<!-- README.md is generated from README.Rmd. Please edit that file -->
# Introduction
`scHiCcompare` is designed for the imputation, joint normalization, and
detection of differential chromatin interactions between two groups of
chromosome-specific single-cell Hi-C datasets (scHi-C). The groups can
be pre-defined based on biological conditions or created by clustering
cells according to their chromatin interaction patterns. Clustering can
be performed using methods like
[Higashi](https://github.com/ma-compbio/Higashi),
[scHiCcluster](https://github.com/zhoujt1994/scHiCluster) methods, etc.
`scHiCcompare` works with processed Hi-C data, specifically
chromosome-specific chromatin interaction matrices, and accepts
five-column tab-separated text files in a sparse matrix format.
The package provides two key functionalities:
- Imputation of single-cell Hi-C data by random forest model with
pooling technique
- Differential analysis to identify differences in chromatin
interactions between groups.
# Installation
``` r
if (!requireNamespace("BiocManager", quietly = TRUE)) {
install.packages("BiocManager")
}
BiocManager::install("scHiCcompare")
# For the latest version install from GitHub
# devtools::install_github("dozmorovlab/scHiCcompare")
```
``` r
library(scHiCcompare)
library(tidyr)
library(ggplot2)
library(gridExtra)
library(lattice)
library(data.table)
```
# Usage
## Input
To use scHiCcompare, you’ll need to define two groups of cells to
compare and save cell-specific scHi-C data (individual files in **.txt**
format) in two folders.
Each cell-specific scHi-C **.txt** file should be formatted as modified
sparse upper triangular matrices in R, which consist of five columns
(chr1, start1, chr2, start2, IF). Since the full matrix of chromatin
interactions is symmetric, only the upper triangular portion, including
the diagonal and excluding any 0, is stored in a sparse matrix format.
The required sparse matrix format of each single-cell Hi-C is:
- “chr1” - Chromosome of the first region.
- “start1” - a start coordinate (in bp) of the first region.
- “chr2” - Chromosome of the second region.
- “start2” - a start coordinate (in bp) of the second region.
- “IF” - the interaction frequency between 2 two regions (IFs).
The ‘.txt’ files need to be saved in tab-separated columns and no row
names, column names, or quotes around character strings with the example
format below.
#> chr1 start1 chr2 start2 IF
#> 17669 chr20 0 chr20 0 128
#> 17670 chr20 0 chr20 1000000 1
#> 17671 chr20 1000000 chr20 1000000 179
#> 17672 chr20 0 chr20 2000000 1
#> 17673 chr20 1000000 chr20 2000000 1
#> 17674 chr20 2000000 chr20 2000000 174
To run `scHiCcompare()`, you need two folders with condition-specific
scHiC ‘.txt’ files. The condition-specific groups of cells should be
pre-defined based on criteria such as experimental conditions,
clustering results, or biological characteristics.
### Prepare input folders
Here is an example workflow using scHiC human brain datasets (Lee et
al., 2019) with ODC and MG cell types at chromosome 20 with a 1MB
resolution.
For the following example sections, we will load samples of 10
single-cell Hi-C data (in ‘.txt’) for each cell type group in two
example folders (`ODCs_example` and `MGs_axample`). The files follow the
same format as those downloaded via `download_schic()` of `Bandnorm`.
You can extract the folder path by the code below, which could be used
as input for `scHiCcompare()` function.
``` r
## Load folder of ODC file path
ODCs_example_path <- system.file("extdata/ODCs_example",
package = "scHiCcompare"
)
## Load folder of MG file path
MGs_example_path <- system.file("extdata/MGs_example",
package = "scHiCcompare"
)
```
Since the data downloaded by `Bandnorm` has the required input format (5
columns of \[chr1, start1, chr2, start2, IF\]), we don’t need an extra
step for data modification. If, after importing your data into R, its
format does not follow the sparse upper triangular [input](#input)
format requirement, you need to modify the data.
## scHiCcompare function
The function requires two *Input Parameter*:
- `file.path.1, file.path.2` - Character strings specifying paths to
folders containing scHi-C data for the first and second cell type or
condition groups.
- `select.chromosome` - Integer or character indicating the chromosome
to be analyzed (e.g., ‘chr1’ or ‘chr10’.)
