fs::dir_create("figures")
+
+
+
+
+
+
+
+Workshop
+Omics 3: Visualising and Interpreting
+Introduction
+Session overview
+In the workshop, you will learn how to merge gene information into our results, conduct and plot a Principle Component Analysis (PCA) as well as how to create a nicely formatted Volcano plot and heatmap.
+Set up
+Either:
+π¬ Open πΈ frogs-88H Project and the cont-fgf-s30.R script.
Or
+π¬ Open π mice-88H Project and the hspc-prog.R script.
π¬ Make a new folder figures in the project directory. You can use the New Folder button in the Files pane but here I have used the fs (Hester, Wickham, and CsΓ‘rdi 2023) package
+
+
+This is where we will save our figure files.
+π¬ Load tidyverse (Wickham et al. 2019) and conflicted (Wickham 2023). You most likely have this code at the top of cont-fgf-s30.R or hspc-prog.R already.
+
+
+ββ Attaching core tidyverse packages βββββββββββββββββββββββββββββββββββββββββββββββ tidyverse 2.0.0 ββ
+β dplyr 1.1.3 β readr 2.1.4
+β forcats 1.0.0 β stringr 1.5.0
+β ggplot2 3.4.3 β tibble 3.2.1
+β lubridate 1.9.3 β tidyr 1.3.0
+β purrr 1.0.2
+ββ Conflicts βββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββ tidyverse_conflicts() ββ
+β dplyr::filter() masks stats::filter()
+β dplyr::lag() masks stats::lag()
+βΉ Use the conflicted package to force all conflicts to become errorsπ¬ Use the dplyr version of filter() by default:
+
+
+conflict_prefer("filter", "dplyr")πΈ Analysis
+We will carry out several steps
+-
+
- Import data and merge statistical results with normalised values +
- Add gene information from Xenbase (Fisher et al. 2023) + +
- log2 transform the data +
- Write the significant genes to file +
- View the relationship between samples using PCA +
- Visualise the expression of the most significant genes using a heatmap +
- Visual all the results with a volcano plot +
Import
+We need to import both the normalised counts and the statistical results. We will need all of these for the visualisation and interpretation.
+π¬ Import files saved from last week from the results folder: S30_normalised_counts.csv and S30_results.csv. I used the names s30_count_norm and s30_results for the dataframes.
+
+
+π¬ Remind yourself what is in the rows and columns and the structure of the dataframes (perhaps using glimpse())
+
+
+
+
+
+
+
+
+
+
+
+#---CODING ANSWER---
+#| echo: false
+#| output: false
+glimpse(s30_count_norm)
+
+Rows: 10,136
+Columns: 7
+$ S30_C_5 <dbl> 228.092879, 480.016357, 111.209463, 48.795989, 439.163β¦
+$ S30_C_6 <dbl> 222.114104, 498.170204, 81.441838, 45.480507, 551.0545β¦
+$ S30_C_A <dbl> 238.647198, 668.212153, 83.141604, 53.118247, 282.5274β¦
+$ S30_F_5 <dbl> 251.794947, 453.047112, 98.328684, 70.759894, 427.3162β¦
+$ S30_F_6 <dbl> 239.567397, 481.986786, 81.757127, 44.681221, 539.9773β¦
+$ S30_F_A <dbl> 245.10704, 607.96159, 62.47827, 36.04515, 279.95069, 1β¦
+$ xenbase_gene_id <chr> "XB-GENE-1000007", "XB-GENE-1000023", "XB-GENE-1000062β¦
+
+
+
+
+
+
+#---CODING ANSWER---
+#| echo: false
+#| output: false
+glimpse(s30_results)
+
+Rows: 10,136
+Columns: 7
+$ baseMean <dbl> 237.553928, 531.565700, 86.392830, 49.813502, 419.9983β¦
+$ log2FoldChange <dbl> 0.096601855, -0.089588528, -0.192811203, -0.008858703,β¦
+$ lfcSE <dbl> 0.2079396, 0.1557384, 0.3253216, 0.4342614, 0.1685420,β¦
+$ stat <dbl> 0.46456683, -0.57525007, -0.59267874, -0.02039947, -0.β¦
+$ pvalue <dbl> 0.64224169, 0.56512218, 0.55339617, 0.98372471, 0.8699β¦
+$ padj <dbl> 0.9998970, 0.9998970, 0.9998970, 0.9998970, 0.9998970,β¦
+$ xenbase_gene_id <chr> "XB-GENE-1000007", "XB-GENE-1000023", "XB-GENE-1000062β¦It is useful to have this information in a single dataframe to which we will add the gene information from xenbase. Having all the information together will make it easier to interpret the results and select genes of interest.
+π¬ Merge the two dataframes:
+
+
+
+# merge the results with the normalised counts
+s30_results <- s30_count_norm |>
+ left_join(s30_results, by = "xenbase_gene_id")This means you have the counts for each sample along with the statistical results for each gene.
+Add gene information from Xenbase
+-
+
I got the information from the Xenbase information pages under Data Reports | Gene Information
+This is listed: Xenbase Gene Product Information [readme] gzipped gpi (tab separated)
+Click on the readme link to see the file format and columns
+I downloaded xenbase.gpi.gz, unzipped it, removed header lines and the Xenopus tropicalis (taxon:8364) entries and saved it as xenbase_info.xlsx
+
If you want to emulate what I did you can use the following commands in the terminal after downloading the file:
+gunzip xenbase.gpi.gz
+less xenbase.gpi
+qgunzip unzips the file and less allows you to view the file. q quits the viewer. You will see the header lines and that the file contains both Xenopus tropicalis and Xenopus laevis. I read the file in with read_tsv (skipping the first header lines) then filtered out the Xenopus tropicalis entries, dropped some columns and saved the file as an excel file.
However, I have already done this for you and saved the file as xenbase_info.xlsx in the meta folder. We will import this file and join it to the results dataframe.
π¬ Load the readxl (Wickham and Bryan 2023) package:
π¬ Import the Xenbase gene information file:
+
+
+
+gene_info <- read_excel("meta/xenbase_info.xlsx") You should view the resulting dataframe to see what information is available. You can use glimpse() or View().
π¬ Merge the gene information with the results:
+
+
+
+# join the gene info with the results
+s30_results <- s30_results |>
+ left_join(gene_info, by = "xenbase_gene_id")We will also find it useful to import the metadata that maps the sample names to treatments. This will allow us to label the samples in the visualisations.
+π¬ Import the metadata that maps the sample names to treatments:
+
+
+
+# Import metadata that maps the sample names to treatments
+meta <- read_table("meta/frog_meta_data.txt")
+row.names(meta) <- meta$sample_id
+# We only need the s30
+meta_s30 <- meta |>
+ dplyr::filter(stage == "stage_30")log2 transform the data
+We use the normalised counts for data visualisations so that the comparisons are meaningful. Since the fold changes are given is log2 it is useful to log2 transform the normalised counts too. We will add columns to the dataframe with these transformed values. Since we have some counts of 0 we will add a tiny amount to avoid -Inf values.
π¬ log2 transform the normalised counts:
+
+
+
+# log2 transform the counts plus a tiny amount to avoid log(0)
+s30_results <- s30_results |>
+ mutate(across(starts_with("s30"),
+ \(x) log2(x + 0.001),
+ .names = "log2_{.col}"))This is a wonderful bit or R wizardy. We are using the across() function to apply a transformation to multiple columns. We have selected all the columns that start with s30. The \(x) is an βanonymousβ function that takes the value of the column and adds 0.001 to it before applying the log2() function. The .names = "log2_{.col}" argument tells across() to name the new columns with the prefix log2_ followed by the original column name. You can read more about across() and anonymous functions from my posit::conf(2023) workshop
I recommend viewing the dataframe to see the new columns.
+We now have dataframe with all the information we need: normalised counts, log2 normalised counts, statistical comparisons with fold changes and p values, and information about the gene other than just the id.
+Write the significant genes to file
+We will create dateframe of the signifcant genes and wrte them to file. These are the files you want to examine in more detail along with the visualisations to select your genes of interest.
+π¬ Create a dataframe of the genes significant at the 0.01 level:
+
+
+
+s30_results_sig0.01 <- s30_results |>
+ filter(padj <= 0.01)π¬ Write the dataframe to file
+
+
+
+#---CODING ANSWER---
+#| echo: false
+#| output: false
+# write to csv file
+write_csv(s30_results_sig0.01,
+ file = "results/s30_results_sig0.01.csv")π¬ Create a dataframe of the genes significant at the 0.05 level and write to file:
+
+
+
+βHow many genes are significant at the 0.01 and 0.05 levels?
+ + + +View the relationship between samples using PCA
+We have 10,136 genes in our dataset. PCA will allow us to plot our samples in the βgene expressionβ space so we can see if FGF-treated sample cluster together and control samples cluster together as we would expect. We do this on the log2 transformed normalised counts.
+Our data have genes in rows and samples in columns which is a common organisation for gene expression data. However, PCA expects samples in rows and genes, the variables, in columns. We can transpose the data to get it in the correct format.
+π¬ Transpose the log2 transformed normalised counts:
+
+
+
+s30_log2_trans <- s30_results |>
+ select(starts_with("log2_")) |>
+ t() |>
+ data.frame()We have used the select() function to select all the columns that start with log2_. We then use the t() function to transpose the dataframe. We then convert the resulting matrix to a dataframe using data.frame(). If you view that dataframe youβll see it has default column name which we can fix using colnames() to set the column names to the Xenbase gene ids.
π¬ Set the column names to the Xenbase gene ids:
+
+
+
+colnames(s30_log2_trans) <- s30_results$xenbase_gene_id㪠Perform PCA on the log2 transformed normalised counts:
+
+
+
+pca <- s30_log2_trans |>
+ prcomp(rank. = 4) The rank. argument tells prcomp() to only calculate the first 4 principal components. This is useful for visualisation as we can only plot in 2 or 3 dimensions. We can see the results of the PCA by viewing the summary() of the pca object.
+
+
+summary(pca)
+
+Importance of first k=4 (out of 6) components:
+ PC1 PC2 PC3 PC4
+Standard deviation 64.0124 47.3351 38.4706 31.4111
+Proportion of Variance 0.4243 0.2320 0.1532 0.1022
+Cumulative Proportion 0.4243 0.6562 0.8095 0.9116The Proportion of Variance tells us how much of the variance is explained by each component. We can see that the first component explains 0.4243 of the variance, the second 0.2320, and the third 0.1532. Together the first three components explain nearly 81% of the total variance in the data. Plotting PC1 against PC2 will capture about 66% of the variance which is likely much better than we would get plotting any two genes against each other. To plot the PC1 against PC2 we will need to extract the PC1 and PC2 score from the pca object and add labels for the samples.
+π¬ Remove log2 from the row names:
+
+
+sample_id <- row.names(s30_log2_trans) |> str_remove("log2_")π¬ Create a dataframe of the PC1 and PC2 scores which are in pca$x and add the sample ids:
+
+
+pca_labelled <- data.frame(pca$x,
+ sample_id)π¬ Merge with the metadata so we can label points by treatment and sibling pair:
+
+
+
+pca_labelled <- pca_labelled |>
+ left_join(meta_s30,
+ by = "sample_id")Since the metadata contained the sample ids, it was especially important to remove the log2_ from the row names so that the join would work. The dataframe should look like this:
+
+
+
+
+
+| PC1 | +PC2 | +PC3 | +PC4 | +sample_id | +stage | +treatment | +sibling_rep | +
|---|---|---|---|---|---|---|---|
| -76.38391 | +0.814699 | +-60.728327 | +-5.820669 | +S30_C_5 | +stage_30 | +control | +five | +
| -67.02571 | +25.668563 | +51.476835 | +28.480254 | +S30_C_6 | +stage_30 | +control | +six | +
| -14.02772 | +-78.474054 | +15.282058 | +-9.213076 | +S30_C_A | +stage_30 | +control | +A | +
| 47.60726 | +49.035510 | +-19.288753 | +20.928290 | +S30_F_5 | +stage_30 | +FGF | +five | +
| 26.04954 | +32.914201 | +20.206072 | +-55.752818 | +S30_F_6 | +stage_30 | +FGF | +six | +
| 83.78054 | +-29.958919 | +-6.947884 | +21.378020 | +S30_F_A | +stage_30 | +FGF | +A | +
π¬ Plot PC1 against PC2 and colour by sibling pair and shape by treatment:
+
+
+
+pca <- pca_labelled |>
+ ggplot(aes(x = PC1, y = PC2,
+ colour = sibling_rep,
+ shape = treatment)) +
+ geom_point(size = 3) +
+ scale_colour_viridis_d(end = 0.95, begin = 0.15,
+ name = "Sibling pair",
+ labels = c("A", ".5", ".6")) +
+ scale_shape_manual(values = c(21, 19),
+ name = NULL,
+ labels = c("Control", "FGF-Treated")) +
+ theme_classic()
+pca
+
+
There is a good separation between treatments on PCA1. The sibling pairs do not seem to cluster together.
+π¬ Save the plot to file:
+
+
+
+ggsave("figures/frog-s30-pca.png",
+ plot = pca,
+ height = 3,
+ width = 4,
+ units = "in",
+ device = "png")Visualise the expression of the most significant genes using a heatmap
+only should do on sig genes. but use the log 2 normalised values
+
+
+
+mat <- s30_results_sig0.01 |>
+ select(starts_with("log2_")) |>
+ as.matrix()
+
+
+
+rownames(mat) <- s30_results_sig0.01$xenbase_gene_symbol
+
+
+n_treatment_clusters <- 2
+n_gene_clusters <- 2
+
+
+heatmaply(mat,
+ scale = "row",
+ hide_colorbar = TRUE,
+ k_col = n_treatment_clusters,
+ k_row = n_gene_clusters,
+ label_names = c("Gene", "Sample", "Expression (normalised, log2)"),
+ fontsize_row = 7, fontsize_col = 10,
+ labCol = str_remove(colnames(mat), pattern = "log2_"),
+ labRow = rownames(mat),
+ heatmap_layers = theme(axis.line = element_blank()))
+
+
+
+Visualise all the results with a volcano plot
+colour the points if padj < 0.05 and log2FoldChange > 1
+ +
+
+
+
+
+
+vol <- s30_results |>
+ ggplot(aes(x = log2FoldChange,
+ y = log10_padj,
+ colour = interaction(sig, bigfc))) +
+ geom_point() +
+ geom_hline(yintercept = -log10(0.05),
+ linetype = "dashed") +
+ geom_vline(xintercept = 2,
+ linetype = "dashed") +
+ geom_vline(xintercept = -2,
+ linetype = "dashed") +
+ scale_x_continuous(expand = c(0, 0)) +
+ scale_y_continuous(expand = c(0, 0)) +
+ scale_colour_manual(values = c("gray",
+ "pink",
+ "gray30",
+ "deeppink")) +
+ geom_text_repel(data = subset(s30_results,
+ bigfc & sig),
+ aes(label = xenbase_gene_symbol),
+ size = 3,
+ max.overlaps = 50) +
+ theme_classic() +
+ theme(legend.position = "none")
+
+
+ggsave("figures/frog-s30-volcano.png",
+ plot = vol,
+ height = 4.5,
+ width = 4.5,
+ units = "in",
+ device = "png")π Analysis
+We will carry out several steps
+-
+
- Import data and merge statistical results with normalised values +
- Add gene information from the NCBI using biomaRt +
- Write the significant genes to file +
- View the relationship between cells using PCA +
- Visualise the expression of the most significant genes using a heatmap +
- Visual all the results with a volcano plot +
Import
+We need to import both the normalised counts and the statistical results. We will need all of these for the visualisation and interpretation.
+π¬ Import the normalised counts for the Prog and HSPC cell types. I used the names prog and hspc for the dataframes.
+
+
+π¬ Combine the two dataframes (minus one set of gene ids) into one dataframe called prog_hspc:
+
+
+
+# combine into one dataframe dropping one of the gene id columns
+prog_hspc <- bind_cols(prog, hspc[-1])π¬ Import the statistical results in results/prog_hspc_results.csv. I used the name prog_hspc_results for the dataframe.
