | 1.500 | 1.000 | 0.000 | -0.000 | -0.000 | 1.000 | 1.000 | 0.500 | 9.396 | 2.531 | 1.781 | -2.042 | -3.062 | -3.063 |
| 2.000 | 1.000 | 1.000 | 2.000 | 1.000 | 1.000 | 0.000 | -0.000 | 1.000 | 0.000 | 1.000 | -0.000 | 2.531 | 7.615 | -2.042 | -0.000 | -3.063 | -0.000 |
| 0.500 | 0.375 | 0.125 | 0.250 | 0.500 | 0.000 | 0.000 | 0.000 | -0.000 | -0.000 | -0.000 | 0.500 | 1.781 | -2.042 | 5.865 | -0.000 | 0.000 | -3.063 |
| -0.000 | 0.000 | -0.000 | -0.000 | 0.000 | -0.000 | 0.000 | 0.000 | 0.000 | -0.000 | -0.000 | 0.000 | -2.042 | 0.000 | 0.000 | 4.083 | -0.000 | -0.000 |
| -0.000 | -0.000 | 0.000 | -0.000 | -0.000 | 0.000 | -0.000 | 0.000 | -0.000 | 0.000 | -0.000 | -0.000 | -3.063 | -3.063 | -0.000 | -0.000 | 6.125 | -0.000 |
| -0.000 | 0.000 | -0.000 | -0.000 | 0.000 | -0.000 | 0.000 | -0.000 | 0.000 | 0.000 | 0.000 | -0.000 | -3.063 | 0.000 | -3.063 | 0.000 | -0.000 | 6.125 |
| Compute ranklhs = rank of the MME = trace of ginvlhs*lhs |
| ranklhs |
|---|
| 16 |
| Compute yhat = vector of solutions for the MME |
| yhat |
|---|
| 133.06942 |
| 71.700685 |
| 61.368738 |
| 8.2498597 |
| 82.390189 |
| 50.679235 |
| 0.8376792 |
| -0.117397 |
| -1.001088 |
| 0.7710314 |
| 0.5901973 |
| -0.72075 |
| 0.4174125 |
| -0.253817 |
| -0.372302 |
| 0.2087062 |
| 0.0817978 |
| 0.0225553 |
| yhat |
|---|
| 133.07 |
| 71.70 |
| 61.37 |
| 8.25 |
| 82.39 |
| 50.68 |
| 0.84 |
| -0.12 |
| -1.00 |
| 0.77 |
| 0.59 |
| -0.72 |
| 0.42 |
| -0.25 |
| -0.37 |
| 0.21 |
| 0.08 |
| 0.02 |
| Compute sesol = standard error of solutions |
| sesol |
|---|
| 2.87 |
| 7.88 |
| 7.61 |
| 8.15 |
| 4.91 |
| 4.95 |
| 5.79 |
| 2.98 |
| 4.34 |
| 4.42 |
| 4.62 |
| 5.26 |
| 3.81 |
| 3.78 |
| 3.94 |
| 3.95 |
| 4.00 |
| 3.98 |
| Computation of Additive, Nonadditive, and Total Genetic Predictions |
| Using matrix computations |
| Define ka = coefficient matrix of additive genetic predictions |
| ka | ||||||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| COL1 | COL2 | COL3 | COL4 | COL5 | COL6 | COL7 | COL8 | COL9 | COL10 | COL11 | COL12 | COL13 | COL14 | COL15 | COL16 | COL17 | COL18 | |
| ROW1 | 0 | 1 | -1 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| ROW2 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| ROW3 | 0 | 0.5 | -0.5 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| ROW4 | 0 | 0.5 | -0.5 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| ROW5 | 0 | 0.5 | -0.5 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| ROW6 | 0 | 0.75 | -0.75 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 |
| ka | |||||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 0.00 | 1.00 | -1.00 | 0.00 | 0.00 | 0.00 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| 0.00 | 0.50 | -0.50 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| 0.00 | 0.50 | -0.50 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| 0.00 | 0.50 | -0.50 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| 0.00 | 0.75 | -0.75 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| Compute kagl = ka*ginvlhs*lhs to check if functions in matrix ka are estimable |
