Stores and operates on sparse expression matrices for single-cell and large bulk RNA-seq, covering dgCMatrix/dgRMatrix/dgTMatrix when-each-is-fast, the dgCMatrix (CSC, R) <-> CSR (Python) implicit transpose, AnnData (cells-rows) <-> SingleCellExperiment (cells-cols) orientation flip, HDF5/h5ad vs Zarr cloud-native shift, HDF5SummarizedExperiment + DelayedArray for out-of-memory bulk, scanpy backed mode for large h5ad, the ~10-15% density crossover where dense beats sparse, 10X format proliferation (MTX vs CellRanger H5 vs h5ad), the dense-conversion memory blow-up, and Dask + Zarr for consortium-scale matrices. Use when choosing sparse format, working with single-cell-sized matrices, importing/exporting 10X, debugging R/Python interop transposes, processing matrices too large for RAM, or building cloud-native pipelines.
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Stores and operates on sparse expression matrices for single-cell and large bulk RNA-seq, covering dgCMatrix/dgRMatrix/dgTMatrix when-each-is-fast, the dgCMatrix (CSC, R) <-> CSR (Python) implicit transpose, AnnData (cells-rows) <-> SingleCellExperiment (cells-cols) orientation flip, HDF5/h5ad vs Zarr cloud-native shift, HDF5SummarizedExperiment + DelayedArray for out-of-memory bulk, scanpy backed mode for large h5ad, the ~10-15% density crossover where dense beats sparse, 10X format proliferation (MTX vs CellRanger H5 vs h5ad), the dense-conversion memory blow-up, and Dask + Zarr for consortium-scale matrices. Use when choosing sparse format, working with single-cell-sized matrices, importing/exporting 10X, debugging R/Python interop transposes, processing matrices too large for RAM, or building cloud-native pipelines.
Before using code patterns, verify installed versions match. If versions differ:
Python: pip show <package> then help(module.function) to check signatures
R: packageVersion('<pkg>') then ?function_name to verify parameters
If code throws ImportError, AttributeError, or TypeError, introspect the installed
package and adapt the example to match the actual API rather than retrying.
Sparse Matrix Handling
"Store / compute on a single-cell matrix without blowing up memory" -> Pick the sparse format that matches the access pattern (CSC for column ops, CSR for row ops), respect the R/Python convention difference (Bioconductor stores cells in columns; AnnData stores cells in rows), and use HDF5/Zarr backed mode for matrices too large for RAM.
The Single Most Important Modern Insight -- The R/Python interop transpose is silent and catastrophic
R Bioconductor (Seurat, SingleCellExperiment) stores cells in COLUMNS and uses dgCMatrix (Column-Compressed Sparse). Python scverse (AnnData, scanpy) stores cells in ROWS and defaults to CSR (Compressed Sparse Row). Round-tripping with anndata2ri, zellkonverter, or rpy2 triggers a TRANSPOSE under the hood -- once per direction. Two flips silently cancel. A debugging session that converts back and forth multiple times can end up with mysteriously transposed data and no error.
Conversion
Implicit transpose
Python CSR -> R dgCMatrix
YES (rows <-> cols)
AnnData .X (cells x genes) -> SingleCellExperiment counts (genes x cells)
YES
Seurat @assays$RNA@counts (genes x cells) -> AnnData .X (cells x genes)
YES
scipy.sparse.csr_matrix(dense)
None (just format conversion)
csr.tocsc() / csc.tocsr()
None (semantically same matrix, different layout)
The safe pattern for one-shot conversions: file-based intermediate. adata.write('file.h5ad') then zellkonverter::readH5AD('file.h5ad') -- avoids the in-memory rpy2/reticulate gymnastics, and the file roundtrip makes orientation explicit.
For a 1M-cell single-cell matrix, the implicit transpose is non-trivial -- minutes of wall time and a temporary memory peak roughly equal to nnz x 12 bytes (CSC) or x 16 bytes (CSR with int64). Avoid unnecessary transposes by aligning the format to the consumer.
Two adjacent insights:
Sparse becomes inefficient above ~10-15% density. Sparse iteration has cache-unfriendly indirection; dense iteration is sequential. Above ~10-15% nonzero, dense is often faster for most operations even though it uses more memory.
