J Labs

A Taste of J (1)

(1 of 35) 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:

(2 of 35) First Steps (ctd)

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.

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

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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:

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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:

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We can now use the assigned names:

(7 of 35) Data Manipulation

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

Define a character string t as follows:

(8 of 35) Data Manipulation (ctd)

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

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Nub of t, i.e. unique characters:

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Count of nub of t:

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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:

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Reverse t:

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Duplicate each letter:

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Make 3 copies of t:

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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:

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Sort words in t:

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

(18 of 35) Numbers

The above examples apply equally well to numbers.

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

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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.

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Add up the first 10,000 positive integers:

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Add up i.3 4 5

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"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.

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

```2.41785 * 10^24```

J has other number notations that use letters:

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Examples:

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The function ? generates random numbers.

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

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

For example, read in the stats functions:

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Example:

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

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Read in the trig and plot functions:

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Try generating sines, here the arguments are in radians:

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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.

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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.

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End of Lab