### Select Start Cells by Cell Type

Source: https://github.com/yzf072/spatrack/blob/main/docs/source/notebooks/01.ST_data_of_axolotl_brain_regeneration_after_injury.ipynb

Defines starting cells by specifying a known cell type.

```python
# start_cells=spt.set_start_cells(adata,select_way='cell_type',cell_type='reaEGC')

# fig, axs = plt.subplots(figsize=(5,5))
# plt.scatter(adata.obsm['X_spatial'][:,0],adata.obsm['X_spatial'][:,1],c='#D3D3D3',s=8)
# plt.scatter(adata.obsm['X_spatial'][start_cells][:,0],adata.obsm['X_spatial'][start_cells][:,1],c='orange',s=8)
```

--------------------------------

### Install spaTrack via pip

Source: https://github.com/yzf072/spatrack/blob/main/README.md

Install the package using pip. Requires Python version 3.7 to 3.9.

```shell
pip install spaTrack
```

--------------------------------

### Select Start Cells by Coordinates

Source: https://github.com/yzf072/spatrack/blob/main/docs/source/notebooks/01.ST_data_of_axolotl_brain_regeneration_after_injury.ipynb

Manually defines starting cells based on specific spatial coordinates and a neighborhood radius.

```python
start_cells = spt.set_start_cells(adata, select_way='coordinates', cell_type='reaEGC', start_point=[-1050,3850], n_neigh=30)

fig, axs = plt.subplots(figsize=(5,5))
plt.scatter(adata.obsm['X_spatial'][:,0], adata.obsm['X_spatial'][:,1], c='#D3D3D3', s=8)
plt.scatter(adata.obsm['X_spatial'][start_cells][:,0], adata.obsm['X_spatial'][start_cells][:,1], c='orange', s=8)
```

--------------------------------

### Assess Start Cluster Entropy

Source: https://github.com/yzf072/spatrack/blob/main/docs/source/notebooks/02.ST_data_of_Intrahepatic_cholangiocarcinoma_cancer.ipynb

Calculates and sorts clusters by entropy value to identify potential starting regions.

```python
adata = spt.assess_start_cluster(adata)
```

--------------------------------

### Select Start Cells via Lasso Tool

Source: https://github.com/yzf072/spatrack/blob/main/docs/source/notebooks/01.ST_data_of_axolotl_brain_regeneration_after_injury.ipynb

Uses an interactive lasso tool to manually select cells of interest for the trajectory start.

```python
# L=spt.Lasso(adata)
# L.vi_plot(basis='X_spatial',cell_type='reaEGC')
```

```python
# start_cells=L.sub_cells
# fig, axs = plt.subplots(figsize=(5, 5))
# plt.scatter(adata.obsm['X_spatial'][:,0],adata.obsm['X_spatial'][:,1],c='#D3D3D3',s=8)
# plt.scatter(adata.obsm['X_spatial'][start_cells][:,0],adata.obsm['X_spatial'][start_cells][:,1],c='orange',s=8)
```

--------------------------------

### Set Start Cells via K-Means

Source: https://github.com/yzf072/spatrack/blob/main/docs/source/notebooks/02.ST_data_of_Intrahepatic_cholangiocarcinoma_cancer.ipynb

Identifies aggregation points within a specific cluster using k-means and selects neighbor cells as starting points for trajectory inference.

```python
fig, axs = plt.subplots(figsize=(6, 9))
start_cells=spt.set_start_cells(adata,select_way='cell_type',split=True,cell_type='P0',n_neigh=100,n_clusters=4)

plt.scatter(adata.obsm['X_spatial'][:,0],adata.obsm['X_spatial'][:,1],c='#D3D3D3',s=20)
plt.scatter(adata.obsm['X_spatial'][start_cells][:,0],adata.obsm['X_spatial'][start_cells][:,1],c='orange',s=25)
```

--------------------------------

### Set starting cells for trajectory analysis

Source: https://github.com/yzf072/spatrack/blob/main/docs/source/notebooks/05.scRNAseq_data_of_HSC.ipynb

Defines the starting cluster for trajectory inference and visualizes the selected cells on a UMAP plot.

```python
start_cells=spt.set_start_cells(adata,select_way='cell_type',cell_type='HSC')
plt.scatter(adata.obsm['X_UMAP'][:,0],adata.obsm['X_UMAP'][:,1],c='#D3D3D3',s=20)
plt.scatter(adata.obsm['X_UMAP'][start_cells][:,0],adata.obsm['X_UMAP'][start_cells][:,1],c='orange',s=25)
```

--------------------------------

### Select start and end points for LAP

Source: https://github.com/yzf072/spatrack/blob/main/docs/source/notebooks/05.scRNAseq_data_of_HSC.ipynb

Identifies the nearest neighbor cells for specified coordinates to serve as start and end points for the Least Action Path.

```python
fig, ax = plt.subplots(figsize=(5, 5))

LAP_start_point=[-20,10]
LAP_end_point=[-30,-10]
LAP_start_cell=spt.nearest_neighbors(LAP_start_point,adata.obsm['X_UMAP'])[0][0]
LAP_end_cell=spt.nearest_neighbors(LAP_end_point,adata.obsm['X_UMAP'])[0][0]

plt.scatter(*adata.obsm["X_UMAP"].T,c='#D3D3D3',s=3)
plt.scatter(*adata[LAP_start_cell].obsm['X_UMAP'].T,s=20)
plt.scatter(*adata[LAP_end_cell].obsm['X_UMAP'].T,s=20)
```

--------------------------------

### Identify Start and End Cells

Source: https://github.com/yzf072/spatrack/blob/main/docs/source/notebooks/01.ST_data_of_axolotl_brain_regeneration_after_injury.ipynb

Locates the nearest cells to specified spatial coordinates to serve as start and end points for the LAP algorithm.

```python
fig, ax = plt.subplots(figsize=(6, 6))

LAP_start_point=[-1050,3900]
LAP_end_point=[-625,3000]
LAP_start_cell=spt.nearest_neighbors(LAP_start_point,adata.obsm['X_spatial'])[0][0]
LAP_end_cell=spt.nearest_neighbors(LAP_end_point,adata.obsm['X_spatial'])[0][0]

plt.scatter(*adata.obsm["X_spatial"].T,c='#D3D3D3',s=15)
plt.scatter(*adata[LAP_start_cell].obsm['X_spatial'].T,s=20)
plt.scatter(*adata[LAP_end_cell].obsm['X_spatial'].T,s=20)
```

--------------------------------

### spaTrack.set_start_cells

Source: https://github.com/yzf072/spatrack/blob/main/docs/source/api_velocity.rst

Sets the starting cells for trajectory inference.

```APIDOC
## spaTrack.set_start_cells

### Description
Sets the starting cells for the trajectory inference process.
```