``` r
scHiCcompare(file.path.1, file.path.2,
select.chromosome,
main.Distances = 1:10000000,
imputation = "RF",
normalization = "LOESS",
differential.detect = "MD.cluster",
pool.style = "progressive", n.imputation = 5,
maxit = 1, outlier.rm = TRUE, missPerc.threshold = 95,
A.min = NULL, fprControl.logfc = 0.8, alpha = 0.05,
Plot = T, Plot.normalize = F, save.output.path = NULL
)
```
*Optional Workflow Parameter* include:
- `main.Distances` - A numeric vector indicating the range of
interacting genomic distances (in base pairs) between two regions
(e.g., loci or bins) to focus on (e.g., `1:100000`, `Inf`). All
genomic range selections can be specified using `Inf`. The
`main.Distances` vector should be proportional to the data’s
resolution (e.g., for 10kb resolution: `1:10000`, `1:50000`,
`1:100000`, `Inf`). As the distance range and resolution increase, the
percentage of ‘0’ or missing values also increases. Selecting a large
distance range at high resolution (e.g., below 200kb) may increase
runtime due to extreme sparsity. By default, `main.Distances` =
`1:10000000`.
- `imputation` - A character string, either `'RF'` or `NULL`, indicating
the imputation method. If `NULL` is selected, the workflow will skip
the `imputation` step. The default is `'RF'` for Random Forest
imputation.
- `normalization` - A character string, either `'LOESS'` or `NULL`,
indicating the normalization method. If `NULL` is selected, the
workflow will skip the `normalization` step. The default is `'LOESS'`.
*Optional Imputation Parameter* include:
- `pool.style` - A character string specifying the pooling style for
`imputation`. Options are `'none'`, `'progressive'`, or `'Fibonacci'`.
The default is `'progressive'`.
- `n.imputation` - An integer specifying the number of multiple
imputations for the imputation step. Because the final imputed values
are calculated as the average of multiple imputations, increasing the
number of imputations improves the accuracy of imputed values;
however, it may also extend the imputation runtime. The default is
`5`.
- `maxit` - An integer specifying the maximum number of iterations for
the internal refinement process within a single `imputation` cycle.
Increasing `maxit` can help stabilize imputed values, although it may
increase the imputation runtime. The default is `1`.
- `outlier.rm` - Logical. If `TRUE`, outliers are removed during
`imputation`. The default is `TRUE`.
- `missPerc.threshold` - A numeric value specifying the maximum
allowable percentage of missing data in pool bands outside the
`main.Distances` to be imputed by the `imputation` method. A higher
threshold includes more extreme sparse distances for imputation (e.g.,
above 95 percent), which increases memory and runtime, while a lower
threshold (e.g., below 50 percent) might reduce the number of
distances imputed. The default is `95`.
*Optional Normalization Parameter* include:
- `A.min` - Numeric value or NULL that sets the A-value quantile cutoff
(eg,. 7, 10, etc) for filtering low average interaction frequencies in
the outlier detection in the differential step of the `hic_compare()`
function from `HiCcompare`. If not provided (NULL), A is
auto-detected.
*Optional Differential Test Parameter* include:
- `fprControl.logfc` - Numeric value to control the false positive rate
for GMM difference clusters (`differential.detect`) (e.g., 0.5, 0.8,
1, 1.5, etc.). Increasing `fprControl.logfc` may lower the false
positive rate but may also reduce the number of detected chromatin
interaction differences. The default is 0.8, equivalent to a 2-fold
change.
- `alpha` - Numeric value specifying the significance level for outlier
detection during the `differential.detect` step with the
`hic_compare()` function from HiCcompare. Default is 0.05.
*Optional Output Parameter* :
- `save.output.path` - Character string specifying the directory to save
outputs, including the imputed cells in the form of a sparse upper
triangular format, normalization result table, and differential
analysis result table. If `save.output.path` = NULL (the default), no
files are saved.
- `Plot` - A logical value indicating whether to plot the
`differential.detect` results in an MD plot. Default is TRUE.
- `Plot.normalize` - A logical value indicating whether to plot the
output of MD plot showing before/after LOESS `normalization`. Default
is FALSE.
### Example of real analysis
In the following example, we will work with scHi-C data from 10 single
cells in both ODC and MG cell types at a 1 MG resolution. We will focus
on chromosome 20, applying the full workflow of scHiCcompare, which
includes imputation, pseudo-bulk normalization, and differential
analysis. Our goal is to detect differences for loci with genomic
distances ranging from 1 to 10,000,000 bp. The progressive pooling style
will be selected to create pool bands for the random forest imputation.
