For..Do

For Temp:= I Do Expr

For each successive value of index I, assigns that value to Variable Temp, and evaluates expression Expr. Expr may refer to I and/or Temp. Temp is a local or temporary Variable that can be referred to only within the expression Expr.

The result of the For control function is an array indexed by I containing the results of evaluating Expr. I must be an index Variable, or be defined as a list or Sequence().

If you make appropriate use of the intelligent array features described earlier in this and preceding chapters, you will rarely need to use For structure (unlike in conventional computer languages, which require extensive use of For loops and related control structures for handling arrays). For is sometimes useful in these specialized cases:

• To avoid the attempted evaluation of out-of-range values by nesting an If-Then-Else inside a For. • To apply an Analytica function that requires a scalar or oneor two-dimensional array input to a higher-dimensioned array. • To reduce the memory needed for calculations with very large arrays by reducing the memory requirement for intermediate results.

Library

Special

Examples

Avoiding out-of-range errors: Consider the following expression:

If X<0 Then 0 Else Sqrt(X)

The If-Then-Else is included in this expression to avoid the warning "Square root of a negative number." However, if X is an array of values, this expression may not avoid the warning since Sqrt(X) is evaluated before If-Then-Else selects which elements of Sqrt(X) to include. To avoid the warning (assuming X is indexed by I) the expression can be rewritten as

For j:=I do
   If X[I=j]<0 then 0 else Sqrt(X[I=j])

or as (see next section):

Var y:=X in I do
   If y<0 Then 0 else Sqrt(y)

Situations like this can often occur during slicing operations. For example, to shift X one position to the right along I, the following expression would encounter an error:

if I<2 then X[I=1] else X[I=I-1]

The error occurs when X[I=I-1] is evaluated since the value corresponding to I-1=0 is out-of-range. The avoid the error, the expression can be rewritten as:

For j:=I do
   If j<2 then X[I=1] else X[I=j-1]

Out-of-range errors can also be avoided without using For by placing the conditional inside an argument. For example, the two examples above can be written without For as follows:

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

Dimensionality reduction: 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 (e.g., by declaring a parameter to be of type Scalar, see page 422). 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):

A: Index_1 v

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_1 v, Index_2 →

	1	2	3
1	A	B	C
2	D	E	F
3	G	H	I

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.

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Analytica Note: For the special case of a dot product (see “Dot product of two matrices” on page 272), where an expression has the form Sum(A*B,I), Analytica performs a similar transformation internally.