solve OLS in linear regression using map reduce

mapReduce.QR.R

# referenece: https://ieeexplore.ieee.org/document/7345473/
# 验证该论文的分布式计算结果


#' 准备数据
X = matrix(rnorm(400), 20, 20)
Y = rnorm(20)

#' 计算分隔数据的 index
splitByRowIndex = function(nrows, size){
  block.len = nrows / size
  res = list()
  for (i in 1:size){
    res[[i]] = c((i-1) * blocksize + 1, i * blocksize)
  }
  res
}

#' 把 `mat 矩阵`按行等分成 `size` 份
splitMatByRow = function(mat, size){
  row.index = splitByRowIndex(nrow(mat), size)
  lapply(row.index, function(val) mat[val[1]:val[2], ])
}


#' Algorithm 1 Main function

block.number = 4  # 数据分成 4 份
x.block = splitMatByRow(X, block.number)
y.block = splitMatByRow(matrix(Y, ncol = 1), block.number)


# Algorithm 2 Mapper function in step1
x.block.qr = lapply(x.block, function(val){
  qrresult = qr(val)
  list(Q=qr.Q(qrresult), R=qr.R(qrresult))
})


# Algorithm 3 Reducer function in step1

Rtemp = do.call(rbind, lapply(x.block.qr, function (l) l$R))
qrresult = qr(Rtemp)
Rtemp.qr = list(Q=qr.Q(qrresult), R=qr.R(qrresult))

R.final = Rtemp.qr$R
Rtemp.Q.divide = splitMatByRow(Rtemp.qr$Q, block.number)


Q.result = list()
for (i in 1:block.number){
  Q.result[[i]] = t(x.block.qr[[i]]$Q  %*% Rtemp.Q.divide[[i]]) # Multiply
}

# Algorithm 4 Reduce function in step2
V = list()
for (i in 1:block.number){
  V[[i]] = Q.result[[i]] %*% matrix(y.block[[i]], ncol = 1)  # Multiply
}


# Algorithm 5 Reduce function in step3
V.sum = Reduce('+', V)
beta = as.numeric(solve(R.final) %*% V.sum)


# real answer
ans = lm(Y ~ X - 1)
coefficients = ans$coefficients

# comare
sum((beta - coefficients) ** 2)