R Under development (unstable) (2026-01-25 r89330 ucrt) -- "Unsuffered Consequences"
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> require("irlba")
Loading required package: irlba
Loading required package: Matrix
> 
> for (FAST in c(FALSE, TRUE))
+ {
+   # Dense matrix
+   set.seed(1)
+   A <- matrix(rnorm(400), 20)
+   L <- irlba(A, nu=2, nv=2, tol=1e-9, fastpath=FAST)
+   S <- svd(A, nu=2, nv=2)
+   if (!isTRUE(all.equal(L$d, S$d[1:2])))
+   {
+     stop("Failed simple dense singular value test", " fastpath=", FAST)
+   }
+ 
+   # restart
+   L1 <- irlba(A, nv=3, v=L, fastpath=FAST)
+   if (!isTRUE(all.equal(L1$d, S$d[1:3])))
+   {
+     stop("Failed restart", " fastpath=", FAST)
+   }
+ 
+   # unequal nu, nv
+   L <- irlba(A, nv=2, nu=3, fastpath=FAST)
+   if (!isTRUE(ncol(L$v) == 2 && ncol(L$u) == 3))
+   {
+     stop("Failed unequal nu,nv", " fastpath=", FAST)
+   }
+ 
+   # Scaling and centering, dense
+   s <- sqrt(apply(A, 2, crossprod))
+   m <- colMeans(A)
+   L <- irlba(A, 3, tol=1e-9, center=m, scale=s, fastpath=FAST)
+   S <- svd(scale(A, center=TRUE, scale=s))
+   if (!isTRUE(all.equal(L$d, S$d[1:3])))
+   {
+     stop("Failed scaling/centering test", " fastpath=", FAST)
+   }
+   # Scale only, non-square, dense
+   A <- matrix(rnorm(200), 10)
+   s <- seq(1, ncol(A))
+   m <- colMeans(A)
+   L <- irlba(A, 3, tol=1e-9, scale=s, fastpath=FAST)
+   S <- svd(scale(A, center=FALSE, scale=s))
+   if (!isTRUE(all.equal(L$d, S$d[1:3])))
+   {
+     stop("Failed dense scaling test", " fastpath=", FAST)
+   }
+   # Center only, non-square, dense
+   L <- irlba(A, 3, tol=1e-9, center=m, fastpath=FAST)
+   S <- svd(scale(A, center=TRUE, scale=FALSE))
+   if (!isTRUE(all.equal(L$d, S$d[1:3])))
+   {
+     stop("Failed dense centering test", " fastpath=", FAST)
+   }
+   # Sparse matrix
+   require("Matrix")
+   K <- 400
+   N <- 2000
+   i <- sample(K, size=N, replace=TRUE)
+   j <- sample(K, size=N, replace=TRUE)
+   A <- sparseMatrix(i, j, x=rnorm(N))
+   L <- irlba(A, nu=2, nv=2, tol=1e-9, fastpath=FAST)
+   S <- svd(A, nu=2, nv=2)
+   if (!isTRUE(all.equal(L$d, S$d[1:2])))
+   {
+     stop("Failed simple sparse singular value test", " fastpath=", FAST)
+   }
+   # Center only, sparse
+   m <- colMeans(A)
+   L <- irlba(A, 3, tol=1e-9, center=m, fastpath=FAST)
+   S <- svd(scale(A, center=TRUE, scale=FALSE))
+   if (!isTRUE(all.equal(L$d, S$d[1:3])))
+   {
+     stop("Failed sparse centering test", " fastpath=", FAST)
+   }
+   # scale only, spase
+   s <- seq(1, ncol(A))
+   L <- irlba(A, 3, tol=1e-9, scale=s, fastpath=FAST)
+   S <- svd(scale(A, center=FALSE, scale=s))
+   if (!isTRUE(all.equal(L$d, S$d[1:3])))
+   {
+     stop("Failed sparse scaling test", " fastpath=", FAST)
+   }
+ 
+   # Symmetric partial eigendecomposition
+   set.seed(1)
+   V <- qr.Q(qr(matrix(runif(100), nrow=10)))
+   x <- V %*% diag(c(10, -9, 8, -7, 6, -5, 4, -3, 2, -1)) %*% t(V)
+   if (!isTRUE(all.equal(partial_eigen(x, 3, fastpath=FAST)$values, c(10, 8, 6))))
+   {
+     stop("Failed partial_eigen test", " fastpath=", FAST)
+   }
+ 
+   # Test right-only option
+   L <- irlba(A, 2, tol=1e-3, right_only=TRUE, fastpath=FAST, work=20)
+   S <- svd(A, nu=2, nv=2)
+   if (isTRUE(max(L$d - S$d[1:2]) > 1e-3))
+   {
+     stop("Failed right_only test", " fastpath=", FAST)
+   }
+ 
+   # Dense complex-valued matrix
+   A <- matrix(rnorm(400), 20) + 1i * matrix(rnorm(400), 20)
+   L <- irlba(A, nu=2, nv=2, tol=1e-9, fastpath=FAST)
+   S <- svd(A, nu=2, nv=2)
+   if (!isTRUE(all.equal(L$d, S$d[1:2])))
+   {
+     stop("Failed complex-valued dense singular value test", " fastpath=", FAST)
+   }
+ 
+   # test extra reorthogonalization
+   L <- irlba(A, nu=2, nv=2, tol=1e-9, reorth=TRUE, fastpath=FAST)
+   if (!isTRUE(all.equal(L$d, S$d[1:2])))
+   {
+     stop("Failed reorthogonalization test", " fastpath=", FAST)
+   }
+ 
+   # very non-square dense matrices
+   set.seed(1)
+   A <- matrix(rnorm(2000), 20)
+   L1 <- irlba(A, nu=2, nv=2, tol=1e-9, fastpath=FAST)
+   L2 <- irlba(t(A), nu=2, nv=2, tol=1e-9, fastpath=FAST)
+   if (!isTRUE(all.equal(L1$d, L2$d)))
+   {
+     stop("Failed nonsquare test", " fastpath=", FAST)
+   }
+ 
+ # This pathological example was provided by Giuseppe Rodriguez, http://bugs.unica.it/~gppe/
+ # The singular values cluster at 1 and 0, making it hard to converge to a truncated
+ # subspace containing the largest few singular values (they are all very close).