For the differential analysis step, we will set the log fold change -
false positive control threshold to 0.8.
The input file path was included in the package and conducted in the
[Prepare input folders](#prepare-input-folders) section.
``` r
## Imputation with 'progressive' pooling
result <- scHiCcompare(
file.path.1 = ODCs_example_path,
file.path.2 = MGs_example_path,
select.chromosome = "chr20",
main.Distances = 1:10000000,
imputation = "RF",
normalization = "LOESS",
differential.detect = "MD.cluster",
pool.style = "progressive",
fprControl.logfc = 0.8,
Plot = TRUE,
Plot.normalize = TRUE
)
```
<img src="man/figures/README-unnamed-chunk-9-1.png" width="100%" /><img src="man/figures/README-unnamed-chunk-9-2.png" width="100%" /><img src="man/figures/README-unnamed-chunk-9-3.png" width="100%" />
From the visualizations above, normalization effectively reduces the
irregular trend in the M values between the imputed pseudo-bulk matrices
of the two cell types. At a 1MB resolution, the differential analysis
reveals that most of the detected differences occur at closer genomic
distances, particularly below 5MB.
## Output
#### Output objects from the R function
The `scHiCcompare()` function will return an object that contains plots,
differential results, pseudo-bulk matrices, normalized results, and
imputation tables. The full differential results are available in
`$Differential_Analysis`. Intermediate results can be accessed with
`$Intermediate`, including the imputation result table
(`$Intermediate$Imputation`), the pseudo-bulk matrix in sparse format
(`$Intermediate$PseudoBulk`), and the normalization table
(`$Intermediate$Bulk.Normalization`). These output table objects have
the following structure:
- `$Intermediate$PseudoBulk` for each condition group (`$condition1` and
`$condition2`) has a standard sparse upper triangular format with 3
columns of \[region1, region2, IF\].
- `$Intermediate$Imputation` for each condition group (`$condition1` and
`$condition2`) has modified sparse upper triangular format:
- Interacting bins coordination \[region1, region2, cell (condition 1
or condition2), chr\]
- Imputed interaction frequency of each single-cell \[imp.IF\_{cell
name 1}, imp.IF\_{cell name 2}, imp.IF\_{cell name 3}, …,etc\]
- `$Intermediate$Bulk.Normalization` has 15 columns
- Interacting bins coordination \[chr1, start1, end1, chr2, start2,
end2, D (scaled genomic distance)\]
- Bulk IF values \[bulk.IF1, bulk.IF2, M (their log fold change,
$log(IF_2/IF_1)$)\]
- Normalized bulk IF values \[adj.bulk.IF1, adj.bulk.IF2, adj.M (their
log fold change, $log(adj.IF_2/adj.IF_1)$)\]
- LOESS correction factor \[mc\];
- Average expression value of bulk IF \[A\].
- `$Differential_Analysis` has same structure as
`$Intermediate$Bulk.Normalization` with addition of 2 differential
detection results columns
- Z score of interaction frequencies’s log fold change \[Z\]
- Differential result cluster \[Difference.cluster\]
#### Externally saved output files
You also can have the option to save the results into the chosen
directory by a parameter in `scHiCcompare()`
[function](#schiccompare-function). This will save the normalization
result table, differential result table, and imputed cell scHi-C data
(each group is a sub-folder). The sample of the saved output folder
structure is:
\|– Bulk_normalization_table.txt
\|– Differential_analysis_table.txt
\|– Imputed\_{group 1’s name}/
- \|– imp\_{cell name}.txt
\|– Imputed\_{group 2’s name}/
- \|– imp\_{cell name}.txt
The normalization result `Bulk_normalization_table.txt` has the same
format as the output object from the `scHiCcompare()` function,
`$Intermediate$Bulk.Normalization`, which is shown in the structure
example below.
The differential result table `Differential_analysis_table.txt` also has
the same format as the output object `$Differential_Analysis` from the
function.
The imputed cell’s scHiC data is saved in a folder for each group, which
has a modified sparse upper triangular format of five columns \[chr1,
start1, chr2, start2, IF\].
### Example of output
Below is a continuous example from [Example of real
anlysis](#example-of-real-anlysis) above, showing how you can extract
different result options from the `scHiCcompare()` function.