--------------------------------

### Plot Cluster Entropy

Source: https://github.com/yzf072/spatrack/blob/main/docs/source/notebooks/02.ST_data_of_Intrahepatic_cholangiocarcinoma_cancer.ipynb

Visualizes the entropy values of clusters to assist in manual selection of the starting cluster.

```python
spt.assess_start_cluster_plot(adata)
```

--------------------------------

### Calculate cell pseudotime

Source: https://github.com/yzf072/spatrack/blob/main/docs/source/notebooks/05.scRNAseq_data_of_HSC.ipynb

Infers pseudotime values for cells based on the previously calculated OT matrix and defined start cells.

```python
adata.obs['ptime']=spt.get_ptime(adata,start_cells)
```

--------------------------------

### Calculate Least Action Path

Source: https://github.com/yzf072/spatrack/blob/main/docs/source/notebooks/05.scRNAseq_data_of_HSC.ipynb

Computes the least action path between defined start and target cells using the vector field.

```python
lap=spt.least_action(adata,
    init_cells=adata.obs_names[LAP_start_cell],
    target_cells=adata.obs_names[LAP_end_cell],
    vecfld=VecFld,
    basis='UMAP',
    adj_key='X_UMAP_distances',
    EM_steps=10,
    n_points=20
)
```

--------------------------------

### Visualize UMAP embeddings and trajectories

Source: https://github.com/yzf072/spatrack/blob/main/docs/source/notebooks/05.scRNAseq_data_of_HSC.ipynb

Generates UMAP plots to visualize clusters, start cells, pseudotime, and inferred vector field trajectories.

```python
fig, axs = plt.subplots(ncols=2, nrows=1, figsize=(10, 5))
sc.pl.embedding(adata, basis='X_UMAP', color='cluster', size=20, legend_loc='on data', ax=axs[0], legend_fontoutline=3, show=False, s=100)

start_points = sc.pl.embedding(adata, basis='X_UMAP',ax=axs[1], show=False, title='start cells')
points = adata.obsm['X_UMAP'][adata.obs['cluster'] == 'HSC']
start_points.scatter(points[:, 0], points[:, 1], s=15, color='orange')
```

```python
fig, axs = plt.subplots(ncols=2, nrows=1, figsize=(10, 4))
sc.pl.embedding(adata, basis='X_UMAP', color='ptime', show=False, ax=axs[0], color_map='Reds', title='ptime')

vf_velocity = sc.pl.embedding(adata, basis='X_UMAP', show=False, ax=axs[1],color='cluster',title='streamplot',  legend_loc=None, alpha=0.4, size=120)
vf_velocity.streamplot(adata.uns['E_grid'][0], adata.uns['E_grid'][1], adata.uns['V_grid'][0], adata.uns['V_grid'][1], color='black', linewidth=1.5,density=1.8,arrowsize=1.2,)
```

--------------------------------

### Initialize environment

Source: https://github.com/yzf072/spatrack/blob/main/docs/source/notebooks/04.ST_data_of_mouse midbrain_with_multiple_times.ipynb

Import necessary libraries and configure scanpy and matplotlib settings.

```python
import spaTrack as spt
import scanpy as sc
import pandas as pd
import matplotlib.pyplot as plt

sc.settings.verbosity = 0
plt.rcParams['figure.dpi'] = 200 #分辨率
```

--------------------------------

### Import libraries and configure settings

Source: https://github.com/yzf072/spatrack/blob/main/docs/source/notebooks/05.scRNAseq_data_of_HSC.ipynb

Initializes spaTrack, scanpy, and plotting parameters for the analysis.

```python
import spaTrack as spt
import scanpy as sc
import pandas as pd
import numpy as np
import matplotlib.pyplot as plt

sc.settings.verbosity = 0
plt.rcParams['figure.dpi'] = 200 #分辨率
```

--------------------------------

### Configure Environment and Imports

Source: https://github.com/yzf072/spatrack/blob/main/docs/source/notebooks/03.ST_data_of_axolotl_brain_slides_with_multiple_times.ipynb

Initializes the environment by suppressing warnings and importing necessary libraries for spatial analysis and plotting.

```python
import warnings

warnings.filterwarnings("ignore")
```

```python
import spaTrack as spt
import scanpy as sc
import pandas as pd
import numpy as np
import matplotlib.pyplot as plt

sc.settings.verbosity = 0
plt.rcParams['figure.dpi'] = 200 #分辨率
```

--------------------------------

### Import Dependencies and Configure Environment

Source: https://github.com/yzf072/spatrack/blob/main/docs/source/notebooks/01.ST_data_of_axolotl_brain_regeneration_after_injury.ipynb

Load necessary libraries for data manipulation, visualization, and spatial analysis, and set global plotting parameters.

```python
import matplotlib.pyplot as plt
import matplotlib.ticker as ticker
import numpy as np
import pandas as pd
import scanpy as sc

import spaTrack as spt

sc.settings.verbosity = 0
plt.rcParams["figure.dpi"] = 200  # 分辨率
```

--------------------------------

### Train the regulatory network model

Source: https://github.com/yzf072/spatrack/blob/main/docs/source/notebooks/04.ST_data_of_mouse midbrain_with_multiple_times.ipynb

Initialize the Trainer with spatial data paths and TF lists, then execute the training process.

```python
gr = spt.Trainer(
    data_type='2_time',
    expression_matrix_path=['./E12.5.adata.h5ad','./E14.5.adata.h5ad'],
    cell_mapping_path='./cell_mapping.csv',
    tfs_path='../../../../data/mouse.midbrain.three.time/ms.TF.tsv', 
    min_cells=[50,20],         #recommend maintaining gene expression in ～ 3% of cells.
    cell_generate_per_time=10000,
    cell_select_per_time=50
)

gr.run(training_times=10,iter_times=30)
```

--------------------------------

### Load and prepare data

Source: https://github.com/yzf072/spatrack/blob/main/docs/source/notebooks/04.ST_data_of_mouse midbrain_with_multiple_times.ipynb

Load expression and metadata files, then assign spatial coordinates and cell identifiers to the AnnData object.

```python
adata_all=sc.read('../../../../data/mouse.midbrain.three.time/mouse midbrain.three.time.point.ST.exp.tsv')
df_annot=pd.read_table('../../../../data/mouse.midbrain.three.time/meta.tsv',sep='\t',index_col=[0])
adata_all.obs=df_annot
adata_all.obs.index=list(df_annot.index)
adata_all.obsm['spatial']=adata_all.obs[['x','y']].values
adata_all.obs['CellID']=adata_all.obs.index
```

