I have updated to the latest version of Elixir ver1.10. I have modified cuMatrix to work.

I wrote addition, subtraction and multiplication code in CUDA and cuBLAS. So I measured it and compared it with the Matrix library.
Multiplication is fast, but addition and subtraction are not much different.

------ cuMatrix ----------------
iex(1)> a = Cumatrix.new(1000,1000,:rand);0
0
iex(2)> b = Cumatrix.new(1000,1000,:rand);0
0
iex(3)> require(Time)
nil
iex(4)> Time.time(Cumatrix.mult(a,b));0
“time: 226896 micro second”
“-------------”
0
iex(5)> Time.time(Cumatrix.mult(a,b));0
“time: 67511 micro second”
“-------------”
0
iex(6)> Time.time(Cumatrix.mult(a,b));0
“time: 33814 micro second”
“-------------”
0
iex(7)> Time.time(Cumatrix.add(a,b));0
“time: 24058 micro second”
“-------------”
0
iex(8)> Time.time(Cumatrix.add(a,b));0
“time: 31787 micro second”
“-------------”
0
iex(9)> Time.time(Cumatrix.add(a,b));0
“time: 28815 micro second”
“-------------”
0
iex(10)> Time.time(Cumatrix.sub(a,b));0
“time: 27208 micro second”
“-------------”
0
iex(11)> Time.time(Cumatrix.sub(a,b));0
“time: 25860 micro second”
“-------------”
0
iex(12)> Time.time(Cumatrix.sub(a,b));0
“time: 24574 micro second”
“-------------”
0

------ Matrix ---------------------
iex(1)> a = Matrix.rand(1000,1000);0
0
iex(2)> b = Matrix.rand(1000,1000);0
0
iex(3)> require(Time)
nil
iex(4)> Time.time(Matrix.mult(a,b));0
“time: 29913660 micro second”
“-------------”
0
iex(5)> Time.time(Matrix.mult(a,b));0
“time: 30599437 micro second”
“-------------”
0
iex(6)> Time.time(Matrix.mult(a,b));0
“time: 30030455 micro second”
“-------------”
0
iex(7)> Time.time(Matrix.add(a,b));0
“time: 21835 micro second”
“-------------”
0
iex(8)> Time.time(Matrix.add(a,b));0
“time: 84429 micro second”
“-------------”
0
iex(9)> Time.time(Matrix.add(a,b));0
“time: 76458 micro second”
“-------------”
0
iex(10)> Time.time(Matrix.sub(a,b));0
“time: 22082 micro second”
“-------------”
0
iex(11)> Time.time(Matrix.sub(a,b));0
“time: 25556 micro second”
“-------------”
0
iex(12)> Time.time(Matrix.sub(a,b));0
“time: 25680 micro second”
“-------------”
0

I was encouraged.
The loss function, the activation function, and the differential calculation are also added. I will start GPU version of Deep Pipe2.