正交变换与数据保密

secu.R

set.seed(123)
x <- seq(1, 20, length = 20)
y <- 4 + 3 * seq(1, 20, length = 20) + rnorm(20, 0, 6)
plot(x, y)

k <- 2
tstMat <- array(runif(k), dim=c(k,k))
A1 <- qr.Q(qr(tstMat))
A2 <- 2

x1 <- cbind(1, x) %*% A1
y1 <- y * A2

k <- 20
tstMat <- array(runif(k), dim=c(k,k))
B <- qr.Q(qr(tstMat))


y2 <- B %*% y1
x2 <- B %*% x1


x3 <- x2 %*% t(A1)
y3 <- y2 * 1/A2

lm1 <- lm(y ~ x)
lm2 <- lm(y3 ~ x3-1)
par(mfrow = c(1, 2))
plot(x, y, xlim = c(-40, 30), ylim = c(-40, 70), pch = 6, xlab = "", ylab = '')
abline(a= lm1$coefficients[1], b =lm1$coefficients[2] )
plot(x3[, 2],y3, xlim = c(-40, 30), ylim = c(-40, 70), pch = 11,col = 2, xlab = '', ylab = '')
abline(a= lm2$coefficients[1], b =lm2$coefficients[2], col = 2 )

plot(lm1)