AnnData backed mode quietly differs from in-memory in important ways.sc.read_h5ad('file.h5ad', backed='r') returns an AnnData where .X is a wrapped HDF5 dataset, read-only. Many scanpy functions silently load to memory; some functions error or hang on backed mode.
Algorithmic Taxonomy
Format
Layout
Fast for
Slow for
dgCMatrix (CSC, R)
i (row indices), p (col pointers), x (values)
Column slicing; per-cell ops in single-cell (cells in cols); matrix-vector with col vector
Row slicing
dgRMatrix (CSR, R)
j (col indices), p (row pointers), x (values)
Row slicing; per-gene ops when genes in rows
Column slicing
dgTMatrix (COO, R triplet)
i, j, x
Random insertion when building; reading MTX
Most operations -- convert to dgCMatrix after build
Random access via chunks; compression; widely supported
Cloud / parallel writes
Zarr
Chunked array, per-chunk file (or S3 object)
Cloud-native; parallel writes; Dask integration
Single-file simplicity
DelayedArray + HDF5Array
Bioc lazy evaluation over HDF5
Out-of-memory bulk ops in R
Speed of in-memory
Decision Tree by Scenario
Scenario
Recommended approach
Single-cell (>10k cells), per-cell ops
dgCMatrix in R (Bioconductor); CSR adata.X in Python (scanpy)
Bulk RNA-seq (60-80% density)
Dense -- sparse overhead exceeds benefit
Single-cell pseudobulk (after donor aggregation)
Dense -- now 60-80% density typically
1M+ cells, can't fit in RAM
scanpy backed mode OR HDF5SummarizedExperiment + DelayedArray
TCGA + GTEx + recount3 scale (100k+ samples)
HDF5Array / Zarr + Dask
10X CellRanger 3.0+ output
sc.read_10x_h5() or Read10X_h5() -- the .h5 is faster than the .mtx triplet
Cloud-native (anndata on S3, dask compute)
Zarr
Local workstation, single-machine
HDF5 -- faster, more widely supported
Building sparse matrix incrementally
COO (dgTMatrix / coo_matrix); convert to CSC/CSR after
R <-> Python conversion
File-based intermediate (adata.write then zellkonverter::readH5AD); aware of the transpose
Check Sparsity
Goal: Decide whether sparse is the right format given the actual data density.
Approach: Compute nonzero fraction; rule of thumb is sparse > ~85% (single-cell). Below that, dense often wins.
import numpy as np
import scipy.sparse as sp
defsparsity(m):
if sp.issparse(m):
return1 - m.nnz / (m.shape[0] * m.shape[1])
return (m == 0).mean()
s = sparsity(adata.X)
print(f'{s:.1%} sparse')
Memory math:
Data
Format
Bytes
30k x 100k single-cell matrix, 5% density
dgCMatrix
(5% * 3e9) * 12 bytes ~= 1.8 GB
Same
Dense double
24 GB
60k x 100k bulk, 70% density
dgCMatrix
50 GB (worse than dense!)
Same
Dense double
48 GB
For single-cell (typically 90-95% sparse), sparse is essential. For bulk RNA-seq (typically 60-80% density), dense is faster and not appreciably larger.
dgCMatrix / scipy CSC / CSR
Goal: Construct, query, and convert sparse matrices in the format matching the consumer's expected layout.
HDF5 (Hierarchical Data Format 5): hierarchical, single-file binary. Random access via chunks; supports compression (gzip, blosc, lz4). On-disk format for AnnData .h5ad, MuData .h5mu, 10x Genomics .h5, HDF5SummarizedExperiment.
Zarr: cloud-native, chunked array storage. Each chunk is a separate file (or S3 object). Parallel-write friendly; splittable by Dask. Format used by recent AnnData (anndata.write_zarr), SpatialData, and large-cohort consortia.
Criterion
HDF5
Zarr
File structure
Single binary file
Directory of chunk files
Parallel writes
Limited (process-level locks)
Native
S3 / cloud object storage
Workarounds (h5cloud); often slow
Native; first-class
Compression options
gzip, blosc, lz4, szip
gzip, blosc, lz4, zstd, custom
Local workstation speed
Faster
Slightly slower (many small files)
Wide ecosystem support
Yes (mature)
Growing; modern scverse
For local workstation work, HDF5 is faster and more widely supported. For cloud-mounted analysis (anndata on S3 with dask-distributed compute), Zarr wins because of object-storage friendliness.
