Extract context-specific region embeddings from ChromBERT¶
This notebook shows how to extract region embeddings using the ChromBERT-tools Python API.
embed_region API: Generate region embeddings for input regions.
umap_plot API: Visualize region embeddings with UMAP using user-defined annotations.
For the bash command-line usage, see `examples/cli/embed_region.ipynb <../cli/embed_region.ipynb>`__
For more details, please refer to the `embed_region <https://chrombert-tools.readthedocs.io/en/latest/commands/embed_region.html>`__ command documentation
[1]:
from chrombert_tools import embed_region, umap_plot
generate region embedding¶
[2]:
import numpy as np
import pandas as pd
[3]:
# Returns:
# - region_emb: Region embedding array with shape ``(n_regions, 768)``. Each row corresponds to one ChromBERT bin overlapping the input regions.
# - overlap_region_bed: Input regions that overlap ChromBERT bins.
# build_region_index maps to ChromBERT's reference regions
results = embed_region(
region="../data/umap_region_1kb_downsample.bed", # your region
odir="./output_emb_region_1kb", # output directory
genome="hg38", # Options: "hg38", "mm10"
resolution="1kb", # Options: "1kb", "2kb", "4kb", "200bp"
)
region_emb=results.region_emb
overlap_region_bed=results.overlap_region_bed
Region summary - total: 3000, overlapping with ChromBERT: 3000 (one region may overlap multiple ChromBERT regions, we keep overlaps with ≥50% coverage of either the ChromBERT bin or the input region), non-overlapping: 0
Using cached region embeddings...
Finished!
Focus region summary - total: 3000, overlapping with ChromBERT: 3000, non-overlapping: 0
Note: It is possible for a single region to overlap multiple ChromBERT regions.
Overlapping regions BED file: ./output_emb_region_1kb/overlap_region.bed
Non-overlapping regions BED file: ./output_emb_region_1kb/no_overlap_region.bed
Region embeddings saved to: ./output_emb_region_1kb/region_emb_emb.npy
Embedding type: general
[4]:
# Region embedding array with shape ``(n_regions, 768)``.
# Each row corresponds to one ChromBERT bin overlapping the input regions.
region_emb
[4]:
array([[ 3.547 , 0.828 , 1.625 , ..., -0.578 , -1.422 , -1.406 ],
[-0.7812, -0.4355, 0.621 , ..., -0.59 , -0.8867, 0.6367],
[-0.9375, -0.2031, 1.016 , ..., -0.377 , -0.2637, 1.547 ],
...,
[-0.336 , -0.9375, 1.07 , ..., -1.234 , -0.953 , -0.5117],
[ 0.0398, 0.287 , -0.2012, ..., 0.2812, 0.0908, 1.781 ],
[ 0.1543, -0.4746, 1.281 , ..., -0.711 , -0.668 , -0.252 ]],
dtype=float16)
[5]:
