259 Lecture 13 Spring 2017
Advanced Excel Topics – Arrays
Topics
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Arrays
Why Use Arrays?
Declaring an Array
Working with Arrays
Multiple Valued User Defined Functions
Cell Ranges as Arguments
Array Formulas
Array Outputs for User Defined Functions
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Arrays
 Definition: An array is a group of
elements of the same type that have a
common name.
 A specific element in an array is referred
to by using the array name and an index
number.
 Arrays are variables that can store
multiple values.
 Arrays very closely resemble matrices
used in mathematics in both form and
operation.
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Why Use Arrays?
(1) Arrays make it possible to solve problems using “Matrices” and
“Linear Algebra” techniques.
(2) Arrays make it possible for user defined functions to work with cell
ranges. For example use the formula =MySum(A1:A5) instead of
the formula =MySum(A1,A2,A3,A4,A5).
(3) Arrays make it possible for a user defined function to return
multiple values. For example:
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=BestFitLine() returns the “Slope” of the best-fit line for a set of N ordered
pairs of data, {(x1, y1), (x2, y2), … , (xN, yN)}.
=BestFitLine() returns the “YIntercept” of the best-fit line for a set of N
ordered pairs of data, {(x1, y1), (x2, y2), … , (xN, yN)}.
=BestFitLine() returns the “Equation” of the best-fit line for a set of N
ordered pairs of data, {(x1, y1), (x2, y2), … , (xN, yN)}.
=BestFitLine() returns the slope, y-intercept, and equation for the best-fit
line for a set of N ordered pairs of data, {(x1, y1), (x2, y2), … , (xN, yN)} in
an array.
(4) Arrays often simplify VBA code.
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Declaring Arrays
 Just like any other variable, arrays
should be declared before they are
used.
 To declare an array, both the size of
the array and the data type of the
values that the array will hold must
be specified.
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Declaring Arrays
 Here are some examples of array declarations:
‘Declare a “1-dimensional” array named “A” that has 5 elements.
‘Think of A as a matrix with 1 row and 5 columns.
Dim A(1 To 5) As Integer
‘Declare a “1-dimensional” array named “Names” that has 10 elements.
‘Think of Names as a matrix with 1 row and 10 columns.
Dim Names(1 To 10) As String
‘Declare a “2-dimensional” array named “Table” that has 24 elements.
‘Think of Table as a matrix with 12 rows and 2 columns.
Dim Table(1 To 12, 1 To 2) As Double
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Working with Arrays
 Remember that a specific element in an
array is referred to by using the array
name and index number.
 For example,
 A(4) is the fourth element in 1-dimensional
array A, or equivalently, the element from
Row 1, Column 4 of array A.
 Names(1) is the first string in 1-dimensional
array Names, or equivalently, the element
from Row 1, Column 1 of array Names.
 Table(2,3) is the element from Row 2,
Column 3 of 2-dimensional array Table.
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Working with Arrays
 Example 1: Set every element in
the array “A” to the value of 1.
‘Assuming that array “A” has already been declared as
well as other variables.
For K = 1 To 5
A(K) = 1
Next K
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Working with Arrays
 Example 2: Set every element in the
array “Table” to a random number in the
interval (0,1).
‘Assuming that array “Table” has already been
declared as well as other variables
For Col = 1 To 2
For Row = 1 To 12
Table(Row,Col) = Rnd()
Next Row
Next Col
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Working with Arrays
 Example 3: Add up all of the elements in the
array “A” pre-loaded with random numbers.
‘Assuming that array “A” has already been declared as
'well as other variables
‘Also assuming that array A has already been pre-loaded
Total = 0
For K = 1 To 5
Total = Total + A(K)
Next K
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Working with Arrays
 Example 4: Increment every element in
the array “A” by 1.
‘Assuming that array “A” has already been declared as
‘well as other variables
‘Also assuming that array A has already been pre-loaded
For K = 1 To 5
A(K) = A(K) + 1
Next K
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Working with Arrays
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Example 5: Determine the frequency of each letter A-Z contained in the phrase
“In any right-angled triangle, the area of the square whose side is the
hypotenuse is equal to the sum of the areas of the squares whose sides are the
two legs” without using arrays.
‘Assume that variables have been previously declared
‘Set counters A-Z to zero
Count_A = 0
Count_B = 0
Count_C = 0
‘ etc., …
Phrase = “In any right-angled triangle, the area of the square whose side is the hypotenuse is equal to
the sum of the areas of the squares whose sides are the two legs”
Phrase = UCase(Phrase)
For K = 1 To Len(Phrase)
Ch = Mid(Phrase,K,1)
If Ch <> “ “ Then
If Ch = “A” Then Count_A = Count_A + 1
If Ch = “B” Then Count_B = Count_B + 1
If Ch = “C” Then Count_C = Count_C + 1
‘ etc., …
End If
Next K
‘Frequencies for letters A-Z are contained in Count_A, Count_B, … , Count_Z
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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
65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90
A B C D E
F G H
I
J
K
L M N O P Q R
S
T U V W X
Working with Arrays
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Example 6: Determine the frequency of each letter A-Z contained in the phrase
“In any right-angled triangle, the area of the square whose side is the
hypotenuse is equal to the sum of the areas of the squares whose sides are the
two legs” using arrays.
Dim Count(1 to 26) As Integer
‘Assume that all other variables have been previously declared
‘Set counters for A-Z to zero
For K = 1 To 26
Count(K) = 0
Next K
Phrase = “In any right-angled triangle, the area of the square whose side is the hypotenuse is equal to
the sum of the areas of the squares whose sides are the two legs”
Phrase = UCase(Phrase)
For K = 1 To Len(Phrase)
Ch = Mid(Phrase,K,1)
If Ch <> “ “ Then
Index = Asc(Ch) - 64
Count(Index) = Count(Index) + 1
End If
Next K
‘Frequencies for letters A-Z are now contained in Count(1-26)
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Y
Z
User Defined Functions and
Arrays
 Recall that in addition to simplifying
VBA code, other advantages of using
“Arrays” were to
(1) make it possible for user defined
functions to work with cell ranges,
and
(2) make it possible for a User
Defined Function to return multiple
values.
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Cell Ranges as Arguments
 It is possible to pass a range of
worksheet cells into a User Defined
Function as an argument to the
function.
 A range of worksheet cells passed
into a User Defined Function will
behave like an “Array” .
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Cell Ranges as Arguments
 Example 7: A function
that takes entries from a
range of column values
as well as two numbers
as inputs!
Function Sample(Q As Variant, X As
Double, Y As Double) As Variant
‘etc., …
End Function
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To call the function, use
=Sample(A2:A7,12,15.2)
A
1
2
3
4
5
6
7
B
2
9
5
4
-1
5
2
9
 