+
+
+π¬ Remind yourself what is in the rows and columns and the structure of the dataframes (perhaps using glimpse())
+
+
+
+
+#---CODING ANSWER---
+#| echo: false
+#| output: false
+glimpse(prog_hspc)
+
+Rows: 280
+Columns: 1,500
+$ ensembl_gene_id <chr> "ENSMUSG00000004730", "ENSMUSG00000027962", "ENSMUSG00β¦
+$ Prog_001 <dbl> 0.000000, 0.000000, 2.447692, 0.000000, 2.447692, 1.07β¦
+$ Prog_002 <dbl> 0.0000000, 0.7859542, 9.8669873, 0.0000000, 7.5139828,β¦
+$ Prog_003 <dbl> 0.000000, 1.049924, 9.466541, 0.000000, 7.636827, 1.04β¦
+$ Prog_004 <dbl> 1.032808, 0.000000, 2.639234, 0.000000, 2.639234, 0.00β¦
+$ Prog_006 <dbl> 0.0000000, 0.9376688, 8.9509200, 0.0000000, 0.5437090,β¦
+$ Prog_007 <dbl> 0.0000000, 0.7008173, 2.2487025, 0.0000000, 2.0451378,β¦
+$ Prog_008 <dbl> 0.0000000, 0.0000000, 9.8216688, 0.0000000, 7.9747826,β¦
+$ Prog_009 <dbl> 0.0000000, 0.0000000, 10.3888553, 0.0000000, 4.4437936β¦
+$ Prog_010 <dbl> 0.000000, 0.000000, 3.277715, 1.453985, 6.670995, 1.45β¦
+$ Prog_011 <dbl> 0.000000, 0.000000, 9.329603, 0.000000, 1.756729, 1.13β¦
+$ Prog_012 <dbl> 1.909353, 1.909353, 3.588040, 0.000000, 0.000000, 0.00β¦
+$ Prog_013 <dbl> 0.0000000, 1.2104051, 0.7285849, 4.6985794, 7.8677891,β¦
+$ Prog_014 <dbl> 0.0000000, 0.0000000, 8.6212214, 0.0000000, 2.4391238,β¦
+$ Prog_015 <dbl> 0.0000000, 0.9646149, 1.5375869, 0.0000000, 0.0000000,β¦
+$ Prog_016 <dbl> 0.000000, 0.000000, 9.604794, 0.000000, 8.631105, 0.00β¦
+$ Prog_017 <dbl> 0.0000000, 0.6852295, 1.4976754, 0.0000000, 5.5232130,β¦
+$ Prog_018 <dbl> 0.000000, 0.000000, 8.815843, 0.000000, 1.775663, 0.00β¦
+$ Prog_019 <dbl> 0.0000000, 1.2988288, 0.7908933, 0.0000000, 4.5175504,β¦
+$ Prog_020 <dbl> 0.000000, 0.000000, 10.912794, 0.000000, 1.588903, 1.0β¦
+$ Prog_021 <dbl> 0.000000, 0.000000, 7.638658, 0.000000, 0.000000, 1.08β¦
+$ Prog_022 <dbl> 0.000000, 0.000000, 8.671409, 0.000000, 0.000000, 0.00β¦
+$ Prog_023 <dbl> 0.0000000, 2.1551569, 1.6194142, 0.0000000, 1.9120124,β¦
+$ Prog_024 <dbl> 1.717498, 0.000000, 9.023824, 0.000000, 7.928356, 0.00β¦
+$ Prog_025 <dbl> 0.000000, 2.368099, 8.553185, 0.000000, 5.413663, 1.62β¦
+$ Prog_026 <dbl> 0.000000, 0.000000, 3.648527, 1.190477, 1.190477, 0.00β¦
+$ Prog_027 <dbl> 0.0000000, 0.0000000, 0.8557008, 0.0000000, 1.3891677,β¦
+$ Prog_028 <dbl> 0.0000000, 0.0000000, 9.9095248, 0.0000000, 8.1128539,β¦
+$ Prog_029 <dbl> 1.152871, 1.152871, 5.870544, 0.000000, 3.060282, 0.00β¦
+$ Prog_030 <dbl> 0.000000, 2.598365, 9.181785, 2.127853, 8.651444, 0.00β¦
+$ Prog_031 <dbl> 0.0000000, 0.8413201, 9.2314616, 0.8413201, 2.5235954,β¦
+$ Prog_032 <dbl> 0.000000, 1.327820, 9.568213, 0.000000, 7.984181, 0.00β¦
+$ Prog_033 <dbl> 0.0000000, 1.3828699, 9.7312399, 0.0000000, 1.3828699,β¦
+$ Prog_035 <dbl> 0.0000000, 1.3171343, 9.3029109, 0.0000000, 6.4998843,β¦
+$ Prog_036 <dbl> 0.000000, 1.499263, 9.081582, 0.000000, 3.054489, 0.00β¦
+$ Prog_037 <dbl> 0.000000, 1.042273, 7.977819, 0.000000, 8.941148, 0.00β¦
+$ Prog_038 <dbl> 0.000000, 1.602107, 10.272361, 0.000000, 1.012878, 1.0β¦
+$ Prog_039 <dbl> 0.0000000, 0.0000000, 8.7123610, 0.0000000, 7.5301015,β¦
+$ Prog_040 <dbl> 0.000000, 0.000000, 2.054034, 8.442082, 2.054034, 1.36β¦
+$ Prog_042 <dbl> 0.000000, 0.000000, 10.345104, 1.507712, 1.507712, 0.0β¦
+$ Prog_043 <dbl> 0.0000000, 0.8515947, 10.7190561, 0.0000000, 1.3834907β¦
+$ Prog_044 <dbl> 0.000000, 1.139041, 1.767524, 1.139041, 5.258244, 0.00β¦
+$ Prog_045 <dbl> 0.6854953, 0.6854953, 9.9645500, 0.0000000, 8.6240290,β¦
+$ Prog_046 <dbl> 0.000000, 0.000000, 9.450093, 0.000000, 1.866185, 0.91β¦
+$ Prog_047 <dbl> 0.000000, 8.678573, 2.850378, 1.165030, 3.874419, 1.16β¦
+$ Prog_048 <dbl> 0.000000, 0.000000, 2.794052, 0.000000, 1.825335, 1.82β¦
+$ Prog_049 <dbl> 0.0000000, 0.6579981, 9.3946513, 0.0000000, 4.7857083,β¦
+$ Prog_050 <dbl> 0.0000000, 0.8386825, 2.0543847, 0.0000000, 6.6143445,β¦
+$ Prog_051 <dbl> 0.000000, 0.000000, 10.468034, 0.000000, 1.066147, 2.0β¦
+$ Prog_052 <dbl> 0.000000, 2.361305, 4.133679, 0.000000, 8.233765, 1.61β¦
+$ Prog_053 <dbl> 0.9224419, 0.9224419, 9.2857331, 0.0000000, 1.8820411,β¦
+$ Prog_055 <dbl> 0.0000000, 0.0000000, 3.4913807, 0.0000000, 6.6568051,β¦
+$ Prog_056 <dbl> 0.000000, 0.000000, 9.725035, 0.000000, 8.116732, 0.00β¦
+$ Prog_057 <dbl> 0.5967097, 0.0000000, 2.3499624, 0.0000000, 2.0262980,β¦
+$ Prog_058 <dbl> 0.000000, 0.000000, 10.114434, 0.000000, 5.739715, 0.0β¦
+$ Prog_059 <dbl> 0.000000, 2.038654, 8.871380, 0.000000, 7.819265, 1.02β¦
+$ Prog_060 <dbl> 0.000000, 1.776961, 9.102002, 0.000000, 2.549440, 1.14β¦
+$ Prog_061 <dbl> 0.0000000, 0.8198795, 10.4280461, 0.0000000, 1.3394322β¦
+$ Prog_062 <dbl> 0.000000, 0.000000, 9.964751, 0.000000, 5.990110, 0.00β¦
+$ Prog_063 <dbl> 0.000000, 8.002331, 2.337480, 1.597934, 3.477092, 0.00β¦
+$ Prog_064 <dbl> 0.000000, 1.007715, 10.123899, 1.007715, 6.687664, 0.0β¦
+$ Prog_065 <dbl> 0.0000000, 0.7570004, 2.1537620, 0.0000000, 8.4055113,β¦
+$ Prog_066 <dbl> 0.000000, 0.000000, 6.895361, 0.000000, 2.160890, 0.00β¦
+$ Prog_067 <dbl> 0.000000, 0.000000, 9.037415, 0.000000, 1.747210, 2.18β¦
+$ Prog_068 <dbl> 0.000000, 0.000000, 1.706107, 0.000000, 7.498985, 0.00β¦
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+$ Prog_733 <dbl> 0.8753909, 1.4163048, 2.5866519, 0.0000000, 2.1170368,β¦
+$ Prog_734 <dbl> 0.000000, 0.000000, 9.663944, 0.000000, 4.813194, 0.00β¦
+$ Prog_735 <dbl> 0.0000000, 0.0000000, 0.8639745, 0.0000000, 0.8639745,β¦
+$ Prog_736 <dbl> 0.0000000, 0.6604615, 0.6604615, 0.0000000, 4.2477932,β¦
+$ Prog_737 <dbl> 0.000000, 2.165385, 1.732880, 0.000000, 10.736052, 2.1β¦
+$ Prog_738 <dbl> 0.000000, 2.017320, 1.335801, 1.335801, 3.342687, 0.00β¦
+$ Prog_739 <dbl> 0.000000, 1.906558, 1.247665, 0.000000, 1.247665, 0.00β¦
+$ Prog_740 <dbl> 0.000000, 0.000000, 2.921112, 0.000000, 1.674204, 0.00β¦
+$ Prog_743 <dbl> 0.0000000, 0.0000000, 0.0000000, 0.0000000, 7.6795528,β¦
+$ Prog_744 <dbl> 0.0000000, 1.5756644, 0.0000000, 0.0000000, 8.0084521,β¦
+$ Prog_745 <dbl> 0.000000, 1.167434, 1.804151, 0.000000, 3.455353, 0.00β¦
+$ Prog_746 <dbl> 0.000000, 0.000000, 9.257702, 0.000000, 0.000000, 0.00β¦
+$ Prog_747 <dbl> 0.000000, 0.000000, 2.651195, 0.000000, 1.214416, 2.92β¦
+$ Prog_748 <dbl> 0.000000, 0.000000, 1.912066, 0.000000, 1.912066, 0.00β¦
+$ Prog_749 <dbl> 0.000000, 0.000000, 7.907326, 0.000000, 7.494291, 0.00β¦
+$ Prog_750 <dbl> 0.000000, 0.000000, 0.000000, 0.000000, 0.000000, 0.00β¦
+$ Prog_751 <dbl> 0.000000, 0.000000, 9.567823, 0.000000, 8.062315, 1.43β¦
+$ Prog_752 <dbl> 0.000000, 1.088315, 8.584688, 0.000000, 1.088315, 2.13β¦
+$ Prog_753 <dbl> 0.4546240, 0.0000000, 1.3113301, 0.0000000, 1.0781157,β¦
+$ Prog_754 <dbl> 2.5350590, 0.9045812, 1.2066442, 0.0000000, 7.1346333,β¦
+$ Prog_757 <dbl> 0.000000, 0.000000, 8.521070, 0.000000, 3.008178, 0.00β¦
+$ Prog_758 <dbl> 0.000000, 1.027425, 10.650493, 0.000000, 6.577320, 0.0β¦
+$ Prog_759 <dbl> 0.0000000, 0.0000000, 1.1091425, 0.0000000, 6.6345901,β¦
+$ Prog_760 <dbl> 0.0000000, 7.3793575, 1.9694755, 0.7899915, 1.6722863,β¦
+$ Prog_761 <dbl> 0.000000, 1.623226, 2.856367, 0.000000, 8.266286, 1.02β¦
+$ Prog_762 <dbl> 0.0000000, 0.6583874, 1.1087820, 0.0000000, 7.1799196,β¦
+$ Prog_763 <dbl> 0.5774134, 0.5774134, 0.5774134, 0.0000000, 8.7733244,β¦
+$ Prog_764 <dbl> 0.0000000, 0.0000000, 2.9788233, 0.0000000, 3.5627696,β¦
+$ Prog_765 <dbl> 0.4887321, 6.8867263, 1.5926631, 0.0000000, 7.2306270,β¦
+$ Prog_767 <dbl> 0.0000000, 0.0000000, 9.0647725, 0.0000000, 9.5066596,β¦
+$ Prog_768 <dbl> 0.0000000, 0.8028968, 1.6932313, 0.0000000, 7.9467204,β¦
+$ Prog_769 <dbl> 0.0000000, 0.0000000, 1.8636357, 0.0000000, 2.8396004,β¦
+$ Prog_770 <dbl> 1.022676, 0.000000, 10.140358, 1.022676, 5.744589, 1.0β¦
+$ Prog_771 <dbl> 0.000000, 0.000000, 7.102581, 0.000000, 4.293110, 0.00β¦
+$ Prog_772 <dbl> 0.9806377, 0.9806377, 2.7740015, 0.0000000, 5.4537430,β¦
+$ Prog_774 <dbl> 0.000000, 0.000000, 1.939114, 0.000000, 6.398148, 1.09β¦
+$ Prog_775 <dbl> 0.0000000, 1.2167722, 1.8673123, 0.0000000, 2.4943937,β¦
+$ Prog_776 <dbl> 0.6768304, 0.0000000, 9.7760819, 0.0000000, 4.9786447,β¦
+$ Prog_777 <dbl> 0.0000000, 0.9423675, 1.5075959, 0.0000000, 0.9423675,β¦
+$ Prog_778 <dbl> 0.000000, 0.000000, 8.986217, 0.000000, 8.551634, 0.00β¦
+$ Prog_779 <dbl> 0.4211472, 0.4211472, 2.1341941, 0.0000000, 1.4302634,β¦
+$ Prog_780 <dbl> 0.5131073, 0.5131073, 9.3775848, 0.8908289, 7.1492370,β¦
+$ Prog_781 <dbl> 0.000000, 1.080345, 0.000000, 0.000000, 2.448417, 1.08β¦
+$ Prog_782 <dbl> 0.000000, 0.774577, 2.578895, 5.923573, 2.186957, 1.64β¦
+$ Prog_783 <dbl> 1.074572, 0.000000, 10.556887, 0.000000, 7.781406, 1.6β¦
+$ Prog_784 <dbl> 0.000000, 0.000000, 2.729708, 4.454398, 9.011330, 0.00β¦
+$ Prog_785 <dbl> 0.000000, 0.000000, 7.680402, 0.000000, 3.650143, 0.00β¦
+$ Prog_786 <dbl> 0.8739354, 0.0000000, 0.8739354, 0.8739354, 1.4143035,β¦
+$ Prog_787 <dbl> 1.738193, 0.000000, 3.370817, 0.000000, 9.072318, 1.73β¦
+$ Prog_788 <dbl> 0.7368005, 1.2221566, 9.1819824, 0.0000000, 8.2710517,β¦
+$ Prog_789 <dbl> 0.0000000, 6.2993373, 3.2689842, 0.0000000, 2.9839948,β¦
+$ Prog_790 <dbl> 0.641878, 0.000000, 11.027752, 0.641878, 1.926681, 1.6β¦
+$ Prog_791 <dbl> 7.354611, 0.888815, 3.115182, 0.000000, 4.584642, 0.00β¦
+$ Prog_792 <dbl> 0.0000000, 0.5602293, 1.7538261, 0.0000000, 7.1441796,β¦
+$ Prog_793 <dbl> 0.0000000, 0.6100055, 0.6100055, 0.6100055, 8.3024400,β¦
+$ Prog_794 <dbl> 0.0000000, 1.2839055, 7.7226264, 1.6564775, 9.9829054,β¦
+$ Prog_795 <dbl> 0.0000000, 0.8871069, 2.1367998, 0.0000000, 7.9894805,β¦
+$ Prog_796 <dbl> 0.000000, 0.000000, 2.296474, 0.000000, 6.034682, 0.00β¦
+$ Prog_797 <dbl> 0.000000, 0.000000, 1.464793, 2.176476, 3.531249, 0.00β¦
+$ Prog_798 <dbl> 0.0000000, 0.8285245, 1.7344840, 8.4849731, 2.1671674,β¦
+$ Prog_799 <dbl> 0.000000, 4.860757, 0.000000, 0.000000, 7.665351, 1.26β¦
+$ Prog_800 <dbl> 0.000000, 8.803266, 2.829021, 0.000000, 2.829021, 0.00β¦
+$ Prog_801 <dbl> 0.5808097, 0.0000000, 1.5766449, 3.4480774, 8.7052117,β¦
+$ Prog_802 <dbl> 0.000000, 1.898890, 8.412752, 0.000000, 8.778230, 0.00β¦
+$ Prog_803 <dbl> 0.000000, 2.543597, 7.878204, 0.000000, 3.708852, 0.00β¦
+$ Prog_804 <dbl> 0.000000, 0.000000, 9.348673, 1.233011, 2.954727, 0.00β¦
+$ Prog_805 <dbl> 0.000000, 0.000000, 8.315664, 0.000000, 9.369724, 0.00β¦
+$ Prog_806 <dbl> 0.000000, 0.935748, 0.935748, 0.935748, 7.896934, 0.00β¦
+$ Prog_807 <dbl> 0.0000000, 0.0000000, 8.6811767, 0.0000000, 8.1350692,β¦
+$ Prog_808 <dbl> 0.0000000, 0.0000000, 3.0377707, 0.0000000, 1.6615960,β¦
+$ Prog_809 <dbl> 0.6287654, 0.0000000, 2.2701368, 0.6287654, 1.6712775,β¦
+$ Prog_810 <dbl> 0.0000000, 0.5049969, 1.1746370, 0.0000000, 7.3167564,β¦
+$ Prog_811 <dbl> 0.000000, 1.329155, 9.629477, 0.000000, 5.626490, 0.00β¦
+$ Prog_812 <dbl> 0.000000, 3.245813, 9.354092, 0.000000, 7.095686, 0.00β¦
+$ Prog_813 <dbl> 0.0000000, 0.8803957, 10.2579542, 0.0000000, 5.5099063β¦
+$ Prog_814 <dbl> 0.0000000, 0.0000000, 9.3443362, 0.8521854, 2.7304517,β¦
+$ Prog_815 <dbl> 0.000000, 0.000000, 9.145702, 0.000000, 1.640454, 1.04β¦
+$ Prog_816 <dbl> 0.0000000, 1.5005517, 7.5725424, 0.0000000, 8.4454565,β¦
+$ Prog_817 <dbl> 0.000000, 0.617522, 1.876247, 0.000000, 1.876247, 0.61β¦
+$ Prog_818 <dbl> 0.000000, 0.000000, 8.817434, 0.000000, 5.110650, 0.00β¦
