This archive contains the source code of a LaTeX guide for using the APL array processing language. The compiled file, which is the only one you may be interested in downloading and reading, is apltutorial.pdf.

I don't claim that I will teach you how to program in APL. I will only show how to use the two most efficient APL systems, April APL and Dyalog APL. For learning APL, I recommend Stefan Kruger's book, "Learning APL," which I use myself.

Learning APL

I found a discussion on a computer languages forum about how fast Dyalog APL is compared to Python. The forum members proposed using matrix multiplication to resolve the issue. Unfortunately, their algorithm was incorrect. Below, you will find the correct method for multiplying two matrices of size (3000, 3000), whose elements are random numbers. As you can see, Dyalog APL finishes the calculation in 14 seconds on my machine, which is not very powerful (the salary of a professor is not large enough to buy a top-of-the-line computer).

     m1 ← ?3000 3000 ⍴1e10
     m2 ← ?3000 3000 ⍴1e10
     ]Performance.runtime '⍴ m1 +.× m2'

* Benchmarking "⍴ m1 +.× m2"
              (ms)
 CPU (avg):  14227
 Elapsed:    14231

The NumPy library relies on BLAS and LAPACK libraries to execute linear algebra functions with vectors and matrices efficiently. Even so, it seems that NumPy is slower than Dyalog APL, according to the conclusion of the members of the forum.

~/apl/apldocs/src$ python -q
>>>> import numpy
i>>>> import time
>>>> def mm():
....    start_time= time.time()
....    a= numpy.random.randint(0, 1e10, (2, 3000, 3000))
....    print((a[0,] @ a[1,]).shape)
....    print(time.time() - start_time)
....    
>>>> mm()
(3000, 3000)
41.086079359054565

As for my part, since I am very fond of BLAS and LAPACK, I refuse to believe in what my eyes are showing me.

Let us see that the algorithm of matrix multiplication used in the Dyalog APL benchmark works. I will create two small random matrices, and multiply them.

      m1 ← ?3 3 ⍴ 5

      m1
3 4 2
3 4 1
1 1 5
      m2 ← ?3 3 ⍴ 4
      m2
2 2 1
3 4 3
3 1 3
      m1 +.× m2
24 24 21
21 23 18
20 11 19