--------------------------------

### Calculate and filter transition probabilities

Source: https://github.com/yzf072/spatrack/blob/main/docs/source/notebooks/04.ST_data_of_mouse midbrain_with_multiple_times.ipynb

Maps data between two sections and provides a commented-out workflow for filtering transition probabilities based on a cutoff.

```python
pi_df=spt.map_data(pi12,adata1_sub,adata2_sub)
```

```python
# import seaborn as sns
# sns.displot(pi_df['pi_value'],bins=200)
# pi_df_new=pi_df.loc[pi_df['pi_value']>cutoff_value]
```

--------------------------------

### Inspect transition probability dataframe

Source: https://github.com/yzf072/spatrack/blob/main/docs/source/notebooks/04.ST_data_of_mouse midbrain_with_multiple_times.ipynb

Displays the first few rows of the integrated transition probability dataframe.

```python
pi_matrix_coord.head()
```

--------------------------------

### Compute Least Action Path

Source: https://github.com/yzf072/spatrack/blob/main/docs/source/notebooks/01.ST_data_of_axolotl_brain_regeneration_after_injury.ipynb

Calculates the optimal transition path between two cells by minimizing the action integral using an Expectation-Maximization algorithm.

```python
lap=spt.least_action(adata,
    init_cells=adata.obs_names[LAP_start_cell],
    target_cells=adata.obs_names[LAP_end_cell],
    vecfld=VecFld,
    basis='spatial',
    adj_key='X_spatial_distances',
    EM_steps=5,
    n_points=20
)
```

--------------------------------

### Prepare data for 3D visualization

Source: https://github.com/yzf072/spatrack/blob/main/docs/source/notebooks/04.ST_data_of_mouse midbrain_with_multiple_times.ipynb

Concatenates observation data from multiple sections and prepares the cell mapping matrix.

```python
df_adata_1=adata1_sub.obs[['CellID','annotation','x','y']]
df_adata_1['batch']='slice1'
df_adata_2=adata2_sub.obs[['CellID','annotation','x','y']]
df_adata_2['batch']='slice2'
df_adata_3=adata3_sub.obs[['CellID','annotation','x','y']]
df_adata_3['batch']='slice3'
df_concat=pd.concat([df_adata_1,df_adata_2,df_adata_3])

df_mapping_cell=pi_matrix_coord[['slice1','slice2','slice3']]
```

```python
df_mapping_cell.head()
```

--------------------------------

### Inspect data

Source: https://github.com/yzf072/spatrack/blob/main/docs/source/notebooks/04.ST_data_of_mouse midbrain_with_multiple_times.ipynb

Display the first few rows of the observation metadata.

```python
adata_all.obs.head()
```

--------------------------------

### Initialize VectorField object

Source: https://github.com/yzf072/spatrack/blob/main/docs/source/notebooks/02.ST_data_of_Intrahepatic_cholangiocarcinoma_cancer.ipynb

Creates a VectorField instance for the spatial basis.

```python
VecFld = spt.VectorField(adata, basis="spatial")
```

--------------------------------

### Initialize Vector Field

Source: https://github.com/yzf072/spatrack/blob/main/docs/source/notebooks/05.scRNAseq_data_of_HSC.ipynb

Initializes the VectorField object required for path analysis.

```python
VecFld=spt.VectorField(adata,basis='UMAP')
```

--------------------------------

### Visualize Least Action Path

Source: https://github.com/yzf072/spatrack/blob/main/docs/source/notebooks/02.ST_data_of_Intrahepatic_cholangiocarcinoma_cancer.ipynb

Plots the inferred path overlaid on the spatial embedding with pseudotime coloring.

```python
LAP_ptime,LAP_nbrs=spt.lap.map_cell_to_LAP(adata)
sub_adata=adata[LAP_nbrs,:]
sub_adata.obs['ptime']=LAP_ptime
sub_adata=sub_adata[np.argsort(sub_adata.obs["ptime"].values), :].copy()

fig, ax = plt.subplots(figsize=(6,8))
plt.axis('off')
ax = sc.pl.embedding(adata,  basis='X_spatial',color='cluster',show=False,ax=ax,frameon=False,legend_loc=None,alpha=0.4,size=150)
ax.streamplot(adata.uns['E_grid'][0], adata.uns['E_grid'][1], adata.uns['V_grid'][0], adata.uns['V_grid'][1],density=1.2,color='black',linewidth=2.5,arrowsize=1.5,minlength=0.1,maxlength=0.8)
ax = spt.plot_least_action_path(adata,basis='spatial',ax=ax,point_size=120,linewidth=5)
sc.pl.embedding(sub_adata, basis='X_spatial',ax=ax, color="ptime", cmap="Purples",frameon=True,size=150,title=' ')
```

--------------------------------

### Load and Prepare ST Data

Source: https://github.com/yzf072/spatrack/blob/main/docs/source/notebooks/03.ST_data_of_axolotl_brain_slides_with_multiple_times.ipynb

Reads gene expression data and metadata, then populates the scanpy adata object with cluster, time, spatial, and UMAP coordinates.

```python
adata = sc.read('../../../../data/03.multiple.ST.slices.axolotl.brain/cell.exp.tsv')
df_annot=pd.read_table('../../../../data/03.multiple.ST.slices.axolotl.brain/cell.meta.tsv')
adata.obs["cluster"] = df_annot['cluster'].values
adata.obs["Time"] = df_annot['Time'].values
adata.obsm["X_spatial"] = df_annot[['x','y']].values
adata.obsm["X_umap"] = df_annot[['UMAP_1','UMAP_2']].values
```

--------------------------------

### spaTrack.plot_least_action_path

Source: https://github.com/yzf072/spatrack/blob/main/docs/source/api_LAP.rst

Visualizes the calculated least action path.

```APIDOC
## spaTrack.plot_least_action_path

### Description
Generates a plot representing the least action path for analysis.
```

--------------------------------

### Visualize 3D mapping across three sections

Source: https://github.com/yzf072/spatrack/blob/main/docs/source/notebooks/04.ST_data_of_mouse midbrain_with_multiple_times.ipynb

Renders a 3D visualization of cell transitions across three sections with connecting lines.

```python
spt.visual_3D_mapping_3(df_concat,df_mapping_cell,point_size=0.8,line_width=0.06,cell_color_list=['#9A154C', '#F3754E', '#5B58A7'])
```

--------------------------------

### Map Cells to Pseudotime and Visualize

Source: https://github.com/yzf072/spatrack/blob/main/docs/source/notebooks/01.ST_data_of_axolotl_brain_regeneration_after_injury.ipynb

