rsvd 2.0.0

Requirements and compatibility

• Require R 4.4 or later and Matrix 1.7-0 or later. CI checks the supported minimum and current R on Linux, Windows, and macOS, and verifies the loaded Matrix version in every job.
• Preserve public function signatures, defaults, result classes, and component names. Singular-vector counts retain their clamping rules, and the existing sampling distributions are unchanged.
• Validate ranks, flags, and sampling parameters before numerical work. Reject invalid randomized settings, including negative oversampling that could produce missing singular values. Reject empty, nonnumeric, and nonfinite matrix inputs with direct errors. Routines that support missing data still omit incomplete rows with a warning. Numeric data frames work consistently across the decompositions.
• Require at least two complete observations for PCA. Prediction checks that new data have the training number of variables and still uses their supplied column order. For compatibility, ordinary missing values propagate and NaN values encountered during scaling become zero.

Numerical fixes

• Deterministic rqb() honors k and returns only the requested basis columns. Randomized QB retains its oversampling columns, with width bounded by both matrix dimensions.
• Complex PCA uses squared magnitudes to compute real scale factors. With center = FALSE, total processed energy agrees with the uncentered SVD; variance proportions use all processed directions, including omitted ones.
• The internal pseudoinverse preserves dimensions when one singular direction remains and returns the correct shape for rectangular zero matrices. Its rank cutoff accounts for matrix dimensions, preventing CUR from inverting roundoff singular values when the requested rank exceeds the true rank. Small, resolved singular directions remain supported.
• Robust PCA handles zero input and thresholding steps that retain no singular values. Dual initialization uses the entrywise maximum norm, and saturated singular-value thresholding increases the sampled rank within the matrix dimensions.
• Robust PCA checks both reconstruction feasibility and stationarity. The penalty increases only after the stationarity test is satisfied. Stalled randomized updates receive bounded power-iteration refinements and then an exact-SVD fallback when needed. These checks can require more time than the former reconstruction-only stop. err remains the reconstruction history; trace = TRUE also displays stationarity. A loose tolerance still completes an update and returns its measured residual.
• PCA plots handle one retained component and fits without stored scores. plot.rpca() routes named options to the helpers that accept them and invisibly returns the last plot. Factor maps require valid integer component indices, matching group and label lengths, and real coordinates. top.n must be a positive integer. Plotting uses supported ggplot2 line-width and legend arguments.

Memory and runtime

• Randomized QB keeps sparse Matrix inputs sparse during multiplication, converting only sketches and projected factors to dense matrices. Randomized ID and CUR use the same sparse products. Missing-row omission in ID and CUR also preserves sparse storage.
• Deterministic QB factors only the leading k columns when a real, independent prefix gives the same basis as full base QR. Complex inputs, deficient prefixes, and other cases use the full dense QR fallback.
• Randomized PCA with an explicit rank centers and scales real sparse inputs implicitly. Prediction applies the same transformation without creating a full dense centered matrix. Sparse column moments account for implicit zeros, nearly constant columns, and overflow in mean accumulation.
• rpca(retx = FALSE) avoids unused left singular vectors. Total-variance calculations reuse column norms or a Frobenius norm instead of applying sample-variance calculations to copied columns.
• Full-column ID avoids a discarded pseudoinverse. CUR reuses its selected row and column matrices. Bounding QB sketch width by the smaller dimension can also reduce the number of random draws for very wide inputs.

Documentation and tests

• Add the testthat entry point so package checks run the test suite. Cover prescribed spectra, invariant subspaces, complex arithmetic, vector counts, rank-deficient decompositions, input validation, and sparse storage formats. Pseudoinverse tests use analytic examples and the Moore-Penrose identities.
• Compare PCA with prcomp() and explicitly processed dense references. Check implicit sparse products, structural zeros, custom matrix dispatch, and allocation limits. Compare partial QR with the full base-QR factors.
• Test robust-PCA rank selection, rescaling, and recovery, including known low-rank-only and sparse-only optima. These distinguish an appropriate split from an arbitrary split with a small reconstruction residual.
• Render the PCA plotting helpers and check component selection, variance denominators, return values, and argument routing. Treat lifecycle deprecations as errors in the relevant tests.
• Edit the README, package description, and all help pages for direct language and concrete explanations. Add an early reconstruction example and method guide, explain how rank differs from oversampling and power iterations, and document sparse storage, preprocessing, and robust-PCA stopping diagnostics.
• Clarify PCA fitted scores versus new-data projections, total versus retained variance, and the loading/correlation interpretation. Explain that robust PCA fits a batch of observations and does not return a prediction method.
• Correct the digit dataset description and image example: the first column contains labels, followed by 784 pixel columns. Complete the tiger image attribution, and update the citation contact to match the maintainer.
• Preserve the recorded README benchmarks and their raw data, including reconstruction errors and cumulative R allocations. Identify their source revision and distinguish them from checks of later release candidates. Provide reproducible tiger and iris illustrations alongside the performance examples.