+$ Prog_819 <dbl> 0.0000000, 0.0000000, 9.9789196, 0.0000000, 7.2226335,β¦
+$ Prog_820 <dbl> 0.0000000, 0.0000000, 7.8202471, 0.6094958, 6.5794013,β¦
+$ Prog_821 <dbl> 0.000000, 0.527402, 9.347671, 0.000000, 7.134023, 0.00β¦
+$ Prog_822 <dbl> 0.000000, 0.000000, 10.830559, 0.000000, 5.611126, 0.7β¦
+$ Prog_823 <dbl> 0.000000, 2.368033, 6.108218, 0.000000, 3.421181, 0.00β¦
+$ Prog_824 <dbl> 0.0000000, 0.0000000, 3.2970935, 0.0000000, 7.2393470,β¦
+$ Prog_825 <dbl> 0.614008, 0.000000, 9.102087, 0.000000, 7.067777, 0.61β¦
+$ Prog_826 <dbl> 0.0000000, 0.0000000, 10.0184296, 0.0000000, 0.8930072β¦
+$ Prog_827 <dbl> 0.000000, 1.153240, 9.651103, 0.000000, 2.224160, 0.00β¦
+$ Prog_828 <dbl> 0.0000000, 0.0000000, 1.4730404, 0.0000000, 7.1366525,β¦
+$ Prog_829 <dbl> 0.000000, 0.000000, 2.002737, 0.679441, 6.402776, 0.00β¦
+$ Prog_830 <dbl> 0.0000000, 0.0000000, 9.9350866, 0.7122405, 2.0675466,β¦
+$ Prog_831 <dbl> 0.0000000, 0.7518682, 8.8581337, 0.0000000, 1.2436351,β¦
+$ Prog_832 <dbl> 0.0000000, 0.9591086, 1.9382199, 0.0000000, 7.2304444,β¦
+$ Prog_833 <dbl> 0.0000000, 0.8376881, 3.0151862, 0.0000000, 3.0151862,β¦
+$ Prog_834 <dbl> 0.0000000, 0.0000000, 2.4274006, 0.0000000, 5.4373805,β¦
+$ Prog_835 <dbl> 0.0000000, 0.9809832, 10.5344381, 0.0000000, 2.5531271β¦
+$ Prog_836 <dbl> 0.0000000, 0.5020465, 1.2967651, 0.5020465, 1.5225555,β¦
+$ Prog_837 <dbl> 0.0000000, 0.9850818, 9.8963349, 0.0000000, 0.0000000,β¦
+$ Prog_838 <dbl> 0.000000, 0.000000, 9.547417, 0.000000, 1.987452, 1.31β¦
+$ Prog_839 <dbl> 0.0000000, 0.0000000, 8.0095143, 0.0000000, 6.1786824,β¦
+$ Prog_840 <dbl> 0.0000000, 0.6485416, 2.4700583, 0.0000000, 8.4397289,β¦
+$ Prog_841 <dbl> 0.000000, 2.018049, 9.332316, 0.000000, 6.751711, 0.00β¦
+$ Prog_842 <dbl> 0.0000000, 0.0000000, 8.9760410, 0.0000000, 6.6732008,β¦
+$ Prog_843 <dbl> 0.0000000, 0.0000000, 2.4085725, 0.0000000, 3.5947323,β¦
+$ Prog_844 <dbl> 1.153513, 1.153513, 10.215305, 0.000000, 2.832433, 0.0β¦
+$ Prog_845 <dbl> 0.0000000, 0.0000000, 1.5265633, 0.0000000, 5.0433788,β¦
+$ Prog_846 <dbl> 0.000000, 0.000000, 2.924854, 2.924854, 7.842922, 1.67β¦
+$ Prog_847 <dbl> 0.0000000, 0.8935156, 2.1475639, 0.8935156, 8.6586321,β¦
+$ Prog_848 <dbl> 0.000000, 0.000000, 9.603595, 0.000000, 3.859249, 0.00β¦
+$ Prog_849 <dbl> 1.653308, 2.403562, 4.344108, 0.000000, 2.403562, 1.65β¦
+$ Prog_850 <dbl> 0.000000, 0.000000, 9.300996, 0.000000, 7.843614, 0.00β¦
+$ Prog_851 <dbl> 0.000000, 1.120675, 9.108092, 0.000000, 7.050312, 1.12β¦
+$ Prog_852 <dbl> 0.000000, 0.000000, 9.579540, 0.000000, 3.070503, 0.00β¦
+$ HSPC_001 <dbl> 0.0000000, 0.0000000, 0.7390988, 0.7390988, 1.2254389,β¦
+$ HSPC_002 <dbl> 0.000000, 0.000000, 2.238601, 0.000000, 2.238601, 0.00β¦
+$ HSPC_003 <dbl> 0.0000000, 0.0000000, 0.9929154, 0.9929154, 1.5755086,β¦
+$ HSPC_004 <dbl> 0.000000, 0.000000, 2.465632, 0.000000, 8.073635, 0.00β¦
+$ HSPC_006 <dbl> 0.000000, 0.000000, 1.941849, 0.000000, 1.941849, 0.00β¦
+$ HSPC_008 <dbl> 0.000000, 1.395221, 0.000000, 0.000000, 0.000000, 0.00β¦
+$ HSPC_009 <dbl> 0.000000, 1.684562, 2.934193, 0.000000, 5.635680, 0.00β¦
+$ HSPC_011 <dbl> 1.237406, 0.000000, 2.685036, 0.000000, 1.237406, 2.34β¦
+$ HSPC_012 <dbl> 0.000000, 0.000000, 2.517338, 0.000000, 7.378370, 1.74β¦
+$ HSPC_014 <dbl> 0.000000, 0.000000, 0.000000, 0.000000, 1.857888, 0.00β¦
+$ HSPC_015 <dbl> 0.000000, 2.398869, 0.000000, 7.717134, 4.177566, 2.39β¦
+$ HSPC_016 <dbl> 0.0000000, 0.9487581, 2.2390441, 0.0000000, 0.9487581,β¦
+$ HSPC_017 <dbl> 0.000000, 0.000000, 0.000000, 0.000000, 4.146951, 0.00β¦
+$ HSPC_018 <dbl> 0.000000, 1.248476, 2.701241, 0.000000, 8.633940, 1.24β¦
+$ HSPC_020 <dbl> 0.000000, 0.000000, 2.277106, 0.000000, 2.277106, 6.73β¦
+$ HSPC_021 <dbl> 0.000000, 0.000000, 2.996123, 0.000000, 8.043618, 2.49β¦
+$ HSPC_022 <dbl> 0.000000, 1.211071, 1.860045, 1.211071, 7.334868, 8.67β¦
+$ HSPC_023 <dbl> 0.000000, 0.000000, 1.539553, 0.000000, 9.321612, 1.53β¦
+$ HSPC_024 <dbl> 0.000000, 0.000000, 1.692191, 0.000000, 9.143541, 0.00β¦
+$ HSPC_025 <dbl> 1.571690, 0.000000, 3.152201, 8.738315, 1.571690, 0.00β¦
+$ HSPC_026 <dbl> 0.000000, 0.000000, 1.384631, 0.000000, 1.384631, 0.00β¦
+$ HSPC_027 <dbl> 0.0000000, 0.0000000, 0.0000000, 0.9302884, 7.0772133,β¦
+$ HSPC_028 <dbl> 0.0000000, 0.8288203, 0.8288203, 0.0000000, 1.7349575,β¦
+$ HSPC_030 <dbl> 0.000000, 1.118674, 1.118674, 0.000000, 5.508301, 0.00β¦
+$ HSPC_031 <dbl> 0.0000000, 0.0000000, 2.9918679, 0.0000000, 9.6855069,β¦
+$ HSPC_033 <dbl> 0.000000, 0.000000, 1.303195, 0.000000, 1.303195, 0.00β¦
+$ HSPC_034 <dbl> 0.0000000, 1.3093499, 2.6262158, 0.7983817, 8.3884282,β¦
+$ HSPC_035 <dbl> 0.000000, 2.175011, 0.000000, 0.000000, 2.649348, 0.00β¦
+$ HSPC_036 <dbl> 0.0000000, 0.0000000, 2.1381879, 5.5782959, 8.5678887,β¦
+$ HSPC_037 <dbl> 0.000000, 1.516975, 2.239950, 0.000000, 3.365905, 0.00β¦
+$ HSPC_038 <dbl> 0.000000, 0.000000, 1.364250, 1.364250, 0.000000, 0.00β¦
+$ HSPC_040 <dbl> 0.0000000, 1.5383598, 1.9474646, 9.3621654, 8.6231804,β¦
+$ HSPC_041 <dbl> 0.000000, 0.000000, 2.579199, 2.579199, 6.743574, 0.00β¦
+$ HSPC_042 <dbl> 0.0000000, 1.4051125, 1.7960064, 0.0000000, 0.8672577,β¦
+$ HSPC_043 <dbl> 0.000000, 0.000000, 3.553494, 1.341668, 6.491814, 7.93β¦
+$ HSPC_044 <dbl> 0.000000, 0.000000, 2.582992, 0.000000, 0.000000, 0.00β¦
+$ HSPC_045 <dbl> 0.000000, 0.000000, 1.346994, 0.000000, 0.000000, 2.03β¦
+$ HSPC_046 <dbl> 0.0000000, 0.8452114, 1.3746533, 0.0000000, 6.7513398,β¦
+$ HSPC_047 <dbl> 0.000000, 8.428296, 4.239537, 0.000000, 3.552610, 2.19β¦
+$ HSPC_048 <dbl> 0.000000, 1.108133, 1.727411, 8.235885, 6.865010, 2.98β¦
+$ HSPC_049 <dbl> 0.000000, 0.000000, 2.394418, 6.252069, 1.274540, 1.94β¦
+$ HSPC_050 <dbl> 0.000000, 0.000000, 3.086078, 0.000000, 6.466053, 0.00β¦
+$ HSPC_051 <dbl> 0.0000000, 0.0000000, 1.9634358, 0.0000000, 0.0000000,β¦
+$ HSPC_052 <dbl> 0.000000, 7.749301, 2.709016, 1.509063, 1.509063, 0.00β¦
+$ HSPC_053 <dbl> 0.0000000, 0.0000000, 2.4796614, 0.0000000, 5.3728144,β¦
+$ HSPC_054 <dbl> 0.000000, 0.000000, 1.158501, 0.000000, 2.231666, 1.15β¦
+$ HSPC_055 <dbl> 0.000000, 1.797473, 3.075245, 0.000000, 3.446842, 0.00β¦
+$ HSPC_056 <dbl> 0.000000, 2.016637, 3.720889, 0.000000, 8.325851, 6.21β¦
+$ HSPC_057 <dbl> 0.000000, 0.000000, 1.847003, 0.000000, 8.239896, 7.42β¦
+$ HSPC_058 <dbl> 1.398955, 0.000000, 3.199362, 0.000000, 2.916174, 0.00β¦
+$ HSPC_060 <dbl> 0.000000, 1.080287, 2.118815, 0.000000, 6.512085, 1.08β¦
+$ HSPC_061 <dbl> 0.000000, 1.725558, 2.985726, 0.000000, 1.725558, 2.48β¦
+$ HSPC_062 <dbl> 0.000000, 0.000000, 2.211545, 0.000000, 0.000000, 0.00β¦
+$ HSPC_063 <dbl> 0.000000, 1.514955, 2.237502, 0.000000, 1.514955, 2.23β¦
+$ HSPC_064 <dbl> 0.000000, 0.000000, 1.718347, 0.000000, 8.222925, 1.10β¦
+$ HSPC_065 <dbl> 0.0000000, 0.0000000, 0.9703625, 0.0000000, 2.2742114,β¦
+$ HSPC_066 <dbl> 0.000000, 0.000000, 2.564196, 5.716981, 9.399772, 1.78β¦
+$ HSPC_067 <dbl> 0.000000, 0.000000, 2.147724, 0.000000, 9.138862, 5.93β¦
+$ HSPC_068 <dbl> 0.000000, 1.870770, 2.658681, 0.000000, 0.000000, 0.00β¦
+$ HSPC_069 <dbl> 0.000000, 1.116169, 1.737865, 7.866496, 3.791268, 8.80β¦
+$ HSPC_070 <dbl> 0.0000000, 0.0000000, 1.4430580, 0.8949015, 4.5972951,β¦
+$ HSPC_071 <dbl> 0.0000000, 0.9271506, 0.0000000, 0.0000000, 1.8892984,β¦
+$ HSPC_072 <dbl> 1.744738, 0.000000, 0.000000, 0.000000, 7.077098, 0.00β¦
+$ HSPC_073 <dbl> 0.000000, 0.000000, 4.134335, 0.000000, 3.387315, 0.00β¦
+$ HSPC_074 <dbl> 0.000000, 0.000000, 1.703855, 0.000000, 3.326366, 1.70β¦
+$ HSPC_075 <dbl> 1.674178, 0.000000, 4.030303, 0.000000, 9.381928, 8.86β¦
+$ HSPC_076 <dbl> 0.000000, 0.000000, 2.821284, 0.000000, 6.891389, 1.14β¦
+$ HSPC_077 <dbl> 0.000000, 0.000000, 1.114630, 0.000000, 8.460932, 0.00β¦
+$ HSPC_078 <dbl> 0.000000, 2.209396, 4.387948, 0.000000, 6.627462, 2.68β¦
+$ HSPC_079 <dbl> 0.000000, 0.000000, 4.095390, 0.000000, 2.076810, 0.00β¦
+$ HSPC_080 <dbl> 0.000000, 1.012596, 2.828881, 0.000000, 1.012596, 0.00β¦
+$ HSPC_081 <dbl> 0.0000000, 1.2652832, 1.2652832, 0.0000000, 5.3328809,β¦
+$ HSPC_082 <dbl> 0.000000, 0.000000, 4.421943, 0.000000, 1.970627, 0.00β¦
+$ HSPC_083 <dbl> 1.895620, 0.000000, 4.114776, 0.000000, 10.864775, 7.8β¦
+$ HSPC_084 <dbl> 0.000000, 0.000000, 3.216417, 0.000000, 4.036024, 0.00β¦
+$ HSPC_085 <dbl> 0.000000, 0.000000, 1.934463, 0.000000, 0.000000, 1.93β¦
+$ HSPC_087 <dbl> 0.000000, 0.000000, 1.859256, 0.000000, 8.387078, 7.44β¦
+$ HSPC_088 <dbl> 0.000000, 0.000000, 2.091761, 1.061818, 1.666812, 0.00β¦
+$ HSPC_089 <dbl> 0.000000, 0.000000, 1.542804, 0.000000, 5.429591, 0.00β¦
+$ HSPC_090 <dbl> 0.0000000, 0.9583485, 0.0000000, 0.9583485, 7.8106423,β¦
+$ HSPC_094 <dbl> 0.000000, 1.001307, 3.002286, 0.000000, 1.001307, 0.00β¦
+$ HSPC_095 <dbl> 0.000000, 2.055264, 3.768162, 0.000000, 5.497828, 0.00β¦
+$ HSPC_096 <dbl> 0.000000, 0.000000, 3.020317, 0.000000, 4.694719, 0.00β¦
+$ HSPC_098 <dbl> 0.000000, 0.000000, 4.033084, 0.000000, 3.353704, 0.00β¦
+$ HSPC_099 <dbl> 0.000000, 0.000000, 1.355566, 8.533241, 1.355566, 7.54β¦
+$ HSPC_100 <dbl> 0.000000, 1.117108, 2.504994, 0.000000, 1.117108, 0.00β¦
+$ HSPC_101 <dbl> 0.000000, 1.007084, 3.182495, 0.000000, 6.058315, 0.00β¦
+$ HSPC_102 <dbl> 0.000000, 1.110882, 2.992525, 0.000000, 1.110882, 6.01β¦
+$ HSPC_103 <dbl> 0.000000, 0.000000, 3.444022, 3.444022, 3.444022, 6.84β¦
+$ HSPC_104 <dbl> 0.000000, 0.000000, 2.720362, 0.000000, 5.326705, 0.00β¦
+$ HSPC_105 <dbl> 0.000000, 0.000000, 2.953351, 0.000000, 2.128535, 0.00β¦
+$ HSPC_106 <dbl> 0.000000, 0.000000, 2.917053, 8.830809, 10.056331, 0.0β¦
+$ HSPC_107 <dbl> 0.000000, 1.539035, 2.266637, 1.539035, 2.266637, 0.00β¦
+$ HSPC_108 <dbl> 0.000000, 0.000000, 2.342599, 1.237188, 9.967793, 0.00β¦
+$ HSPC_109 <dbl> 0.000000, 1.595174, 3.183524, 1.595174, 6.584986, 0.00β¦
+$ HSPC_110 <dbl> 0.000000, 0.000000, 2.667372, 0.000000, 9.520268, 2.66β¦
+$ HSPC_111 <dbl> 0.000000, 1.495539, 2.691330, 3.780086, 1.495539, 0.00β¦
+$ HSPC_114 <dbl> 0.0000000, 0.0000000, 2.1872025, 0.0000000, 0.9172819,β¦
+$ HSPC_115 <dbl> 0.000000, 2.348960, 4.119213, 6.801590, 2.348960, 2.34β¦
+$ HSPC_117 <dbl> 0.000000, 0.000000, 2.662801, 0.000000, 2.662801, 0.00β¦
+$ HSPC_118 <dbl> 0.000000, 0.000000, 2.731892, 0.000000, 7.192924, 1.26β¦
+$ HSPC_119 <dbl> 0.000000, 2.432480, 3.827272, 0.000000, 2.432480, 8.53β¦
+$ HSPC_120 <dbl> 0.000000, 0.000000, 1.186672, 0.000000, 1.186672, 9.49β¦
+$ HSPC_121 <dbl> 0.000000, 0.000000, 4.264196, 0.000000, 2.822082, 0.00β¦
+$ HSPC_122 <dbl> 0.000000, 1.435059, 2.140080, 0.000000, 0.000000, 0.00β¦
+$ HSPC_123 <dbl> 0.000000, 0.000000, 2.244368, 0.000000, 6.093587, 0.00β¦
+$ HSPC_125 <dbl> 0.000000, 0.000000, 1.285018, 0.000000, 5.553951, 6.70β¦
+$ HSPC_126 <dbl> 0.0000000, 0.0000000, 1.5017883, 0.0000000, 2.6995085,β¦
+$ HSPC_127 <dbl> 0.000000, 0.000000, 0.000000, 0.000000, 2.822566, 0.00β¦
+$ HSPC_130 <dbl> 0.000000, 0.000000, 0.000000, 0.000000, 9.443009, 0.00β¦
+$ HSPC_131 <dbl> 0.000000, 0.000000, 2.384852, 0.000000, 4.161211, 0.00β¦
+$ HSPC_132 <dbl> 0.0000000, 0.7827224, 0.4438051, 0.0000000, 1.6604369,β¦
+$ HSPC_133 <dbl> 2.234359, 3.072289, 0.000000, 2.234359, 8.065004, 0.00β¦
+$ HSPC_134 <dbl> 0.000000, 2.768568, 0.000000, 0.000000, 6.641594, 0.00β¦
+$ HSPC_135 <dbl> 0.000000, 0.000000, 0.000000, 0.000000, 3.600652, 8.08β¦