Assigns pseudotime values to cells along the trajectory and visualizes the path over the spatial embedding.

```python
LAP_ptime,LAP_nbrs=spt.map_cell_to_LAP(adata,cell_neighbors=80)
sub_adata=adata[LAP_nbrs,:]
sub_adata.obs['ptime']=LAP_ptime
sub_adata=sub_adata[np.argsort(sub_adata.obs["ptime"].values), :].copy()

fig, ax = plt.subplots(figsize=(6,5))
plt.axis('off')
ax = sc.pl.embedding(adata,  basis='X_spatial',color='cluster',show=False,ax=ax,frameon=False,legend_loc=None,alpha=0.6,size=150)
ax.streamplot(adata.uns['E_grid'][0], adata.uns['E_grid'][1], adata.uns['V_grid'][0], adata.uns['V_grid'][1],density=1.2,color='black',linewidth=2,arrowsize=1.2)
ax = spt.plot_least_action_path(adata,basis='spatial',ax=ax,point_size=120,linewidth=5)
sc.pl.embedding(sub_adata, basis='X_spatial',ax=ax, color="ptime", cmap="YlGnBu",frameon=True,size=150,title=' ')
```

--------------------------------

### Calculate cell transition probability matrix

Source: https://github.com/yzf072/spatrack/blob/main/docs/source/notebooks/01.ST_data_of_axolotl_brain_regeneration_after_injury.ipynb

Computes the transition probability matrix using optimal transport with spatial information integration.

```python
adata.obsp["trans"] = spt.get_ot_matrix(adata, data_type="spatial",alpha1=0.6,alpha2=0.4)
```

--------------------------------

### Visualize TF-target relationships

Source: https://github.com/yzf072/spatrack/blob/main/docs/source/notebooks/04.ST_data_of_mouse midbrain_with_multiple_times.ipynb

Generate a scatter plot to visualize the relationship between transcription factors and target genes.

```python
gr.plot_scatter()
```

--------------------------------

### Calculate cell-transition probability and velocity

Source: https://github.com/yzf072/spatrack/blob/main/docs/source/notebooks/03.ST_data_of_axolotl_brain_slides_with_multiple_times.ipynb

Iterates through time points to compute optimal transport matrices, pseudotime, and cell velocity for spatial transcriptomics data.

```python
time_and_start = {"D5": "reaEGC", "D10": "reaEGC", "D15": "reaEGC", "D20": "rIPC"}
alpha = {
    "D5": [0.693, 0.307],
    "D10": [0.7, 0.3],
    "D15": [0.75, 0.25],
    "D20": [0.704, 0.296],
}

P_all = V_all = np.array([]).reshape(0, 2)

for time_point in time_and_start.keys():
    print(time_point)
    subadata = adata[adata.obs["Time"] == time_point]
    subadata.obsp["trans"] = spt.get_ot_matrix(subadata, data_type="spatial",alpha1=alpha[time_point][0],alpha2=alpha[time_point][1])
    start_cluster = time_and_start[time_point]
    start_cells = spt.set_start_cells(
        subadata, select_way="cell_type", cell_type=start_cluster
    )
    subadata.obs["ptime"] = spt.get_ptime(subadata, start_cells)
    _, _ = spt.get_velocity(subadata, basis="umap", n_neigh_pos=80, n_neigh_gene=0)

    P_all = np.vstack((P_all, subadata.obsm["X_umap"]))
    V_all = np.vstack((V_all, subadata.obsm["velocity_umap"]))
```

--------------------------------

### Calculate cell transition probability

Source: https://github.com/yzf072/spatrack/blob/main/docs/source/notebooks/02.ST_data_of_Intrahepatic_cholangiocarcinoma_cancer.ipynb

Estimates the transition matrix using gene expression and spatial distance parameters.

```python
adata.obsp['trans']=spt.get_ot_matrix(adata,data_type='spatial',alpha1=0.587,alpha2=0.413)
```

--------------------------------

### Load and Format Spatial Data

Source: https://github.com/yzf072/spatrack/blob/main/docs/source/notebooks/01.ST_data_of_axolotl_brain_regeneration_after_injury.ipynb

Read gene expression and annotation files, then map them into a scanpy AnnData object structure required by spaTrack.

```python
adata = sc.read("../../../../data/axolotl brain regeneration.ST/D15_4.ST.exp.tsv")
df_annot = pd.read_table("../../../../data/axolotl brain regeneration.ST/D15_4.ST.annot.tsv")

adata.obs["cluster"] = df_annot["cluster"].values
adata.obsm["X_spatial"] = df_annot[["x", "y"]].values
adata.layers["counts"] = adata.X
```

--------------------------------

### Save spatial data to disk

Source: https://github.com/yzf072/spatrack/blob/main/docs/source/notebooks/04.ST_data_of_mouse midbrain_with_multiple_times.ipynb

Export subsetted AnnData objects to h5ad format for use in the regulatory network construction pipeline.

```python
adata1_sub.write('./E12.5.adata.h5ad')
adata2_sub.write('./E14.5.adata.h5ad')
```

--------------------------------

### Prepare ICC AnnData object

Source: https://github.com/yzf072/spatrack/blob/main/docs/source/notebooks/02.ST_data_of_Intrahepatic_cholangiocarcinoma_cancer.ipynb

Load expression counts and annotation data from TSV files, then populate the AnnData object with spatial coordinates and cluster information.

```python
adata = sc.read("../../../../data/ICC.ST.data/ICC.primary.ST.exp_count.tsv", cache=True)
anno = pd.read_table("../../../../data/ICC.ST.data/ICC.primary.ST.annot.tsv")

adata.obs.index = anno["ID"].values
adata.obs["cluster"] = anno["cluster"].values
adata.obsm["X_spatial"] = anno[["x", "y"]].values
adata.layers["counts"] = adata.X
```

--------------------------------

### Generate integrated transition probability data

Source: https://github.com/yzf072/spatrack/blob/main/docs/source/notebooks/04.ST_data_of_mouse midbrain_with_multiple_times.ipynb

Integrates transition probability results across multiple sections into a single dataframe and exports it to a CSV file.

```python
pi_matrix_coord = spt.generate_animate_input(pi_list=[pi12,pi23], adata_list=[adata1_sub,adata2_sub,adata3_sub],time ='Time point',annotation='annotation')
# pi_matrix_coord=pi_matrix_coord.loc[(pi_matrix_coord['pi_value1']> value1) & (pi_matrix_coord['pi_value1']> value2) ]
pi_matrix_coord.to_csv("./cell.transfer.csv")
```

--------------------------------

### spaTrack.Lasso

Source: https://github.com/yzf072/spatrack/blob/main/docs/source/api_velocity.rst

Lasso class for trajectory analysis.

```APIDOC
## spaTrack.Lasso

### Description
A class used for Lasso-based trajectory analysis.
```