# Input regions that overlap ChromBERT bins.
# DataFrame columns: [chrom, start, end, build_region_index, start_input, end_input].
# The region order matches the order of embeddings in `region_emb`.
overlap_region_bed
[5]:
| chrom | start | end | build_region_index | start_input | end_input | |
|---|---|---|---|---|---|---|
| 0 | chr1 | 54000 | 55000 | 6 | 54000 | 55000 |
| 1 | chr1 | 916000 | 917000 | 213 | 916000 | 917000 |
| 2 | chr1 | 960000 | 961000 | 255 | 960000 | 961000 |
| 3 | chr1 | 1004000 | 1005000 | 296 | 1004000 | 1005000 |
| 4 | chr1 | 1013000 | 1014000 | 305 | 1013000 | 1014000 |
| ... | ... | ... | ... | ... | ... | ... |
| 2995 | chr1 | 248839000 | 248840000 | 183893 | 248839000 | 248840000 |
| 2996 | chr1 | 248857000 | 248858000 | 183907 | 248857000 | 248858000 |
| 2997 | chr1 | 248861000 | 248862000 | 183911 | 248861000 | 248862000 |
| 2998 | chr1 | 248873000 | 248874000 | 183923 | 248873000 | 248874000 |
| 2999 | chr1 | 248945000 | 248946000 | 183981 | 248945000 | 248946000 |
3000 rows × 6 columns
[6]:
# Map each region to its user-defined annotation class
region_anno = pd.read_csv("../data/umap_region_1kb_downsample.bed",sep="\t",header=None,names=["chrom","start_input","end_input","build_region_index","anno"])
overlap_region_bed = overlap_region_bed.merge(region_anno[["chrom","start_input","end_input","anno"]],on=["chrom","start_input","end_input"])
overlap_region_bed
[6]:
| chrom | start | end | build_region_index | start_input | end_input | anno | |
|---|---|---|---|---|---|---|---|
| 0 | chr1 | 54000 | 55000 | 6 | 54000 | 55000 | repressive |
| 1 | chr1 | 916000 | 917000 | 213 | 916000 | 917000 | promoter |
| 2 | chr1 | 960000 | 961000 | 255 | 960000 | 961000 | promoter |
| 3 | chr1 | 1004000 | 1005000 | 296 | 1004000 | 1005000 | promoter |
| 4 | chr1 | 1013000 | 1014000 | 305 | 1013000 | 1014000 | promoter |
| ... | ... | ... | ... | ... | ... | ... | ... |
| 2995 | chr1 | 248839000 | 248840000 | 183893 | 248839000 | 248840000 | promoter |
| 2996 | chr1 | 248857000 | 248858000 | 183907 | 248857000 | 248858000 | promoter |
| 2997 | chr1 | 248861000 | 248862000 | 183911 | 248861000 | 248862000 | repressive |
| 2998 | chr1 | 248873000 | 248874000 | 183923 | 248873000 | 248874000 | promoter |
| 2999 | chr1 | 248945000 | 248946000 | 183981 | 248945000 | 248946000 | repressive |
3000 rows × 7 columns
[7]:
# umap plot
umap_plot(region_emb, overlap_region_bed["anno"], "./output_emb_region_1kb")
/mnt/Storage/home/chenqianqian/miniconda3/envs/chrombert/lib/python3.9/site-packages/umap/umap_.py:1952: UserWarning: n_jobs value 1 overridden to 1 by setting random_state. Use no seed for parallelism.
warn(
generate gene (promoter region) embeddings¶
[8]:
# gene_emb_dict: Python dictionary mapping each matched gene to a 768-dimensional embedding.
results = embed_region(
gene="ENSG00000170921;TANC2;ENSG00000200997;DPYD;SNORA70;tp53;brd4", # your genes
odir="./output_emb_genes", # output directory
genome="hg38", # Options: "hg38", "mm10"
resolution="1kb", # Options: "1kb", "2kb", "4kb", "200bp"
)
gene_emb_dict = results.gene_emb_dict
Using cached region embeddings for gene pooling...
Finished!
Note: All gene names were converted to lowercase for matching.
Gene count summary - requested: 7, matched: 7, not found: 0
Matched gene meta saved to: ./output_emb_genes/overlap_genes_meta.tsv
Gene embeddings saved to: ./output_emb_genes/gene_emb_emb.pkl
Embedding type: general
[9]:
# Python dictionary mapping each matched gene to a 768-dimensional embedding.
for key, value in gene_emb_dict.items():
print(key,value.shape)
ensg00000170921 (768,)
tanc2 (768,)
ensg00000200997 (768,)
dpyd (768,)
snora70 (768,)
tp53 (768,)
brd4 (768,)
Generate cell-type-specific embeddings¶
We use cell-type-specific chromatin accessibility peak and signal files as input.
The embed_region API uses these data to build a cell-type-specific model and generate cell-type-specific embeddings.
