Chapter 6

Introduction to arrays

What is an Array?• Group of variables or constants, all of the same type, referred to by a single

name.

• Array values occupy consecutive memory locations in the computer.

• Single value in an array called array element and referred to by the array name and a subscript (of type integer) that is pointing to its location in the group.

• Arrays allow a powerful computation that apply the same algorithm to many different items with a simple DO loop.

• Example:Find square root of 100 different real numbers.

DO i= 1, 100a(i) = SQRT(a(i))

END DO

Rather than

a1 = SQRT(a1)

a2= SQRT(a2)

…

a100 = SQRT(a100)

a ( 3 )

a ( 1 )

a ( 2 )

a ( 4 )

a ( 5 )

Computer Memory

Array a

Arrays

• Arrays can be multi-dimensions.• Number of subscripts called rank.• Extent of array in one dimension is the number of values in that

given dimension of the array.• Shape of the array is the combination of its rank and the extent in

each dimension.• Size of array is the total number of elements in all dimensions.

Rank:

Extent:

Shape: Rank, extent

Size:

1 , 1 1 , 41 , 31 , 2

2 , 1 2 , 42 , 32 , 2

3 , 1 3 , 43 , 33 , 2

4 , 1 4 , 44 , 34 , 2

5 , 1 5 , 45 , 35 , 2

Two dimension array

Vector(i , j)

Dimension - 2

Dim

ensi

on -

1

Arrays1

2

3

4

12

13

14

15

One dimension array

Vector(i)

Rank:

Extent:

Shape: Rank, extent

Size:

1

15

15

2

5 , 4

20

Dim

ensi

on -

1

1, 1 , 3 1, 4, 31, 3, 31, 2, 3

2, 1, 1 2, 4, 32, 3, 1 2, 2, 1

3, 1 , 1 3, 4, 33, 3, 13, 2, 1

4, 1, 1 4, 4, 34, 3, 14 , 2, 1

5, 1, 1 5, 4, 35, 3, 15, 2, 1

1, 1 , 2 1, 4, 21, 3, 21, 2, 2

2, 1, 1 2, 4, 22, 3, 1 2, 2, 1

3, 1 , 1 3, 4, 23, 3, 13, 2, 1

4, 1, 1 4, 4, 24, 3, 14 , 2, 1

5, 1, 1 5, 4, 25, 3, 15, 2, 1

1, 1 , 1 1, 4, 11, 3, 11, 2, 1

2, 1, 1 2, 4, 12, 3, 1 2, 2, 1

3, 1 , 1 3, 4, 13, 3, 13, 2, 1

4, 1, 1 4, 4, 14, 3, 14 , 2, 1

5, 1, 1 5, 4, 15, 3, 15, 2, 1

Dim

ensi

on -

1

Dimension - 2

Dimen

sion -

3

Three dimension array

Vector(i, j, k)

Rank:

Extent:

Shape: Rank, extent

Size:

3

5, 4, 3

60

Declaring Arrays

• Define type and size

REAL, DIMENSION(16) :: voltageINTEGER, DIMENSION(5, 6):: matrix, valuesCHARACTER(len=20), DIMENSION(50) :: last_name

Find rank, extent, shape and size of above arrays.

• Array constant(/ 3, 4, 5, 1, 3/)

Array example

• Declares an array that stores the student ID of all students in the class. (43 students)

• Make a WRITE statement that makes the program display the first student in the class.

• Make a WRITE statement that makes the program display the student number 25 in the list.

INTEGER, DIMENSION(43) :: studentID

WRITE(*,*) ‘ ID of first student: ’, studentID(1)

WRITE(*,*) ‘ ID of 25th student: ’, studentID(25)

Array example• Make two arrays that represent a building that consists of 7 floors. Each

floor has 15 rooms. • First array values indicates if the room is occupied or not. (True or False)• The second array indicates how many persons in the room in case it is

occupied. (Integer)

• Please, write to the customer if room number 9 in the 6th floor is occupied or not.

• Please, write how many persons in room 2 in the 7th floor.

LOGICAL, DIMENSION (7,15) :: occupied

INTEGER, DIMENSION (7,15) :: persons

WRITE(*,*) ‘Is room 9 in floor 6 occupied ? ’, occupid(6,9)

WRITE(*,*) ‘persons in room 2 at floor 7 are: ’, persons(7,2)

Using array elements in FORTRAN

• Each element in the array is treated as any regular FORTRAN variable.