--------------------------------

### spaTrack.least_action

Source: https://github.com/yzf072/spatrack/blob/main/docs/source/api_LAP.rst

Calculates the least action path between specified points.

```APIDOC
## spaTrack.least_action

### Description
Calculates the least action path based on the defined vector field and constraints.
```

--------------------------------

### Calculate cell pseudotime

Source: https://github.com/yzf072/spatrack/blob/main/docs/source/notebooks/01.ST_data_of_axolotl_brain_regeneration_after_injury.ipynb

Assigns pseudotime values between 0 and 1 based on the sorted sum of transition probabilities from initial cells.

```python
adata.obs["ptime"] = spt.get_ptime(adata, start_cells)
```

--------------------------------

### spaTrack.get_ot_matrix

Source: https://github.com/yzf072/spatrack/blob/main/docs/source/api_velocity.rst

Calculates the optimal transport matrix.

```APIDOC
## spaTrack.get_ot_matrix

### Description
Computes the optimal transport matrix used for trajectory inference.
```

--------------------------------

### Plot Least Action Path

Source: https://github.com/yzf072/spatrack/blob/main/docs/source/notebooks/05.scRNAseq_data_of_HSC.ipynb

Visualizes the computed least action path overlaid on the UMAP embedding and vector field.

```python
LAP_ptime,LAP_nbrs=spt.lap.map_cell_to_LAP(adata,basis='UMAP')
sub_adata=adata[LAP_nbrs,:]
sub_adata.obs['ptime']=LAP_ptime
sub_adata=sub_adata[np.argsort(sub_adata.obs["ptime"].values), :].copy()

fig, ax = plt.subplots(figsize=(8,8))
plt.axis('off')
ax = sc.pl.embedding(adata,  basis='X_UMAP',color='cluster',show=False,ax=ax,frameon=False,legend_loc=None,alpha=0.8,size=150)
ax.streamplot(adata.uns['E_grid'][0], adata.uns['E_grid'][1], adata.uns['V_grid'][0], adata.uns['V_grid'][1],density=1.2,color='black',linewidth=2.5,arrowsize=1.5,minlength=0.1,maxlength=0.8)
ax = spt.plot_least_action_path(adata,basis='UMAP',ax=ax,point_size=120,linewidth=5)
sc.pl.embedding(sub_adata, basis='X_UMAP',ax=ax, color="ptime", cmap="Purples",frameon=True,size=150,title=' ')
```

--------------------------------

### Suppress warnings

Source: https://github.com/yzf072/spatrack/blob/main/docs/source/notebooks/05.scRNAseq_data_of_HSC.ipynb

Configures the environment to ignore warnings during execution.

```python
import warnings

warnings.filterwarnings("ignore")
```

--------------------------------

### Subset data by time point

Source: https://github.com/yzf072/spatrack/blob/main/docs/source/notebooks/04.ST_data_of_mouse midbrain_with_multiple_times.ipynb

Split the main AnnData object into subsets based on time points and define annotation colors.

```python
adata1_sub=adata_all[adata_all.obs['Time point']=='E12.5']
adata2_sub=adata_all[adata_all.obs['Time point']=='E14.5']
adata3_sub=adata_all[adata_all.obs['Time point']=='E16.5']
adata_all.uns['annotation_colors']=['#9A154C', '#F3754E', '#5B58A7']
```

--------------------------------

### Preprocess and visualize data

Source: https://github.com/yzf072/spatrack/blob/main/docs/source/notebooks/05.scRNAseq_data_of_HSC.ipynb

Filters genes, normalizes counts, and generates a UMAP embedding plot colored by cluster.

```python
sc.pp.filter_genes(adata,min_cells=30)
sc.pp.normalize_total(adata,target_sum=1e4)
sc.pp.log1p(adata)
fig, axs = plt.subplots(figsize=(6, 6))
ax = sc.pl.embedding(adata,  basis='X_UMAP',show=False,color='cluster',ax=axs,frameon=False,title=' ',palette='tab20b',size=150, legend_fontsize=20)
```

--------------------------------

### Load and format HSC data

Source: https://github.com/yzf072/spatrack/blob/main/docs/source/notebooks/05.scRNAseq_data_of_HSC.ipynb

Reads expression and UMAP coordinate files, then populates the AnnData object with cluster annotations and UMAP embeddings.

```python
adata = sc.read("../../../../data/HSPC.Sc-RNA.data/HSPC.sc.expression.tsv")
anno = pd.read_table("../../../../data/HSPC.Sc-RNA.data/UMAP_coor.annot.tsv",)

adata.obs.index = anno["Cell_id"].values
adata.obs["cluster"] = anno["Annot"].values
adata.obsm["X_UMAP"] = anno[['UMAP_1','UMAP_2']].values

adata.var_names_make_unique()
```

--------------------------------

### Visualize 3D mapping between two sections

Source: https://github.com/yzf072/spatrack/blob/main/docs/source/notebooks/04.ST_data_of_mouse midbrain_with_multiple_times.ipynb

Renders a 3D visualization of cell transfer between two specific sections.

```python
spt.visual_3D_mapping_2(df_concat,pi_df[['slice1','slice2']],point_size=1,line_width=0.05,cell_color_list=['#9A154C', '#F3754E', '#5B58A7'])
```

--------------------------------

### Fit GAM model for pseudotime genes

Source: https://github.com/yzf072/spatrack/blob/main/docs/source/notebooks/02.ST_data_of_Intrahepatic_cholangiocarcinoma_cancer.ipynb

Apply a generalized additive model to identify genes associated with pseudotime.

```python
df_res  = spt.ptime_gene_GAM(sub_adata_path,core_number=5)
```

--------------------------------

### Visualize pseudotime distribution

Source: https://github.com/yzf072/spatrack/blob/main/docs/source/notebooks/01.ST_data_of_axolotl_brain_regeneration_after_injury.ipynb

Plots the pseudotime values on the spatial embedding using a red color map.

```python
fig, axs = plt.subplots(figsize=(5, 5))
sc.pl.embedding(adata, basis='spatial', color='ptime', show=False, ax=axs, color_map='Reds', title='ptime', size=100)
axs.xaxis.set_major_locator(ticker.MultipleLocator(500))
axs.yaxis.set_major_locator(ticker.MultipleLocator(500))
```

--------------------------------

### Preprocess and visualize spatial data

Source: https://github.com/yzf072/spatrack/blob/main/docs/source/notebooks/02.ST_data_of_Intrahepatic_cholangiocarcinoma_cancer.ipynb

Filter genes, normalize data, and generate a spatial embedding plot colored by cluster.

```python
sc.pp.filter_genes(adata,min_cells=10)
sc.pp.normalize_total(adata,target_sum=1e4)
sc.pp.log1p(adata)
fig, axs = plt.subplots(figsize=(6, 9))
ax = sc.pl.embedding(adata,  basis='X_spatial', show=False, color='cluster', ax=axs, frameon=False, title=' ', palette='tab20c', size=150, legend_fontsize=20)
```

