How to "melt" `pandas.DataFrame` objects in Python 3?

Question

I'm trying to melt certain columns of a pd.DataFrame while preserving columns of the other. In this case, I want to melt sine and cosine columns into values and then which column they came from (ie sine or cosine ) into a new columns entitled data_type then preserving the original desc column.

How can I use pd.melt to achieve this without melting and concatenating each component manually?

# Data
a = np.linspace(0,2*np.pi,100)
DF_data = pd.DataFrame([a, np.sin(np.pi*a), np.cos(np.pi*a)], index=["t", "sine", "cosine"], columns=["t_%d"%_ for _ in range(100)]).T
DF_data["desc"] = ["info about this" for _ in DF_data.index]

The round about way I did it:

# Melt each part
DF_melt_A = pd.DataFrame([DF_data["t"],
                          DF_data["sine"],
                          pd.Series(DF_data.shape[0]*["sine"], index=DF_data.index, name="data_type"), 
                          DF_data["desc"]]).T.reset_index()
DF_melt_A.columns = ["idx","t","values","data_type","desc"]
DF_melt_B = pd.DataFrame([DF_data["t"],
                          DF_data["cosine"],
                          pd.Series(DF_data.shape[0]*["cosine"], index=DF_data.index, name="data_type"),
                          DF_data["desc"]]).T.reset_index()
DF_melt_B.columns = ["idx","t","values","data_type","desc"]

# Merge
pd.concat([DF_melt_A, DF_melt_B], axis=0, ignore_index=True)

If I do pd.melt(DF_data I get a complete meltdown

In response to the comments:

Answer 1

allright so I had to create a similar df because I did not have access to your a variable. I change your a variable for a list from 0 to 99... so t will be 0 to 99

you could do this :

a = range(0, 100)
DF_data = pd.DataFrame([a, [np.sin(x)for x in a], [np.cos(x)for x in a]], index=["t", "sine", "cosine"], columns=["t_%d"%_ for _ in range(100)]).T
DF_data["desc"] = ["info about this" for _ in DF_data.index]

df = pd.melt(DF_data, id_vars=['t','desc'])
df.head(5)

this should return what you are looking for.

     t             desc variable     value
0  0.0  info about this     sine  0.000000
1  1.0  info about this     sine  0.841471
2  2.0  info about this     sine  0.909297
3  3.0  info about this     sine  0.141120
4  4.0  info about this     sine -0.756802