| (kagl = ka if functions in ka are estimable) |
| kagl | |||||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| -0.00 | 1.00 | -1.00 | -0.00 | -0.00 | 0.00 | 1.00 | -0.00 | 0.00 | -0.00 | -0.00 | 0.00 | 0.00 | -0.00 | 0.00 | -0.00 | -0.00 | -0.00 |
| -0.00 | -0.00 | 0.00 | -0.00 | -0.00 | 0.00 | -0.00 | 1.00 | 0.00 | 0.00 | -0.00 | 0.00 | -0.00 | -0.00 | 0.00 | -0.00 | 0.00 | -0.00 |
| -0.00 | 0.50 | -0.50 | 0.00 | -0.00 | 0.00 | 0.00 | -0.00 | 1.00 | -0.00 | -0.00 | 0.00 | 0.00 | -0.00 | -0.00 | -0.00 | -0.00 | -0.00 |
| -0.00 | 0.50 | -0.50 | -0.00 | -0.00 | 0.00 | 0.00 | -0.00 | 0.00 | 1.00 | -0.00 | 0.00 | 0.00 | -0.00 | 0.00 | -0.00 | -0.00 | -0.00 |
| -0.00 | 0.50 | -0.50 | -0.00 | -0.00 | 0.00 | 0.00 | -0.00 | 0.00 | -0.00 | 1.00 | 0.00 | 0.00 | -0.00 | -0.00 | -0.00 | -0.00 | -0.00 |
| -0.00 | 0.75 | -0.75 | -0.00 | -0.00 | -0.00 | 0.00 | -0.00 | 0.00 | -0.00 | -0.00 | 1.00 | 0.00 | -0.00 | 0.00 | -0.00 | -0.00 | -0.00 |
| difkaglka | |||||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| -0.00 | -0.00 | -0.00 | -0.00 | -0.00 | 0.00 | 0.00 | -0.00 | 0.00 | -0.00 | -0.00 | 0.00 | 0.00 | -0.00 | 0.00 | -0.00 | -0.00 | -0.00 |
| -0.00 | -0.00 | 0.00 | -0.00 | -0.00 | 0.00 | -0.00 | 0.00 | 0.00 | 0.00 | -0.00 | 0.00 | -0.00 | -0.00 | 0.00 | -0.00 | 0.00 | -0.00 |
| -0.00 | -0.00 | 0.00 | 0.00 | -0.00 | 0.00 | 0.00 | -0.00 | 0.00 | -0.00 | -0.00 | 0.00 | 0.00 | -0.00 | -0.00 | -0.00 | -0.00 | -0.00 |
| -0.00 | -0.00 | 0.00 | -0.00 | -0.00 | 0.00 | 0.00 | -0.00 | 0.00 | -0.00 | -0.00 | 0.00 | 0.00 | -0.00 | 0.00 | -0.00 | -0.00 | -0.00 |
| -0.00 | -0.00 | 0.00 | -0.00 | -0.00 | 0.00 | 0.00 | -0.00 | 0.00 | -0.00 | -0.00 | 0.00 | 0.00 | -0.00 | -0.00 | -0.00 | -0.00 | -0.00 |
| -0.00 | -0.00 | -0.00 | -0.00 | -0.00 | -0.00 | 0.00 | -0.00 | 0.00 | -0.00 | -0.00 | 0.00 | 0.00 | -0.00 | 0.00 | -0.00 | -0.00 | -0.00 |
| Compute uaka = vector of multibreed additive genetic predictions |
| uaka |
|---|
| 11.17 |
| -0.12 |
| 4.16 |
| 5.94 |
| 5.76 |
| 7.03 |
| Compute vepuaka = matrix of variance of errors of additive genetic predictions |
| vepuaka | |||||
|---|---|---|---|---|---|
| 213.34 | 11.27 | 99.91 | 99.86 | 122.74 | 158.88 |
| 11.27 | 8.88 | 9.36 | 5.98 | 10.06 | 10.35 |
| 99.91 | 9.36 | 70.83 | 48.88 | 60.55 | 84.56 |
| 99.86 | 5.98 | 48.88 | 58.98 | 58.19 | 75.37 |
| 122.74 | 10.06 | 60.55 | 58.19 | 82.55 | 93.65 |
| 158.88 | 10.35 | 84.56 | 75.37 | 93.65 | 135.68 |
| Compute sepuaka = vector of standard errors of additive genetic predictions |
| sepuaka |
|---|
| 14.61 |
| 2.98 |
| 8.42 |
| 7.68 |
| 9.09 |
| 11.65 |
| Define kn = coefficient matrix of nonadditive genetic predictions |
