# For..Do

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## For Temp := I Do Expr

For each successive value of «I», assigns that value to the local variable «Temp», and evaluates expression «Expr». «Expr» may refer to «I» and «Temp». «Temp» becomes a local variable that can be referred to only within the expression «Expr».

In the most common usage, «I» is an index, and the result of evaluating the For loop is an array indexed by «I», with each slice along «I» containing the result of evaluating «Expr» at that value. When «I» is a self-indexed variable, «Temp» is set successively to each of «I»'s index values.

Prior to Analytica 4.0, when I was a 1-D self-indexed variable, the context value of «I», rather than the index value of «I», was used.

## For Temp := loopExpr Do bodyExpr

For can also be used to loop over every element of an array result, with «loopExpr» being an arbitrary expression. If «loopExpr» is an identifer, and that identifier is a valid index, then its index value is used (as described in the previous section), otherwise «loopExpr» is evaluated in context, and «Temp» loops over all elements of the array result. The result of evaluating For in this case is an array containing all of the dimensions of «loopExpr», with each slice among those dimensions being the result of evaluating «bodyExpr».

## For Temp[I, J] := loopExpr Do bodyExpr

In this usage of For, with indexes of «Temp» explicitly specified, «loopExpr» is evaluated, and then For loops over all indexes of this result that are not listed, leaving «Temp» indexed by those that are listed. For example, if the result of «loopExpr» is indexed by I, J, K and L, then For Temp[I, J] loops over all combinations of K, L. At each iteration, a slice along «I» and «J» is assigned to «Temp», which in this case would itself be an array indexed by K and L. With an empty list of indexes, For Temp[] := loopExpr, For loops over all dimensions of «loopExpr», so that «Temp» is atomic in each iteration.

## When to use a For loop

You rarely need to to use a For loop with Analytica, unlike most other computer languages: Analytica's Intelligent Array features mean that most functions and operations iterate over the dimensions (indexes) of array values automatically. Adding unnecessary For loops (sometimes known as Vacuous For Loops) make expressions much harder to read and slower to evaluate. If you find yourself using a lot of For loops, you might want to review Intelligent Arrays to see if the For loops are really necessary -- e.g. Indexes and arrays: An introduction in the Analytica User Guide.

There are just a few rare situations when an explicit For loop is useful:

• To update a local variable as a side-effect in each iteration.
• To apply one of the few constructs (such as While..Do) or functions (such as Sequence) that are not Array-abstractable, since they require one or more parameters that are scalar or vector (i.e., zero or one indexes respectively).
• To avoid the attempted evaluation of out-of-range values by nesting an If-Then-Else inside a For.
• To avoid expensive conditional computations.
• To reduce the memory needed for calculations with very large arrays by reducing the memory requirement for intermediate results.

Special

## Detailed Notes

When looping over a self-indexed variable, there is a subtlety as to whether the index value or main value of the variable is used. Consider the following two variations:

For Temp := X Do expr
For Temp[] := X Do expr

When «X» is a self-indexed variable, there is a subtle difference between these two variations. The first case loops over the index values of «X», while the second case loops over the main value of «X». Consider the following self-indexed variable, X, indexed by Self and In1:

In1 ▶
X ▼ 'a' 'b' 'c' 'd'
1 11 12 13 14
2 21 22 23 24
3 31 32 33 34

The For Temp:=X variation loops three times, setting Temp to 1, 2, and 3. The For Temp[] := X variation loops 12 times, setting X to 11, 12, .., 33, 34.

Other than this subtlety, for expressions where «X» is not a self-indexed variable, the two syntaxes produce the same result.

Prior to 4.0, For Temp := X required «X» to be an index or sequence, but used «X»'s value rather than index value. Analytica 4.0 loops all elements of «X» for any dimensionality.

There is another equivalence in Analytica. Consider the following two expressions:

For Temp[I, J] := X Do expr
 Var Temp[I, J] := X Do expr

Although these may be conceptualized differently, the first as a procedural expression, the second as a declarative expression, they are functionally identical. The first says to loop over all dimensions of «X» except «I» and «J». The second declares «Temp» to be a local variable indexed only by «I» and «J» while «expr» is evaluated. In order to guarantee that «Temp» is indexed only by «I» and «J», Analytica will iterate over all dimensions in «X» other than «I» and «J». Hence, these two are functionally identical. In general, declarative expressions tend to be clearer and conceptually simpler, allowing the modeller or reader to express their logic and letting the software worry about the evaluation details; therefore, in most cases the Var..Do is the preferred form.