--------------------------------

### spaTrack.get_ptime

Source: https://github.com/yzf072/spatrack/blob/main/docs/source/api_velocity.rst

Calculates pseudotime.

```APIDOC
## spaTrack.get_ptime

### Description
Calculates the pseudotime values for the cells.
```

--------------------------------

### Visualize spatial data

Source: https://github.com/yzf072/spatrack/blob/main/docs/source/notebooks/04.ST_data_of_mouse midbrain_with_multiple_times.ipynb

Generate a spatial embedding plot to visualize cell annotations across the time points.

```python
fig, axs = plt.subplots(ncols=1, nrows=1, figsize=(12, 6))
sc.pl.embedding(adata_all, basis='spatial', color='annotation', size=50, legend_loc='right margin', legend_fontsize=20,ax=axs, legend_fontoutline=3, show=False, s=80)
axs.set_title('spatial',fontsize=18)
```

--------------------------------

### Perform Quality Control and Normalization

Source: https://github.com/yzf072/spatrack/blob/main/docs/source/notebooks/01.ST_data_of_axolotl_brain_regeneration_after_injury.ipynb

Filter low-abundance genes and normalize expression data to prepare for downstream trajectory inference.

```python
sc.pp.filter_genes(adata, min_cells=10)
sc.pp.normalize_total(adata, target_sum=1e4)
sc.pp.log1p(adata)
sc.pp.calculate_qc_metrics(adata, percent_top=None, log1p=False, inplace=True)
```

--------------------------------

### Visualize trajectory gene heatmap

Source: https://github.com/yzf072/spatrack/blob/main/docs/source/notebooks/05.scRNAseq_data_of_HSC.ipynb

Orders genes by trajectory and generates a heatmap of their expression.

```python
sort_exp_sig = spt.order_trajectory_genes(sub_adata,df_sig_res,cell_number=30)
spt.plot_trajectory_gene_heatmap(sort_exp_sig,smooth_length=200,gene_label_size=15,cmap_name='twilight_shifted')
```

--------------------------------

### Visualize cell pseudotime and trajectory

Source: https://github.com/yzf072/spatrack/blob/main/docs/source/notebooks/02.ST_data_of_Intrahepatic_cholangiocarcinoma_cancer.ipynb

Plots the embedding of cells colored by pseudotime and overlays the inferred vector field trajectory.

```python
fig, axs = plt.subplots(ncols=2, nrows=1, figsize=(9, 6))

sc.pl.embedding(adata, basis='X_spatial', color='ptime', show=False, ax=axs[0], color_map='Reds', title='Ptime',size=120)
vf_velocity = sc.pl.embedding(adata, basis='X_spatial', show=False, ax=axs[1],color='cluster', legend_loc=None, frameon=False, title='Trajectory', alpha=0.6, size=120)
vf_velocity.streamplot(adata.uns['E_grid'][0], adata.uns['E_grid'][1], adata.uns['V_grid'][0], adata.uns['V_grid'][1], color='black', linewidth=2,density=1.2,arrowsize=1.2)
```

--------------------------------

### Plot gene expression vs pseudotime

Source: https://github.com/yzf072/spatrack/blob/main/docs/source/notebooks/05.scRNAseq_data_of_HSC.ipynb

Plots the expression of a specific gene against pseudotime.

```python
spt.plot_trajectory_gene(sub_adata_path,gene_name='VIM',show_cell_type=False)
```

--------------------------------

### Map cells between time points

Source: https://github.com/yzf072/spatrack/blob/main/docs/source/notebooks/04.ST_data_of_mouse midbrain_with_multiple_times.ipynb

Compute cell mapping between two time points and save the result to a CSV file.

```python
pi_df=spt.map_data(pi12,adata1_sub,adata2_sub)
pi_df.to_csv('./cell_mapping.csv')
```

--------------------------------

### Retrieve network weights

Source: https://github.com/yzf072/spatrack/blob/main/docs/source/notebooks/04.ST_data_of_mouse midbrain_with_multiple_times.ipynb

Access the DataFrame containing the inferred weights between transcription factors and target genes.

```python
gr.network_df
```

--------------------------------

### Calculate transfer matrices between ST sections

Source: https://github.com/yzf072/spatrack/blob/main/docs/source/notebooks/04.ST_data_of_mouse midbrain_with_multiple_times.ipynb

Computes the transfer matrix between pairs of spatial transcriptomics sections using an unbalanced and structured optimal transport algorithm.

```python
pi12 = spt.transfer_matrix(adata1_sub,adata2_sub,epsilon=0.01,alpha=0.5)
pi23 = spt.transfer_matrix(adata2_sub,adata3_sub,epsilon=0.01,alpha=0.5)
```

--------------------------------

### spaTrack.map_cell_to_LAP

Source: https://github.com/yzf072/spatrack/blob/main/docs/source/api_LAP.rst

Maps individual cells to their corresponding least action path.

```APIDOC
## spaTrack.map_cell_to_LAP

### Description
Maps cell data to the calculated least action path trajectories.
```

--------------------------------

### Plot individual pseudotime-dependent genes

Source: https://github.com/yzf072/spatrack/blob/main/docs/source/notebooks/02.ST_data_of_Intrahepatic_cholangiocarcinoma_cancer.ipynb

Visualize the expression of specific genes along the pseudotime trajectory.

```python
spt.plot_trajectory_gene(sub_adata_path,gene_name='AQP1')
```

```python
spt.plot_trajectory_gene(sub_adata_path,gene_name='ITGA3')
```

--------------------------------

### Calculate Velocity Grid

Source: https://github.com/yzf072/spatrack/blob/main/docs/source/notebooks/03.ST_data_of_axolotl_brain_slides_with_multiple_times.ipynb

Converts cell-level velocity data into a grid-based representation for trajectory analysis.

```python
P_grid, V_grid = spt.velocity.get_velocity_grid(
    adata, P=P_all, V=V_all
)
```

--------------------------------

### Identify pseudotime-dependent genes

Source: https://github.com/yzf072/spatrack/blob/main/docs/source/notebooks/05.scRNAseq_data_of_HSC.ipynb

Fits gene expression to pseudotime using a GAM and filters results by model fit and FDR.

```python
df_res=spt.ptime_gene_GAM(sub_adata_path,core_number=5)
df_sig_res = df_res.loc[(df_res['model_fit']>0.4) & (df_res['fdr']<0.05)]
```

