qr.coef
随着qr
似乎可以完成这项工作:
(A <- matrix(c((1:8)^2, 0, 0, 0, 0), nrow = 3, ncol = 4, byrow = TRUE))
# [,1] [,2] [,3] [,4]
# [1,] 1 4 9 16
# [2,] 25 36 49 64
# [3,] 0 0 0 0
(B <- c(1, 2, 0))
# [1] 1 2 0
(X0 <- qr.coef(qr(A), B))
# [1] -0.437500 0.359375 NA NA
X0[is.na(X0)] <- 0
X0
# [1] -0.437500 0.359375 0.000000 0.000000
# Verification:
A %*% X0
# [,1]
# [1,] 1
# [2,] 2
# [3,] 0
第二个例子:
(A<-matrix(c(1, 2, 0, 0, 1, 2, 0, 0, 1, 2, 1, 0), nrow = 3, ncol = 4, byrow = TRUE))
# [,1] [,2] [,3] [,4]
# [1,] 1 2 0 0
# [2,] 1 2 0 0
# [3,] 1 2 1 0
(B<-c(1, 1, 2))
# [1] 1 1 2
qr.solve(A, B)
# Error in qr.solve(A, B) : singular matrix 'a' in solve
(X0 <- qr.coef(qr(A), B))
# [1] 1 NA 1 NA
X0[is.na(X0)] <- 0
X0
# [1] 1 0 1 0
A %*% X0
# [,1]
# [1,] 1
# [2,] 1
# [3,] 2