Iterate | JMP 12

Iterate

JSL provides the For(), While(), Summation(), and Product() functions to repeat (or iterate) actions according to the conditions that you specify.

Note: A similar function called For Each Row() is for iterating actions over rows of a data table. See If for an example. Additional Ways to Access Data Values in Data Tables also describes iterating through table rows.

For

The For() function expects four arguments separated by commas. The first three arguments are rules for how many times to repeat the loop, and the fourth is what to do each time the loop is executed.

The basic syntax for For() is as follows:

For(initialization, while, iteration, body);

For example, the following script sums the numbers from 0 to 20:

s = 0;

For(i = 0, i <= 20, i++, s += i);

The script works like this:


s = 0;	Sets the s variable to 0. This variable holds the sum.
For(	Begins the For() loop.
i = 0,	Sets the initialization variable (i) to 0. This expression is performed only once.
i <= 20,	Each time the loop begins, compares i to 20. As long as i is less than or equal to 20, continue evaluating the loop. If i is greater than 20, immediately break out of the loop.
i++,	At the end of the loop, increments i by 1. Note that this step is done after the body of the loop (next line) is evaluated.
s += i	Evaluates the body of the loop. Adds the value of i to s. After the body is finished, i is incremented (previous line).
);	Ends the loop.

Infinite Loops

For loops that always evaluate as true create an infinite loop, which never stops. To stop the script, press ESC on Windows (or COMMAND-PERIOD on Macintosh). You can also select Edit > Stop Script. On Macintosh, Edit > Stop Script is available only when the script is running.

Comparing For Loops in JSL to C and C++

The JSL For() loop works just like it does in the C (and C++) programming language, although the punctuation is different.

Tip: If you know C, watch out for the difference between JSL and C in the use of semicolons and commas. In JSL, For() is a function where commas separate arguments and semicolons join expressions. In C, for is a special clause where semicolons separate arguments and commas join them.

While

A related function is While(), which repeatedly tests the condition and evaluates its body script as long as the condition is true. The syntax is:

While(condition, body);

For example, here are two different programs that use a While() loop to find the least power of 2 that is greater than or equal to x (287). The result of both programs is 512.

x = 287;

// loop 1:

y = 1;

While(y < x, y *= 2);

Show(y);

// loop 2:

k = 0;

While(2 ^ k < x, k++);

Show(2 ^ k);

The scripts work like this:


x = 287;	Sets x to 287.
// loop 1
y = 1;	Sets y to 1.
While(	Begins the While() loop.
y < x,	As long as y is less than x, continues evaluating the loop.
y *= 2	Multiplies 1 by 2 and then assigns the result to y. The loop then repeats while y is less than 287.
);	Ends the loop.
Show(y);	Shows the value of y (512).
// loop 2
k = 0;	Sets k to 0.
While(	Begins the While() loop.
2 ^ k < x,	Raises 2 to the exponent power of k and continues evaluating the loop as long as the result is less than 287.
k++	Increments k to 1. The loop then repeats while 2 ^ k is less than 287.
);	Ends the loop.
Show(2 ^ k);	Shows the value of 2 ^ k (512).

As with For() loops, While() loops that always evaluate as true create an infinite loop, which never stops. To stop the script, press ESC on Windows (or COMMAND-PERIOD on Macintosh). You can also select Edit > Stop Script. On Macintosh, Edit > Stop Script is available only when the script is running.

Summation

The Summation() function adds the body results over all i values. The syntax is:

Summation(initialization, limitvalue, body);

For example:

s = Summation(i = 1, 10, i);

returns 55, the result of 1+2+3+4+5+6+7+8+9+10.

The script works like this:


s =	Sets the s variable to the value of the function.
Summation(	Begins the Summation() loop.
i = 1,	Sets i to 1.
10,	Sets the limit of i to 10.
i	All values of i from 1 to 10 are added together, resulting in 55.
);	Ends the loop.

This behavior is similar to Σ in the Formula Editor. The following expression:

Summation(i = 1, N Row(), x ^ 2);

is equivalent to the following formula in the Formula Editor:

Product

The Product() function is similar to Summation() except that it multiplies the body results rather than adding them. The syntax is the same as for Summation(). For example:

p = Product(i = 1, 5 , i);

returns 120, the result of 1*2*3*4*5.

In this example, the initial value of i is 1, the upper limit is 5, then all integer values of i up to 5 are multiplied.

Here is the equivalent in the Formula Editor:

Break and Continue

The Break() and Continue() functions give you more control over looping. Break() immediately stops the loop and proceeds to the next expression that follows the loop. Continue() is a gentler form of Break(). It immediately stops the current iteration of the loop and continues with the next iteration of the loop.

Break

Break() is typically used inside a conditional expression. For example:

For(i = 1, i <= 5, i++,

If(i == 3, Break());

Print("i=" || Char(i));

The script works like this:


For(	Begins the For() loop.
i = 1,	Sets i to 1.
i <= 5,	As long as i is less than or equal to 5, continues evaluating the loop.
i++,	Increments i by 1. Note that this step is done after the If loop is evaluated.
If(	Begins the If() loop.
i == 3, Break()	If i is equal to 3, breaks the loop.
);	Ends the loop.
Print(	When i equals 3, opens the Print() loop.
"i="	Prints the string "i=" to the log.
\|\|	Places "i=" on the same line as the value that follows.
Char(i));	Prints the value of i to the log. The For() loop then repeats until the value of i is less than or equal to 5, breaking and printing only when i is less than 3.
);	Ends the loop.

Note that when the If() and Break() expressions follow Print(), the script prints the values of i from 1 to 3, because the loop breaks after "i=3" is printed.

As with Break(), Continue() is typically used inside a conditional expression. For example:

For(i = 1, i <= 5, i++,

If(i < 3, Continue());

Print("i=" || Char(i));

The script works like this:


For(	Begins the For() loop.
i = 1,	Sets i to 1.
i <= 5,	Evaluates 1 as less than or equal to 5.
i++,	Increments i by 1. Note that this step is done after the If loop is evaluated.
If(	Begins the If() loop.
i < 3, Continue()	Evaluates i as 1 and continues as long as i is less than 3.
);	Ends the If() loop.
Print(	When i is no longer less than 3, opens the Print() loop.
"i="	Prints the string "i=" to the log.
\|\|	Places "i=" on the same line as the value that follows.
Char(i));	Prints the value of i to the log. The For() loop then repeats until the value of i is less than or equal to 5, continuing and printing only when i is equal to or greater than 3.
);	Ends the loop.