Add PCA and dot plots; make the incomplete beta fast at every argument

README.md

@@ -38,6 +38,7 @@ what is planned.
 | Replication across studies | `sumrank`: SumRank (Nakatsuka et al. 2025), which ranks every gene within each study by its signed -log10 p-value and sums its best normalized ranks across studies, for genes up and down, with p-values from the Irwin-Hall distribution and from a null pooled over permutations; `differential_expression_sumrank`: the same for one cell type and contrast of the studies of a `CubeCollection`, with permutations that re-run each study's limma analysis from a seeded generator; `held_out_prediction`: each study left out in turn, genes chosen from the others by SumRank and by meta-analysis, its cases scored by UCell's rank score, and the AUC by study and method; with SumRank's Manhattan plot and the held-out AUC of every study | the authors' code, mpmath, scikit-learn |
 | Composition tests | `propeller`: differences in cell-type proportions between conditions, from the cell numbers of a cube or a table of them, with the logit or arcsine square-root transform, a design matched by sample id, t-tests of its contrasts and the F-test of a factor, robust empirical Bayes moderation, speckle's columns (baseline and mean proportions, proportion ratio, statistic, p-value, FDR) and a provenance record | speckle, limma |
 | Figures | `cytepool.plotting` (optional extra `plot`, matplotlib): the plots of limma, edgeR, DESeq2, speckle and metafor from CytePool's results, in one call each: MDS plots of pseudobulk samples (`plotMDS`), the cells pooled into each sample and cell type, cell-type composition and `propeller`'s results, voom's mean-variance trend, residual variances and their prior (`plotSA`), sample quality weights, MD and volcano plots, p-value histograms, the genes up and down in each cell type, barcode plots and summaries of gene-set tests, DESeq2's dispersions (`plotDispEsts`), edgeR's quasi-dispersions (`plotQLDisp`), forest plots of meta-analyses, the fractions of variance of every variable over the genes (`plotVarPart`) and of chosen genes (`plotPercentBars`), and heatmaps of pathway scores | limma, edgeR, DESeq2, metafor, speckle, variancePartition, GSVA |
+| Samples and cells at a glance | `principal_components` and `plot_pca`: samples on the principal components of their most variable genes, from a matrix or a cell type of a cube, as DESeq2's `plotPCA` computes and draws them; `plot_dotplot`: the fraction of cells that express each gene and their mean expression in each cell type, from a cube's sums and so without the cells, as scanpy's `dotplot` draws them | DESeq2, edgeR, scanpy |
 | Distributions and smoothers | Tails of the normal, t, F, chi-squared, gamma, beta and hypergeometric distributions, and quantiles of the first four; LOWESS, and limma's rule for its span; natural spline bases | mpmath, R, limma |
 
 ## Planned

THIRD_PARTY_NOTICES.md

@@ -187,6 +187,49 @@ of neurodegenerative diseases through meta-analysis. Nature Communications 16, 7
 doi:10.1038/s41467-025-62579-z. The code is distributed under the Apache License,
 Version 2.0 (Copyright 2024 Nathan Nakatsuka; http://www.apache.org/licenses/LICENSE-2.0).
 
+### scanpy
+
+`plot_dotplot` in `cytepool/plotting.py` follows three conventions of scanpy 1.12.4's
+dot plot (https://github.com/scverse/scanpy, `src/scanpy/plotting/_dotplot.py`) that its
+documentation leaves open: the largest fraction rounded up to a tenth, the steps of the
+key of the dots' areas (0.2, 0.1 or 0.05), and a scaled row of equal values drawn as 0.
+No code is copied. scanpy is described in Wolf FA, Angerer P, Theis FJ (2018). SCANPY:
+large-scale single-cell gene expression data analysis. Genome Biology 19, 15.
+doi:10.1186/s13059-017-1382-0. It is distributed under the BSD 3-Clause License:
+
+```text
+BSD 3-Clause License
+
+Copyright (c) 2025 scverse®
+Copyright (c) 2017 F. Alexander Wolf, P. Angerer, Theis Lab
+All rights reserved.
+
+Redistribution and use in source and binary forms, with or without
+modification, are permitted provided that the following conditions are met:
+
+* Redistributions of source code must retain the above copyright notice, this
+  list of conditions and the following disclaimer.
+
+* Redistributions in binary form must reproduce the above copyright notice,
+  this list of conditions and the following disclaimer in the documentation
+  and/or other materials provided with the distribution.
+
+* Neither the name of the copyright holder nor the names of its
+  contributors may be used to endorse or promote products derived from
+  this software without specific prior written permission.
+
+THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
+AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
+IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
+DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE
+FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
+DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR
+SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
+CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY,
+OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
+OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+```
+
 ### numba
 
 `cytepool/_jit.py` places the cache of its compiled routines with subclasses of numba's