``` r
### Extract imputed differential result
diff_result <- result$Differential_Analysis
head(diff_result)
#> chr1 start1 end1 chr2 start2 end2 bulk.IF1 bulk.IF2 D M
#> <char> <num> <num> <char> <num> <num> <num> <num> <num> <num>
#> 1: chr20 0e+00 1e+06 chr20 1e+06 2e+06 43 35 1 -0.29698174
#> 2: chr20 1e+06 2e+06 chr20 2e+06 3e+06 38 45 1 0.24392558
#> 3: chr20 2e+06 3e+06 chr20 3e+06 4e+06 33 32 1 -0.04439412
#> 4: chr20 3e+06 4e+06 chr20 4e+06 5e+06 26 28 1 0.10691520
#> 5: chr20 4e+06 5e+06 chr20 5e+06 6e+06 41 33 1 -0.31315789
#> 6: chr20 5e+06 6e+06 chr20 6e+06 7e+06 35 20 1 -0.80735492
#> adj.bulk.IF1 bulk.adj.IF2 adj.M mc A Z
#> <num> <num> <num> <num> <num> <num>
#> 1: 40.49493 37.16514 -0.1237912 -0.1731905 38.83004 -0.3167693
#> 2: 35.78622 47.78376 0.4171161 -0.1731905 41.78499 1.0969765
#> 3: 31.07751 33.97956 0.1287964 -0.1731905 32.52853 0.3434079
#> 4: 24.48531 29.73211 0.2801057 -0.1731905 27.10871 0.7388785
#> 5: 38.61145 35.04142 -0.1399674 -0.1731905 36.82643 -0.3590482
#> 6: 32.96099 21.23722 -0.6341644 -0.1731905 27.09911 -1.6507094
#> Difference.cluster
#> <num>
#> 1: 1
#> 2: 1
#> 3: 1
#> 4: 1
#> 5: 1
#> 6: 1
```
``` r
### Extract imputed pseudo bulk matrices normalization
norm_result <- result$Intermediate$Bulk.Normalization
head(norm_result)
#> chr1 start1 end1 chr2 start2 end2 bulk.IF1 bulk.IF2 D M
#> <char> <num> <num> <char> <num> <num> <num> <num> <num> <num>
#> 1: chr20 1e+06 2e+06 chr20 1e+06 2e+06 1830 2246 0 0.2955143
#> 2: chr20 2e+06 3e+06 chr20 2e+06 3e+06 2009 2260 0 0.1698452
#> 3: chr20 3e+06 4e+06 chr20 3e+06 4e+06 1502 1956 0 0.3810216
#> 4: chr20 4e+06 5e+06 chr20 4e+06 5e+06 1749 2317 0 0.4057278
#> 5: chr20 5e+06 6e+06 chr20 5e+06 6e+06 2040 2400 0 0.2344653
#> 6: chr20 6e+06 7e+06 chr20 6e+06 7e+06 2020 2361 0 0.2250427
#> adj.bulk.IF1 bulk.adj.IF2 adj.M mc A
#> <num> <num> <num> <num> <num>
#> 1: 1992.411 2062.918 0.05017112 0.2453432 2027.664
#> 2: 2187.297 2075.777 -0.07549795 0.2453432 2131.537
#> 3: 1635.301 1796.557 0.13567840 0.2453432 1715.929
#> 4: 1904.222 2128.130 0.16038459 0.2453432 2016.176
#> 5: 2221.048 2204.365 -0.01087791 0.2453432 2212.706
#> 6: 2199.273 2168.544 -0.02030041 0.2453432 2183.908
```
``` r
### Extract imputed ODC cell type table
imp_ODC_table <- result$Intermediate$Imputation$condition1
head(imp_ODC_table)
#> region1 region2 cell chr imp.IF_ODC.bandnorm_chr20_1
#> 1 1e+06 1e+06 condition1 chr20 179
#> 2 2e+06 2e+06 condition1 chr20 189
#> 3 3e+06 3e+06 condition1 chr20 204
#> 4 4e+06 4e+06 condition1 chr20 177
#> 5 5e+06 5e+06 condition1 chr20 181
#> 6 6e+06 6e+06 condition1 chr20 199
#> imp.IF_ODC.bandnorm_chr20_2 imp.IF_ODC.bandnorm_chr20_3
#> 1 174 194
#> 2 191 217
#> 3 197 190
#> 4 187 156
#> 5 196 218
#> 6 167 184
#> imp.IF_ODC.bandnorm_chr20_4 imp.IF_ODC.bandnorm_chr20_5
#> 1 201 171
#> 2 179 180
#> 3 200 108
#> 4 178 146
#> 5 200 263
#> 6 200 214
#> imp.IF_ODC.bandnorm_chr20_6 imp.IF_ODC.bandnorm_chr20_7
#> 1 142 198
#> 2 201 215
#> 3 25 184
#> 4 144 150
#> 5 162 215
#> 6 218 232
#> imp.IF_ODC.bandnorm_chr20_8 imp.IF_ODC.bandnorm_chr20_9
#> 1 175 208
#> 2 205 214
#> 3 176 54
#> 4 199 208
#> 5 191 191
#> 6 209 173
#> imp.IF_ODC.bandnorm_chr20_10
#> 1 188
#> 2 218
#> 3 164
#> 4 204
#> 5 223
#> 6 224
```
``` r
