R Under development (unstable) (2025-08-17 r88631 ucrt) -- "Unsuffered Consequences"
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> library(Matrix, quietly=TRUE)
> library(sparsesvd)
> 
> ## Stress test:
> ##  - apply sparsesvd() to a large number of random sparse nonnegative matrices
> ##  - check that original matrix M can be reconstructed with reasonable accuracy
> ##  - compare truncated SVD against first components of full SVD
> 
> ## Run interactively with:
> ##   R --slave -f stress_test.R --args <n.run> <k> <n> <r> <torture?> <fillrate> <tol>
> ## (all arguments are optional with default values set below)
> argv <- commandArgs(trailingOnly=TRUE)
> argc <- length(argv)
> 
> ## arguments and their default values
> n.run    <- if (argc >= 1) as.integer(argv[1]) else 100   # number of runs
> k        <- if (argc >= 2) as.integer(argv[2]) else 500   # k = number of rows of M
> n        <- if (argc >= 3) as.integer(argv[3]) else 100   # n = number of columns of M
> r        <- if (argc >= 4) as.integer(argv[4]) else 10    # r = rank of truncated SVD
> torture  <- if (argc >= 5) as.logical(argv[5]) else FALSE # run with gctorture()?
> fillrate <- if (argc >= 6) as.numeric(argv[6]) else .10   # fill rate of sparse matrix (10%)
> tol      <- if (argc >= 7) as.numeric(argv[7]) else 1e-6  # acceptable approx. error per cell
> 
> cat("sparsesvd() Stress Test:\n")
sparsesvd() Stress Test:
> cat(sprintf(" - %d runs testing full and rank-%d sparse SVD\n", n.run, r))
 - 100 runs testing full and rank-10 sparse SVD
> cat(sprintf(" - based on %d x %d nonnegative matrix with %.1f%% nonzero cells\n", k, n, 100 * fillrate))
 - based on 500 x 100 nonnegative matrix with 10.0% nonzero cells
> cat(sprintf(" - reconstruction accuracy < %g, gctorture() is %s\n", tol, if (torture) "ON" else "OFF"))
 - reconstruction accuracy < 1e-06, gctorture() is OFF
> 
> ## approximate matrix comparison
> assert.mat.equal <- function (x, y, tol=1e-6, msg="") {
+   if (!all(dim(x) ==  dim(y))) stop(sprintf("error: matrix dimensions differ %s", msg))
+   err <- max(abs(x - y))
+   if (err > tol) stop(sprintf("approximation error %g > tolerance %g %s", err, tol, msg))
+ }
> 
> ## now perform n.run iterations of the test procedure
> gctorture(torture)
> 
> pb <- txtProgressBar(min=0, max=n.run, style=3)

  |                                                                            
  |                                                                      |   0%> for (i in 1:n.run) {
+   setTxtProgressBar(pb, i)
+   x <- ifelse(runif(k * n) < fillrate, runif(k * n), 0)
+   M <- matrix(x, k, n) # random non-negative matrix with specified fill rate
+   Ms <- Matrix(M, sparse=TRUE)
+ 
+   ## complete sparse SVD
+   svdM <- sparsesvd(Ms)
+   R <- with(svdM, u %*% diag(d) %*% t(v)) # reconstructed matrix
+   assert.mat.equal(R, M, tol=tol, msg=sprintf("(full SVD at iteration #%d)", i))
+ 
+   ## complete sparse SVD of transposed matrix
+   svdMt <- sparsesvd(t(Ms))
+   R <- with(svdMt, v %*% diag(d) %*% t(u)) # reconstructed matrix
+   assert.mat.equal(R, M, tol=tol, msg=sprintf("(full transposed SVD at iteration #%d)", i))
+ 
+   Mr <- with(svdM, u[, 1:r] %*% diag(d[1:r]) %*% t(v[, 1:r])) # r-dimensional approximation
+ 
+   ## truncated sparse SVD
+   svdMr <- sparsesvd(Ms, rank=r)
+   Rr <- with(svdMr, u %*% diag(d) %*% t(v)) # reconstructed r-dim approximation
+   assert.mat.equal(Rr, Mr, tol=tol, msg=sprintf("(%d-rank truncated SVD at iteration #%d)", r, i))
+ 
+   ## truncated sparse SVD of transposed matrix
+   svdMrt <- sparsesvd(t(Ms), rank=r)
+   Rr <- with(svdMrt, v %*% diag(d) %*% t(u)) # reconstructed r-dim approximation
+   assert.mat.equal(Rr, Mr, tol=tol, msg=sprintf("(%d-rank truncated transposed SVD at iteration #%d)", r, i))
+ }

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  |======================================================================| 100%> close(pb)

> 
> proc.time()
   user  system elapsed 
   5.32    0.26    5.54