Goal: Work with bulk SummarizedExperiment objects too large to fit in RAM by keeping the matrix on disk.
Approach:HDF5Array wraps an HDF5 dataset as a DelayedArray. Subsetting builds a delayed operation tree -- no I/O until realization. DelayedMatrixStats provides delayed-friendly stat functions.
library(HDF5Array)
library(SummarizedExperiment)
library(DelayedMatrixStats)
se <- loadHDF5SummarizedExperiment('saved_se_dir')
s <- se[1:1000,1:50]
row_means <- rowMeans2(assay(se))
saveHDF5SummarizedExperiment(se,'saved_se_dir', replace =TRUE)
The assay(se) returns a DelayedMatrix backed by HDF5. DESeq2, edgeR, limma have varying levels of DelayedArray support; consult package docs before assuming all ops work in delayed mode.
For TCGA + GTEx + recount3 scale (100k+ samples, 60k genes), a dense matrix is ~48 GB (double); dgCMatrix at 70% density is ~50 GB (sparse loses). HDF5Array + chunk-aware ops keeps memory at whatever-fits-in-RAM.
scanpy Backed Mode
Goal: Work with h5ad files too large for memory by loading only accessed slices on demand.
Approach:sc.read_h5ad(..., backed='r') returns an AnnData with .X as a wrapped HDF5 dataset. Subset operations are lazy; .to_memory() realizes.
import scanpy as sc
adata = sc.read_h5ad('large_dataset.h5ad', backed='r')
print(f'Shape: {adata.shape}, X type: {type(adata.X)}')
t_cells = adata[adata.obs['cell_type'] == 'T_cell', :].to_memory()
Limitations:
.X is read-only in backed='r'. Use backed='r+' for in-place updates, but only .X updates supported.
.obs and .var are fully loaded -- only .X supports backed access.
Very large sparse h5ad (>35 GB) can still cause memory issues even in backed mode (anndata library overhead).
Many scanpy functions internally load to memory; check ?function docs for backed compatibility.
Functions like sc.tl.pca, sc.pp.neighbors typically require in-memory; subset first with .to_memory().
For datasets too large for backed mode, process in chunks:
import anndata as ad
defprocess_in_chunks(h5ad_path, chunk_size=10000, func=None):
adata = sc.read_h5ad(h5ad_path, backed='r')
n_cells = adata.shape[0]
results = []
for start inrange(0, n_cells, chunk_size):
end = min(start + chunk_size, n_cells)
chunk = adata[start:end].to_memory()
if func:
chunk = func(chunk)
results.append(chunk)
return ad.concat(results)
HDF5 with /matrix/data, /matrix/indices, /matrix/indptr, /matrix/shape; single file, fast
H5AD
data.h5ad
AnnData; convert on import
kallisto
bustools output
output.bus + barcode and gene mappings
import scanpy as sc
adata = sc.read_10x_h5('filtered_feature_bc_matrix.h5')
adata = sc.read_10x_mtx('filtered_feature_bc_matrix/')
library(Seurat)
mat <- Read10X_h5('filtered_feature_bc_matrix.h5')
mat <- Read10X(data.dir ='filtered_feature_bc_matrix/')
library(DropletUtils)
sce <- read10xCounts('filtered_feature_bc_matrix/')
For 10X output, prefer the .h5 over the MTX triplet -- typically 5-10x faster for large matrices.
Dense Conversion -- The Memory Blow-Up
adata.X.toarray() (Python) or as.matrix(seurat_obj@assays$RNA@counts) (R) on a 30k x 100k single-cell matrix instantiates a ~24 GB dense double array. Common triggers:
Passing sparse to a function that internally calls as.matrix() (older R cor() implementations).
Heatmap functions (pheatmap, ComplexHeatmap) that require dense.
ML libraries with no sparse support (some sklearn models; XGBoost requires specific sparse API).
Plotting functions (plot(), ggplot2) called on the full matrix.