## Extract Pseudo-bulk matrix from imputed scHi-C data
## Pseudo bulk matrix in standard sparse format
psudobulk_result <- result$Intermediate$PseudoBulk$condition1
head(psudobulk_result)
#> region1 region2 IF
#> 1 1e+06 1e+06 1830
#> 2 2e+06 2e+06 2009
#> 3 3e+06 3e+06 1502
#> 4 4e+06 4e+06 1749
#> 5 5e+06 5e+06 2040
#> 6 6e+06 6e+06 2020
```
Furthermore, you also have some parameter options in the function to
indicate which plots to output and an option to save the results in a
given directory.
# Helper functions
There are several other functions included in `scHiCcompare` package.
## Heatmap HiC matrix plot
`plot_HiCmatrix_heatmap()` produces a heatmap visualization for HiC and
scHiC matrices. It requires, as input, a modified sparse matrix, the
same format from `scHiCcompare()` [Input](#input) with five columns of
chr1, start1, chr2 start2, IF. More information can be found in its help
document and the example below.
``` r
data("ODC.bandnorm_chr20_1")
plot_HiCmatrix_heatmap(scHiC.sparse = ODC.bandnorm_chr20_1, main = "scHiC matrix of a ODC cell", zlim = c(0, 5))
#> Matrix dimensions: 63x63
```
<img src="man/figures/README-unnamed-chunk-14-1.png" width="100%" />
## Imputation Diagnostic plot
`plot_imputed_distance_diagnostic()` generates a diagnostic
visualization of imputation across genomic distances for all single
cells. It compares the distribution of all cells’ interaction frequency
at a given distance data before and after imputation. It requires, as
input, the scHiC table format of the original and imputed scHiC
datasets. ScHiC table format includes columns of genomic loci
coordinates and interaction frequencies (IF) of each cell (cell,
chromosome, start1, end1, IF1, IF2, IF3, etc).
The output of `$Intermediate$Imputation` of `scHiCcompare()` function is
directly compatible with this format. For more details, see the sections
on [Output](#output))
``` r
# Extract imputed table result
imp_MG_table <- result$Intermediate$Imputation$condition2
imp_ODC_table <- result$Intermediate$Imputation$condition1
```
#> region1 region2 cell chr imp.IF_ODC.bandnorm_chr20_1
#> 1 1e+06 1e+06 condition1 chr20 179
#> 2 2e+06 2e+06 condition1 chr20 189
#> 3 3e+06 3e+06 condition1 chr20 204
#> 4 4e+06 4e+06 condition1 chr20 177
#> 5 5e+06 5e+06 condition1 chr20 181
#> 6 6e+06 6e+06 condition1 chr20 199
#> imp.IF_ODC.bandnorm_chr20_2 imp.IF_ODC.bandnorm_chr20_3
#> 1 174 194
#> 2 191 217
#> 3 197 190
#> 4 187 156
#> 5 196 218
#> 6 167 184
#> imp.IF_ODC.bandnorm_chr20_4 imp.IF_ODC.bandnorm_chr20_5
#> 1 201 171
#> 2 179 180
#> 3 200 108
#> 4 178 146
#> 5 200 263
#> 6 200 214
#> imp.IF_ODC.bandnorm_chr20_6 imp.IF_ODC.bandnorm_chr20_7
#> 1 142 198
#> 2 201 215
#> 3 25 184
#> 4 144 150
#> 5 162 215
#> 6 218 232
#> imp.IF_ODC.bandnorm_chr20_8 imp.IF_ODC.bandnorm_chr20_9
#> 1 175 208
#> 2 205 214
#> 3 176 54
#> 4 199 208
#> 5 191 191
#> 6 209 173
#> imp.IF_ODC.bandnorm_chr20_10
#> 1 188
#> 2 218
#> 3 164
#> 4 204
#> 5 223
#> 6 224
We need to create the table input for original IFs values in the same
format. Below is a continuous example from [Example of real
anlysis](#example-of-real-anlysis) above, showing how you can construct
scHiC table for original IF values and compare them with the output of
imputed IF values.