• FORTRAN statements can access its values, assign values and make operations on them.

• Back to student ID example:

INTEGER, DIMENSION(43) :: studentID

studentID(5)=999999

IF (studentID(5)==999999) studentID(4)=888888

studentID(6) = MAX(studentID(4), studentID(5))

WRITE(*,*) ‘ ID of sixth student: ’, studentID(6)

Initialization of array elements

• Un-initialized arrayINTEGER, DIMENSION(10) :: j

WRITE (*,*) ‘ j(1) = ’, j(1)

• Initialization with assignment statementREAL, DIMENSION(10) :: array1

DO I = 1, 10

array1(i) = REAL(i)

END DO

• Initialization with assignment using array constructorREAL, DIMENSION(10) :: array1

array1 = (/1., 2., 3., 4., 5., 6., 7., 8., 9., 10./)

• Possible to assign one value to all array elements.REAL, DIMENSION(10) :: array1

array1 = 0.

Example-1PROGRAM squaresIMPLICIT NONE

INTEGER :: iINTEGER, DIMENSION(10) :: number, square

DO i=1, 10number(i)=isquare(i)=number(i)**2END DO

DO i=1, 10WRITE(*,*) number(i), ' ', square(i)END DO

END PROGRAM

Initialization of array elements

• Named constants in array declarationINTEGER, PARAMETER :: max_size=1000

INTEGER, DIMENSION(max_size) :: array1

REAL, DIMENSION(2*max_size) :: array2

Do i = 1, max_size

array2(i) = array1(i) * 2.0 / 3.0

END DO

• Initializing with READ statementINTEGER, DIMENSION(5) :: array1

Do i=1,5

READ(*,*) array1(i)

END DO

• Initializing arrays in declaration (OK for small arrays)INTEGER, DIMENSION(5) :: array1 =(/1,2,3,4,5/)

Number of values must be equal to the array size

• Declaring arrays using implied loopsINTEGER, DIMENSION(100) :: array1 = ( / ( i , i=1,100) / )

General form of implied loop (arg1, arg2, …, index = istart, iend, incr)

Initialization of array elements

Example-2PROGRAM square_rootsIMPLICIT NONE

INTEGER :: iINTEGER, DIMENSION(10) :: value = (/ (i, i = 1, 10) /)INTEGER, DIMENSION(10) :: s_root

DO i=1, 10s_root(i) = SQRT(value(i))END DO

DO i=1, 10WRITE(*,*) values(i), ' ', s_root(i)END DO

END PROGRAM

More Implied loops

• INTEGER, DIMENSION(25) :: array = (\ ((0, i=1, 4), 5*j, j=1,5) \)

(arg1, arg2, …, index = istart, iend, incr)

• array = 0, 0, 0, 0, 5, 0, 0, 0, 0, 10, 0, 0, 0, 0, 15, 0, 0, 0, 0, 20, 0, 0, 0, 0, 25

• INTEGER, DIMENSION(25) :: array = (\ ((j, 2*j, 3*j, j=1,3) \)

• array = 1, 2, 3, 2, 4, 6, 3, 6, 9

Whole array operations

• REAL, DIMENSION(4):: a = (/ 1, 2, 3, 4 /)• REAL, DIMENSION(4):: b = (/ 2, 2, 1, 0 /)• REAL, DIMENSION(4):: c

• DO i = 1, 4• c(i) = a(i) + b(i)• END DO

• DO i = 1, 4• WRITE(*,*) c(i)• END DO

c = a + b

WRITE(*,*) ‘ c = ’, c

Output :c = 3.0 4.0 4.0 4.0

2210

1234

3444

+ =

a b c

Out of bound subscripts

• REAL, DIMENSION(5) :: array

• array should have 5 values numbered 1 to 5• Any other subscript out of these bounds (1, 5)

will result in an out of bounds error either detected by compiler (if compiler bounds check is turned on) or at run time.

Example-3

PROGRAM summationIMPLICIT NONEINTEGER :: iREAL, DIMENSION(6) :: x=(/ 1., 2., 3., 4., 5., 6./)REAL, DIMENSION(6) :: a=(/ .1, .1, .1, .2, .2, .2/)REAL :: total=0

DO i=1, 6total = total + (2*x(i)+a(i))END DO

WRITE (*,*) 'Total = ', total

END PROGRAM_____________________________________________

What does this program do?