+$ HSPC_136 <dbl> 0.000000, 0.000000, 0.000000, 0.000000, 2.962552, 0.00β¦
+$ HSPC_138 <dbl> 0.0000000, 0.7062338, 0.7062338, 0.0000000, 1.8180968,β¦
+$ HSPC_139 <dbl> 0.000000, 0.000000, 4.345514, 0.000000, 0.000000, 4.09β¦
+$ HSPC_140 <dbl> 0.000000, 0.000000, 4.660038, 0.000000, 0.000000, 0.00β¦
+$ HSPC_141 <dbl> 0.000000, 0.000000, 0.000000, 0.000000, 4.543589, 0.00β¦
+$ HSPC_142 <dbl> 0.000000, 0.000000, 2.523431, 0.000000, 0.000000, 0.00β¦
+$ HSPC_143 <dbl> 0.000000, 1.958674, 2.760027, 0.000000, 8.379422, 0.00β¦
+$ HSPC_144 <dbl> 0.000000, 0.000000, 1.075288, 0.000000, 0.000000, 0.00β¦
+$ HSPC_146 <dbl> 0.000000, 2.277948, 2.277948, 3.120975, 1.548407, 0.00β¦
+$ HSPC_148 <dbl> 0.000000, 0.000000, 2.428270, 0.000000, 0.000000, 0.00β¦
+$ HSPC_149 <dbl> 0.000000, 0.000000, 0.000000, 7.370990, 9.039081, 0.00β¦
+$ HSPC_151 <dbl> 0.000000, 0.000000, 1.942220, 0.000000, 6.477871, 0.00β¦
+$ HSPC_152 <dbl> 0.000000, 0.000000, 0.000000, 0.000000, 8.948497, 0.00β¦
+$ HSPC_153 <dbl> 0.000000, 0.000000, 0.000000, 0.000000, 0.000000, 0.00β¦
+$ HSPC_154 <dbl> 0.000000, 0.000000, 0.000000, 0.000000, 6.567172, 0.00β¦
+$ HSPC_155 <dbl> 0.000000, 0.000000, 0.000000, 0.000000, 5.981102, 2.73β¦
+$ HSPC_156 <dbl> 0.0000000, 0.5544683, 0.5544683, 0.0000000, 1.2665659,β¦
+$ HSPC_157 <dbl> 0.000000, 1.992960, 3.313476, 0.000000, 6.056835, 2.79β¦
+$ HSPC_158 <dbl> 0.000000, 1.681202, 1.681202, 0.000000, 2.436668, 1.68β¦
+$ HSPC_159 <dbl> 0.000000, 0.000000, 0.000000, 4.189894, 9.099914, 9.05β¦
+$ HSPC_161 <dbl> 0.000000, 0.000000, 1.701367, 0.000000, 3.323133, 8.08β¦
+$ HSPC_162 <dbl> 0.715249, 0.715249, 1.191268, 0.000000, 6.603848, 1.54β¦
+$ HSPC_164 <dbl> 0.000000, 1.780116, 4.173269, 0.000000, 3.053739, 0.00β¦
+$ HSPC_165 <dbl> 0.000000, 0.000000, 2.521243, 0.000000, 1.752913, 2.52β¦
+$ HSPC_166 <dbl> 0.000000, 1.680351, 3.830900, 0.000000, 2.435661, 0.00β¦
+$ HSPC_168 <dbl> 0.000000, 0.000000, 2.587724, 0.000000, 1.587172, 0.00β¦
+$ HSPC_169 <dbl> 0.000000, 2.231654, 2.231654, 0.000000, 2.840202, 1.15β¦
+$ HSPC_170 <dbl> 0.000000, 2.323845, 3.702651, 0.000000, 0.000000, 0.00β¦
+$ HSPC_171 <dbl> 0.000000, 2.249267, 0.000000, 0.000000, 6.986101, 0.00β¦
+$ HSPC_172 <dbl> 0.0000000, 0.0000000, 1.2663678, 1.6361385, 3.8432543,β¦
+$ HSPC_173 <dbl> 0.000000, 0.000000, 2.202687, 0.000000, 2.202687, 0.00β¦
+$ HSPC_174 <dbl> 0.000000, 0.000000, 0.000000, 0.000000, 0.000000, 1.25β¦
+$ HSPC_175 <dbl> 0.000000, 0.000000, 2.214143, 0.000000, 3.959792, 1.49β¦
+$ HSPC_176 <dbl> 0.000000, 0.000000, 2.023933, 0.000000, 6.539273, 2.02β¦
+$ HSPC_177 <dbl> 0.000000, 1.971046, 1.971046, 0.000000, 3.664721, 0.00β¦
+$ HSPC_178 <dbl> 0.000000, 1.002574, 1.002574, 0.000000, 8.129245, 0.00β¦
+$ HSPC_179 <dbl> 0.0000000, 0.8360365, 1.7464921, 0.0000000, 2.3003274,β¦
+$ HSPC_180 <dbl> 0.000000, 0.000000, 2.753903, 0.000000, 6.624564, 6.08β¦
+$ HSPC_181 <dbl> 0.000000, 0.000000, 5.739487, 0.000000, 5.969896, 0.00β¦
+$ HSPC_182 <dbl> 0.000000, 0.000000, 3.778793, 0.000000, 3.245451, 3.24β¦
+$ HSPC_183 <dbl> 0.000000, 0.000000, 3.206129, 1.020477, 7.802033, 0.00β¦
+$ HSPC_185 <dbl> 0.000000, 0.000000, 5.514029, 6.498157, 9.703008, 0.00β¦
+$ HSPC_186 <dbl> 0.000000, 1.605849, 9.300294, 0.000000, 3.729280, 0.00β¦
+$ HSPC_187 <dbl> 0.000000, 0.000000, 3.016892, 0.000000, 8.206576, 2.18β¦
+$ HSPC_189 <dbl> 2.651507, 1.465231, 0.000000, 0.000000, 1.465231, 2.17β¦
+$ HSPC_190 <dbl> 0.000000, 0.000000, 0.000000, 0.000000, 0.000000, 0.00β¦
+$ HSPC_191 <dbl> 0.000000, 0.000000, 0.000000, 0.000000, 1.406826, 0.00β¦
+$ HSPC_192 <dbl> 0.000000, 0.000000, 2.111369, 0.000000, 0.000000, 1.41β¦
+$ HSPC_193 <dbl> 0.0000000, 2.2721907, 2.9455106, 0.0000000, 9.1712813,β¦
+$ HSPC_195 <dbl> 0.0000000, 0.0000000, 2.4446955, 0.0000000, 1.4738612,β¦
+$ HSPC_196 <dbl> 0.000000, 1.379440, 2.888830, 0.000000, 0.000000, 0.00β¦
+$ HSPC_198 <dbl> 2.155150, 0.000000, 3.506202, 1.105265, 1.105265, 0.00β¦
+$ HSPC_199 <dbl> 1.676720, 0.000000, 2.102827, 4.774209, 2.102827, 1.06β¦
+$ HSPC_200 <dbl> 1.572132, 2.306518, 0.000000, 0.000000, 2.790837, 1.57β¦
+$ HSPC_202 <dbl> 1.3178909, 0.0000000, 0.0000000, 0.0000000, 1.6957804,β¦
+$ HSPC_203 <dbl> 0.000000, 0.000000, 0.000000, 0.000000, 0.000000, 0.00β¦
+$ HSPC_204 <dbl> 0.000000, 1.342435, 1.342435, 0.000000, 2.487324, 1.34β¦
+$ HSPC_205 <dbl> 0.000000, 1.996780, 0.000000, 0.000000, 2.803674, 4.95β¦
+$ HSPC_206 <dbl> 1.076411, 0.000000, 1.076411, 0.000000, 1.076411, 0.00β¦
+$ HSPC_207 <dbl> 0.000000, 0.000000, 1.482035, 0.000000, 9.592779, 0.00β¦
+$ HSPC_208 <dbl> 0.000000, 0.000000, 3.104133, 0.000000, 2.262852, 2.26β¦
+$ HSPC_210 <dbl> 0.000000, 1.021329, 1.021329, 0.000000, 1.613332, 1.02β¦
+$ HSPC_211 <dbl> 0.000000, 0.000000, 3.567889, 1.351210, 6.755381, 2.03β¦
+$ HSPC_212 <dbl> 0.000000, 0.000000, 2.570024, 0.000000, 0.000000, 0.00β¦
+$ HSPC_213 <dbl> 0.000000, 1.935211, 1.935211, 0.000000, 1.270332, 1.27β¦
+$ HSPC_214 <dbl> 1.4766124, 0.0000000, 1.8775155, 0.0000000, 1.4766124,β¦
+$ HSPC_215 <dbl> 0.000000, 0.000000, 3.551326, 0.000000, 2.403099, 6.60β¦
+$ HSPC_216 <dbl> 0.0000000, 1.3146495, 0.8021597, 0.8021597, 6.2917837,β¦
+$ HSPC_218 <dbl> 0.000000, 2.567330, 3.440186, 0.000000, 3.980149, 0.00β¦
+$ HSPC_219 <dbl> 0.000000, 1.620715, 2.040160, 0.000000, 2.364726, 0.00β¦
+$ HSPC_220 <dbl> 0.000000, 0.000000, 4.645420, 0.000000, 6.439808, 0.00β¦
+$ HSPC_221 <dbl> 0.000000, 1.932925, 3.617433, 1.268520, 8.054842, 1.26β¦
+$ HSPC_222 <dbl> 0.000000, 2.630291, 3.270905, 0.000000, 2.157369, 1.44β¦
+$ HSPC_223 <dbl> 0.000000, 3.195293, 3.195293, 0.000000, 3.195293, 0.00β¦
+$ HSPC_224 <dbl> 0.000000, 0.000000, 3.235910, 0.000000, 2.381448, 3.23β¦
+$ HSPC_225 <dbl> 0.000000, 1.892444, 0.000000, 0.000000, 0.000000, 1.89β¦
+$ HSPC_227 <dbl> 0.000000, 0.000000, 2.269803, 0.000000, 1.541657, 0.00β¦
+$ HSPC_228 <dbl> 0.000000, 0.000000, 2.193480, 0.000000, 2.193480, 3.02β¦
+$ HSPC_229 <dbl> 0.000000, 2.483864, 4.276180, 0.000000, 3.348781, 0.00β¦
+$ HSPC_230 <dbl> 0.000000, 0.000000, 2.376256, 0.000000, 9.125464, 6.25β¦
+$ HSPC_231 <dbl> 0.000000, 2.442191, 3.838346, 0.000000, 10.045009, 2.4β¦
+$ HSPC_232 <dbl> 0.000000, 1.868824, 3.834078, 0.000000, 4.080153, 0.00β¦
+$ HSPC_233 <dbl> 0.000000, 0.000000, 3.219022, 0.000000, 3.219022, 0.00β¦
+$ HSPC_235 <dbl> 0.000000, 0.000000, 6.066406, 0.000000, 3.382760, 0.00β¦
+$ HSPC_236 <dbl> 0.000000, 0.000000, 3.747550, 0.000000, 5.733689, 3.08β¦
+$ HSPC_237 <dbl> 0.000000, 2.058995, 2.058995, 0.000000, 2.874584, 2.05β¦
+$ HSPC_239 <dbl> 0.000000, 2.206777, 3.951001, 0.000000, 3.951001, 0.00β¦
+$ HSPC_240 <dbl> 0.0000000, 0.0000000, 1.8347816, 0.0000000, 1.4390643,β¦
+$ HSPC_243 <dbl> 0.000000, 1.118272, 0.000000, 0.000000, 1.740598, 0.00β¦
+$ HSPC_244 <dbl> 0.7871557, 0.7871557, 0.7871557, 0.0000000, 8.1826024,β¦
+$ HSPC_245 <dbl> 0.000000, 1.459488, 0.000000, 0.000000, 1.459488, 0.00β¦
+$ HSPC_246 <dbl> 0.000000, 0.000000, 1.629406, 0.000000, 0.000000, 0.00β¦
+$ HSPC_247 <dbl> 0.000000, 0.000000, 4.129612, 0.000000, 6.233964, 3.74β¦
+$ HSPC_248 <dbl> 0.000000, 0.000000, 3.844645, 0.000000, 0.000000, 1.69β¦
+$ HSPC_249 <dbl> 0.000000, 0.000000, 1.595836, 0.000000, 1.595836, 2.33β¦
+$ HSPC_250 <dbl> 0.000000, 1.277977, 3.022356, 0.000000, 4.572877, 7.32β¦
+$ HSPC_251 <dbl> 0.0000000, 0.0000000, 2.2758529, 0.0000000, 1.9568480,β¦
+$ HSPC_253 <dbl> 0.000000, 0.000000, 1.265413, 0.000000, 8.470854, 0.00β¦
+$ HSPC_254 <dbl> 0.000000, 2.017054, 2.826829, 2.017054, 5.231539, 0.00β¦
+$ HSPC_255 <dbl> 0.0000000, 0.0000000, 0.0000000, 0.0000000, 1.8624297,β¦
+$ HSPC_256 <dbl> 0.824835, 1.346341, 9.308939, 0.000000, 1.346341, 0.82β¦
+$ HSPC_257 <dbl> 0.000000, 0.000000, 1.897882, 0.000000, 6.591455, 0.00β¦
+$ HSPC_258 <dbl> 0.0000000, 0.8526372, 0.0000000, 0.0000000, 7.0828772,β¦
+$ HSPC_261 <dbl> 0.0000000, 0.9300646, 0.9300646, 0.0000000, 1.4909411,β¦
+$ HSPC_263 <dbl> 1.537503, 0.000000, 1.537503, 0.000000, 0.000000, 2.26β¦
+$ HSPC_264 <dbl> 0.000000, 1.425741, 1.425741, 0.000000, 0.000000, 8.70β¦
+$ HSPC_265 <dbl> 0.000000, 2.672373, 4.308280, 0.000000, 3.554532, 7.62β¦
+$ HSPC_266 <dbl> 0.000000, 0.000000, 3.498974, 0.000000, 8.164818, 2.62β¦
+$ HSPC_267 <dbl> 0.0000000, 0.0000000, 0.0000000, 0.0000000, 1.9510360,β¦
+$ HSPC_268 <dbl> 0.0000000, 0.7786889, 3.0278105, 0.0000000, 1.9494543,β¦
+$ HSPC_269 <dbl> 0.0000000, 0.0000000, 1.9511222, 0.0000000, 2.5642396,β¦
+$ HSPC_270 <dbl> 0.0000000, 0.0000000, 2.2633366, 0.0000000, 6.3366603,β¦
+$ HSPC_271 <dbl> 1.351781, 1.351781, 4.404598, 1.351781, 2.037221, 6.96β¦
+$ HSPC_274 <dbl> 0.000000, 0.000000, 2.990962, 0.000000, 9.428474, 8.26β¦
+$ HSPC_275 <dbl> 0.5251597, 6.3066729, 1.8617796, 0.0000000, 6.2986480,β¦
+$ HSPC_276 <dbl> 0.000000, 1.155802, 2.836006, 0.000000, 0.000000, 8.56β¦
+$ HSPC_278 <dbl> 0.000000, 1.185387, 2.881903, 0.000000, 2.269850, 3.64β¦
+$ HSPC_279 <dbl> 3.563514, 1.487393, 2.204027, 0.000000, 7.109467, 1.48β¦
+$ HSPC_280 <dbl> 0.000000, 0.000000, 2.837358, 0.000000, 3.939531, 0.00β¦
+$ HSPC_281 <dbl> 3.488013, 0.000000, 3.488013, 0.000000, 3.488013, 0.00β¦
+$ HSPC_282 <dbl> 0.0000000, 1.1722813, 2.0476063, 0.0000000, 1.1722813,β¦
+$ HSPC_283 <dbl> 0.000000, 3.590649, 4.529495, 1.911441, 1.911441, 0.00β¦
+$ HSPC_285 <dbl> 0.0000000, 0.0000000, 3.0705949, 0.0000000, 8.1491892,β¦
+$ HSPC_286 <dbl> 0.000000, 0.000000, 2.259352, 0.000000, 2.259352, 0.00β¦
+$ HSPC_287 <dbl> 0.000000, 1.048672, 3.408389, 1.649500, 1.649500, 0.00β¦
+$ HSPC_288 <dbl> 0.0000000, 1.3879010, 3.0490024, 0.0000000, 8.9178718,β¦
+$ HSPC_289 <dbl> 0.000000, 0.000000, 3.641902, 0.000000, 3.940529, 0.00β¦
+$ HSPC_290 <dbl> 0.000000, 0.000000, 2.594545, 0.000000, 7.607623, 2.59β¦
+$ HSPC_291 <dbl> 0.000000, 1.175842, 1.175842, 0.000000, 9.326333, 0.00β¦
+$ HSPC_292 <dbl> 0.000000, 0.000000, 2.804302, 0.000000, 5.422785, 8.43β¦
+$ HSPC_293 <dbl> 1.077036, 0.000000, 2.711161, 7.608787, 4.047517, 1.07β¦
+$ HSPC_294 <dbl> 0.0000000, 0.0000000, 0.9161348, 0.0000000, 1.8723003,β¦
+$ HSPC_295 <dbl> 0.0000000, 1.8799200, 3.0264680, 0.9210673, 4.2380463,β¦
+$ HSPC_296 <dbl> 0.000000, 2.157001, 2.157001, 2.157001, 5.287566, 0.00β¦
+$ HSPC_297 <dbl> 0.000000, 1.687785, 2.444464, 0.000000, 0.000000, 0.00β¦
+$ HSPC_298 <dbl> 0.0000000, 0.7784226, 2.4036840, 0.0000000, 2.4036840,β¦
+$ HSPC_299 <dbl> 0.000000, 1.099428, 1.716067, 0.000000, 8.068194, 2.74β¦
+$ HSPC_300 <dbl> 0.0000000, 0.0000000, 2.0342975, 0.0000000, 2.0342975,β¦
+$ HSPC_301 <dbl> 0.000000, 3.073359, 6.232145, 0.000000, 4.938720, 0.00β¦
+$ HSPC_302 <dbl> 3.078836, 0.000000, 4.545226, 0.000000, 3.078836, 3.07β¦
+$ HSPC_303 <dbl> 0.000000, 0.000000, 3.009431, 0.000000, 7.544693, 0.00β¦
+$ HSPC_304 <dbl> 0.0000000, 1.5484583, 2.7602490, 0.0000000, 5.4055991,β¦
+$ HSPC_305 <dbl> 0.000000, 0.000000, 2.558256, 0.000000, 4.669580, 1.15β¦
+$ HSPC_306 <dbl> 0.000000, 0.000000, 3.185666, 0.000000, 5.689777, 3.33β¦
+$ HSPC_307 <dbl> 0.000000, 1.976472, 4.777034, 0.000000, 3.293648, 2.78β¦
+$ HSPC_308 <dbl> 0.000000, 0.000000, 3.975296, 6.548101, 3.526101, 0.00β¦
+$ HSPC_309 <dbl> 0.000000, 1.804026, 3.455193, 0.000000, 3.083349, 1.80β¦
+$ HSPC_310 <dbl> 1.743404, 0.000000, 2.510071, 0.000000, 2.510071, 1.74β¦
+$ HSPC_312 <dbl> 0.0000000, 1.4203264, 1.8133978, 0.0000000, 7.5148795,β¦
