Calculating temporal and sptial gradients while using groupby in multi-index pandas dataframe - pandas

Question

Say I have the following sample pandas dataframe of water content (i.e. "wc") values at specified depths along a column of soil:
import pandas as pd
df = pd.DataFrame([[1, 2,5,3,1], [1, 3, 5,3, 2], [4, 6, 6,3,1], [1, 2,5,3,1], [1, 3, 5,3, 2], [4, 6, 6,3,1]], columns=pd.MultiIndex.from_product([['wc'], [10, 20, 30, 45, 80]]))
df['model'] = [5,5, 5, 6,6,6]
df['time'] = [0, 1, 2,0, 1, 2]
df.set_index(['time', 'model'], inplace=True)
>> df
[Out]:
wc
10 20 30 45 80
time model
0 5 1 2 5 3 1
1 5 1 3 5 3 2
2 5 4 6 6 3 1
0 6 1 2 5 3 1
1 6 1 3 5 3 2
2 6 4 6 6 3 1
I would like to calulate the spatial (between columns) and temporal (between rows) gradients for each model "group" in the following structure:
wc temp_grad spat_grad
10 20 30 45 80 10 20 30 45 80 10 20 30 45
time model
0 5 1 2 5 3 1
1 5 1 3 5 3 2
2 5 4 6 6 3 1
0 6 1 2 5 3 1
1 6 1 3 5 3 2
2 6 4 6 6 3 1
My attempt involved writing a function first for the temporal gradients and combining this with groupby:
def temp_grad(df):
temp_grad = np.gradient(df[('wc', 10.0)], df.index.get_level_values(0))
return pd.Series(temp_grad, index=x.index)
df[('temp_grad', 10.0)] = (df.groupby(level = ['model'], group_keys=False)
.apply(temp_grad))
but I am not sure how to automate this to apply for all wc columns as well as navigate the multi-indexing issues.

Answer 1

Assuming the function you write is actually what you want, then for temp_grad, you can do at once all the columns in the apply. use np.gradient the same way you did in your function but specify along the axis=0 (rows). Built a dataframe with index and columns as the original data. For the spat_grad, I think the model does not really matter, so no need of the groupby, do np.gradient directly on df['wc'], and along the axis=1 (columns) this time. Built a dataframe the same way. To get the expected output, concat all three of them like:
df = pd.concat([
df['wc'], # original data
# add the temp_grad
df['wc'].groupby(level = ['model'], group_keys=False)
.apply(lambda x: #do all the columns at once, specifying the axis in gradient
pd.DataFrame(np.gradient(x, x.index.get_level_values(0), axis=0),
columns=x.columns, index=x.index)), # build a dataframe
# for spat, no need of groupby as it is row-wise operation
# change the axis, and the values for the x
pd.DataFrame(np.gradient(df['wc'], df['wc'].columns, axis=1),
columns=df['wc'].columns, index=df['wc'].index)
],
keys=['wc','temp_grad','spat_grad'], # redefine the multiindex columns
axis=1 # concat along the columns
)
and you get
print(df)
wc temp_grad spat_grad \
10 20 30 45 80 10 20 30 45 80 10 20
time model
0 5 1 2 5 3 1 0.0 1.0 0.0 0.0 1.0 0.1 0.2
1 5 1 3 5 3 2 1.5 2.0 0.5 0.0 0.0 0.2 0.2
2 5 4 6 6 3 1 3.0 3.0 1.0 0.0 -1.0 0.2 0.1
0 6 1 2 5 3 1 0.0 1.0 0.0 0.0 1.0 0.1 0.2
1 6 1 3 5 3 2 1.5 2.0 0.5 0.0 0.0 0.2 0.2
2 6 4 6 6 3 1 3.0 3.0 1.0 0.0 -1.0 0.2 0.1
30 45 80
time model
0 5 0.126667 -0.110476 -0.057143
1 5 0.066667 -0.101905 -0.028571
2 5 -0.080000 -0.157143 -0.057143
0 6 0.126667 -0.110476 -0.057143
1 6 0.066667 -0.101905 -0.028571
2 6 -0.080000 -0.157143 -0.057143