我正在尝试快速求解R CRAN中大型数组的方程式(形式为x％*％res = y)。
我有数据x和y并想计算res。
如何最好地做到这一点，即快速？非常感谢!
这是一个示例和一些方法:(似乎“解决”是最快的？)
# setup:
p = 20 # dimension of matrix to solve
nmkt= 3000 # length of array, i.e., number of equations to solve
res = matrix(0,p,nmkt) # result matrix
x = array(rnorm(p*p*nmkt),c(p,p,nmkt)) # data
# make x symetric and invertible
for(i in 1:nmkt){ x[, , i]= crossprod(x[, , i])+diag(p)*0.01}
y = matrix(rnorm(p*nmkt),nmkt,p) # data
# computation and test:
R=100 # number of replications (actually much larger than 100 in my application R=1e5 or 1e7)
system.time(for(r in 1:R){ for(i in 1:nmkt){res[,i] = qr.solve(x[, , i], y[i,], tol = 1e-7)}})
system.time(for(r in 1:R){ for(i in 1:nmkt){res[,i] = solve(x[, , i], y[i,], tol = 1e-7)}})
system.time(for(r in 1:R){ for(i in 1:nmkt){res[,i] = crossprod( chol2inv(chol( x[, , i] )) , y[i,] )}})
通过数组的循环是一个好的解决方案吗？
最佳答案
还是使用稀疏矩阵？ :
require(Matrix)
j = c(matrix(1:(p*nmkt),p,p*nmkt,byrow=TRUE))
i = c(aperm( array(j,c(p,p,nmkt)), c(2,1,3)))
system.time(for(r in 1:R){ res= solve(sparseMatrix(i=i, j=j, x = c(x)), c(t(y)), tol = 1e-7)} )