| Assume that males will be mated to (1/2A 1/2B) females and viceversa |
| kn | ||||||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| COL1 | COL2 | COL3 | COL4 | COL5 | COL6 | COL7 | COL8 | COL9 | COL10 | COL11 | COL12 | COL13 | COL14 | COL15 | COL16 | COL17 | COL18 | |
| ROW1 | 0 | 0 | 0 | 0.5 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0.5 | 0 | 0 | 0 | 0 | 0 |
| ROW2 | 0 | 0 | 0 | 0.5 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0.5 | 0 | 0 | 0 | 0 |
| ROW3 | 0 | 0 | 0 | 0.5 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0.5 | 0 | 0 | 0 |
| ROW4 | 0 | 0 | 0 | 0.5 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0.5 | 0 | 0 |
| ROW5 | 0 | 0 | 0 | 0.5 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0.5 | 0 |
| ROW6 | 0 | 0 | 0 | 0.5 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0.5 |
| kn | |||||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 0.00 | 0.00 | 0.00 | 0.50 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.50 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| 0.00 | 0.00 | 0.00 | 0.50 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.50 | 0.00 | 0.00 | 0.00 | 0.00 |
| 0.00 | 0.00 | 0.00 | 0.50 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.50 | 0.00 | 0.00 | 0.00 |
| 0.00 | 0.00 | 0.00 | 0.50 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.50 | 0.00 | 0.00 |
| 0.00 | 0.00 | 0.00 | 0.50 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.50 | 0.00 |
| 0.00 | 0.00 | 0.00 | 0.50 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.50 |
| Compute kngl = kn*ginvlhs*lhs to check if functions in matrix kn are estimable |
| (kngl = kn if functions in kn are estimable) |
| kngl | |||||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| -0.00 | 0.00 | -0.00 | 0.50 | -0.00 | 0.00 | -0.00 | 0.00 | -0.00 | 0.00 | 0.00 | -0.00 | 0.50 | 0.00 | -0.00 | 0.00 | 0.00 | 0.00 |
| 0.00 | 0.00 | -0.00 | 0.50 | 0.00 | 0.00 | -0.00 | 0.00 | -0.00 | 0.00 | 0.00 | -0.00 | -0.00 | 0.50 | -0.00 | 0.00 | 0.00 | -0.00 |
| 0.00 | 0.00 | -0.00 | 0.50 | -0.00 | 0.00 | -0.00 | 0.00 | -0.00 | 0.00 | -0.00 | -0.00 | -0.00 | 0.00 | 0.50 | 0.00 | 0.00 | 0.00 |
| -0.00 | 0.00 | -0.00 | 0.50 | 0.00 | 0.00 | -0.00 | 0.00 | -0.00 | 0.00 | -0.00 | -0.00 | -0.00 | 0.00 | -0.00 | 0.50 | 0.00 | -0.00 |
| 0.00 | 0.00 | -0.00 | 0.50 | -0.00 | 0.00 | -0.00 | 0.00 | -0.00 | 0.00 | -0.00 | -0.00 | -0.00 | 0.00 | -0.00 | 0.00 | 0.50 | -0.00 |
| -0.00 | 0.00 | -0.00 | 0.50 | -0.00 | 0.00 | -0.00 | 0.00 | -0.00 | 0.00 | 0.00 | -0.00 | -0.00 | 0.00 | -0.00 | 0.00 | 0.00 | 0.50 |
| difknglkn | |||||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| -0.00 | 0.00 | -0.00 | -0.00 | -0.00 | 0.00 | -0.00 | 0.00 | -0.00 | 0.00 | 0.00 | -0.00 | -0.00 | 0.00 | -0.00 | 0.00 | 0.00 | 0.00 |