There is an alternative syntax that may be seen in older models and is still supported. The following two syntax forms are treated identically:

For Temp[I, J] := X Do expr
For Temp := X in each I, J Do expr

## Examples

### Using For loops for their side-effects

The following loop computes ratios of successive Fibonacci numbers (which converges to the golden ratio):

var a := 0;
var b := 1;
for i := 1..100 do (
var c := a + b;
a := b;
b := c;
a/b
)

The result of each iteration through the loop depends on side-effects in the local variables a and b that were updated in the previous iteration.

### Abstracting over Non-Abstractable Functions

For can be used to apply a function that requires a scalar, one- or two- dimensional input to a multidimensional result. This usage is rare in Analytica since array abstraction normally does this automatically; however, the need occasionally arises in some circumstances.

Suppose you have an array A indexed by I, and you wish to apply a function f(x) to each element of A along I. In a conventional programming language, this would require a loop over the elements of A; however, in almost all cases, Analytica’s array abstraction does this automatically — the expression is simply: f(A), the result remains indexed by I. However, there are a few cases where Analytica does not automatically array abstract, or it is possible to write a user-defined function that does not automatically array abstract. For example, Analytica does not array abstract over functions such as Sequence, Split, Subset, or Unique, since these return unindexed lists of varying lengths that are unknown until the function evaluates. Suppose we have the following variables defined (note: A is an array of text values):

Variable A :=
Index_1 ▶
1 A, B, C
2 D, E, F
3 G, H, I

We wish to split the text values in A and obtain a two dimensional array of letters indexed by Index_1 and Index_2 Since Split does not array abstract, we must do each row separately and reindex by Index_2 before the result rows are recombined into a single array. This is accomplished by the following loop.

for Row := Index_1 do
Array(Index_2, Split(A[Index_1 = Row], ', '))

resulting in

Index_2 ▶
Index_1 ▼ 1 2 3
1 A B C
2 D E F
3 G H I

### Avoiding Out-Of-Range or Type Mismatch Errors

Consider the following expression:

If IsNumber(X) then Mod(X, 2) else 0

The If-Then-Else is included here to avoid the error "the first parameter to Mod must be numeric". However, when X is an array of values, this expression may not avoid the error because Mod(X, 2) will if any element of X is numeric, and will encounter the error if any element of X is non-numeric. To avoid the error, the expression can be re-written as

For j :=X do
If IsNumber(j) then Mod(j, 2) else 0

In most cases of this form where a warning results, Analytica can figure out whether the warning impacts the final result without an explicit For loop. For example, even though Sqrt(X) or X[I = I - 1] may cause a warning for some elements of X when X is an array, the expressions

If X < 0 Then 0 Else Sqrt(X)
if I < 2 then X[I = 1] else X[I = I-1]

do not need an explicit For loops to avoid the warnings.

### Expensive Conditional Computation

Suppose you have user-defined functions, f(X, I) and g(X, I), that are very computationally expensive, and a criteria, SomeCondition(A, I) to determine which is the most appropriate to use. If you evaluate:

If SomeCondition(A, I) Then f(A , I) Else g(A, I)

when A is indexed by I and J, then f(A, I) and g(A, I) are both evaluated for every slice of J, even though only one or the other is used at every slice. A For loop can avoid unnecessary evaluations of f and g:

For X[I] := A Do
If SomeCondition(X, I) Then f(X, I) Else g(X, I)

For small computations, the overhead of the For loop will far outweigh the saving in avoiding function evaluations. In the absence of a For loop, Analytica's array abstraction is able to carry out operations over entire arrays in native code, rather than having to interpret a For loop, and so is much faster. So you should use this approach only when the computational cost of f(X, I) or g(X, I) is substantial.

### Reducing Memory Requirements

In some cases, it is possible to reduce the amount of memory required for intermediate results during the evaluation of expressions involving large arrays. For example, consider the following expression:

MatrixA: A two dimensional array indexed by M and N.
MatrixB: A two dimensional array indexed by N and P.
Average(MatrixA * MatrixB, N)

During the calculation, Analytica needs memory to compute MatrixA * MatrixB, an array indexed by M, N, and P. If these indexes have sizes 100, 200, and 300 respectively, then MatrixA * MatrixB contains 6,000,000 numbers, requiring over 60 megabytes of memory at 10 bytes per number.

To reduce the memory required, use the following expression instead

For L := M Do Average(MatrixA[M = L]*MatrixB, N)

Each element MatrixA[M = L]*MatrixB has dimensions N and P, needing only 200x300x10= 600 kilobytes of memory at a time.

Note
For the special case of a dot product, where an expression has the form Sum(A*B, I), Analytica performs a similar transformation internally.