+$ HSPC_313 <dbl> 0.000000, 1.591589, 4.096808, 1.591589, 2.329876, 0.00β¦
+$ HSPC_314 <dbl> 0.000000, 0.000000, 3.527058, 1.634863, 3.236083, 7.90β¦
+$ HSPC_315 <dbl> 0.000000, 2.261631, 2.261631, 2.261631, 3.630638, 0.00β¦
+$ HSPC_317 <dbl> 0.000000, 2.335038, 3.715556, 0.000000, 2.335038, 0.00β¦
+$ HSPC_318 <dbl> 0.000000, 0.000000, 3.357051, 0.000000, 0.000000, 0.00β¦
+$ HSPC_320 <dbl> 0.000000, 0.000000, 3.189910, 2.339927, 3.479868, 3.18β¦
+$ HSPC_321 <dbl> 0.000000, 1.191188, 1.191188, 0.000000, 2.616741, 1.19β¦
+$ HSPC_322 <dbl> 0.0000000, 0.0000000, 0.0000000, 0.0000000, 1.9762562,β¦
+$ HSPC_323 <dbl> 0.0000000, 0.0000000, 0.9890293, 0.0000000, 2.5666314,β¦
+$ HSPC_324 <dbl> 0.000000, 1.088036, 2.728840, 0.000000, 2.728840, 0.00β¦
+$ HSPC_325 <dbl> 1.428402, 1.428402, 4.810635, 0.000000, 2.131908, 0.00β¦
+$ HSPC_326 <dbl> 0.000000, 0.000000, 5.321205, 0.000000, 6.303048, 0.00β¦
+$ HSPC_327 <dbl> 0.0000000, 0.6422346, 2.7240929, 0.0000000, 3.1457469,β¦
+$ HSPC_328 <dbl> 0.000000, 0.000000, 3.620927, 0.000000, 2.733670, 1.27β¦
+$ HSPC_329 <dbl> 1.954249, 0.000000, 3.800965, 0.000000, 1.954249, 0.00β¦
+$ HSPC_330 <dbl> 1.870221, 0.000000, 3.695045, 0.000000, 2.317254, 2.65β¦
+$ HSPC_331 <dbl> 0.000000, 0.000000, 2.953080, 0.000000, 2.953080, 0.00β¦
+$ HSPC_332 <dbl> 0.000000, 1.044806, 2.883335, 0.000000, 6.444771, 1.04β¦
+$ HSPC_333 <dbl> 0.8059525, 1.3199644, 1.3199644, 0.0000000, 1.9975449,β¦
+$ HSPC_334 <dbl> 0.000000, 0.000000, 0.000000, 0.000000, 1.931089, 0.00β¦
+$ HSPC_335 <dbl> 0.000000, 0.000000, 2.751133, 0.000000, 7.599859, 0.00β¦
+$ HSPC_336 <dbl> 0.000000, 0.000000, 1.959737, 0.000000, 0.000000, 3.27β¦
+$ HSPC_337 <dbl> 0.000000, 0.000000, 5.147478, 0.000000, 4.187618, 0.00β¦
+$ HSPC_338 <dbl> 0.0000000, 0.0000000, 10.1024666, 0.0000000, 7.9043216β¦
+$ HSPC_339 <dbl> 0.0000000, 0.9599543, 2.5175886, 5.1304754, 7.6196067,β¦
+$ HSPC_341 <dbl> 0.0000000, 0.0000000, 2.2497917, 7.5891885, 2.2497917,β¦
+$ HSPC_342 <dbl> 0.0000000, 0.7849552, 1.4893359, 0.4452176, 8.7833506,β¦
+$ HSPC_343 <dbl> 0.0000000, 0.7869497, 0.7869497, 0.7869497, 1.9640992,β¦
+$ HSPC_344 <dbl> 0.000000, 1.425890, 1.425890, 0.000000, 8.886625, 2.59β¦
+$ HSPC_345 <dbl> 0.000000, 0.000000, 2.093666, 1.397341, 0.000000, 1.39β¦
+$ HSPC_346 <dbl> 0.000000, 0.000000, 1.637347, 0.000000, 1.637347, 1.03β¦
+$ HSPC_348 <dbl> 0.000000, 1.733815, 2.768747, 7.794259, 2.166424, 1.73β¦
+$ HSPC_349 <dbl> 0.000000, 0.000000, 3.434533, 0.000000, 2.783890, 0.00β¦
+$ HSPC_350 <dbl> 0.000000, 0.000000, 4.536066, 5.820193, 0.000000, 0.00β¦
+$ HSPC_351 <dbl> 0.000000, 1.910297, 2.704369, 0.000000, 7.827990, 1.91β¦
+$ HSPC_352 <dbl> 0.000000, 0.000000, 1.855727, 0.000000, 0.000000, 0.00β¦
+$ HSPC_353 <dbl> 0.000000, 0.000000, 0.899194, 0.000000, 0.000000, 0.89β¦
+$ HSPC_354 <dbl> 0.000000, 2.331123, 4.869071, 0.000000, 7.191315, 0.00β¦
+$ HSPC_356 <dbl> 0.000000, 0.000000, 4.138465, 0.000000, 1.914037, 0.00β¦
+$ HSPC_358 <dbl> 0.000000, 1.322769, 3.323190, 1.322769, 3.524842, 0.00β¦
+$ HSPC_359 <dbl> 0.0000000, 0.9071742, 1.8584210, 0.0000000, 8.1305324,β¦
+$ HSPC_360 <dbl> 0.000000, 0.000000, 2.544055, 0.000000, 9.351724, 0.00β¦
+$ HSPC_361 <dbl> 0.000000, 0.000000, 4.073667, 0.000000, 9.554073, 2.05β¦
+$ HSPC_362 <dbl> 0.000000, 0.000000, 7.448528, 0.000000, 4.768353, 0.00β¦
+$ HSPC_363 <dbl> 0.000000, 0.000000, 2.749745, 8.987973, 7.432788, 7.45β¦
+$ HSPC_365 <dbl> 0.000000, 0.000000, 4.965616, 2.594802, 9.358295, 8.09β¦
+$ HSPC_367 <dbl> 0.000000, 2.528168, 4.327223, 0.000000, 6.909409, 5.10β¦
+$ HSPC_368 <dbl> 0.000000, 0.000000, 0.000000, 0.000000, 8.951178, 0.00β¦
+$ HSPC_370 <dbl> 0.000000, 0.000000, 1.307598, 0.000000, 0.797134, 0.00β¦
+$ HSPC_371 <dbl> 0.000000, 1.257081, 1.257081, 0.000000, 1.257081, 1.25β¦
+$ HSPC_372 <dbl> 0.000000, 0.000000, 2.221252, 0.000000, 8.278550, 0.00β¦
+$ HSPC_373 <dbl> 0.000000, 0.000000, 4.730281, 2.884763, 3.783634, 6.93β¦
+$ HSPC_374 <dbl> 0.000000, 0.000000, 2.862633, 0.000000, 10.146380, 7.7β¦
+$ HSPC_376 <dbl> 0.000000, 0.000000, 3.171475, 8.276931, 2.537496, 0.00β¦
+$ HSPC_377 <dbl> 0.000000, 0.000000, 3.297929, 0.000000, 8.087149, 1.30β¦
+$ HSPC_380 <dbl> 1.219391, 0.000000, 2.934029, 1.219391, 3.165253, 1.21β¦
+$ HSPC_382 <dbl> 0.0000000, 0.0000000, 1.5486445, 0.0000000, 9.8626042,β¦
+$ HSPC_383 <dbl> 0.000000, 0.000000, 3.684053, 0.000000, 2.521370, 1.75β¦
+$ HSPC_386 <dbl> 0.000000, 1.412425, 2.934964, 3.837412, 2.112261, 4.60β¦
+$ HSPC_387 <dbl> 0.000000, 0.000000, 2.464120, 0.000000, 2.004298, 2.00β¦
+$ HSPC_388 <dbl> 0.0000000, 0.0000000, 0.0000000, 0.0000000, 7.0965225,β¦
+$ HSPC_389 <dbl> 0.000000, 0.000000, 8.902540, 0.000000, 1.263307, 0.00β¦
+$ HSPC_390 <dbl> 0.000000, 1.531571, 3.386125, 7.733304, 3.625976, 0.00β¦
+$ HSPC_391 <dbl> 0.000000, 1.423235, 2.125560, 0.000000, 2.125560, 0.00β¦
+$ HSPC_392 <dbl> 1.166291, 0.000000, 2.242760, 0.000000, 0.000000, 1.16β¦
+$ HSPC_393 <dbl> 0.000000, 1.110847, 8.026679, 0.000000, 7.310363, 1.11β¦
+$ HSPC_395 <dbl> 0.000000, 0.000000, 1.923747, 0.000000, 1.923747, 1.26β¦
+$ HSPC_396 <dbl> 0.0000000, 0.9279096, 2.8713748, 0.0000000, 8.4108606,β¦
+$ HSPC_398 <dbl> 0.000000, 1.052478, 2.405000, 0.000000, 1.654517, 7.24β¦
+$ HSPC_399 <dbl> 0.000000, 0.000000, 1.198818, 0.000000, 9.267652, 0.00β¦
+$ HSPC_400 <dbl> 0.000000, 0.000000, 2.368347, 0.000000, 1.255700, 0.00β¦
+$ HSPC_402 <dbl> 0.000000, 0.000000, 2.004052, 0.000000, 8.950833, 8.75β¦
+$ HSPC_403 <dbl> 0.000000, 0.000000, 2.797093, 0.000000, 0.000000, 0.00β¦
+$ HSPC_404 <dbl> 0.0000000, 0.0000000, 3.7817437, 0.0000000, 4.2260011,β¦
+$ HSPC_405 <dbl> 0.000000, 1.099247, 1.715831, 0.000000, 1.099247, 5.31β¦
+$ HSPC_406 <dbl> 0.000000, 0.000000, 2.135083, 1.430987, 3.245124, 0.00β¦
+$ HSPC_407 <dbl> 0.0000000, 0.5650490, 1.5448568, 0.0000000, 3.8016573,β¦
+$ HSPC_408 <dbl> 0.0000000, 1.5700909, 10.4839578, 0.0000000, 8.0221142β¦
+$ HSPC_409 <dbl> 0.000000, 0.000000, 3.044399, 0.000000, 3.044399, 0.00β¦
+$ HSPC_410 <dbl> 0.904751, 0.000000, 1.854660, 0.000000, 5.165464, 0.00β¦
+$ HSPC_411 <dbl> 0.0000000, 0.0000000, 0.9059253, 0.0000000, 7.5067273,β¦
+$ HSPC_412 <dbl> 0.0000000, 0.0000000, 0.6614079, 8.5121379, 7.3252186,β¦
+$ HSPC_413 <dbl> 0.000000, 1.169683, 1.807043, 1.169683, 9.674198, 0.00β¦
+$ HSPC_415 <dbl> 0.000000, 0.000000, 5.273790, 0.000000, 3.093809, 0.00β¦
+$ HSPC_416 <dbl> 0.000000, 1.337731, 3.110643, 0.000000, 0.000000, 0.00β¦
+$ HSPC_417 <dbl> 0.0000000, 0.7221578, 1.5601978, 0.0000000, 1.2011916,β¦
+$ HSPC_418 <dbl> 0.000000, 0.000000, 2.348200, 0.000000, 1.241207, 0.00β¦
+$ HSPC_419 <dbl> 0.000000, 0.000000, 1.158302, 0.692403, 0.000000, 0.69β¦
+$ HSPC_420 <dbl> 0.0000000, 0.7442525, 1.5970870, 0.0000000, 1.5970870,β¦
+$ HSPC_421 <dbl> 0.000000, 0.000000, 3.682417, 0.000000, 1.985374, 0.00β¦
+$ HSPC_422 <dbl> 0.000000, 0.000000, 1.630076, 1.033967, 1.630076, 7.51β¦
+$ HSPC_423 <dbl> 0.0000000, 0.0000000, 1.4797402, 0.0000000, 1.1326799,β¦
+$ HSPC_424 <dbl> 0.000000, 1.267474, 2.728919, 0.000000, 3.439860, 0.00β¦
+$ HSPC_425 <dbl> 0.000000, 0.000000, 1.016015, 0.000000, 6.474436, 0.00β¦
+$ HSPC_426 <dbl> 0.000000, 0.000000, 3.133563, 0.000000, 0.000000, 1.55β¦
+$ HSPC_427 <dbl> 0.000000, 2.152076, 4.835791, 0.000000, 7.220338, 0.00β¦
+$ HSPC_431 <dbl> 0.000000, 2.150174, 3.639547, 1.101833, 5.618926, 2.97β¦
+$ HSPC_432 <dbl> 0.000000, 0.000000, 1.949682, 0.000000, 3.261333, 4.18β¦
+$ HSPC_435 <dbl> 0.000000, 1.097512, 2.970692, 0.000000, 7.647274, 6.35β¦
+$ HSPC_436 <dbl> 0.0000000, 0.0000000, 1.1114827, 0.0000000, 5.7023734,β¦
+$ HSPC_440 <dbl> 0.000000, 1.385247, 1.385247, 0.000000, 2.545103, 5.12β¦
+$ HSPC_441 <dbl> 0.000000, 0.000000, 1.696075, 1.084126, 8.589432, 1.08β¦
+$ HSPC_442 <dbl> 0.0000000, 0.0000000, 0.0000000, 0.0000000, 3.6713853,β¦
+$ HSPC_443 <dbl> 0.000000, 1.546895, 2.276125, 0.000000, 2.276125, 1.54β¦
+$ HSPC_444 <dbl> 1.374089, 0.000000, 0.000000, 0.000000, 1.374089, 0.00β¦
+$ HSPC_446 <dbl> 0.000000, 2.439029, 1.683195, 0.000000, 1.683195, 1.68β¦
+$ HSPC_447 <dbl> 0.000000, 1.113089, 1.113089, 0.000000, 2.166474, 7.12β¦
+$ HSPC_448 <dbl> 0.000000, 1.139444, 0.000000, 0.000000, 9.257634, 0.00β¦
+$ HSPC_449 <dbl> 0.000000, 1.344056, 2.489522, 0.000000, 5.057946, 2.02β¦
+$ HSPC_450 <dbl> 0.000000, 0.000000, 2.979455, 0.000000, 5.551901, 0.00β¦
+$ HSPC_451 <dbl> 0.000000, 0.000000, 0.000000, 0.000000, 9.322231, 1.75β¦
+$ HSPC_453 <dbl> 0.0000000, 0.0000000, 1.4937200, 0.0000000, 2.4699783,β¦
+$ HSPC_454 <dbl> 0.0000000, 0.0000000, 0.0000000, 0.0000000, 9.1805553,β¦
+$ HSPC_455 <dbl> 0.000000, 0.000000, 0.000000, 0.000000, 7.204120, 0.00β¦
+$ HSPC_456 <dbl> 0.0000000, 0.0000000, 1.4363752, 0.0000000, 7.5943576,β¦
+$ HSPC_457 <dbl> 0.000000, 0.000000, 0.000000, 0.000000, 4.535876, 7.75β¦
+$ HSPC_459 <dbl> 0.000000, 1.282562, 1.282562, 1.282562, 9.214660, 1.95β¦
+$ HSPC_460 <dbl> 0.000000, 0.000000, 0.000000, 0.000000, 2.601133, 0.00β¦
+$ HSPC_461 <dbl> 0.000000, 0.000000, 0.000000, 7.294303, 7.224373, 0.00β¦
+$ HSPC_462 <dbl> 0.000000, 0.000000, 0.000000, 0.000000, 5.732804, 0.00β¦
+$ HSPC_463 <dbl> 0.000000, 0.000000, 1.566104, 0.725680, 0.000000, 0.00β¦
+$ HSPC_465 <dbl> 0.000000, 4.053991, 0.000000, 3.894882, 2.159925, 0.00β¦
+$ HSPC_466 <dbl> 0.000000, 1.163197, 0.000000, 0.000000, 3.274518, 0.00β¦
+$ HSPC_467 <dbl> 0.000000, 1.176891, 1.176891, 1.176891, 8.628113, 2.25β¦
+$ HSPC_468 <dbl> 0.000000, 1.297938, 1.297938, 0.000000, 10.108305, 0.0β¦
+$ HSPC_470 <dbl> 0.000000, 0.000000, 0.000000, 0.000000, 0.000000, 3.23β¦
+$ HSPC_471 <dbl> 0.000000, 0.000000, 1.535633, 0.000000, 5.948904, 0.00β¦
+$ HSPC_472 <dbl> 0.0000000, 0.0000000, 0.0000000, 3.3032627, 0.9896601,β¦
+$ HSPC_473 <dbl> 0.000000, 0.000000, 0.000000, 0.000000, 6.756343, 6.88β¦
+$ HSPC_474 <dbl> 1.040938, 1.040938, 0.000000, 0.000000, 2.386883, 0.00β¦
+$ HSPC_475 <dbl> 7.447608, 0.000000, 3.318667, 0.000000, 3.318667, 1.99β¦
+$ HSPC_477 <dbl> 0.0000000, 0.0000000, 0.0000000, 0.0000000, 1.3981912,β¦
+$ HSPC_478 <dbl> 0.000000, 0.000000, 4.083810, 0.000000, 2.884169, 0.00β¦
+$ HSPC_479 <dbl> 0.000000, 0.000000, 3.027550, 0.000000, 8.194229, 1.94β¦
+$ HSPC_480 <dbl> 0.000000, 1.034469, 3.059791, 0.000000, 2.376690, 1.03β¦
+$ HSPC_482 <dbl> 6.620967, 0.000000, 0.000000, 0.000000, 0.000000, 0.00β¦
+$ HSPC_483 <dbl> 0.000000, 0.000000, 3.006419, 0.000000, 8.010120, 2.17β¦
+$ HSPC_485 <dbl> 0.0000000, 1.0279164, 0.6036333, 0.6036333, 0.6036333,β¦
+$ HSPC_486 <dbl> 0.000000, 0.000000, 1.410572, 0.000000, 1.410572, 5.75β¦
+$ HSPC_488 <dbl> 0.000000, 0.000000, 0.000000, 0.000000, 9.802316, 0.00β¦
+$ HSPC_489 <dbl> 0.000000, 1.882197, 0.000000, 0.000000, 0.000000, 0.00β¦
+$ HSPC_490 <dbl> 0.000000, 0.000000, 0.000000, 0.000000, 2.790270, 1.30β¦
+$ HSPC_491 <dbl> 0.000000, 1.469639, 0.000000, 4.081147, 8.733647, 0.00β¦
+$ HSPC_492 <dbl> 1.163132, 0.000000, 0.000000, 0.000000, 9.050494, 0.00β¦
+$ HSPC_493 <dbl> 0.000000, 0.000000, 2.223299, 0.000000, 3.586020, 4.73β¦
+$ HSPC_494 <dbl> 0.000000, 0.000000, 0.000000, 0.000000, 3.680132, 8.44β¦
+$ HSPC_495 <dbl> 0.000000, 2.419005, 0.000000, 0.000000, 5.543935, 2.41β¦
+$ HSPC_496 <dbl> 0.000000, 0.000000, 0.000000, 1.788287, 1.788287, 10.6β¦
+$ HSPC_497 <dbl> 0.000000, 0.000000, 1.945149, 0.000000, 1.945149, 1.94β¦