+ # Or, for that matter, the smallest.
+ #
+ #   Reference:
+ #   J. M. Varah. The Prolate matrix. Linear Algebra and Appl.,
+ #   187:269-278, 1993.
+ #  Michela Redivo-Zaglia, University of Padova, Italy
+ #       Email: Michela.RedivoZaglia@unipd.it
+ #  Giuseppe Rodriguez, University of Cagliari, Italy
+ #       Email: rodriguez@unica.it
+   tprolate <- function(n, w=0.25)
+   {
+     a <- rep(0, n)
+     a[1] <- 2 * w
+     a[2:n] <- sin(2 * pi * w * (1:(n-1))) / (pi * (1:(n-1)))
+     toeplitz(a)
+   }
+ 
+   x <- tprolate(512)
+   set.seed(1)
+   l <- irlba(x, nv=20, fastpath=FAST)
+   if (isTRUE(max(abs(l$d - 1)) > 1e-3))
+   {
+     stop("Failed tprolate test fastpath=", FAST)
+   }
+ 
+   # test for issue #7 and issue #14
+   mx <- matrix(sample(1:100, 100 * 100, replace=TRUE), nrow=100)
+   set.seed(1)
+   l <- irlba(mx, nv=30, center=colMeans(mx), fastpath=FAST)
+   s <- svd(scale(mx, center=TRUE, scale=FALSE))
+   if (isTRUE(max(abs(l$d - s$d[1:30])) > 1e-3))
+   {
+     stop("Failed integer matrix test fastpath=", FAST)
+   }
+ 
+   # test for https://github.com/bwlewis/irlba/issues/22
+   set.seed(1000)
+   ncells <- 50
+   ngenes <- 1000
+   counts <- matrix(as.double(rpois(ncells*ngenes, lambda=100)), nrow=ncells)
+   centers <- colMeans(counts)
+   set.seed(1)
+   out <- irlba(scale(counts, scale=FALSE, center=centers), nu=10, nv=10)
+   set.seed(1)
+   l <- irlba(counts, center=centers, nu=10, nv=10, fastpath=FAST)
+   if (isTRUE(max(abs(out$d - l$d)) > 1e-3))
+   {
+     stop("Failed centering test (n > m) fastpath=", FAST)
+   }
+ 
+   # test for https://github.com/bwlewis/irlba/issues/42
+   set.seed(1234)
+   a <- matrix(rnorm(10000), ncol=20)
+   center <- runif(ncol(a))
+   scale <- runif(ncol(a))
+   L <- irlba(a, 5, scale=scale, center=center, fastpath=FAST)
+   S <- svd(scale(a, center=center, scale=scale))
+   if (isTRUE(max(abs(S$d[1:5] - L$d)) > 1e-3))
+   {
+     stop("Failed scale + center test fastpath=", FAST)
+   }
+ }
> 
> # smallest=TRUE, m > n  (fastpath always FALSE in this case)
> x <- matrix(rnorm(5000), 100)
> set.seed(1)
> L <- irlba(x, nv=5, smallest=TRUE)
> if (!isTRUE(all.equal(L$d, tail(svd(x)$d, 5))))
+ {
+   stop("Failed smallest svd test")
+ }
> 
> # smallest=TRUE, n > m
> x <- matrix(rnorm(5000), 50)
> set.seed(1)
> L <- irlba(x, nv=5, smallest=TRUE)
> if (!isTRUE(all.equal(L$d, tail(svd(x)$d, 5))))
+ {
+   stop("Failed smallest svd test")
+ }
> 
> # test for https://github.com/bwlewis/irlba/issues/47 (again, fastpath always FALSE)
> set.seed(2345)
> a <- spMatrix(50, 40, x=runif(200), i=sample(50, 200, replace=TRUE), j=sample(40, 200, replace=TRUE))
> center <- runif(ncol(a))
> scale <- runif(ncol(a))
> L <- irlba(a, 5, scale=scale, center=center)
> S <- svd(scale(a, center=center, scale=scale))
> if (isTRUE(max(abs(S$d[1:5] - L$d)) > 1e-3))
+ {
+   stop("Failed scale + center test for non-fastpath'able matrices")
+ }
> 
> proc.time()
   user  system elapsed 
   4.57    0.29    4.87