``` r
# Create scHiC table object for original ODC interaction frequencies (IF)
scHiC.table_ODC <- imp_ODC_table[c("region1", "region2", "cell", "chr")]
# List all files in the specified directory for original ODC data
file.names <- list.files(path = ODCs_example_path, full.names = TRUE, recursive = TRUE)
# Loop through each file to read and merge data
for (i in 1:length(file.names)) {
# Read the current file into a data frame
data <- read.delim(file.names[[i]])
names(data) <- c("chr", "region1", "chr2", "region2", paste0("IF_", i))
data <- data[, names(data) %in%
c("chr", "region1", "region2", paste0("IF_", i))]
# Merge the newly read data with the existing scHiC.table_ODC
scHiC.table_ODC <- merge(scHiC.table_ODC, data,
by = c("region1", "region2", "chr"), all = TRUE
)
}
# Create scHiC table object for original MG interaction frequencies (IF)
scHiC.table_MG <- imp_MG_table[c("region1", "region2", "cell", "chr")]
# List all files in the specified directory for original MG data
file.names <- list.files(path = MGs_example_path, full.names = TRUE, recursive = TRUE)
# Loop through each file to read and merge data
for (i in 1:length(file.names)) {
# Read the current file into a data frame
data <- read.delim(file.names[[i]])
names(data) <- c("chr", "region1", "chr2", "region2", paste0("IF_", i))
data <- data[, names(data) %in%
c("chr", "region1", "region2", paste0("IF_", i))]
# Merge the newly read data with the existing scHiC.table_MG
scHiC.table_MG <- merge(scHiC.table_MG, data,
by = c("region1", "region2", "chr"), all = TRUE
)
}
```
``` r
# plot imputed Distance Diagnostic of MG
plot1 <- plot_imputed_distance_diagnostic(
raw_sc_data = scHiC.table_MG,
imp_sc_data = imp_MG_table, D = 1
)
plot2 <- plot_imputed_distance_diagnostic(
raw_sc_data = scHiC.table_MG,
imp_sc_data = imp_MG_table, D = 2
)
plot3 <- plot_imputed_distance_diagnostic(
raw_sc_data = scHiC.table_MG,
imp_sc_data = imp_MG_table, D = 3
)
plot4 <- plot_imputed_distance_diagnostic(
raw_sc_data = scHiC.table_MG,
imp_sc_data = imp_MG_table, D = 4
)
grid.arrange(plot1, plot2, plot3, plot4, ncol = 2, nrow = 2)
```
<img src="man/figures/README-unnamed-chunk-18-1.png" width="100%" />
The diagnostic visualizations demonstrate that with a sample of only 10
single cells per group (note: this small sample size is for
demonstration purposes only), the imputed values for MG closely match
the original distribution only at shorter genomic distances (e.g., D1,
D2). Increasing the number of single cells per group enhances imputation
accuracy across distances. We recommend using a minimum of 80 single
cells per group for optimal imputation performance.
# Session Info
#> R version 4.2.3 (2023-03-15)
#> Platform: x86_64-apple-darwin17.0 (64-bit)
#> Running under: macOS Big Sur ... 10.16
#>
#> Matrix products: default
#> BLAS: /Library/Frameworks/R.framework/Versions/4.2/Resources/lib/libRblas.0.dylib
#> LAPACK: /Library/Frameworks/R.framework/Versions/4.2/Resources/lib/libRlapack.dylib
#>
#> locale:
#> [1] en_US.UTF-8/en_US.UTF-8/en_US.UTF-8/C/en_US.UTF-8/en_US.UTF-8
#>
#> attached base packages:
#> [1] stats graphics grDevices utils datasets methods base
#>
#> other attached packages:
#> [1] data.table_1.16.4 lattice_0.22-6 gridExtra_2.3
#> [4] ggplot2_3.5.1 tidyr_1.3.1 scHiCcompare_0.99.5
#>
#> loaded via a namespace (and not attached):
#> [1] minqa_1.2.6 colorspace_2.1-1
#> [3] CGHcall_2.60.0 mclust_6.0.1
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