+$ HSPC_498 <dbl> 0.000000, 0.000000, 0.000000, 0.000000, 7.967779, 0.00β¦
+$ HSPC_499 <dbl> 0.000000, 0.000000, 1.614671, 0.000000, 8.977937, 0.00β¦
+$ HSPC_500 <dbl> 0.000000, 1.779610, 1.779610, 0.000000, 7.269594, 2.55β¦
+$ HSPC_501 <dbl> 0.000000, 2.304226, 0.000000, 0.000000, 2.304226, 0.00β¦
+$ HSPC_502 <dbl> 0.0000000, 0.0000000, 1.4698900, 0.0000000, 7.2171885,β¦
+$ HSPC_503 <dbl> 0.000000, 0.000000, 0.000000, 0.000000, 7.932863, 8.79β¦
+$ HSPC_504 <dbl> 0.000000, 0.000000, 2.201356, 0.000000, 9.317511, 2.20β¦
+$ HSPC_505 <dbl> 0.000000, 0.000000, 2.180019, 0.000000, 2.180019, 0.00β¦
+$ HSPC_506 <dbl> 0.000000, 0.000000, 1.878328, 0.000000, 2.667432, 0.00β¦
+$ HSPC_507 <dbl> 0.000000, 1.878372, 2.667483, 0.000000, 3.549225, 1.87β¦
+$ HSPC_508 <dbl> 0.0000000, 0.2296644, 0.2296644, 0.2296644, 4.6628473,β¦
+$ HSPC_509 <dbl> 0.000000, 0.000000, 0.000000, 0.000000, 2.942680, 7.82β¦
+$ HSPC_510 <dbl> 0.000000, 1.166340, 1.802743, 6.721521, 1.166340, 6.59β¦
+$ HSPC_512 <dbl> 0.000000, 0.000000, 1.738345, 0.000000, 0.000000, 1.11β¦
+$ HSPC_514 <dbl> 1.237955, 0.000000, 2.962215, 0.000000, 8.674516, 0.00β¦
+$ HSPC_515 <dbl> 1.108707, 1.108707, 1.108707, 0.000000, 1.108707, 8.57β¦
+$ HSPC_516 <dbl> 0.0000000, 0.0000000, 1.4299322, 0.0000000, 9.6466954,β¦
+$ HSPC_518 <dbl> 0.000000, 0.000000, 0.000000, 0.000000, 2.617584, 0.00β¦
+$ HSPC_520 <dbl> 0.000000, 0.000000, 1.644413, 0.000000, 8.591871, 0.00β¦
+$ HSPC_521 <dbl> 0.000000, 0.000000, 0.000000, 0.000000, 9.290520, 0.00β¦
+$ HSPC_522 <dbl> 0.000000, 0.000000, 0.000000, 0.000000, 2.182446, 0.00β¦
+$ HSPC_523 <dbl> 0.0000000, 0.0000000, 0.7295826, 9.9573376, 1.8610172,β¦
+$ HSPC_524 <dbl> 0.000000, 0.000000, 0.000000, 0.000000, 3.266931, 0.00β¦
+$ HSPC_526 <dbl> 1.301071, 1.301071, 0.000000, 0.000000, 1.301071, 0.00β¦
+$ HSPC_527 <dbl> 0.0000000, 0.0000000, 0.0000000, 1.2793196, 7.6901603,β¦
+$ HSPC_528 <dbl> 0.000000, 0.000000, 1.669689, 7.592221, 2.423018, 0.00β¦
+$ HSPC_530 <dbl> 1.746336, 0.000000, 0.000000, 0.000000, 8.986799, 1.74β¦
+$ HSPC_532 <dbl> 0.000000, 0.000000, 0.000000, 1.176792, 10.454235, 0.0β¦
+$ HSPC_533 <dbl> 0.0000000, 0.0000000, 0.7536668, 0.0000000, 1.9046925,β¦
+$ HSPC_534 <dbl> 0.000000, 0.000000, 0.000000, 0.000000, 2.227399, 0.00β¦
+$ HSPC_535 <dbl> 0.000000, 0.000000, 3.918443, 0.000000, 8.372526, 0.00β¦
+$ HSPC_537 <dbl> 0.000000, 0.000000, 1.665647, 1.665647, 6.776472, 2.91β¦
+$ HSPC_538 <dbl> 0.000000, 0.000000, 2.242435, 0.000000, 2.851982, 8.64β¦
+$ HSPC_539 <dbl> 0.000000, 3.354010, 1.725182, 7.588085, 7.535255, 0.00β¦
+$ HSPC_540 <dbl> 0.0000000, 0.0000000, 0.0000000, 0.0000000, 1.9846071,β¦
+$ HSPC_541 <dbl> 0.000000, 0.000000, 0.000000, 0.000000, 10.016742, 0.0β¦
+$ HSPC_543 <dbl> 0.000000, 0.000000, 0.000000, 0.000000, 8.753904, 7.96β¦
+$ HSPC_544 <dbl> 0.0000000, 0.0000000, 0.8221823, 0.0000000, 7.1295118,β¦
+$ HSPC_545 <dbl> 0.000000, 0.000000, 0.000000, 1.484735, 3.764537, 2.20β¦
+$ HSPC_546 <dbl> 0.000000, 2.211853, 3.047085, 0.000000, 0.000000, 0.00β¦
+$ HSPC_547 <dbl> 0.000000, 0.000000, 0.000000, 0.654750, 9.253559, 0.65β¦
+$ HSPC_548 <dbl> 0.000000, 0.000000, 2.165553, 1.455855, 1.455855, 0.00β¦
+$ HSPC_549 <dbl> 0.000000, 0.000000, 0.000000, 0.000000, 1.557210, 1.55β¦
+$ HSPC_550 <dbl> 1.750214, 0.000000, 1.750214, 0.000000, 3.680372, 0.00β¦
+$ HSPC_551 <dbl> 0.000000, 0.000000, 1.287115, 0.000000, 5.908242, 8.49β¦
+$ HSPC_552 <dbl> 0.000000, 0.000000, 1.226425, 0.000000, 4.650625, 8.64β¦
+$ HSPC_553 <dbl> 0.0000000, 0.4708726, 0.4708726, 0.0000000, 7.2724626,β¦
+$ HSPC_554 <dbl> 1.449277, 1.449277, 1.449277, 0.000000, 1.449277, 9.03β¦
+$ HSPC_555 <dbl> 0.000000, 0.000000, 1.802172, 0.000000, 0.000000, 0.00β¦
+$ HSPC_556 <dbl> 0.0000000, 0.0000000, 0.9369457, 0.0000000, 0.9369457,β¦
+$ HSPC_557 <dbl> 1.141542, 0.000000, 1.141542, 0.000000, 1.770759, 0.00β¦
+$ HSPC_559 <dbl> 0.000000, 0.000000, 0.000000, 0.000000, 2.411402, 0.00β¦
+$ HSPC_560 <dbl> 0.000000, 2.929589, 1.680915, 0.000000, 6.116774, 6.74β¦
+$ HSPC_562 <dbl> 0.000000, 0.000000, 2.717569, 0.000000, 0.000000, 8.61β¦
+$ HSPC_563 <dbl> 0.000000, 1.199800, 1.845653, 0.000000, 1.845653, 0.00β¦
+$ HSPC_566 <dbl> 0.000000, 0.000000, 2.959197, 0.000000, 2.959197, 2.13β¦
+$ HSPC_567 <dbl> 0.000000, 0.000000, 1.812523, 0.000000, 1.812523, 6.68β¦
+$ HSPC_568 <dbl> 0.000000, 0.000000, 2.956854, 0.000000, 2.131637, 2.95β¦
+$ HSPC_569 <dbl> 0.0000000, 1.2707229, 0.7709662, 0.0000000, 1.2707229,β¦
+$ HSPC_571 <dbl> 0.000000, 1.041987, 1.041987, 0.000000, 1.041987, 1.64β¦
+$ HSPC_573 <dbl> 0.000000, 0.000000, 1.461676, 0.000000, 3.288566, 0.00β¦
+$ HSPC_574 <dbl> 0.0000000, 0.7547277, 1.9066029, 0.0000000, 5.9897178,β¦
+$ HSPC_575 <dbl> 0.000000, 1.183227, 2.604870, 4.577438, 2.878570, 1.18β¦
+$ HSPC_576 <dbl> 0.000000, 0.000000, 2.741129, 0.000000, 10.233110, 6.7β¦
+$ HSPC_577 <dbl> 0.000000, 0.000000, 0.000000, 0.000000, 2.834036, 1.60β¦
+$ HSPC_578 <dbl> 0.000000, 0.000000, 1.404000, 7.371858, 2.101881, 1.40β¦
+$ HSPC_579 <dbl> 0.000000, 0.000000, 0.000000, 0.000000, 7.491585, 1.82β¦
+$ HSPC_580 <dbl> 0.000000, 0.000000, 1.510090, 0.000000, 1.510090, 0.00β¦
+$ HSPC_582 <dbl> 4.342803, 9.749104, 0.000000, 0.000000, 5.826065, 1.65β¦
+$ HSPC_584 <dbl> 0.000000, 0.000000, 2.565813, 0.000000, 3.733595, 7.76β¦
+$ HSPC_585 <dbl> 0.000000, 0.000000, 1.449121, 0.000000, 1.449121, 5.35β¦
+$ HSPC_586 <dbl> 0.0000000, 0.8914714, 1.4383643, 0.0000000, 1.8339836,β¦
+$ HSPC_589 <dbl> 0.000000, 1.963326, 2.765365, 0.000000, 7.352066, 0.00β¦
+$ HSPC_590 <dbl> 0.000000, 0.000000, 1.835966, 1.192227, 1.192227, 6.95β¦
+$ HSPC_592 <dbl> 0.000000, 0.000000, 0.000000, 5.165700, 1.227806, 0.00β¦
+$ HSPC_593 <dbl> 0.000000, 0.000000, 0.000000, 0.000000, 3.554248, 0.00β¦
+$ HSPC_594 <dbl> 1.950098, 0.000000, 1.950098, 0.000000, 4.395615, 5.71β¦
+$ HSPC_595 <dbl> 1.756544, 0.000000, 1.756544, 0.000000, 2.796431, 3.54β¦
+$ HSPC_596 <dbl> 0.000000, 0.000000, 0.000000, 0.000000, 2.086691, 7.95β¦
+$ HSPC_597 <dbl> 0.000000, 0.000000, 1.563392, 0.000000, 0.000000, 2.29β¦
+$ HSPC_598 <dbl> 0.000000, 0.000000, 1.220673, 1.220673, 0.000000, 1.22β¦
+$ HSPC_599 <dbl> 0.000000, 1.349651, 2.034571, 0.000000, 1.349651, 0.00β¦
+$ HSPC_600 <dbl> 0.000000, 0.000000, 0.000000, 0.000000, 4.377207, 0.00β¦
+$ HSPC_601 <dbl> 0.000000, 0.000000, 2.865429, 0.000000, 2.376203, 1.63β¦
+$ HSPC_602 <dbl> 0.000000, 0.000000, 0.000000, 0.000000, 3.806407, 2.41β¦
+$ HSPC_603 <dbl> 0.000000, 2.004660, 1.589106, 0.000000, 9.490018, 0.00β¦
+$ HSPC_604 <dbl> 1.748474, 0.000000, 2.516030, 0.000000, 1.748474, 0.00β¦
+$ HSPC_606 <dbl> 0.000000, 0.000000, 1.075087, 0.000000, 2.111214, 0.00β¦
+$ HSPC_607 <dbl> 0.000000, 0.000000, 3.717957, 0.000000, 9.191362, 0.00β¦
+$ HSPC_608 <dbl> 0.000000, 1.574605, 1.574605, 0.000000, 3.156098, 1.57β¦
+$ HSPC_610 <dbl> 0.000000, 0.000000, 0.000000, 0.000000, 0.000000, 0.00β¦
+$ HSPC_612 <dbl> 0.000000, 1.356545, 2.043143, 0.000000, 6.275658, 0.00β¦
+$ HSPC_613 <dbl> 0.000000, 0.000000, 1.438703, 6.081511, 2.144549, 6.95β¦
+$ HSPC_614 <dbl> 0.000000, 1.315161, 3.077500, 0.000000, 4.543775, 1.31β¦
+$ HSPC_615 <dbl> 0.000000, 0.000000, 0.000000, 0.000000, 2.450652, 0.00β¦
+$ HSPC_617 <dbl> 0.0000000, 1.3847809, 2.3300729, 0.0000000, 0.8525275,β¦
+$ HSPC_618 <dbl> 0.000000, 0.000000, 3.542103, 0.000000, 2.885428, 2.39β¦
+$ HSPC_620 <dbl> 0.000000, 0.000000, 0.000000, 0.000000, 2.517983, 0.00β¦
+$ HSPC_623 <dbl> 0.000000, 0.000000, 0.000000, 0.000000, 8.705469, 1.70β¦
+$ HSPC_624 <dbl> 0.0000000, 0.7200995, 0.0000000, 0.0000000, 8.9490659,β¦
+$ HSPC_625 <dbl> 0.000000, 0.000000, 0.000000, 3.458561, 8.847668, 2.93β¦
+$ HSPC_626 <dbl> 0.000000, 0.000000, 0.000000, 0.000000, 3.424363, 0.00β¦
+$ HSPC_627 <dbl> 0.000000, 0.000000, 0.000000, 0.000000, 8.000538, 6.99β¦
+$ HSPC_628 <dbl> 0.000000, 1.638219, 0.000000, 0.000000, 1.638219, 0.00β¦
+$ HSPC_629 <dbl> 1.196665, 0.000000, 0.000000, 0.000000, 1.841645, 0.00β¦
+$ HSPC_630 <dbl> 0.000000, 0.000000, 0.000000, 0.000000, 2.098177, 2.09β¦
+$ HSPC_631 <dbl> 0.000000, 1.893172, 1.237108, 0.000000, 9.108643, 1.23β¦
+$ HSPC_633 <dbl> 0.000000, 0.000000, 2.731996, 0.000000, 2.731996, 0.00β¦
+$ HSPC_634 <dbl> 0.000000, 0.000000, 0.000000, 0.000000, 8.501517, 0.00β¦
+$ HSPC_635 <dbl> 0.000000, 0.000000, 0.000000, 0.000000, 2.892953, 0.00β¦
+$ HSPC_636 <dbl> 0.000000, 1.087599, 1.700617, 1.087599, 6.627788, 0.00β¦
+$ HSPC_637 <dbl> 0.0000000, 0.9389313, 2.4816963, 0.0000000, 7.3021856,β¦
+$ HSPC_638 <dbl> 0.0000000, 0.0000000, 1.1842890, 0.0000000, 2.5023010,β¦
+$ HSPC_639 <dbl> 0.996580, 1.994867, 2.579258, 0.000000, 2.316452, 0.99β¦
+$ HSPC_640 <dbl> 0.000000, 1.025432, 2.362406, 0.000000, 2.627103, 1.02β¦
+$ HSPC_641 <dbl> 0.000000, 0.000000, 2.000512, 0.000000, 2.000512, 1.00β¦
+$ HSPC_643 <dbl> 0.000000, 2.465561, 1.705628, 0.000000, 9.092947, 1.70β¦
+$ HSPC_644 <dbl> 0.0000000, 0.4904320, 0.8557752, 0.0000000, 6.1750519,β¦
+$ HSPC_645 <dbl> 0.0000000, 0.0000000, 0.7156666, 0.0000000, 2.0742346,β¦
+$ HSPC_646 <dbl> 0.0000000, 0.0000000, 0.0000000, 0.9959057, 9.3159931,β¦
+$ HSPC_648 <dbl> 0.000000, 2.242718, 0.000000, 0.000000, 3.081640, 1.51β¦
+$ HSPC_649 <dbl> 0.0000000, 0.7139349, 0.7139349, 0.0000000, 0.7139349,β¦
+$ HSPC_651 <dbl> 0.000000, 2.253619, 7.476806, 0.000000, 6.023902, 2.73β¦
+$ HSPC_652 <dbl> 1.352094, 0.000000, 2.500412, 0.000000, 2.037610, 0.00β¦
+$ HSPC_654 <dbl> 0.000000, 0.000000, 0.000000, 0.000000, 9.886385, 7.53β¦
+$ HSPC_656 <dbl> 0.000000, 1.355844, 1.355844, 0.000000, 0.000000, 0.00β¦
+$ HSPC_657 <dbl> 0.000000, 2.238724, 3.077173, 0.000000, 6.951322, 3.07β¦
+$ HSPC_658 <dbl> 0.000000, 0.000000, 2.796922, 3.846645, 8.942041, 0.00β¦
+$ HSPC_660 <dbl> 0.000000, 1.253314, 1.253314, 0.000000, 7.108572, 1.25β¦
+$ HSPC_661 <dbl> 0.000000, 1.491329, 3.043680, 1.491329, 9.643608, 0.00β¦
+$ HSPC_662 <dbl> 0.000000, 0.000000, 0.000000, 0.000000, 1.688146, 4.39β¦
+$ HSPC_663 <dbl> 0.000000, 0.000000, 0.000000, 0.000000, 0.000000, 6.57β¦
+$ HSPC_664 <dbl> 0.0000000, 1.5053124, 0.9406784, 0.0000000, 1.5053124,β¦
+$ HSPC_665 <dbl> 0.000000, 1.290390, 1.290390, 0.000000, 6.107672, 1.29β¦
+$ HSPC_666 <dbl> 0.000000, 1.130141, 0.000000, 7.631839, 8.362422, 6.31β¦
+$ HSPC_667 <dbl> 0.000000, 0.000000, 1.776997, 0.000000, 6.465588, 1.77β¦
+$ HSPC_668 <dbl> 0.000000, 0.000000, 0.000000, 0.000000, 9.302290, 0.00β¦
+$ HSPC_669 <dbl> 0.000000, 0.000000, 2.425594, 0.000000, 1.671860, 0.00β¦
+$ HSPC_670 <dbl> 0.000000, 2.337848, 3.718794, 0.000000, 0.000000, 2.33β¦
+$ HSPC_671 <dbl> 0.000000, 0.000000, 0.000000, 0.000000, 2.158776, 0.00β¦
+$ HSPC_672 <dbl> 0.000000, 0.000000, 0.000000, 0.000000, 1.038159, 0.00β¦
+$ HSPC_673 <dbl> 0.000000, 1.519487, 1.519487, 0.000000, 8.786551, 5.68β¦
+$ HSPC_674 <dbl> 0.000000, 1.235988, 0.000000, 0.000000, 1.891750, 1.89β¦
+$ HSPC_676 <dbl> 0.000000, 0.000000, 0.000000, 0.000000, 4.975163, 1.74β¦
+$ HSPC_678 <dbl> 0.000000, 2.249420, 1.524795, 0.000000, 3.089130, 0.00β¦
+$ HSPC_679 <dbl> 2.256522, 2.256522, 0.000000, 1.530665, 2.737162, 1.53β¦
+$ HSPC_680 <dbl> 0.000000, 2.323337, 0.000000, 5.359270, 8.465280, 0.00β¦
+$ HSPC_681 <dbl> 0.0000000, 1.6627807, 0.0000000, 0.0000000, 1.9591579,β¦
+$ HSPC_682 <dbl> 0.000000, 1.043463, 0.000000, 7.477477, 2.064713, 1.04β¦
+$ HSPC_683 <dbl> 0.000000, 0.000000, 2.261955, 0.000000, 3.631015, 0.00β¦