--------------------------------

### Visualize Spatial and UMAP Embeddings

Source: https://github.com/yzf072/spatrack/blob/main/docs/source/notebooks/03.ST_data_of_axolotl_brain_slides_with_multiple_times.ipynb

Plots the integrated data across spatial coordinates and UMAP space to observe batch-corrected distributions.

```python
fig, axs = plt.subplots(ncols=2, nrows=1, figsize=(18, 6))
sc.pl.embedding(adata, basis='X_spatial', color='Time', size=50, legend_fontsize=15,legend_loc='on data', ax=axs[0], legend_fontoutline=3, show=False, s=40)
axs[0].set_title('spatial',fontsize=18)
sc.pl.umap(adata,color='cluster',ax=axs[1],legend_loc='on data',size=50,legend_fontoutline=3, legend_fontsize=15,palette='tab20b',show=False,s=60)
axs[1].set_title('UMAP',fontsize=18)
```

--------------------------------

### Visualize Spatial Cell Clusters

Source: https://github.com/yzf072/spatrack/blob/main/docs/source/notebooks/01.ST_data_of_axolotl_brain_regeneration_after_injury.ipynb

Generate a spatial embedding plot to visualize cell type distribution across the tissue sample.

```python
fig, axs = plt.subplots(figsize=(7, 7))
ax = sc.pl.embedding(adata, basis='X_spatial', show=False, 
    color='cluster', ax=axs, frameon=False, title=' ', palette='tab20c', size=100)
```

--------------------------------

### Plot Cell Clusters on Spatial Slides

Source: https://github.com/yzf072/spatrack/blob/main/docs/source/notebooks/03.ST_data_of_axolotl_brain_slides_with_multiple_times.ipynb

Sets custom colors for clusters and visualizes them on the spatial embedding.

```python
adata.uns['cluster_colors']=['#5254a3', '#8c6d31','#EEDC82','#d6616b']
```

```python
fig, axs = plt.subplots(ncols=1, nrows=1, figsize=(12, 6))
sc.pl.embedding(adata, basis='X_spatial', color='cluster', size=50, legend_loc='right margin', legend_fontsize=20,ax=axs, legend_fontoutline=3, show=False, s=80)
axs.set_title('spatial',fontsize=18)
```

--------------------------------

### Animate cell transfer across ST sections

Source: https://github.com/yzf072/spatrack/blob/main/docs/source/notebooks/04.ST_data_of_mouse midbrain_with_multiple_times.ipynb

Generates an HTML animation showing cell transfer between multiple spatial transcriptomics sections.

```python
spt.animate_transfer(adata_list=[adata1_sub,adata2_sub,adata3_sub],
                 transfer_path='./cell.transfer.csv',
                 fig_title = " Cell transfer from E12.5 E14.5 to E16.5",
                 time ='Time point',
                 color=['#5B58A7', '#9A154C', '#F3754E'],
                 annotation='annotation',
                 save_path='./cell.transfer.animation.html',
                 times=['E12.5','E14.5','E16.5'])
```

--------------------------------

### spaTrack.get_velocity

Source: https://github.com/yzf072/spatrack/blob/main/docs/source/api_velocity.rst

Calculates trajectory velocity.

```APIDOC
## spaTrack.get_velocity

### Description
Computes the velocity of the trajectory.
```

--------------------------------

### Plot gene regulatory network

Source: https://github.com/yzf072/spatrack/blob/main/docs/source/notebooks/04.ST_data_of_mouse midbrain_with_multiple_times.ipynb

Visualize the gene regulatory network with optional filtering for minimum weight and node count.

```python
gr.plot_gene_regulation(min_weight=0.012,min_node_num=10)
```

--------------------------------

### Calculate cell transition probability

Source: https://github.com/yzf072/spatrack/blob/main/docs/source/notebooks/05.scRNAseq_data_of_HSC.ipynb

Computes the optimal transport (OT) matrix between cells. If PCA coordinates are missing, the function automatically performs PCA.

```python
adata.obsp['trans']=spt.get_ot_matrix(adata,data_type='single-cell')
```

--------------------------------

### Compute spatial neighbors

Source: https://github.com/yzf072/spatrack/blob/main/docs/source/notebooks/02.ST_data_of_Intrahepatic_cholangiocarcinoma_cancer.ipynb

Calculates the neighbor graph based on spatial coordinates.

```python
sc.pp.neighbors(adata, use_rep="X_spatial", key_added="X_spatial", n_neighbors=100)
```

--------------------------------

### Calculate vector field velocity

Source: https://github.com/yzf072/spatrack/blob/main/docs/source/notebooks/05.scRNAseq_data_of_HSC.ipynb

Computes the vector field velocity on a grid for trajectory visualization.

```python
adata.uns['E_grid'],adata.uns['V_grid']=spt.get_velocity(adata,basis='UMAP',n_neigh_pos=100,n_neigh_gene=0)
```

--------------------------------

### Plot single gene expression along pseudotime

Source: https://github.com/yzf072/spatrack/blob/main/docs/source/notebooks/01.ST_data_of_axolotl_brain_regeneration_after_injury.ipynb

Visualizes the expression of a specific gene across pseudotime points.

```python
spt.plot_trajectory_gene(sub_adata,gene_name='VIM',point_size=80)
```

```python
spt.plot_trajectory_gene(sub_adata,gene_name='SYP',point_size=80)
```

--------------------------------

### Filter cells and genes for trajectory analysis

Source: https://github.com/yzf072/spatrack/blob/main/docs/source/notebooks/02.ST_data_of_Intrahepatic_cholangiocarcinoma_cancer.ipynb

Select specific clusters and filter genes based on minimum expression proportion and high variability.

```python
sub_adata_path = sub_adata[sub_adata.obs["cluster"].isin(["P0", "P3", "P4"])]
sub_adata_path = spt.filter_gene(sub_adata_path, min_exp_prop=0.1, hvg_gene=5000)
```

--------------------------------

### Reconstruct Vector Field

Source: https://github.com/yzf072/spatrack/blob/main/docs/source/notebooks/01.ST_data_of_axolotl_brain_regeneration_after_injury.ipynb

Reconstructs the grid-level vector field into a cell-level format for trajectory analysis.

```python
VecFld=spt.VectorField(adata,basis='spatial')
```

--------------------------------

### Filter genes for LAP analysis

Source: https://github.com/yzf072/spatrack/blob/main/docs/source/notebooks/05.scRNAseq_data_of_HSC.ipynb

Selects specific cell types and filters genes based on expression proportion and variability.

```python
sub_adata_path=sub_adata[sub_adata.obs['cluster'].isin(['HSC','BMEP','MKP'])]
sub_adata_path=spt.filter_gene(sub_adata_path,min_exp_prop=0.1,hvg_gene=5000)
```

