I decided to rebuild the Cygwin environment on Windows, so I made a note of the procedure.

Python 3.6
Fortran90
C/C++

For those who do scientific and technological calculations using.

First, ** Let's give up matplotlib on Cygwin ** It may be possible if you do your best. But if you devote that time to development, your productivity will increase many times. You can get a sufficient environment with a little patience.

Introduced Anaconda

I don't think about anything. Download and install Python 3.6 Version 64bit-installer (32bit for 32bit). ~~https://www.continuum.io/Downloads~~ 2019/03/22 postscript The domain of Anaconda has changed, so click here. https://www.anaconda.com/distribution/

Introducing Cygwin

For the time being, download setup-x86_64.exe (setup-x86.exe for 32bit) from Official. Execute as it is and hit the next repeatedly until the package is selected.

This time C/C++

gcc-core
gcc-g++

Fortran

gcc-fortran

Python I left it to Anaconda.

Common

make
git
wget

After selecting these, go to the next. The packages required for the dependency will be automatically output, so proceed directly to the next installation.

Introduced apt-cyg

Although it deviates from the main subject, apt-cyg will be introduced for future package management. Please refer to here for this. http://qiita.com/hkuno/items/df06db4bb406a17d2494

Introduced matplotlib

The difficulty with cygwin is the introduction of matplotlib. As I wrote at the beginning, ** give up **. However, if the Python path on the Anaconda side is in the path, calling iPython with Cygwin will call Anaconda's. Both scipy and matplotlib work fine on this iPython. In this case, the Python environment will be that of Anaconda, so install the Python package with conda. (In this case, you don't have to move X windows, so it's a lot of work.)

** 2017/10/02 postscript ** Pass Anaconda through cygwin. Add the following to .bashrc in the cygwin user directory.

PATH=/cygdrive/c/Anaconda3:/cygdrive/c/Anaconda3/Scripts:/cygdrive/c/Anaconda3/Library/bin:$PATH
export PATH

.bashrc is automatically done by starting mintty (a terminal often used in cygwin) even once. If you have changed the installation location of Anaconda on the Windows side, change the PATH as appropriate. Now you can hit anaconda's python on cygwin without going through ipython.

Summary

Get a Mac or Linux.