+$ HSPC_687 <dbl> 0.000000, 0.000000, 3.811941, 9.810273, 3.430744, 2.09β¦
+$ HSPC_689 <dbl> 0.000000, 0.000000, 0.000000, 2.085635, 10.065718, 2.0β¦
+$ HSPC_690 <dbl> 2.196289, 2.196289, 3.029625, 0.000000, 6.808290, 7.65β¦
+$ HSPC_692 <dbl> 2.555176, 0.000000, 4.919547, 0.000000, 5.637318, 2.55β¦
+$ HSPC_695 <dbl> 0.0000000, 0.2681148, 1.3971816, 0.2681148, 10.7977224β¦
+$ HSPC_696 <dbl> 0.000000, 2.265383, 4.020705, 0.000000, 8.976227, 0.00β¦
+$ HSPC_697 <dbl> 0.000000, 1.271303, 3.012385, 0.000000, 0.000000, 7.59β¦
+$ HSPC_698 <dbl> 0.000000, 0.000000, 4.694712, 0.000000, 0.000000, 0.00β¦
+$ HSPC_699 <dbl> 0.000000, 0.000000, 2.930008, 0.000000, 0.000000, 0.00β¦
+$ HSPC_700 <dbl> 0.000000, 0.000000, 1.083768, 0.000000, 1.695606, 0.00β¦
+$ HSPC_701 <dbl> 0.000000, 1.156584, 3.066217, 1.156584, 5.095538, 1.79β¦
+$ HSPC_702 <dbl> 0.000000, 0.000000, 3.185800, 0.000000, 2.336223, 2.33β¦
+$ HSPC_703 <dbl> 0.000000, 3.026458, 2.193467, 4.488271, 7.306130, 6.31β¦
+$ HSPC_704 <dbl> 0.000000, 1.708092, 1.708092, 0.000000, 1.708092, 8.37β¦
+$ HSPC_705 <dbl> 0.0000000, 0.0000000, 0.0000000, 0.0000000, 7.8292660,β¦
+$ HSPC_706 <dbl> 0.000000, 1.272727, 0.000000, 1.272727, 6.221902, 7.03β¦
+$ HSPC_707 <dbl> 0.000000, 0.000000, 0.000000, 0.000000, 3.917498, 1.36β¦
+$ HSPC_708 <dbl> 0.000000, 0.000000, 0.000000, 4.944545, 9.429525, 9.22β¦
+$ HSPC_709 <dbl> 0.000000, 0.000000, 6.392596, 0.000000, 5.005898, 0.00β¦
+$ HSPC_714 <dbl> 0.000000, 0.000000, 3.784587, 0.000000, 2.395136, 1.64β¦
+$ HSPC_716 <dbl> 0.000000, 0.000000, 0.000000, 1.311350, 8.040385, 1.31β¦
+$ HSPC_717 <dbl> 0.000000, 1.153655, 1.153655, 0.000000, 2.224752, 0.00β¦
+$ HSPC_719 <dbl> 0.000000, 0.000000, 3.146515, 6.492252, 4.618557, 0.00β¦
+$ HSPC_720 <dbl> 0.0000000, 0.8205612, 1.3403833, 0.0000000, 1.7217133,β¦
+$ HSPC_721 <dbl> 0.000000, 2.935568, 3.456262, 0.000000, 0.000000, 2.11β¦
+$ HSPC_722 <dbl> 0.000000, 0.000000, 2.268643, 0.000000, 9.095591, 1.18β¦
+$ HSPC_723 <dbl> 0.8420975, 0.8420975, 2.5250483, 0.0000000, 4.8843811,β¦
+$ HSPC_724 <dbl> 0.0000000, 1.0942930, 1.7093650, 0.0000000, 3.2499204,β¦
+$ HSPC_725 <dbl> 1.577147, 0.000000, 3.159495, 0.000000, 2.312545, 2.79β¦
+$ HSPC_727 <dbl> 0.000000, 1.576167, 3.894561, 0.000000, 8.810183, 0.00β¦
+$ HSPC_729 <dbl> 0.0000000, 0.0000000, 1.9363149, 0.0000000, 7.5873035,β¦
+$ HSPC_730 <dbl> 1.134736, 1.761952, 2.197661, 0.000000, 7.311461, 0.00β¦
+$ HSPC_731 <dbl> 0.000000, 1.129768, 1.129768, 4.039758, 1.755516, 5.09β¦
+$ HSPC_732 <dbl> 0.0000000, 0.6937047, 2.2340688, 0.6937047, 2.0310980,β¦
+$ HSPC_733 <dbl> 0.000000, 0.000000, 1.435585, 0.000000, 4.173862, 2.14β¦
+$ HSPC_734 <dbl> 0.000000, 1.217180, 1.578880, 0.000000, 9.362294, 1.21β¦
+$ HSPC_735 <dbl> 0.000000, 0.000000, 2.048558, 0.000000, 9.326379, 2.04β¦
+$ HSPC_736 <dbl> 0.0000000, 0.0000000, 0.6789402, 0.0000000, 2.2034453,β¦
+$ HSPC_737 <dbl> 0.0000000, 0.0000000, 0.7110779, 0.0000000, 7.7355892,β¦
+$ HSPC_738 <dbl> 0.000000, 2.715943, 0.000000, 0.000000, 3.362289, 8.20β¦
+$ HSPC_740 <dbl> 0.000000, 0.000000, 0.000000, 0.000000, 2.620463, 6.54β¦
+$ HSPC_742 <dbl> 0.0000000, 0.8436636, 0.8436636, 0.0000000, 1.7586463,β¦
+$ HSPC_743 <dbl> 1.122102, 0.000000, 0.000000, 0.000000, 0.000000, 6.91β¦
+$ HSPC_744 <dbl> 0.000000, 7.472712, 1.212953, 0.000000, 1.212953, 0.00β¦
+$ HSPC_745 <dbl> 0.000000, 0.000000, 0.000000, 2.402561, 2.402561, 0.00β¦
+$ HSPC_746 <dbl> 0.000000, 2.183740, 0.000000, 0.000000, 6.837761, 0.00β¦
+$ HSPC_747 <dbl> 0.000000, 0.000000, 1.777355, 0.000000, 7.778192, 2.54β¦
+$ HSPC_748 <dbl> 0.000000, 2.263816, 0.000000, 0.000000, 3.303450, 0.00β¦
+$ HSPC_749 <dbl> 0.000000, 0.000000, 1.443774, 0.000000, 3.501043, 0.00β¦
+$ HSPC_750 <dbl> 0.000000, 1.029692, 0.000000, 0.000000, 8.102961, 0.00β¦
+$ HSPC_751 <dbl> 0.000000, 0.000000, 3.435201, 0.000000, 3.435201, 7.28β¦
+$ HSPC_752 <dbl> 2.227867, 0.000000, 2.227867, 0.000000, 3.065024, 9.23β¦
+$ HSPC_753 <dbl> 0.000000, 0.000000, 2.092163, 0.000000, 2.420031, 3.10β¦
+$ HSPC_755 <dbl> 0.0000000, 0.0000000, 0.0000000, 0.0000000, 5.3881500,β¦
+$ HSPC_756 <dbl> 0.000000, 1.730911, 0.000000, 0.000000, 6.980096, 6.68β¦
+$ HSPC_757 <dbl> 0.000000, 1.394821, 1.394821, 0.000000, 3.193425, 0.00β¦
+$ HSPC_758 <dbl> 0.0000000, 0.8647569, 1.4016663, 0.0000000, 7.1436038,β¦
+$ HSPC_759 <dbl> 1.5063802, 0.9414682, 1.9112870, 0.9414682, 2.2271023,β¦
+$ HSPC_760 <dbl> 0.000000, 9.073516, 1.653873, 0.000000, 1.051989, 0.00β¦
+$ HSPC_761 <dbl> 0.0000000, 2.0270678, 1.5086587, 0.0000000, 2.4076406,β¦
+$ HSPC_762 <dbl> 0.000000, 1.935807, 1.935807, 0.000000, 7.772123, 0.00β¦
+$ HSPC_764 <dbl> 0.000000, 1.784134, 1.784134, 0.000000, 3.969445, 1.78β¦
+$ HSPC_765 <dbl> 0.000000, 2.116018, 2.116018, 0.000000, 11.306195, 2.1β¦
+$ HSPC_766 <dbl> 0.0000000, 0.9827582, 0.9827582, 0.0000000, 3.5531934,β¦
+$ HSPC_767 <dbl> 0.6646406, 0.0000000, 1.4623246, 0.0000000, 10.4507620β¦
+$ HSPC_768 <dbl> 0.000000, 1.703127, 1.703127, 1.703127, 9.992206, 2.46β¦
+$ HSPC_769 <dbl> 0.000000, 2.429943, 4.213728, 0.000000, 4.772537, 2.42β¦
+$ HSPC_770 <dbl> 0.000000, 1.760248, 1.760248, 1.760248, 6.134208, 2.52β¦
+$ HSPC_771 <dbl> 0.000000, 0.000000, 1.818104, 0.000000, 8.774881, 1.81β¦
+$ HSPC_772 <dbl> 0.000000, 1.600797, 0.000000, 0.000000, 2.340909, 0.00β¦
+$ HSPC_773 <dbl> 0.0000000, 0.9900713, 1.5717090, 0.0000000, 5.2659904,β¦
+$ HSPC_774 <dbl> 0.0000000, 0.0000000, 1.5496423, 0.0000000, 2.5406754,β¦
+$ HSPC_776 <dbl> 0.000000, 0.000000, 3.691348, 2.314052, 8.369556, 0.00β¦
+$ HSPC_777 <dbl> 0.000000, 0.000000, 2.079090, 0.000000, 8.370977, 1.05β¦
+$ HSPC_778 <dbl> 0.000000, 0.000000, 3.691686, 1.434589, 4.532296, 0.00β¦
+$ HSPC_780 <dbl> 0.000000, 1.178249, 1.818049, 0.000000, 7.874420, 0.00β¦
+$ HSPC_781 <dbl> 0.000000, 2.884261, 2.884261, 0.000000, 3.783095, 2.88β¦
+$ HSPC_782 <dbl> 0.000000, 0.000000, 2.691145, 0.000000, 7.913867, 0.00β¦
+$ HSPC_783 <dbl> 0.000000, 0.000000, 1.775679, 0.000000, 8.938539, 9.20β¦
+$ HSPC_784 <dbl> 0.000000, 0.000000, 0.000000, 0.000000, 2.668054, 1.05β¦
+$ HSPC_785 <dbl> 0.000000, 0.000000, 2.465903, 0.000000, 3.530782, 1.32β¦
+$ HSPC_786 <dbl> 0.000000, 1.148465, 1.779704, 0.000000, 2.552651, 8.42β¦
+$ HSPC_787 <dbl> 0.000000, 0.000000, 3.897091, 2.161763, 3.513976, 4.84β¦
+$ HSPC_788 <dbl> 0.000000, 0.000000, 3.844884, 0.000000, 1.877270, 6.68β¦
+$ HSPC_789 <dbl> 0.000000, 0.000000, 1.822053, 0.000000, 2.264164, 1.18β¦
+$ HSPC_790 <dbl> 0.000000, 0.000000, 2.851872, 0.000000, 9.272098, 0.00β¦
+$ HSPC_791 <dbl> 1.789964, 0.000000, 4.930584, 0.000000, 6.443477, 2.56β¦
+$ HSPC_794 <dbl> 0.000000, 1.112719, 0.000000, 1.112719, 2.498279, 3.78β¦
+$ HSPC_795 <dbl> 0.0000000, 0.0000000, 0.0000000, 0.0000000, 2.2924736,β¦
+$ HSPC_796 <dbl> 0.0000000, 0.7001062, 1.5229964, 1.1694432, 6.1361361,β¦
+$ HSPC_797 <dbl> 0.000000, 0.872225, 1.411951, 0.872225, 3.217981, 0.87β¦
+$ HSPC_798 <dbl> 0.000000, 1.531160, 0.000000, 2.257120, 4.314828, 0.00β¦
+$ HSPC_799 <dbl> 0.000000, 0.000000, 4.059222, 2.637723, 3.516894, 0.00β¦
+$ HSPC_800 <dbl> 0.000000, 0.000000, 1.766326, 0.000000, 5.615808, 3.03β¦
+$ HSPC_801 <dbl> 0.000000, 1.335456, 0.000000, 0.000000, 1.335456, 0.00β¦
+$ HSPC_802 <dbl> 0.000000, 0.000000, 0.000000, 2.881726, 4.081151, 0.00β¦
+$ HSPC_803 <dbl> 0.000000, 0.000000, 0.000000, 0.000000, 7.326296, 0.00β¦
+$ HSPC_804 <dbl> 0.000000, 0.000000, 1.871913, 0.000000, 2.660005, 6.23β¦
+$ HSPC_806 <dbl> 0.000000, 0.000000, 0.000000, 0.000000, 4.774769, 0.00β¦
+$ HSPC_807 <dbl> 0.0000000, 1.2411117, 0.0000000, 0.0000000, 2.3480676,β¦
+$ HSPC_808 <dbl> 0.0000000, 0.0000000, 1.1139506, 2.5001649, 1.1139506,β¦
+$ HSPC_809 <dbl> 1.788499, 0.000000, 0.000000, 1.788499, 3.064135, 1.78β¦
+$ HSPC_810 <dbl> 0.000000, 0.000000, 1.651345, 0.000000, 3.549216, 0.00β¦
+$ HSPC_812 <dbl> 0.0000000, 0.0000000, 2.0668334, 0.0000000, 8.1782380,β¦
+$ HSPC_813 <dbl> 0.0000000, 0.0000000, 0.6277581, 4.3663804, 1.8975541,β¦
+$ HSPC_814 <dbl> 0.000000, 1.109763, 2.161664, 0.000000, 0.000000, 0.00β¦
+$ HSPC_815 <dbl> 0.9630613, 0.9630613, 2.7434401, 0.9630613, 7.9310753,β¦
+$ HSPC_816 <dbl> 0.000000, 0.000000, 1.346034, 1.346034, 6.498939, 1.34β¦
+$ HSPC_818 <dbl> 0.0000000, 0.0000000, 3.4534483, 0.9967122, 9.8653293,β¦
+$ HSPC_819 <dbl> 0.000000, 0.000000, 3.149725, 1.364557, 7.496230, 2.05β¦
+$ HSPC_820 <dbl> 0.0000000, 0.8098885, 2.4642646, 0.0000000, 9.0793660,β¦
+$ HSPC_821 <dbl> 0.000000, 0.000000, 3.792154, 0.000000, 3.175252, 0.00β¦
+$ HSPC_822 <dbl> 0.000000, 1.386534, 3.957031, 0.000000, 2.080316, 0.00β¦
+$ HSPC_824 <dbl> 0.000000, 1.236780, 1.236780, 2.342030, 2.342030, 1.23β¦
+$ HSPC_825 <dbl> 0.000000, 0.000000, 2.079118, 0.000000, 5.922947, 2.07β¦
+$ HSPC_826 <dbl> 0.000000, 2.002994, 2.002994, 0.000000, 4.811203, 0.00β¦
+$ HSPC_827 <dbl> 1.746375, 0.000000, 3.381363, 0.000000, 7.353191, 1.74β¦
+$ HSPC_828 <dbl> 0.000000, 0.000000, 1.588492, 0.000000, 2.326162, 0.00β¦
+$ HSPC_831 <dbl> 0.000000, 1.304384, 0.000000, 0.000000, 6.405611, 6.06β¦
+$ HSPC_832 <dbl> 0.000000, 0.000000, 2.376979, 0.000000, 9.076790, 1.03β¦
+$ HSPC_833 <dbl> 0.0000000, 0.0000000, 1.8371808, 0.0000000, 0.0000000,β¦
+$ HSPC_834 <dbl> 0.0000000, 0.9245023, 1.8852183, 0.0000000, 8.9614736,β¦
+$ HSPC_835 <dbl> 0.000000, 0.000000, 2.595404, 0.000000, 6.141626, 6.76β¦
+$ HSPC_836 <dbl> 0.000000, 0.000000, 3.994019, 0.000000, 4.386241, 0.00β¦
+$ HSPC_837 <dbl> 0.000000, 0.000000, 2.792826, 0.000000, 0.000000, 0.00β¦
+$ HSPC_838 <dbl> 0.0000000, 0.0000000, 3.2926469, 0.0000000, 0.9838061,β¦
+$ HSPC_839 <dbl> 0.000000, 0.000000, 2.452494, 0.000000, 2.720721, 1.69β¦
+$ HSPC_840 <dbl> 0.000000, 0.000000, 3.534585, 0.000000, 1.866730, 5.03β¦
+$ HSPC_841 <dbl> 0.000000, 0.000000, 1.438567, 0.000000, 1.438567, 1.43β¦
+$ HSPC_842 <dbl> 0.000000, 2.545827, 2.545827, 0.000000, 7.622029, 2.54β¦
+$ HSPC_843 <dbl> 1.256817, 0.000000, 1.256817, 0.000000, 1.256817, 0.00β¦
+$ HSPC_844 <dbl> 0.000000, 0.000000, 1.584047, 0.000000, 7.433263, 0.00β¦
+$ HSPC_845 <dbl> 0.000000, 1.227393, 1.880830, 7.669286, 6.989762, 0.00β¦
+$ HSPC_846 <dbl> 0.000000, 1.401354, 1.401354, 0.000000, 2.919525, 7.30β¦
+$ HSPC_848 <dbl> 0.000000, 0.000000, 1.391594, 0.000000, 2.553619, 7.94β¦
+$ HSPC_849 <dbl> 0.000000, 0.000000, 1.601976, 0.000000, 8.387312, 2.82β¦
+$ HSPC_851 <dbl> 0.000000, 0.000000, 3.910752, 0.000000, 6.824279, 7.81β¦
+$ HSPC_852 <dbl> 0.000000, 1.658355, 2.409562, 1.658355, 1.658355, 0.00β¦
+
+
+
+
+
+
+#---CODING ANSWER---
+#| echo: false
+#| output: false
+glimpse(prog_hspc_results)
+
+Rows: 280
+Columns: 6
+$ Top <dbl> 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16,β¦
+$ p.value <dbl> 7.038138e-117, 4.736622e-90, 1.832630e-88, 4.211954e-7β¦
+$ FDR <dbl> 1.970679e-114, 6.631271e-88, 1.710455e-86, 2.948368e-7β¦
+$ summary.logFC <dbl> 1.596910, 3.035165, 3.261056, -2.146491, -3.056730, 3.β¦
+$ logFC.hspc <dbl> 1.596910, 3.035165, 3.261056, -2.146491, -3.056730, 3.β¦
+$ ensembl_gene_id <chr> "ENSMUSG00000028639", "ENSMUSG00000024053", "ENSMUSG00β¦It is useful to have this information in a single dataframe to which we will add the gene information from Ensembl Having all the information together will make it easier to interpret the results and select genes of interest.