| 0.00 | 0.00 | -0.00 | -0.00 | 0.00 | 0.00 | -0.00 | 0.00 | -0.00 | 0.00 | 0.00 | -0.00 | -0.00 | 0.00 | -0.00 | 0.00 | 0.00 | -0.00 |
| 0.00 | 0.00 | -0.00 | -0.00 | -0.00 | 0.00 | -0.00 | 0.00 | -0.00 | 0.00 | -0.00 | -0.00 | -0.00 | 0.00 | -0.00 | 0.00 | 0.00 | 0.00 |
| -0.00 | 0.00 | -0.00 | -0.00 | 0.00 | 0.00 | -0.00 | 0.00 | -0.00 | 0.00 | -0.00 | -0.00 | -0.00 | 0.00 | -0.00 | 0.00 | 0.00 | -0.00 |
| 0.00 | 0.00 | -0.00 | -0.00 | -0.00 | 0.00 | -0.00 | 0.00 | -0.00 | 0.00 | -0.00 | -0.00 | -0.00 | 0.00 | -0.00 | 0.00 | 0.00 | -0.00 |
| -0.00 | 0.00 | -0.00 | -0.00 | -0.00 | 0.00 | -0.00 | 0.00 | -0.00 | 0.00 | 0.00 | -0.00 | -0.00 | 0.00 | -0.00 | 0.00 | 0.00 | 0.00 |
| Compute uakn = vector of multibreed nonadditive genetic predictions |
| uakn |
|---|
| 4.33 |
| 4.00 |
| 3.94 |
| 4.23 |
| 4.17 |
| 4.14 |
| Compute vepuaks = matrix of variance of errors of nonadditive genetic predictions |
| vepuakn | |||||
|---|---|---|---|---|---|
| 14.06 | 11.00 | 12.21 | 13.79 | 12.53 | 13.13 |
| 11.00 | 14.38 | 14.08 | 12.35 | 12.69 | 12.54 |
| 12.21 | 14.08 | 17.51 | 13.66 | 13.14 | 14.86 |
| 13.79 | 12.35 | 13.66 | 17.42 | 13.07 | 13.72 |
| 12.53 | 12.69 | 13.14 | 13.07 | 14.61 | 12.84 |
| 13.13 | 12.54 | 14.86 | 13.72 | 12.84 | 16.00 |
| Compute sepuakn = vector of standard errors of nonadditive genetic predictions |
| sepuakn |
|---|
| 3.75 |
| 3.79 |
| 4.18 |
| 4.17 |
| 3.82 |
| 4.00 |
| Define kt = coefficient matrix of total genetic predictions |
| Assume that males will be mated to (1/2A 1/2B) females and viceversa |
| kt | ||||||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| COL1 | COL2 | COL3 | COL4 | COL5 | COL6 | COL7 | COL8 | COL9 | COL10 | COL11 | COL12 | COL13 | COL14 | COL15 | COL16 | COL17 | COL18 | |
| ROW1 | 0 | 1 | -1 | 0.5 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0.5 | 0 | 0 | 0 | 0 | 0 |
| ROW2 | 0 | 0 | 0 | 0.5 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0.5 | 0 | 0 | 0 | 0 |
| ROW3 | 0 | 0.5 | -0.5 | 0.5 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0.5 | 0 | 0 | 0 |
| ROW4 | 0 | 0.5 | -0.5 | 0.5 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0.5 | 0 | 0 |
| ROW5 | 0 | 0.5 | -0.5 | 0.5 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0.5 | 0 |
| ROW6 | 0 | 0.75 | -0.75 | 0.5 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0.5 |
| kt | |||||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 0.00 | 1.00 | -1.00 | 0.50 | 0.00 | 0.00 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.50 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| 0.00 | 0.00 | 0.00 | 0.50 | 0.00 | 0.00 | 0.00 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.50 | 0.00 | 0.00 | 0.00 | 0.00 |
| 0.00 | 0.50 | -0.50 | 0.50 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.50 | 0.00 | 0.00 | 0.00 |
| 0.00 | 0.50 | -0.50 | 0.50 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.50 | 0.00 | 0.00 |
