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社区首页 >专栏 >【康普森GS专栏】基因组选择中构建H矩阵需要设置哪些参数?

【康普森GS专栏】基因组选择中构建H矩阵需要设置哪些参数?

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邓飞
发布2019-06-13 20:33:09
1.6K1
发布2019-06-13 20:33:09
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1. 基因组选择中H矩阵的构建

这里的1为非测序个体, 2为测序个体. A11, A12, A21, A22可以由系谱构建的A矩阵提取. G为基因组构建的矩阵. H矩阵构建的相关代码见: 【GS专栏】全基因组选择中如何构建H矩阵.

2. 直接构建H^{-1}矩阵

一步法混合线性方程组中, 直接利用的是H逆矩阵, 因此直接构建H逆矩阵更加方便.

H逆矩阵构建方法:

3. 构建H逆矩阵需要考虑的参数

3.1 G矩阵矫正到A22矩阵的尺度

原因:

G矩阵构建是由测序个体的基因频率构建的,它的频率可能与A矩阵的基因频率(可以追溯到基础群体base population)不一样, 这导致G矩阵和A22矩阵存在尺度上的差异, 因此需要矫正.

矫正方法是建立两个方程组:

  • G矩阵对角线的平均值与A22对角线平均值一致
  • G矩阵非对角线的平均值与A22非对角线平均值一致
3.2 调整G矩阵和A22矩阵的相对权重

原因: 对于某些性状, G矩阵可能无法解释所有的变异, 这时可以设定A矩阵解释的比例.

3.3 设置tau 和omega

对于某些性状, 适当设置tau 和 omega, 可以矫正估算的无偏性.

4. 完整的H逆矩阵构建方法

5. 构建H逆矩阵Julia代码展示

Julia是新一代的计算科学语言, 速度非常快, 比R语言、Python要快很多, 内存占用也比较少. 比C语言、Fortran要简单很多,是一门未来的明星语言. 是时候尝试一下新东西了.

代码思路:

  • 依赖的包: NamedArray, 主要用于矩阵提取
  • 参数介绍:
    • id_full: 为所有的ID, A矩阵的id
    • id_geno: 为测序的ID, G矩阵的id
    • Amatrix: A矩阵
    • Gmatrix: G矩阵
    • a = 0.95, 表示G矩阵的比例, 默认0.95
    • b = 0.05, 表示A22矩阵的比例, 默认1-0.95=0.05
    • tau =1, 默认值为1
    • omega=1, 默认值为1
  • 首先定义一个函数diag, 因为julia中没有diag函数.
  • 提取A11, A12, A21, A22
  • 根据对角线和非对角线方程组, 计算a和b
  • 将相关参数加进去, 构建H逆矩阵
代码语言:javascript
复制
function hmatrix_julia_adjust(id_full,id_geno,Amatrix,Gmatrix,a =0.95,b=0.05,tau=1,omega=1)    print("G* = a*G + b*A22, a is ",a,"; b is ",b,"\n")    print("iG = tau*G - omega*A22, tau is ",tau,"; omega is ",omega,"\n\n")
    function diag(mat)        dd = [mat[i,i] for i in 1:size(mat,1)]        return dd    end
     id1 = id_full     idb = id_geno     A = Amatrix     G = Gmatrix     ida = setdiff(id1,idb)     A = NamedArray(A,(id1,id1))     G = NamedArray(G,(idb,idb))     reb = idb     rea = ida
    A22 = A[reb,reb]    diagA22 = diag(A22)    offdiagA22 = []    for i in 1:size(A22,1)        for j in 1:size(A22,2)            if(i != j )                push!(offdiagA22,A22[i,j])            end        end    end
    diagG = diag(G)    offdiagG = []    for i in 1:size(G,1)        for j in 1:size(G,2)            if(i != j )                push!(offdiagG,G[i,j])            end        end    end    print("\n\nStatistic of Rel Matrix G\n","\t\t","N","\t","Mean","\t","Min","\t","Max","\t","\n",      "Diagonal\t",length(diagG),"\t",round.(mean(diagG),digits=3),"\t",      round.(minimum(diagG),digits=3),"\t",      round.(maximum(diagG),digits=3),"\t",      "\nOff-diagonal\t",length(offdiagG),"\t",      round.(mean(offdiagG),digits=3),"\t",round.(minimum(offdiagG),digits=3),"\t",      round.(maximum(offdiagG),digits=3),"\t","\n\n")
    print("\n\nStatistic of Rel Matrix A22\n","\t\t","N","\t","Mean","\t","Min","\t","Max","\t","\n",    "Diagonal\t",length(diagA22),"\t",round.(mean(diagA22),digits=3),"\t",    round.(minimum(diagA22),digits=3),"\t",    round.(maximum(diagA22),digits=3),"\t",    "\nOff-diagonal\t",length(offdiagA22),"\t",    round.(mean(offdiagA22),digits=3),"\t",round.(minimum(offdiagA22),digits=3),"\t",    round.(maximum(offdiagA22),digits=3),"\t","\n\n")
    # 根据方程计算alpha和beta两个参数值    meanoffdiagG=mean(offdiagG)    meandiagG=mean(diagG)    meanoffdiagA22=mean(offdiagA22)    meandiagA22=mean(diagA22)    print("Means_off_diag\t","Means_diag:\n","G\t",meanoffdiagG,"\t",meandiagG,    "\nA22\t",meanoffdiagA22,"\t",meandiagA22,"\n")
    beta=(meandiagA22 - meanoffdiagA22)/(meandiagG - meanoffdiagG)    alpha=meandiagA22-meandiagG*beta    print("Adjust G, and the value of alpha and beta is:",alpha,beta,"\n\n\n")    G=alpha .+ beta .* G #    # 在将a和b的参数加上    G = a .* G + b .* A22
    iA22 = inv(A22)    iG =inv(G)    iA = inv(A)    x22 = tau*iG - omega*iA22
    diagx22 = diag(x22)    offdiagx22 = []    for i in 1:size(x22,1)        for j in 1:size(x22,2)            if(i != j )                push!(offdiagx22,x22[i,j])            end        end    end
    print("\n\nStatistic of Rel Matrix x22\n","\t\t","N","\t","Mean","\t","Min","\t","Max","\t","\n",      "Diagonal\t",length(diagx22),"\t",round.(mean(diagx22),digits=3),"\t",      round.(minimum(diagx22),digits=3),"\t",      round.(maximum(diagx22),digits=3),"\t",      "\nOff-diagonal\t",length(offdiagx22),"\t",      round.(mean(offdiagx22),digits=3),"\t",round.(minimum(offdiagx22),digits=3),"\t",      round.(maximum(offdiagx22),digits=3),"\t","\n\n")
   # 构建H逆矩阵   iHaa = iA[rea,rea]   iHab = iA[rea,reb]   iHba = iHab'   iHbb = iA[reb,reb] + x22   function cbind(A,B)       X = vcat(A',B')'       return(X)   end   function rbind(A,B)       X = vcat(A,B)       return(X)   end   iH = cbind(rbind(iHaa,iHba),rbind(iHab,iHbb))   return(round.(iH,digits=6))end
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目录
  • 3.2 调整G矩阵和A22矩阵的相对权重
  • 3.3 设置tau 和omega
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