A Taste of J - Part 1

First Steps

You can use J as a calculator - just type sentences into the window and press Enter.

J is ready for input when the message in the status bar at the foot of the screen displays Ready.

Typically, the cursor is indented 3 spaces to distinguish user entries from the response of the computer, which are shown aligned to the left.

For example, add 5 to the three numbers 10 20 30 :

5 + 10 20 30 15 25 35

You are encouraged to experiment when going through labs.

You can type in your own sentences, or re-enter sentences by moving the cursor up to the line, pressing Enter, then making any modifications.

Try this now with the sentence 5 + 10 20 30 shown above.

The standard mathematical functions are + - * % ^ ^. , i.e. plus, minus, times, divide, power and log:

5 + 10 20 30 15 25 35 5 - 10 20 30 _5 _15 _25 5 * 10 20 30 50 100 150 5 % 10 20 30 0.5 0.25 0.166667 5 ^ 10 20 30 9.76563e6 9.53674e13 9.31323e20 5 ^. 10 20 30 1.43068 1.86135 2.11328

Note that the symbol for log " ^. " has two characters. In general, J functions are written with either a single character as in power " ^ ", or with two characters, where the second character is either a period " . " or colon " : ".

For example, *: squares its argument:

*: 10 20 30 100 400 900

Use =: to assign names.

No result is shown if a sentence is an assignment; otherwise the result is displayed.

Note that character strings are entered using quotes:

a=: 5 b=: 10 20 30 log=: ^. plus=: + square=: *: sum=: +/ text=: 'hello world'

We can now use the assigned names:

a plus b 15 25 35 square b 100 400 900 sum b 60 c=: a plus b sum c 75 text hello world

Data Manipulation

J excels at manipulating data. Let us try some examples.

Define a character string t as follows:

t=: 'earl of chatham' t earl of chatham

Count of t , i.e. number of characters in the string:

#t 15

Nub of t , i.e. unique characters:

~. t earl ofchtm

Count of nub of t :

# ~. t 11

Sort t in ascending order. "sort" is a predefined utility.

The sort order is the standard ASCII alphabet, where blanks are sorted before other characters:

sort t aaacefhhlmort

Reverse t :

|. t mahtahc fo lrae

Duplicate each letter:

2 # t eeaarrll ooff cchhaatthhaamm

Make 3 copies of t :

3 # ,: t earl of chatham earl of chatham earl of chatham

Chop t into words.

Note J puts each word in a box - when something is in a box it is treated as a single item, even though it may contain several numbers or characters:

;: t +----+--+-------+ |earl|of|chatham| +----+--+-------+

Sort words in t :

sort ;: t +-------+----+--+ |chatham|earl|of| +-------+----+--+

The utility " each " applies a function to each boxed item. For example, count the length of each word:

# each ;: t +-+-+-+ |4|2|7| +-+-+-+

Numbers

The above examples apply equally well to numbers.

Other facilities are defined just for numbers. For example, the integer function ( i. ) generates numbers:

i.10 NB. first 10 numbers 0 1 2 3 4 5 6 7 8 9 i.4 3 NB. first 12 numbers in a 4 by 3 table 0 1 2 3 4 5 6 7 8 9 10 11 i.3 4 5 NB. first 60 numbers in a 3 by 4 by 5 table 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59

The function +/ sums its argument. It is made up of + (add) with / (insert), meaning insert + between each item of the argument.

So +/ 10 20 30 means: 10 + 20 + 30 .

Similarly */ is "multiply insert", i.e. multiply all elements together.

+/ 10 20 30 60 */ 10 20 30 6000

Add up the first 10,000 positive integers:

+/i.10001 NB. 10001 - since J starts counting at 0 50005000

Add up i.3 4 5

+/i.3 4 5 60 63 66 69 72 75 78 81 84 87 90 93 96 99 102 105 108 111 114 117

"power insert" of 10 20 30 is a big number! It exceeds the representation used by the machine, so J returns infinity.

Can you figure out the other examples below?

(Try 3 ^ 4 , then take 2 to the power of this number.)

The ' x ' used here means "extended" and instructs J to use extended precision in performing the calculations, instead of converting to floating point.

^/ 10 20 30 _ ^/ 2 3 4 2.41785e24 ^/ 2 3 4x 2417851639229258349412352

Note the " e " notation used in 2.41785e24, meaning:

2.41785 * 10^24

J has other number notations that use letters:

3b102 NB. base (102 in base 3) 11 3r5 NB. ratio (3 % 5) 3r5 3j5 NB. complex number 3j5 3p5 NB. Pi (3 * Pi ^ 5) 918.059 3x5 NB. Exponentional (3 * 2.71828... ^ 5) 445.239

Examples:

1p1 2p1 NB. Pi, 2 * Pi 3.14159 6.28319 %: -i.6 NB. square roots of minus 0 to minus 5 0 0j1 0j1.41421 0j1.73205 0j2 0j2.23607

The function ? generates random numbers.

For example, generate 20 random numbers in the range 0-99:

? 20#100 13 75 45 53 21 4 67 67 93 38 51 83 3 5 52 67 0 38 6 41 ? 20#100 68 58 93 84 52 9 65 41 70 91 76 26 4 73 32 63 75 99 36 24

The function " load " reads in definitions from "script" files.

For example, read in the stats functions:

load 'stats'

Example:

dstat ? 20#100 sample size: 20 minimum: 6 maximum: 98 median: 55.5 mean: 54.25 std devn: 30.1765 skewness: _0.140884 kurtosis: 1.66846

normalrand generates random numbers in a normal distribution with mean 0 and standard deviation 1:

normalrand 6 2.4598 0.120974 _0.269407 _3.27581 _1.73646 _0.60928 dstat normalrand 10000 sample size: 10000 minimum: _4.79869 maximum: 4.05703 median: 0.0095872 mean: 0.00343015 std devn: 0.997596 skewness: _0.0475715 kurtosis: 3.03493

Read in the trig and plot functions:

load 'trig plot'

Try generating sines, here the arguments are in radians:

sin i.6 0 0.841471 0.909297 0.14112 _0.756802 _0.958924 sin i.3 4 0 0.841471 0.909297 0.14112 _0.756802 _0.958924 _0.279415 0.656987 0.989358 0.412118 _0.544021 _0.99999

You can plot numbers directly. The next section plots the sin of i.3 4 . The lines are jagged because each point is joined by a straight line and there are very few points.

plot sin i.3 4

The next two sections plot sin 0.2 * i.30 30 , first as a series of lines, then as a surface. This time there are enough data points to show smooth lines.

plot sin 0.2 * i.30 30

'surface' plot sin 0.2 * i.30 30

End of lab