Defensive pattern: subset to a manageable gene/cell set BEFORE dense conversion.
For per-cell PCA-style ops, use sparse-aware solvers:
from scipy.sparse.linalg import svds
U, s, Vt = svds(adata.X, k=50)
irlba (R) and scipy.sparse.linalg.svds (Python) compute truncated SVD without densifying.
SCE vs AnnData vs MuData -- Where Bulk Fits
Container
Library
Cells/samples
Multi-modal
Bulk fit
SummarizedExperiment / RangedSummarizedExperiment
Bioconductor
n/a; bulk
No
YES -- standard for DESeq2/edgeR/limma bulk
SingleCellExperiment (Amezquita 2020)
Bioconductor
cells in cols
Via altExps
scRNA-seq with spike-ins, ADT
AnnData
scverse/Python
cells in rows
Via layers
scRNA-seq; bulk is unusual
MuData
scverse/Python
cells in rows
Yes, multiple AnnData
Multi-modal scRNA + ATAC + protein
MultiAssayExperiment
Bioconductor
samples
Yes
R-side multi-modal analog
Bulk RNA-seq rarely uses AnnData -- it shines on the single-cell dimensionality reduction / neighbors / clustering machinery. For bulk in R, use SummarizedExperiment. For bulk in Python, a tidy DataFrame + numpy array is usually sufficient.
Dask + Zarr for Consortium-Scale Matrices
For TCGA + GTEx + recount3 (Wilks 2021 Genome Biol 22:323) or pancancer assemblies:
import zarr
import dask.array as da
z = zarr.open('counts.zarr', mode='r')
da_arr = da.from_zarr(z)
col_sums = da_arr.sum(axis=0).compute()
filtered = da_arr[da_arr.sum(axis=1) > 100, :]
import anndata as ad
adata_disk = ad.read_zarr('large_data.zarr')
For R: HDF5Array + DelayedArray is the equivalent, but R doesn't have a true Dask analog. BiocParallel can parallelize chunks, but lazy planning is more manual.
Subsetting: select genes (rows) or samples (cols) by index:
gene_idx = [gene_names.index(g) for g in ['TP53', 'BRCA1', 'MYC'] if g in gene_names]
subset = sparse_matrix[gene_idx, :]
CPM Normalization on Sparse
Goal: Apply CPM normalization without densifying.
Approach: Compute library sizes from column sums; broadcast scaling factors with sparse multiply for CPM; transform only the nonzero data array in-place with log1p.
import numpy as np
import scipy.sparse as sp
defnormalize_sparse_cpm(sparse_matrix):
lib_sizes = np.array(sparse_matrix.sum(axis=0)).flatten()
scaling = 1e6 / lib_sizes
return sparse_matrix.multiply(scaling)
deflog1p_inplace(sparse_matrix):
out = sparse_matrix.copy()
out.data = np.log1p(out.data)
return out
cpm = normalize_sparse_cpm(adata.X)
log_cpm = log1p_inplace(cpm)
After log-transformation, sparsity is PRESERVED (log1p(0) = 0). After CPM with pseudocount, zeros become nonzero -- check sparsity and convert to dense if density drops below ~15%.
Save / Load Sparse Matrices
import scipy.sparse as sp
import numpy as np
sp.save_npz('counts_sparse.npz', sparse_matrix)
loaded = sp.load_npz('counts_sparse.npz')
np.savez('counts_with_meta.npz',
data = sparse_matrix.data,
indices = sparse_matrix.indices,
indptr = sparse_matrix.indptr,
shape = sparse_matrix.shape,
genes = np.array(gene_names),
samples = np.array(sample_names))
For interop and durable storage, prefer h5ad or zarr:
Trigger: AnnData with cells in rows passed to a SingleCellExperiment workflow that expects cells in cols; downstream colSums returns gene-level totals.
Mechanism: AnnData stores cells in rows; SCE in cols. The conversion auto-transposes ONCE per direction; two roundtrips silently restore.
Symptom: Per-cell stats look like per-gene stats; QC plots have wrong axes.
Fix: Use file-based intermediate (adata.write('file.h5ad'); zellkonverter::readH5AD('file.h5ad')). Always verify dimensions and orientation after conversion.