| 0.00 | 0.50 | -0.50 | 0.50 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.50 | 0.00 |
| 0.00 | 0.75 | -0.75 | 0.50 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.50 |
| Compute ktgl = kt*ginvlhs*lhs to check if functions in matrix kt are estimable |
| (ktgl = kt if functions in kt are estimable) |
| ktgl | |||||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| -0.00 | 1.00 | -1.00 | 0.50 | -0.00 | 0.00 | 1.00 | -0.00 | 0.00 | -0.00 | -0.00 | 0.00 | 0.50 | -0.00 | 0.00 | -0.00 | -0.00 | -0.00 |
| 0.00 | 0.00 | 0.00 | 0.50 | -0.00 | 0.00 | -0.00 | 1.00 | 0.00 | 0.00 | -0.00 | -0.00 | -0.00 | 0.50 | -0.00 | -0.00 | 0.00 | -0.00 |
| -0.00 | 0.50 | -0.50 | 0.50 | -0.00 | 0.00 | 0.00 | 0.00 | 1.00 | -0.00 | -0.00 | 0.00 | 0.00 | -0.00 | 0.50 | -0.00 | -0.00 | -0.00 |
| -0.00 | 0.50 | -0.50 | 0.50 | -0.00 | 0.00 | 0.00 | -0.00 | 0.00 | 1.00 | -0.00 | 0.00 | -0.00 | 0.00 | 0.00 | 0.50 | -0.00 | -0.00 |
| -0.00 | 0.50 | -0.50 | 0.50 | -0.00 | 0.00 | 0.00 | -0.00 | 0.00 | -0.00 | 1.00 | 0.00 | 0.00 | 0.00 | -0.00 | -0.00 | 0.50 | -0.00 |
| -0.00 | 0.75 | -0.75 | 0.50 | -0.00 | 0.00 | 0.00 | -0.00 | 0.00 | -0.00 | -0.00 | 1.00 | 0.00 | 0.00 | 0.00 | -0.00 | -0.00 | 0.50 |
| difktglkt | |||||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| -0.00 | -0.00 | -0.00 | -0.00 | -0.00 | 0.00 | 0.00 | -0.00 | 0.00 | -0.00 | -0.00 | 0.00 | 0.00 | -0.00 | 0.00 | -0.00 | -0.00 | -0.00 |
| 0.00 | 0.00 | 0.00 | -0.00 | -0.00 | 0.00 | -0.00 | 0.00 | 0.00 | 0.00 | -0.00 | -0.00 | -0.00 | 0.00 | -0.00 | -0.00 | 0.00 | -0.00 |
| -0.00 | -0.00 | -0.00 | -0.00 | -0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 | -0.00 | 0.00 | 0.00 | -0.00 | -0.00 | -0.00 | -0.00 | -0.00 |
| -0.00 | -0.00 | -0.00 | -0.00 | -0.00 | 0.00 | 0.00 | -0.00 | 0.00 | -0.00 | -0.00 | 0.00 | -0.00 | 0.00 | 0.00 | -0.00 | -0.00 | -0.00 |
| -0.00 | -0.00 | 0.00 | -0.00 | -0.00 | 0.00 | 0.00 | -0.00 | 0.00 | -0.00 | -0.00 | 0.00 | 0.00 | 0.00 | -0.00 | -0.00 | 0.00 | -0.00 |
| -0.00 | -0.00 | -0.00 | -0.00 | -0.00 | 0.00 | 0.00 | -0.00 | 0.00 | -0.00 | -0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.00 | -0.00 | -0.00 |
| Compute uakt = vector of multibreed total genetic predictions |
| uakt |
|---|
| 15.50 |
| 3.88 |
| 8.10 |
| 10.17 |
| 9.92 |
| 11.16 |
| Compute vepuaks = matrix of variance of errors of total genetic predictions |
| vepuakt | |||||
|---|---|---|---|---|---|
| 212.50 | 15.41 | 97.44 | 98.05 | 121.67 | 156.97 |
| 15.41 | 24.06 | 15.76 | 14.02 | 16.84 | 15.83 |
| 97.44 | 15.76 | 70.92 | 49.21 | 59.87 | 82.92 |
| 98.05 | 14.02 | 49.21 | 62.70 | 58.56 | 74.41 |
| 121.67 | 16.84 | 59.87 | 58.56 | 84.61 | 92.75 |
| 156.97 | 15.83 | 82.92 | 74.41 | 92.75 | 135.57 |
| Compute sepuakt = vector of standard errors of total genetic predictions |
| sepuakt |
|---|
| 14.58 |
| 4.90 |
| 8.42 |
| 7.92 |
| 9.20 |
| 11.64 |