--------------------------------

### Filter and order significant trajectory genes

Source: https://github.com/yzf072/spatrack/blob/main/docs/source/notebooks/02.ST_data_of_Intrahepatic_cholangiocarcinoma_cancer.ipynb

Filter genes by model fit and FDR thresholds, then order them based on trajectory expression.

```python
df_sig_res = df_res.loc[(df_res['model_fit']>0.15) & (df_res['fdr']<0.05)]
sort_exp_sig = spt.order_trajectory_genes(sub_adata_path,df_sig_res,cell_number=20)
```

--------------------------------

### Visualize Trajectory on UMAP

Source: https://github.com/yzf072/spatrack/blob/main/docs/source/notebooks/03.ST_data_of_axolotl_brain_slides_with_multiple_times.ipynb

Generates a UMAP embedding plot overlaid with a streamplot representing the calculated velocity grid.

```python
fig,axs=plt.subplots(ncols=1,nrows=1,figsize=(8,6))

ax = sc.pl.embedding(adata, basis ='X_umap',show=False,color='cluster',ax=axs,legend_loc='on data',frameon=False,title=' ',legend_fontsize=20,
                     legend_fontoutline =3,legend_fontweight='bold',alpha=0.5,size=300)

ax.streamplot(adata.uns['P_grid'][0], adata.uns['P_grid'][1], adata.uns['V_grid'][0], adata.uns['V_grid'][1],density=2,color='black',linewidth=3,arrowsize=2,minlength=0.2,maxlength=0.8)

plt.tight_layout()
```

--------------------------------

### spaTrack.VectorField

Source: https://github.com/yzf072/spatrack/blob/main/docs/source/api_LAP.rst

Computes the vector field for the given data.

```APIDOC
## spaTrack.VectorField

### Description
Computes the vector field for the provided data structure.
```

--------------------------------

### Visualize cell quiver plot

Source: https://github.com/yzf072/spatrack/blob/main/docs/source/notebooks/01.ST_data_of_axolotl_brain_regeneration_after_injury.ipynb

Displays the velocity field as a quiver plot over the spatial embedding, with arrow length controlled by the scale parameter.

```python
fig, axs = plt.subplots(figsize=(5, 5))
sc.pl.embedding(adata, basis='spatial',show=False,title=' ',color='cluster',ax=axs,frameon=False,palette='tab20b',legend_fontweight='normal',alpha=0.1,size=600)
axs.quiver(adata.uns['E_grid'][0],adata.uns['E_grid'][1],adata.uns['V_grid'][0],adata.uns['V_grid'][1],scale=0.008)
```

--------------------------------

### Visualize cell trajectory streamplot

Source: https://github.com/yzf072/spatrack/blob/main/docs/source/notebooks/01.ST_data_of_axolotl_brain_regeneration_after_injury.ipynb

Generates a streamline plot to visualize the inferred cell differentiation trajectory.

```python
fig,axs=plt.subplots(ncols=1,nrows=1,figsize=(6,6))
ax = sc.pl.embedding(adata,  basis='spatial',show=False,title=' ',color='cluster',ax=axs,frameon=False,palette='tab20b',legend_fontweight='normal',alpha=0.8,size=150)
ax.streamplot(adata.uns['E_grid'][0], adata.uns['E_grid'][1], adata.uns['V_grid'][0], adata.uns['V_grid'][1],density=1.8,color='black',linewidth=2.5,arrowsize=1.5)
```

--------------------------------

### spaTrack.plot_trajectory_gene_heatmap

Source: https://github.com/yzf072/spatrack/blob/main/docs/source/api_Pgene.rst

Generates a heatmap of gene expression along a trajectory.

```APIDOC
## spaTrack.plot_trajectory_gene_heatmap

### Description
Visualizes the expression of trajectory-dependent genes using a heatmap.
```

--------------------------------

### spaTrack.ptime_gene_GAM

Source: https://github.com/yzf072/spatrack/blob/main/docs/source/api_Pgene.rst

Calculates pseudotime-dependent gene expression using Generalized Additive Models (GAM).

```APIDOC
## spaTrack.ptime_gene_GAM

### Description
Fits a Generalized Additive Model to gene expression data relative to pseudotime.
```

--------------------------------

### Calculate vector field velocity

Source: https://github.com/yzf072/spatrack/blob/main/docs/source/notebooks/02.ST_data_of_Intrahepatic_cholangiocarcinoma_cancer.ipynb

Computes the vector field velocity by averaging velocities of cells and their spatial neighbors.

```python
adata.uns['E_grid'],adata.uns['V_grid']=spt.get_velocity(adata,basis='spatial',n_neigh_pos=100)
```

--------------------------------

### spaTrack.order_trajectory_genes

Source: https://github.com/yzf072/spatrack/blob/main/docs/source/api_Pgene.rst

Orders genes based on their expression patterns along a trajectory.

```APIDOC
## spaTrack.order_trajectory_genes

### Description
Sorts genes according to their dynamic expression changes across the inferred trajectory.
```

--------------------------------

### Display significant genes

Source: https://github.com/yzf072/spatrack/blob/main/docs/source/notebooks/05.scRNAseq_data_of_HSC.ipynb

Displays the dataframe containing significant pseudotime-dependent genes.

```python
df_sig_res
```

--------------------------------

### Calculate cell velocity field

Source: https://github.com/yzf072/spatrack/blob/main/docs/source/notebooks/01.ST_data_of_axolotl_brain_regeneration_after_injury.ipynb

Computes the velocity field based on spatial coordinates and pseudotime, storing results in the AnnData object.

```python
adata.uns["E_grid"], adata.uns["V_grid"] = spt.get_velocity(adata, basis="spatial", n_neigh_pos=50)
```

--------------------------------

### Filter significant pseudotime-dependent genes

Source: https://github.com/yzf072/spatrack/blob/main/docs/source/notebooks/01.ST_data_of_axolotl_brain_regeneration_after_injury.ipynb

Filters results based on model fit R2 value and FDR threshold.

```python
df_sig_res = df_res.loc[(df_res['model_fit']>0.2) & (df_res['fdr']<0.05)]
```

--------------------------------

### spaTrack.filter_gene

Source: https://github.com/yzf072/spatrack/blob/main/docs/source/api_Pgene.rst

Filters genes based on specified criteria.

```APIDOC
## spaTrack.filter_gene

### Description
Filters genes from the dataset based on provided criteria.
```

--------------------------------

### spaTrack.plot_trajectory_gene

Source: https://github.com/yzf072/spatrack/blob/main/docs/source/api_Pgene.rst

Plots the expression of a specific gene along a trajectory.

```APIDOC
## spaTrack.plot_trajectory_gene

### Description
Creates a plot showing the expression trend of a selected gene over pseudotime.
```

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