Dense conversion blew up memory
Trigger:as.matrix(seurat_obj@assays$RNA@counts) on a 100k-cell dataset; R session crashes with OOM.
Symptom: R session killed; "cannot allocate vector of size N GB".
Fix: Don't densify the full matrix. Subset to genes/cells of interest first. For dimensionality reduction, use irlba::irlba() (sparse SVD).
scanpy backed mode silently loaded to memory
Trigger:adata = sc.read_h5ad(path, backed='r') then sc.tl.pca(adata); memory spikes to dense-equivalent.
Mechanism: Many scanpy functions internally call .to_memory() because they cannot operate on backed mode. sc.tl.pca, sc.pp.neighbors, sc.tl.umap all materialize.
Symptom: OOM despite backed mode.
Fix: Subset first (adata[mask].to_memory()), then operate. Or use a streaming-aware alternative (Dask + Zarr).
Sparse stored where dense would be faster
Trigger: Bulk RNA-seq with 70% density stored as dgCMatrix; per-gene rowVars is slow.
Symptom: Operations notably slower than expected; profiler shows time in sparse indexing.
Fix: Convert to dense for the hot path: as.matrix(sparse_mat) (R) or sparse_matrix.toarray() (Python). Memory may go up but speed improves substantially.
10X MTX read is slow
Trigger: Reading a 100k-cell 10X dataset via the MTX three-file format; takes 10+ minutes.
Mechanism: MTX is a text format; parsing is slow for large matrices.
Symptom: Long load times; user kills the process before completion.
Fix: Use the CellRanger H5 (.h5) instead -- typically 5-10x faster.
Common errors
Error / symptom
Cause
Fix
cannot allocate vector of size N GB
Implicit dense conversion
Subset first; use sparse-aware solver (irlba)
Sparse-dense arithmetic returns numpy.matrix
Deprecated NumPy type from sparse+dense
np.asarray(sparse + dense) to force ndarray
KeyError: '_index' reading h5ad
anndata version mismatch
Update anndata; or sc.read_h5ad(..., backed=None)
Empty rows/cols after sparse subset
Subset removed all data
Verify the index list; cross-check sample/gene names
Backed mode AnnData crash on sc.tl.umap
Function not backed-compatible
.to_memory() on the subset first
Per-cell totals look wrong after R<->Python conversion
Implicit transpose
Verify dimensions; use file-based intermediate
CSR (Python) <-> dgCMatrix (R) treated as same
Convention difference
They're transposes of each other; verify shape and a known cell-gene pair
References
Amezquita RA, Lun ATL, Becht E et al. 2020. Orchestrating single-cell analysis with Bioconductor. Nat Methods 17:137-145. doi:10.1038/s41592-019-0654-x
Wolf FA, Angerer P, Theis FJ. 2018. SCANPY: large-scale single-cell gene expression data analysis. Genome Biol 19:15. doi:10.1186/s13059-017-1382-0
Wilks C et al. 2021. recount3: summaries and queries for large-scale RNA-seq expression and splicing. Genome Biol 22:323. doi:10.1186/s13059-021-02533-6
Bates D, Maechler M. 2023. Matrix: Sparse and Dense Matrix Classes and Methods. R package version 1.6-x.
Pages H et al. 2020. HDF5Array: HDF5 backend for DelayedArray objects. Bioconductor package.
Miles A et al. 2020. zarr-python. Python package documentation.
Rocklin M. 2015. Dask: Parallel Computation with Blocked algorithms and Task Scheduling. Proc Python Sci Conf. (canonical Dask reference)
Lachmann A et al. 2018. Massive mining of publicly available RNA-seq data from human and mouse. Nat Commun 9:1366. doi:10.1038/s41467-018-03751-6
Related Skills
counts-ingest - Reading 10X formats; building sparse matrices from quantification output
gene-id-mapping - Var (gene) metadata in AnnData
metadata-joins - Obs (sample) metadata in AnnData
normalization - log1p and CPM patterns on sparse
differential-expression/deseq2-basics - Pseudobulk aggregation makes dense
single-cell/data-io - Single-cell file format ecosystem
single-cell/preprocessing - Standard single-cell sparse pipeline