[10]:
import os
os.environ["CUDA_VISIBLE_DEVICES"]='0'
[ ]:
# download example data
# Myoblast cell-type-specific chromatin accessibility peak and signal files
import subprocess
if not os.path.exists('../data/myoblast_ENCFF647RNC_peak.bed'):
cmd = f'wget https://www.encodeproject.org/files/ENCFF647RNC/@@download/ENCFF647RNC.bed.gz -O ../data/myoblast_ENCFF647RNC_peak.bed.gz'
subprocess.run(cmd, shell=True)
cmd = f"gzip -d ../data/myoblast_ENCFF647RNC_peak.bed.gz"
subprocess.run(cmd, shell=True)
# import subprocess
if not os.path.exists('../data/myoblast_ENCFF149ERN_signal.bigwig'):
cmd = f'wget https://www.encodeproject.org/files/ENCFF149ERN/@@download/ENCFF149ERN.bigWig -O ../data/myoblast_ENCFF149ERN_signal.bigwig'
subprocess.run(cmd, shell=True)
[ ]:
# We only use the first 100 lines of the peak file for demonstration
!head -n 100 ../data/myoblast_ENCFF647RNC_peak.bed > ../data/myoblast_ENCFF647RNC_peak_100.bed
[13]:
# Generate cell-type-specific embeddings using chromatin accessibility peak and signal files as input
# Build a cell-type-specific model from the input data
# Generate embeddings using the fine-tuned model
results_myoblast_specific = embed_region(
region = "../data/myoblast_ENCFF647RNC_peak_100.bed", # your focus region
odir = "./output_cell_specific_emb_train", # output directory
cell_type_bw = "../data/myoblast_ENCFF149ERN_signal.bigwig", # your focus cell-type accessibility data
cell_type_peak = "../data/myoblast_ENCFF647RNC_peak.bed", # your focus cell-type peak data
genome = "hg38", # genome
resolution = "1kb", # resolution
)
Preparing dataset ...
Region summary - total: 373422, overlapping with ChromBERT: 368260 (one region may overlap multiple ChromBERT regions, we keep overlaps with ≥50% coverage of either the ChromBERT bin or the input region), non-overlapping: 7920
Total regions: 324690
Fast mode: downsampling to 20k regions
Fine-tuning cell-specific model...
[Attempt 0/2] seed=55
Load pretrained ckpt /mnt/Storage/home/chenqianqian/.cache/chrombert/data/checkpoint/hg38_6k_1kb_pretrain.ckpt successfully!
/mnt/Storage/home/chenqianqian/miniconda3/envs/chrombert/lib/python3.9/site-packages/torchmetrics/utilities/prints.py:43: UserWarning: Metric `SpearmanCorrcoef` will save all targets and predictions in the buffer. For large datasets, this may lead to large memory footprint.
warnings.warn(*args, **kwargs)
Using bfloat16 Automatic Mixed Precision (AMP)
GPU available: True (cuda), used: True
TPU available: False, using: 0 TPU cores
HPU available: False, using: 0 HPUs
You are using a CUDA device ('NVIDIA A100-PCIE-40GB') that has Tensor Cores. To properly utilize them, you should set `torch.set_float32_matmul_precision('medium' | 'high')` which will trade-off precision for performance. For more details, read https://pytorch.org/docs/stable/generated/torch.set_float32_matmul_precision.html#torch.set_float32_matmul_precision
LOCAL_RANK: 0 - CUDA_VISIBLE_DEVICES: [0]
Loading `train_dataloader` to estimate number of stepping batches.
/mnt/Storage/home/chenqianqian/miniconda3/envs/chrombert/lib/python3.9/site-packages/lightning/pytorch/utilities/model_summary/model_summary.py:231: Precision bf16-mixed is not supported by the model summary. Estimated model size in MB will not be accurate. Using 32 bits instead.
| Name | Type | Params | Mode
---------------------------------------------------
0 | model | ChromBERTGeneral | 62.8 M | train
---------------------------------------------------
18.9 M Trainable params
43.9 M Non-trainable params
62.8 M Total params
251.095 Total estimated model params size (MB)
153 Modules in train mode
0 Modules in eval mode
/mnt/Storage/home/chenqianqian/miniconda3/envs/chrombert/lib/python3.9/site-packages/lightning/pytorch/trainer/connectors/data_connector.py:484: Your `val_dataloader`'s sampler has shuffling enabled, it is strongly recommended that you turn shuffling off for val/test dataloaders.
Metric default_validation/pcc improved. New best score: 0.269
Metric default_validation/pcc improved by 0.166 >= min_delta = 0.01. New best score: 0.435
Metric default_validation/pcc improved by 0.089 >= min_delta = 0.01. New best score: 0.524
Metric default_validation/pcc improved by 0.085 >= min_delta = 0.01. New best score: 0.609
Metric default_validation/pcc improved by 0.133 >= min_delta = 0.01. New best score: 0.742
Metric default_validation/pcc improved by 0.022 >= min_delta = 0.01. New best score: 0.764
Metric default_validation/pcc improved by 0.068 >= min_delta = 0.01. New best score: 0.832
Metric default_validation/pcc improved by 0.010 >= min_delta = 0.01. New best score: 0.842
Metric default_validation/pcc improved by 0.018 >= min_delta = 0.01. New best score: 0.860
Metric default_validation/pcc improved by 0.012 >= min_delta = 0.01. New best score: 0.872
Metric default_validation/pcc improved by 0.013 >= min_delta = 0.01. New best score: 0.885
Metric default_validation/pcc improved by 0.017 >= min_delta = 0.01. New best score: 0.902
Monitored metric default_validation/pcc did not improve in the last 5 records. Best score: 0.902. Signaling Trainer to stop.
