Nothing

```
test_that('Fixed-design equicorrelated knockoffs have the right correlation structure', {
n = 20; p = 10
X = knockoff:::normc(knockoff:::rnorm_matrix(n,p))
knock_variables_default = create.fixed(X, method='equi', randomize=F)
knock_variables_randomized = create.fixed(X, method='equi', randomize=T)
X = knock_variables_default$X
Xko_default = knock_variables_default$Xk
Xko_randomized = knock_variables_randomized$Xk
G = t(X) %*% X
s = min(2*min(eigen(G)$values), 1)
for (Xko in list(Xko_default, Xko_randomized)) {
expect_equal(t(Xko) %*% Xko, G)
expect_equal(t(X) %*% Xko, G - diag(s,p,p))
}
})
# Test case from Weijie Su.
test_that('equicorrelated knockoffs are created in numerically sensitive case', {
n = 15; p = 5
M = matrix(0, p, p)
diag(M) = 1
for (i in 1:p) {
for (j in 1:p) {
if ((i==j+1) || (j==i+1))
M[i,j] <- 0.6
if ((i==j+2) || (j==i+2))
M[i,j] <- 0.1
}
}
X = knockoff:::with_seed(2, matrix(rnorm(n*p),n) %*% chol(M) )
k = 4
Z = knockoff:::normc(X[,-k])
Z_ko = create.fixed(Z, method='equi', randomize=F)$Xk
expect_false(any(is.nan(Z_ko)))
})
test_that('Fixed-design SDP knockoffs have the right correlation structure', {
skip_on_cran()
n = 20; p = 10
X = knockoff:::normc(knockoff:::rnorm_matrix(n,p))
knock_variables_default = create.fixed(X, method='sdp', randomize=F)
knock_variables_randomized = create.fixed(X, method='sdp', randomize=T)
X = knock_variables_default$X
Xko_default = knock_variables_default$Xk
Xko_randomized = knock_variables_randomized$Xk
offdiag <- function(A) A - diag(diag(A))
G = t(X) %*% X
tol = 1e-4
for (Xko in list(Xko_default, Xko_randomized)) {
expect_equal(t(Xko) %*% Xko, G, tolerance=tol)
expect_equal(offdiag(t(X) %*% Xko), offdiag(G), tolerance=tol)
expect_true(all(diag(t(X) %*% Xko) < 1+tol))
}
})
test_that('Gaussian equicorrelated knockoffs have the right correlation structure', {
# Problem parameters
n = 10000000 # number of observations
p = 3 # number of variables
# Generate the variables from a multivariate normal distribution
mu = c(1,2,3); Sigma = matrix(c(1,0.55,0.2, 0.55,1,0.55, 0.2, 0.55, 1),3)
X = matrix(rep(mu,each=n),n) + matrix(rnorm(n*p),n) %*% chol(Sigma)
Xk = create.gaussian(X, mu, Sigma, method='equi')
SigmaHat = cov(Xk)
SigmaHatCross = cov(X, y=Xk)
muHat = colMeans(Xk)
lambda_min = eigen(Sigma, symmetric=T, only.values = T)$values[p]
diag_s = diag(rep(1, nrow(Sigma)) * min(2*lambda_min, min(diag(Sigma))))
expect_equal(mu, muHat, tolerance=2e-3)
expect_equal(Sigma, SigmaHat, tolerance=2e-3)
expect_equal(Sigma-diag_s, SigmaHatCross, tolerance=2e-3)
})
```

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