5
Q 
4
 1
 
5
X  12
Y  15.2
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Cell Ranges as Arguments
 Example 8: A
function that takes
more than one array
as an argument.
Function Sample2(Q As
Variant, R As Variant, Z As
Variant) As Variant
‘etc., …
End Function
 To call this function,
use
A
B
C
D
1
12
14
2
-4
7
E
F
G
12
13
14
H
3
4
5
6
12
7
19
8
-2
12 14
R

 4 7 
 12 
Q   19 
 
 2 
Z  12 13 14
=Sample2(B6:B8,C1:D2,E4:G4)
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Cell Ranges as Arguments
 Example 8: Create
a user defined
function MyDet22()
that will return the
determinant of a 2x2
matrix given a range
of 2x2 cell range.
 For example,
MyDet22(C2:D3)
should return a value
of -2 .
A
B
C
D
2
4
5
3
2
2
E
1
4
Function MyDet22(Mat As Variant)
As Double
‘Returns the “Determinant” of
a 2x2 matrix
‘The 2x2 matrix is passed into
this function as a cell range
MyDet22 = Mat(2,2)*Mat(1,1)Mat(2,1)*Mat(1,2)
End Function
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Array Formulas
 When working with arrays, it is useful to know how to
work with array formulas!
 An array formula is a formula that can perform
multiple calculations on one or more of the items in
an array.
 Array formulas can return either multiple results or a
single result.
 For example, an array formula can be placed in a
range of cells, such as a column or row, and used to
calculate a column or row of subtotals.
 An array formula can also be placed in a single cell
and be used to calculate a single amount.
 An array formula that resides in multiple cells is called
a multi-cell formula, and an array formula that resides
in a single cell is called a single-cell formula.
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Array Formulas
 Example 9: Go to
the help file web
page for Guidelines
and examples of
array formulas.
 Try the examples
 Create a multi-cell
array formula
 Create a single-cell
array formula
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Array Formulas
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2.
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Ex. 9 (cont.): Create a multi-cell
array formula
Open a new, blank workbook.
Copy the example worksheet
data, and then paste it into the
new workbook starting at cell A1.
To multiply the values in the
array (the cell range C2 through
D11), select cells E2 through
E11, and then enter the following
formula in the formula bar:
=C2:C11*D2:D11
Press CTRL+SHIFT+ENTER.
Excel surrounds the formula with
braces ({ }) and places an
instance of the formula in each
cell of the selected range.
What appears in column E is the
total sales amount for each car
type for each salesperson.
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Array Formulas
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1.
2.
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Ex. 9 (cont.): Create a single-cell
array formula
In cell A13 of the workbook, type
Total Sales.
In cell B13, type the following
formula, and then press
CTRL+SHIFT+ENTER
=SUM(C2:C11*D2:D11)
In this case, Excel multiplies the
values in the array (the cell
range C2 through D11) and then
uses the SUM function to add the
totals together.
Note that the single-cell formula
(in cell B13) is completely
independent of the multi-cell
formula (the formula in cells E2
through E11).
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Array Formulas
 For the most part, array formulas use standard
formula syntax.
 All array formulas begin with an equal sign, and
any of the built-in Excel functions can be used in
array formulas.
 The key difference is that when using an array
formula, CTRL+SHIFT+ENTER must be pressed
to enter the array formula.
 When this is done, Excel surrounds the array
formula with braces — if the braces are typed
manually, the formula will be converted to a text
string, and will not work.
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Array Formulas
 When working with multi-cell formulas, one
needs to follow these rules:
 Select the range of cells to hold output results before
entering the formula.
 The contents of an individual cell in an array formula
cannot be changed.
 An entire array formula can be moved or deleted, but
part of an array formula cannot be moved or deleted.
 To “shrink” an array formula, first delete the existing
formula, then start over.
 To delete an array formula, select the entire formula
press DELETE, and then press CTRL+SHIFT+ENTER.
 Blank cells cannot be inserted into or deleted from a
multi-cell array formula.
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Array Outputs for User Defined
Functions
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For multiple values output
as an array for a user
defined function, use the
idea of array formulas!
For example, try the
following function,
Sample():
Function Sample(A As Variant, B As
Variant) As Variant
Dim K As Integer, C(1 To 4, 1 To 2) As
Integer
For K = 1 To 4
C(K, 1) = A(K) + B(K)
C(K, 2) = A(K) + A(K)
Next K
Sample = C
End Function
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References
 Notes on Arrays – John Albers
 Array Formulas (pp. 19-24) – Excel
Help Files (Guidelines and examples
of array formulas)
http://office.microsoft.com/enus/excel-help/guidelines-andexamples-of-array-formulasHA010228458.aspx
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