+π¬ Merge the two dataframes:
+
+
+
+# merge stats results with normalise values
+prog_hspc_results <- prog_hspc_results |>
+ left_join(prog_hspc, by = "ensembl_gene_id")This means you have the counts for each sample along with the statistical results for each gene.
+Add gene information from Ensembl using biomaRt
+Ensembl (Martin et al. 2023; Birney et al. 2004)is a bioinformatics project to organise all the biological information around the sequences of large genomes. The are a large number of databases but BioMart (Smedley et al. 2009) provides a consistent interface to the material. There are web-based tools to use these but the R package biomaRt (Durinck et al. 2009) gives you programmatic access making it easier to integrate information into R dataframes
π¬ Load the biomaRt (Durinck et al. 2009) package:
π¬ Connect to the mouse database and see what information we can retrieve:
+
+
+
+# Connect to the mouse database
+ensembl <- useMart(biomart = "ensembl",
+ dataset = "mmusculus_gene_ensembl")
+
+# See what information we can retrieve
+listAttributes(mart = ensembl) |> View()This may take a moment
+We use the getBM() function to retrieve information from the database. The filters argument is used to specified what kind of identifier we are supplying to retrieve information. The attributes argument is used to select the information we want to retrieve. The values argument is used to specify the identifers. The mart argument is used to specify the connection we created.
π¬ Get the gene information:
+
+
+
+We are getting the gene name and and a description. We also need to get the id because we will use that to merge the gene_info dataframe with the prog_hspc_results dataframe. Notice the dataframe returned only has 279 rows - one of the ids does not have information.
π¬ We can find which is missing with:
+
+
+
+prog_hspc_results |> select(ensembl_gene_id) |>
+ filter(!ensembl_gene_id %in% gene_info$ensembl_gene_id)
+
+Error:
+! [conflicted] select found in 2 packages.
+Either pick the one you want with `::`:
+β’ biomaRt::select
+β’ plotly::select
+Or declare a preference with `conflicts_prefer()`:
+β’ `conflicts_prefer(biomaRt::select)`
+β’ `conflicts_prefer(plotly::select)`Oh, conflicted has flagged a conflict for us.
π¬ Take the appropriate action to resolve the conflict:
+
+
+
+β What is the id which is missing information?
+ + +We might want to look that up - but letβs worry about it later if it turns out to be something important.
+π¬ Merge the gene information with the results:
+
+
+
+prog_hspc_results <- prog_hspc_results |>
+ left_join(gene_info, by = "ensembl_gene_id")I recommend viewing the dataframe to see the new columns. We now have dataframe with all the info we need, normalised counts, log2 normalised counts, statistical comparisons with fold changes and p values, information about the gene other than just the id
+Write the significant genes to file
+We will create dateframe of the signifcant genes and write them to file. These are the files you want to examine in more detail along with the visualisations to select your genes of interest.
+π¬ Create a dataframe of the genes significant at the 0.01 level:
+
+
+
+prog_hspc_results_sig0.01 <- prog_hspc_results |>
+ filter(FDR <= 0.01)π¬ Write the dataframe to file
+
+
+
+#---CODING ANSWER---
+#| echo: false
+#| output: false
+write_csv(prog_hspc_results_sig0.01,
+ file = "results/prog_hspc_results_sig0.01.csv")π¬ Create a dataframe of the genes significant at the 0.05 level and write to file:
+
+
+
+βHow many genes are significant at the 0.01 and 0.05 levels?
+ + + +View the relationship between cells using PCA
+We have 280 genes in our dataset. PCA will allow us to plot our cells in the βgene expressionβ space so we can see if Prog cells cluster together and HSPC cells cluster together as we would expect. We do this on the log2 transformed normalised counts.
+Our data have genes in rows and samples in columns which is a common organisation for gene expression data. However, PCA expects cells in rows and genes, the variables, in columns. We can transpose the data to get it in the correct format.
+π¬ Transpose the log2 transformed normalised counts:
+
+
+
+prog_hspc_trans <- prog_hspc_results |>
+ dplyr::select(starts_with(c("Prog_", "HSPC_"))) |>
+ t() |>
+ data.frame()We have used the select() function to select all the columns that start with Prog_ or HSPC_. We then use the t() function to transpose the dataframe. We then convert the resulting matrix to a dataframe using data.frame(). If you view that dataframe youβll see it has default column name which we can fix using colnames() to set the column names to the gene ids.
π¬ Set the column names to the gene ids:
+
+
+
+colnames(prog_hspc_trans) <- prog_hspc_results$ensembl_gene_idperform PCA using standard functions
+
+
+
+pca <- prog_hspc_trans |>
+ prcomp(rank. = 15) The rank. argument tells prcomp() to only calculate the first 15 principal components. This is useful for visualisation as we can only plot in 2 or 3 dimensions. We can see the results of the PCA by viewing the summary() of the pca object.
+
+
+summary(pca)
+
+Importance of first k=15 (out of 280) components:
+ PC1 PC2 PC3 PC4 PC5 PC6 PC7
+Standard deviation 12.5612 8.36646 5.98988 5.41386 4.55730 4.06142 3.84444
+Proportion of Variance 0.1099 0.04874 0.02498 0.02041 0.01446 0.01149 0.01029
+Cumulative Proportion 0.1099 0.15861 0.18359 0.20400 0.21846 0.22995 0.24024
+ PC8 PC9 PC10 PC11 PC12 PC13 PC14
+Standard deviation 3.70848 3.66899 3.5549 3.48508 3.44964 3.42393 3.37882
+Proportion of Variance 0.00958 0.00937 0.0088 0.00846 0.00829 0.00816 0.00795
+Cumulative Proportion 0.24982 0.25919 0.2680 0.27645 0.28473 0.29290 0.30085
+ PC15
+Standard deviation 3.33622
+Proportion of Variance 0.00775
+Cumulative Proportion 0.30860The Proportion of Variance tells us how much of the variance is explained by each component. We can see that the first component explains 0.1099 of the variance, the second 0.04874, and the third 0.2498. Together the first three components explain 18% of the total variance in the data. Plotting PC1 against PC2 will capture about 16% of the variance. This is not that high but it likely better than we would get plotting any two genes against each other. To plot the PC1 against PC2 we will need to extract the PC1 and PC2 score from the pca object and add labels for the cells.
+π¬ Create a dataframe of the PC1 and PC2 scores which are in pca$x and add the cell ids:
+
+
+pca_labelled <- data.frame(pca$x,
+ cell_id = row.names(prog_hspc_trans))It will be helpful to add a column for the cell type so we can label points. One way to do this is to extract the information in the cell_id column into two columns.
+π¬ Extract the cell type and cell number from the cell_id column (keeping the cell_id column):
+
+
+"([a-zA-Z]{4})_([0-9]{3})" is a regular expression - or regex. [a-zA-Z] means any lower or upper case letter, {4} means 4 of them, and [0-9] means any number, {3} means 3 of them. The brackets around the two parts of the regex mean we want to extract those parts. The first part goes into cell_type and the second part goes into cell_number. The _ between the two patterns matches the underscore and the fact it isnβt in a bracket means we donβt want to keep it.
We can now plot the PC1 and PC2 scores.
+π¬ Plot PC1 against PC2 and colour the points by cell type:
+
+
+
+pca <- pca_labelled |>
+ ggplot(aes(x = PC1, y = PC2,
+ colour = cell_type)) +
+ geom_point(alpha = 0.4) +
+ scale_colour_viridis_d(end = 0.8, begin = 0.15,
+ name = "Cell type") +
+ theme_classic()
+pca
+
+
Fairly good separation of cell types but plenty of overlap
+π¬ Save the plot to file:
+
+
+
+ggsave("figures/prog_hspc-pca.png",
+ plot = pca,
+ height = 3,
+ width = 4,
+ units = "in",
+ device = "png")Visualise the expression of the most significant genes using a heatmap
+ +we will use the most significant genes on a random subset of the cells since ~1500 columns is a lot
+
+
+
+
+
+
+rownames(mat) <- prog_hspc_results_sig0.01$external_gene_name
+
+
+n_cell_clusters <- 2
+n_gene_clusters <- 2
+
+
+heatmaply(mat,
+ scale = "row",
+ hide_colorbar = TRUE,
+ k_col = n_cell_clusters,
+ k_row = n_gene_clusters,
+ label_names = c("Gene", "Cell id", "Expression (normalised, log2)"),
+ fontsize_row = 7, fontsize_col = 10,
+ labCol = colnames(mat),
+ labRow = rownames(mat),
+ heatmap_layers = theme(axis.line = element_blank()))
+
+
+
+will take a few mins to run, and longer to appear in the viewer separation is not as strong as for the frog data run a few times to see different subset
+Visualise all the results with a volcano plot
+colour the points if FDR < 0.05 and prog_hspc_results > 1
+ +
+
+
+
+
+
+vol <- prog_hspc_results |>
+ ggplot(aes(x = summary.logFC,
+ y = log10_FDR,
+ colour = interaction(sig, bigfc))) +
+ geom_point() +
+ geom_hline(yintercept = -log10(0.05),
+ linetype = "dashed") +
+ geom_vline(xintercept = 1,
+ linetype = "dashed") +
+ geom_vline(xintercept = -1,
+ linetype = "dashed") +
+ scale_x_continuous(expand = c(0, 0)) +
+ scale_y_continuous(expand = c(0, 0)) +
+ scale_colour_manual(values = c("gray",
+ "pink",
+ "deeppink")) +
+ geom_text_repel(data = subset(prog_hspc_results,
+ bigfc & sig),
+ aes(label = external_gene_name),
+ size = 3,
+ max.overlaps = 50) +
+ theme_classic() +
+ theme(legend.position = "none")
+
+
+
+
+
+
+
+
+ggsave("figures/prog-hspc-volcano.png",
+ plot = vol,
+ height = 4.5,
+ width = 4.5,
+ units = "in",
+ device = "png")π€ Look after future you!
+π¬ Go through your script (cont-fgf-s30.R or hspc-prog.R) and tidy up. I would suggest restarting R and trying to run the full pipeline from start to finish. You might need to :
-
+
- collect together library statements at the top of the script +
- remove code that you needed to start today but which wouldnβt be needed running the script from the top (e.g., importing) +
- edit your comments for clarity +
- rename variables for consistency or clarity +
- remove house keeping or exploratory code +
- restyle code, add code section headers etc +
π₯³ Finished
+Well Done!
+Independent study following the workshop
+ +The Code file
+These contain all the code needed in the workshop even where it is not visible on the webpage.
+The workshop.qmd file is the file I use to compile the practical. Qmd stands for Quarto markdown. It allows code and ordinary text to be interleaved to produce well-formatted reports including webpages. Right-click on the link and choose Save-As to download. You will be able to open the Qmd file in RStudio. Alternatively, View in Browser. Coding and thinking answers are marked with #---CODING ANSWER--- and #---THINKING ANSWER---
Pages made with R (R Core Team 2023), Quarto (Allaire et al. 2022), knitr (Xie 2022), kableExtra (Zhu 2021)
References
+
+Allaire, J. J., Charles Teague, Carlos Scheidegger, Yihui Xie, and Christophe Dervieux. 2022. Quarto. https://doi.org/10.5281/zenodo.5960048.
+
+
+Birney, Ewan, T. Daniel Andrews, Paul Bevan, Mario Caccamo, Yuan Chen, Laura Clarke, Guy Coates, et al. 2004. βAn Overview of Ensembl.β Genome Research 14 (5): 925β28. https://doi.org/10.1101/gr.1860604.
+
+
+Durinck, Steffen, Paul T. Spellman, Ewan Birney, and Wolfgang Huber. 2009. βMapping Identifiers for the Integration of Genomic Datasets with the r/Bioconductor Package biomaRtβ 4.
+
+
+Fisher, Malcolm, Christina James-Zorn, Virgilio Ponferrada, Andrew J Bell, Nivitha Sundararaj, Erik Segerdell, Praneet Chaturvedi, et al. 2023. βXenbase: Key Features and Resources of the Xenopus Model Organism Knowledgebase.β Genetics 224 (1): iyad018. https://doi.org/10.1093/genetics/iyad018.
+
+
+Hester, Jim, Hadley Wickham, and GΓ‘bor CsΓ‘rdi. 2023. βFs: Cross-Platform File System Operations Based on βLibuvβ.β
+
+
+Martin, Fergal J, M Ridwan Amode, Alisha Aneja, Olanrewaju Austine-Orimoloye, Andrey G Azov, If Barnes, Arne Becker, et al. 2023. βEnsembl 2023.β Nucleic Acids Research 51 (D1): D933β41. https://doi.org/10.1093/nar/gkac958.
+
+
+R Core Team. 2023. R: A Language and Environment for Statistical Computing. Vienna, Austria: R Foundation for Statistical Computing. https://www.R-project.org/.
+
+
+Smedley, Damian, Syed Haider, Benoit Ballester, Richard Holland, Darin London, Gudmundur Thorisson, and Arek Kasprzyk. 2009. βBioMart Biological Queries Made Easy.β BMC Genomics 10 (1): 22. https://doi.org/10.1186/1471-2164-10-22.
+
+
+Wickham, Hadley. 2023. βConflicted: An Alternative Conflict Resolution Strategy.β
+
+
+Wickham, Hadley, Mara Averick, Jennifer Bryan, Winston Chang, Lucy DβAgostino McGowan, Romain FranΓ§ois, Garrett Grolemund, et al. 2019. βWelcome to the Tidyverseβ 4: 1686. https://doi.org/10.21105/joss.01686.
+
+
+Wickham, Hadley, and Jennifer Bryan. 2023. βReadxl: Read Excel Files.β https://CRAN.R-project.org/package=readxl.
+
+
+Xie, Yihui. 2022. βKnitr: A General-Purpose Package for Dynamic Report Generation in r.β https://yihui.org/knitr/.
+
+
+Zhu, Hao. 2021. βkableExtra: Construct Complex Table with βKableβ and Pipe Syntax.β https://CRAN.R-project.org/package=kableExtra.
+
+