`Trainer.fit` stopped: `max_epochs=5` reached.
Evaluating the finetuned model performance
Load pretrained ckpt /mnt/Storage/home/chenqianqian/.cache/chrombert/data/checkpoint/hg38_6k_1kb_pretrain.ckpt successfully!
Loading checkpoint from /mnt/Storage2/home/chenqianqian/projects/chrombert/chrombert_tools/ChromBERT-tools/examples/api/output_cell_specific_emb_train/train/try_00_seed_55/lightning_logs/lightning_logs/version_0/checkpoints/epoch=3-step=239.ckpt
Loading from pl module, remove prefix 'model.'
Loading from pl module, replace 'pretrain_model' with 'pretrain_model.chrombert'
Loaded 111/111 parameters
/mnt/Storage/home/chenqianqian/miniconda3/envs/chrombert/lib/python3.9/site-packages/torchmetrics/utilities/prints.py:43: UserWarning: Metric `SpearmanCorrcoef` will save all targets and predictions in the buffer. For large datasets, this may lead to large memory footprint.
warnings.warn(*args, **kwargs)
ft_ckpt: /mnt/Storage2/home/chenqianqian/projects/chrombert/chrombert_tools/ChromBERT-tools/examples/api/output_cell_specific_emb_train/train/try_00_seed_55/lightning_logs/lightning_logs/version_0/checkpoints/epoch=3-step=239.ckpt, test_metrics: {'pearsonr': 0.8920528888702393, 'spearmanr': 0.8251720666885376, 'mse': 0.028753146529197693, 'mae': 0.0986708402633667, 'r2': 0.7648238203557352}
Attempt metrics: pearsonr=0.8920528888702393
Accepted run (pearsonr=0.8921 >= 0.4).
Finished stage 2: obtained a fine-tuned ChromBERT
Best pearsonr=0.8920528888702393, metrics={'pearsonr': 0.8920528888702393, 'spearmanr': 0.8251720666885376, 'mse': 0.028753146529197693, 'mae': 0.0986708402633667, 'r2': 0.7648238203557352, 'ft_ckpt': '/mnt/Storage2/home/chenqianqian/projects/chrombert/chrombert_tools/ChromBERT-tools/examples/api/output_cell_specific_emb_train/train/try_00_seed_55/lightning_logs/lightning_logs/version_0/checkpoints/epoch=3-step=239.ckpt'}
Region summary - total: 100, overlapping with ChromBERT: 101 (one region may overlap multiple ChromBERT regions, we keep overlaps with ≥50% coverage of either the ChromBERT bin or the input region), non-overlapping: 0
Your supervised_file does not contain the 'label' column. Please verify whether ground truth column ('label') is required. If it is not needed, you may disregard this message.
100%|██████████| 26/26 [00:02<00:00, 12.59it/s]
Finished!
Focus region summary - total: 100, overlapping with ChromBERT: 101, non-overlapping: 0
Note: It is possible for a single region to overlap multiple ChromBERT regions.
Overlapping regions BED file: ./output_cell_specific_emb_train/overlap_region.bed
Non-overlapping regions BED file: ./output_cell_specific_emb_train/no_overlap_region.bed
Region embeddings saved to: ./output_cell_specific_emb_train/region_emb_emb.npy
Embedding type: cell-specific
[14]:
region_emb = results_myoblast_specific.region_emb # cell-type-specific region embeddings
region_emb
[14]:
array([[ 1.2109375 , -0.06298828, 0.66015625, ..., -0.19921875,
-1.0234375 , -0.453125 ],
[-0.19433594, -0.02001953, 1.21875 , ..., -0.38476562,
-0.5625 , 0.45507812],
[ 2.171875 , 0.3515625 , 0.38867188, ..., -0.41796875,
-1.390625 , -0.68359375],
...,
[-1.265625 , -0.6328125 , 0.59375 , ..., -0.58203125,
-1.2109375 , 0.33984375],
[-1.5546875 , -0.68359375, 0.58984375, ..., -0.35546875,
-1. , 0.6328125 ],
[-1.1875 , -0.58203125, 0.66015625, ..., -0.45898438,
-0.6875 , 0.6328125 ]], dtype=float32)
Generate cell-type-specific embeddings using a fine-tuned checkpoint¶
We use a fine-tuned checkpoint as input.