Changing the Subscript Range of an Array

• REAL, DIMENSION(5):: arrElements arr(1), arr(2), arr(3), arr(4), arr(5)

Change range

• REAL, DIMESION(-2:2)Elements arr(-2), arr(-1), arr(0), arr(1), arr(2)

• What is he sixze of the following array?REAL, DIMENSION(-1:19)

Size = upper – lower +1 = 19 - -1 +1 = 21

Out of boundsINTEGER, DIMESION(5):: arrDo i=1,5WRITE(*,*) arr(i)END DO

INTEGER, DIMESION(-2:2):: arrDo i=1,5WRITE(*,*) arr(i)END DO

INTEGER, DIMESION(-2:2):: arrDo i=-2,2WRITE(*,*) arr(i)END DO

Array subset

arr(subscript1 : subscript2: increment)

INTEGER, DIMENSION(10):: a=(/1., -2., 3., -4., 5., -6., 7., -8., 9., -10./)

• Find the following subsets:– arr(:)– arr(3:7)– arr(3:7:2)– arr(3:7:7)– arr(:6)– arr(5:)– arr(::2)

Example

INTEGER, DIMENSION(3):: x=(/2, 5, 8/)

INTEGER, DIMENSION(5):: y=(/1, 3, 2, 4, 7/)

INTEGER, DIMENSION(2):: z

z = x(1:2) + y(3:4)

WRITE(*,*) z

z = 4, 9

Vector Subscript

• The subset in previous slides used subscript triplets array(a:b:c)

• Vector subscript is using a vector or array as index values of another array.

INTEGER, DIMENSION(5):: vec=(/1,6,4,1,9/)REAL, DIMENSION(10):: a=(/1, -2, 3, -4, 5, -6, 7, -8, 9, -10/)WRITE(*,*) a(vec)Output: a(1), a(6), a(4), a(1), a(9)

1, -6, -4, 1, 9

Subset Assignment

INTEGER, DIMENSION(5):: vec=(/1,6,4,1,9/)

REAL, DIMENSION(10):: a=(/1, -2, 3, -4, 5, -6, 7, -8, 9, -10/)

REAL, DIMENSION(10):: b=(/1, -2, 3, -4, 5, -6, 7, -8, 9, -10/)

a(2:8:2)=(/1, -1, 1, -1/)

b(vec)=(/1,-1,1, -1, 1/)

WRITE(*,*) ‘a = ’, a

WRITE (*,*) ‘b = ’, b

Output :

a = 1, 1, 3, -1, 5, 1, 7, -1, 9, -10

b = -1, -2, 3, 1, 5, -1, 7, -8, 1, -10

Simple Output FormatINTEGER :: a=10REAL :: b=5.1

WRITE(*,*) a, bOutput: 10 5.10000000

WRITE(*,100) a, b100 FORMAT(I2, F10.8)Output: 105.10000000

WRITE(*,100) a, b100 FORMAT(I2, 1X, F10.8)Output: 10 5.10000000

WRITE(*,100) a, b100 FORMAT(I2, 3X, F3.1)Output: 10 5.1

WRITE(*,100) a, b100 FORMAT(' a= ',I2, 3X, 'b= ', F3.1)Output: a= 10 b= 5.1

Input/output of array elementsREAL, DIMENSION(5) :: a= (/0.5,-1,0.1,2., 10.4/)

WRITE(*,*) (a(i), i=1, 5)Output: 0.500000000 -1.00000000 0.100000001 2.00000000 10.40000000

Do i=1,5WRITE(*,*) a(i)END DOOutput: 0.500000000 -1.00000000 0.100000000 2.00000000 10.40000000

WRITE(*,100) a(1), a(2), a(3), a(4), a(5)100 FORMAT (1X, 'a =', 5F7.2)Output: a = 0.50 -1.00 0.10 2.00 10.40

WRITE(*,100) (a(i), i=1, 5)100 FORMAT (F10.2)Output: 0.50 -1.00 0.10 2.00 10.40

WRITE(*,100) (a(i), i=1, 5)100 FORMAT (5F10.2)Output: 0.50 -1.00 0.10 2.00 10.40

Input/Output with implied loopsWRITE(unit, format)(arg1, ar2,.., index=istart, iend, incr)READ(unit, format)(arg1, ar2,.., index=istart, iend, incr)