The embed_region API uses this checkpoint to generate cell-type-specific embeddings.
[ ]:
# import glob
# ft_ckpt_dir = "./output_cell_specific_emb_train/train/**/*.ckpt"
# ft_ckpt = glob.glob(ft_ckpt_dir, recursive=True)[0]
ft_ckpt = results_myoblast_specific.model_ckpt # Path to the cell-type-specific model checkpoint generated in the previous step
[16]:
from chrombert_tools import embed_region
[17]:
# Generate cell-type-specific embeddings using a fine-tuned checkpoint as input
# Loading fine-tuned model using the checkpoint
# Generate embeddings using the fine-tuned model
results_myoblast_specific_2 = embed_region(
region = "../data/myoblast_ENCFF647RNC_peak_100.bed", # your focus region
gene="ENSG00000170921;TANC2;ENSG00000200997;DPYD;SNORA70;tp53;brd4", # your genes
odir = "./output_cell_specific_emb_cistrome_2", # output directory
ft_ckpt = ft_ckpt, # fine-tuned checkpoint
genome = "hg38", # genome
resolution = "1kb", # resolution
)
Using provided fine-tuned checkpoint: /mnt/Storage2/home/chenqianqian/projects/chrombert/chrombert_tools/ChromBERT-tools/examples/api/output_cell_specific_emb_train/train/try_00_seed_55/lightning_logs/lightning_logs/version_0/checkpoints/epoch=3-step=239.ckpt
Load pretrained ckpt /mnt/Storage/home/chenqianqian/.cache/chrombert/data/checkpoint/hg38_6k_1kb_pretrain.ckpt successfully!
Loading checkpoint from /mnt/Storage2/home/chenqianqian/projects/chrombert/chrombert_tools/ChromBERT-tools/examples/api/output_cell_specific_emb_train/train/try_00_seed_55/lightning_logs/lightning_logs/version_0/checkpoints/epoch=3-step=239.ckpt
Loading from pl module, remove prefix 'model.'
Loading from pl module, replace 'pretrain_model' with 'pretrain_model.chrombert'
Loaded 111/111 parameters
Region summary - total: 100, overlapping with ChromBERT: 101 (one region may overlap multiple ChromBERT regions, we keep overlaps with ≥50% coverage of either the ChromBERT bin or the input region), non-overlapping: 0
Your supervised_file does not contain the 'label' column. Please verify whether ground truth column ('label') is required. If it is not needed, you may disregard this message.
100%|██████████| 26/26 [00:02<00:00, 12.52it/s]
Finished!
Focus region summary - total: 100, overlapping with ChromBERT: 101, non-overlapping: 0
Note: It is possible for a single region to overlap multiple ChromBERT regions.
Overlapping regions BED file: ./output_cell_specific_emb_cistrome_2/overlap_region.bed
Non-overlapping regions BED file: ./output_cell_specific_emb_cistrome_2/no_overlap_region.bed
Region embeddings saved to: ./output_cell_specific_emb_cistrome_2/region_emb_emb.npy
Embedding type: cell-specific
Your supervised_file does not contain the 'label' column. Please verify whether ground truth column ('label') is required. If it is not needed, you may disregard this message.
100%|██████████| 7/7 [00:00<00:00, 8.87it/s]
Finished!
Note: All gene names were converted to lowercase for matching.
Gene count summary - requested: 7, matched: 7, not found: 0
Matched gene meta saved to: ./output_cell_specific_emb_cistrome_2/overlap_genes_meta.tsv
Gene embeddings saved to: ./output_cell_specific_emb_cistrome_2/gene_emb_emb.pkl
Embedding type: cell-specific
[18]:
results_myoblast_specific_2.region_emb
[18]:
array([[ 1.2109375 , -0.06298828, 0.66015625, ..., -0.19921875,
-1.0234375 , -0.453125 ],
[-0.19433594, -0.02001953, 1.21875 , ..., -0.38476562,
-0.5625 , 0.45507812],
[ 2.171875 , 0.3515625 , 0.38867188, ..., -0.41796875,
-1.390625 , -0.68359375],
...,
[-1.265625 , -0.6328125 , 0.59375 , ..., -0.58203125,
-1.2109375 , 0.33984375],
[-1.5546875 , -0.68359375, 0.58984375, ..., -0.35546875,
-1. , 0.6328125 ],
[-1.1875 , -0.58203125, 0.66015625, ..., -0.45898438,
-0.6875 , 0.6328125 ]], dtype=float32)
[19]:
results_myoblast_specific_2.model_ckpt
[19]:
'/mnt/Storage2/home/chenqianqian/projects/chrombert/chrombert_tools/ChromBERT-tools/examples/api/output_cell_specific_emb_train/train/try_00_seed_55/lightning_logs/lightning_logs/version_0/checkpoints/epoch=3-step=239.ckpt'
[20]:
results_myoblast_specific_2.gene_emb_dict
[20]:
{'ensg00000170921': array([-7.18750000e-01, -3.10058594e-02, 7.07031250e-01, -1.67236328e-02,
-9.88281250e-01, -3.06640625e-01, 8.16406250e-01, 3.82812500e-01,
1.01562500e+00, 5.74218750e-01, -4.95605469e-02, 6.21093750e-01,
-6.40625000e-01, -2.98828125e-01, 6.32812500e-01, 3.14941406e-02,
1.46875000e+00, 7.81250000e-01, -5.31250000e-01, -9.92187500e-01,
6.79687500e-01, 5.42968750e-01, -9.10156250e-01, 1.36718750e-01,
-4.31640625e-01, 8.90625000e-01, -4.35546875e-01, 7.38281250e-01,
1.73828125e-01, -3.84765625e-01, -2.98828125e-01, -8.51562500e-01,
9.02343750e-01, -2.57812500e-01, -5.29785156e-02, 6.52343750e-01,
1.00000000e+00, 1.40625000e+00, 3.94531250e-01, -5.22460938e-02,
1.11718750e+00, 4.55078125e-01, -9.13085938e-02, 2.89062500e-01,
-3.78906250e-01, -9.47265625e-02, -1.23291016e-02, 1.42578125e-01,
1.85546875e-01, -1.26953125e-01, -1.61132812e-01, -2.81250000e-01,
3.06640625e-01, -5.62500000e-01, 3.49121094e-02, 2.32421875e-01,
8.32031250e-01, 2.38281250e-01, 3.45703125e-01, 3.73046875e-01,
-2.33398438e-01, 2.65625000e-01, 8.32031250e-01, 3.33984375e-01,
-2.87109375e-01, -6.01562500e-01, -4.88281250e-01, 1.01562500e+00,
5.82031250e-01, -8.49609375e-02, 3.22265625e-01, 3.37890625e-01,
-3.51562500e-01, 4.19921875e-01, -4.12109375e-01, 3.60107422e-03,
4.57031250e-01, 5.35156250e-01, -8.78906250e-01, 8.39843750e-01,
2.65625000e-01, 9.80468750e-01, 6.40625000e-01, -5.54687500e-01,
1.92187500e+00, 8.98437500e-02, -3.75000000e-01, 5.07812500e-01,
2.50000000e-01, 9.42382812e-02, -2.79541016e-02, -6.34765625e-02,
-8.75000000e-01, -2.46093750e-01, -1.96533203e-02, 9.25781250e-01,
-7.38281250e-01, -1.12500000e+00, 1.02343750e+00, 1.84570312e-01,
-2.55859375e-01, -3.33984375e-01, 1.16406250e+00, 2.00195312e-01,
-5.35156250e-01, 1.84570312e-01, -6.13281250e-01, -9.92187500e-01,
1.19531250e+00, 2.69531250e-01, -2.24609375e-02, 7.42187500e-01,
-4.43359375e-01, -1.17968750e+00, 1.65625000e+00, 1.37695312e-01,
-1.94531250e+00, 1.12304688e-01, 4.31640625e-01, 3.51562500e-01,
1.26562500e+00, 1.70898438e-01, -5.89843750e-01, -7.76367188e-02,
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