WRITE(*, *) (i, 2*I, 3*I, i=1,3)Output: 1 2 3 2 4 6 3 6 9

WRITE(*,100) (a(i), i=1, 5)100 (1X, ‘a= ’, 5F7.2)

WRITE(*,200) ((i,j, j=1,3), i=1, 2)200 FORMAT(1X, I5, 1X, I5)Output: 1 1 1 2 1 3 2 1 2 2 2 3

Two-Dimensional Array

• Rank-2 array require 2 subscripts as an address to retrieve one value.

array(a,b)a is the index in the first dimension

b is the index in the second dimension

• Declaring 2-D arrayREAL, DIMENSION(3,6) :: arr1

REAL, DIMENSION(-1:9, 0:19) :: arr2

INTEGER, DIMENSION(10, 0:19) :: arr3

Initializing 2-D arrays

• Using DO loopsINTEGER, DIMENSION(4,3):: arrDO i=1, 4

DO j=1, 3arr(i, j)= j

END DOEND DO

• Using Constructorarr=(/ 1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3 /)Memory arrangement in computer(/ arr(1,1), arr(2,1), arr(3,1), arr(4,1), arr(1,2), arr(2,2), arr(3,2), arr(4,2), arr(1,3), …, arr(4,3) /)

Is array shape correct?? NO that is 1-D arrayarr=RESHAPE( (/ 1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3 /), (/4, 3/))

1 2 3

1 2 3

1 2 3

1 2 3

• Initializing in DeclarationINTEGER, DIMENSION(4,3):: arr=RESHAPE ( (/ 1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3 /), (/4,3/))

• Initializing using READREAD(*,*) arr

READ(*,*) ((arr(i,j), j=1,3), i=1,4)

Initializing 2-D arrays

2-D array subsets

arr(:, 1)arr(1, :)arr(1:3, 1:4:2)arr(1:4:2, :)list = (/ 1, 2, 4/)arr(:, list)

• How to access the third column?• How to access the fourth row?• How to access the second and fourth columns together?

1 2 3 4

5 6 7 8

1 1 2 2

3 3 4 4

arr(:,3)

arr(4,:)

arr(:,2:4:2)

2-D array outputWRITE (*,*) arr1 1 1 1 2 2 2 2 3 3 3 3

DO j=1, 3 DO i=1, 4 WRITE (*,*) arr(i, j) END DOEND DO

DO i=1, 4 DO j=1, 3 WRITE (*,*) arr(i, j) END DOEND DO

WRITE (*,*) ((arr(i,j), i=1,4), j=1,3)1 1 1 1 2 2 2 2 3 3 3 3

DO i=1, 4 WRITE (*,*) (arr(i, j), j=1,3)END DO

1 2 3

1 2 3

1 2 3

1 2 3

1

1

1

1

2

2

2

2

3

3

3

3

1

2

3

1

2

3

1

2

3

1

2

3

1 2 3

1 2 3

1 2 3

1 2 3

2-D array example-1

1. Write a program that initializes a 3X4 matrix as shown below. The program should make search for minimum and maximum values in the 2-D array.

2. Repeat the above program but let the user now enter the values of the matrix via the keyboard.

1.5 2. -3.1 4.0

5. 9.6 7.7 -8.

1.1 0.1 2.1 -2.

2-D array example-2

1. Write a program that initializes a 3X4 matrix as shown below. The program should count how many positive numbers, negative numbers and zeros in the matrix.

2. Repeat the above program but let the user now enter the values of the matrix via the keyboard.

1.5 2. -3.1 4.0

5. 9.6 7.7 -8.

1.1 0.1 2.1 -2.

Matrix Operations• Write a program that accepts two matrices from the user and store

them in two 2-D arrays. Then, the program prompt the user to select the operation he is seeking by entering 1 for matrix addition, 2 for matrix subtraction, and 3 for matrix multiplication. Addition and subtraction are done element by element for two matrices that are having the same size. The multiplication is done for two matrixes where the number of columns in the first matrix is equal to the number of rows in the second one.

C = A + B (MXN) = (MXN) + (MXN)

C = A - B (MXN) = (MXN) - (MXN)

C = A X B (MXN) = (MXL) + (LXN)

Multiplication can be done as follows

l

jjkijik baC

1

*