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Arrays

Learn the concept of arrays in scientific and engineering computing, and how to manipulate and operate on ordered sets of values. Understand array declarations, constants, initialization, input/output, and usage within loops.

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Arrays

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  1. Arrays Introduction Week 7

  2. Introduction In scientific and engineering computing, it is very common to need to manipulate ordered sets of values, such as vectors and matrices. There is a common requirement in many applications to repeat the same sequence of operations on successive sets of data. In order to handle both of these requirements, F provides extensive facilities for grouping a set of items of the same type into an array which can be operated on ·either as an object in its own right ·or by reference to each of its individual elements.

  3. 1 2 3 4 5 6 A The array concept

  4. The array concept • A set with n (=6) object, named A • In mathematical terms, we can call A, a vector • And we refer to its elements asA1, A2, A3, …

  5. The array concept • In F, we call such an ordered set of related variables an array • Individual items within an arrayarray elements • A(1), A(2), A(3), …, A(n)

  6. Array Concept In all the programs we have used one name to refer to one location in the computer’s memory. It is possible to refer a complete set of data obtained for example from repeating statements, etc. To do this is to define a group called “array” with locations in the memory so that its all elements are identified by an index or subscript of integer type. An array element is designated by the name of the array along with a parenthesized list of subscript expressions.

  7. The array concept • Subscripts can be: x(10) y(i+4) z(3*i+max(i, j, k)) x(int(y(i)*z(j)+x(k))) x(1)=x(2)+x(4)+1 print*,x(5)

  8. -1 0 1 2 3 1 2 3 4 A The array concept A20 A31

  9. Array declarations type, dimension(subscript bounds) :: list_of_array_names type, dimension(n:m) :: variable_name_list real, dimension(0:4) :: gravity, pressure integer, dimension(1:100) :: scores logical, dimension(-1, 3) :: table

  10. Examples for Shape Arrays real, dimension ( 0 : 49 ) : : z ! the array “z” has 50 elements real, dimension ( 11 : 60 ) : : a, b, c ! a,b,c has 50 elements real, dimension ( -20 : -1 ) : : x ! the array “x” has 20 elements real, dimension ( -9 : 10 ) : : y ! the array “y” has 20 elements

  11. Array declarations • Up to 7 dimensions • Number of permissible subscripts:rank • Number of elements in a particular dimension: extent • Total number of elements of an array:size • Shape of an array is determined by its rank and the extent of each dimension

  12. Array constants and initial values Since an array consists of a number of array elements, it is necessary to provide values for each of these elements by means of an “ array constructor “. In its simplest form, an array constructor consists of a list of values enclosed between special delimiters : ·the first of which consists of the 2 characters : ( / ·the second of the 2 characters : / ) ( /value_1, value_2, ……………………., value_n/)

  13. Examples integer, dimension ( 10 ) : : arr arr = (/ 3, 5, 7, 3, 27, 8, 12, 31, 4, 22 /)  arr ( 1 ) = 3  arr ( 5 ) = 27 ! the value 27 is storen in the 5th location of the array “arr”  arr ( 7 ) = 12 arr ( 10 ) = 22

  14. Array constructors • (/ value_1, value_2, … /) • arr = (/ 123, 234, 567, 987 /) • Regular patterns are common:implied do(/ value_list, implied_do_control /) • arr = (/ (i, i = 1, 10) /) • arr = (/ -1, (0, i = 1, 48), 1 /)

  15. Initialization • You can declare and initialize an array at the same time: integer, dimension(50) :: my_array = (/ (0, i = 1, 50) /)

  16. Input and output • Array elements treated as scalar variables • Array name may appear: whole array • Subarrays can be referred too EXAMPLE : integer, dimension ( 5 ) : : value read *, value read *, value(3)

  17. Examples real, dimension(5) :: p, qinteger, dimension(4) :: rprint *, p, q(3), rread *, p(3), r(1), q print *, p, q (3), q (4), r print *, q (2) ! displays the value in the 2nd location of the array “q” print *, p ! displays all the values storen in the array “p”

  18. Using arrays and array elements... The use of array variables within a loop , therefore,greatly increases the power and flexibility of a program.F enables an array to be treated as a single object in its own right, in much the same way as a scalar object.Assignment of an array constant to an array variable will be performed as is seen below : array_name = (/ list_of_values /) array_name = (/ value_1, value_2, ….., value_n /) An array element can be used anywhere that a scalar variable can be used a(2) = t(5) - t(3)*q(2)a(i) = t(j) - f(k)

  19. Using arrays and array elements... • An array can be treated as a single object • Two arrays are conformable if they have the same shape • A scalar, including a constant, is conformable with any array • All intrinsic operations are defined between two conformable objects

  20. Using arrays and array elements... Arrays having the same number of elements may be applied to arrays and simple expressions.In this case, operation applied toan array are carried out elementwise. . real, dimension(20) :: a, b, c . . a = b*c do i = 1, 20 a(i) = b(i)*c(i) end do

  21. Example integer, dimension ( 4 ) : : a, b integer, dimension ( 0 : 3 ) : : c integer, dimension ( 6 : 9 ) : : d a = (/ 1, 2, 3, 4 /) b = (/ 5, 6, 7, 8 /) c = (/ -1, 3, -5, 7 /) c(0) c(1) c(2) c(3) a = a + b! will result a = (/ 6, 8, 10, 12 /) d = 2 * abs ( c ) + 1! will result d = (/ 3, 7, 11, 15 /) d(6) d(7) d(8) d(9)

  22. Intrinsic procedures with arrays • Elemental intrinsic procedures with arrays array_1 = sin(array_2) arr_max = max(100.0, a, b, c, d, e) • Some special intrinsic functions: maxval(arr) maxloc(arr) minval(arr) minloc(arr) size(arr) sum(arr)

  23. Sub-arrays • Array sections can be extracted from a parent array in a rectangular grid usinf subscript triplet notation or using vectorsubscript notation • Subscript triplet:subscript_1 : subscript_2 : stride Similar to the do – loops, a subscript triplet defines an ordered set of subscripts beginning with subscript_1, ending with subscript_2 and considering a seperation of stride between the consecutive subscripts.The value of stride must not be “zero”.

  24. Sub-arrays • Subscript triplet:subscript_1 : subscript_2 : stride • Simpler forms: subscript_1 : subscript_2 subscript_1 : subscript_1 : : stride : subscript_2 : subscript_2 : stride : : stride :

  25. Example real, dimension ( 10 ) : : arr arr ( 1 : 10 ) ! rank-one array containing all the elements of arr. arr ( : ) ! rank-one array containing all the elements of arr. arr ( 3 : 5 ) ! rank-one array containing the elements arr (3), arr(4), arr(5). arr ( : 9 ) ! rank-one array containing the elements arr (1), arr(2),…., arr(9). arr ( : : 4 ) ! rank-one array containing the elements arr (1), arr(5),arr(9).

  26. Example integer, dimension ( 10 ) : : a integer, dimension ( 5 ) : : b, i integer: : j a = (/ 11, 22, 33, 44, 55, 66, 77, 88, 99, 110 /) i = (/ 6, 5, 3, 9, 1 /) b = a ( i )! will result b = ( 66, 55, 33, 99, 11 /) a ( 2 : 10 : 2 )! will result a = ( 22, 44, 66, 88, 110 /) a ( 1 : 10 : 2 ) = (/ j ** 2, ( j = 1, 5 ) /) ! will result a = ( 1, 4, 9, 16, 25 /) a(1) a(3) a(5) a(7) a(9)

  27. Type of printing sub-arrays work = ( / 3, 7, 2 /) print *, work (1), work (2), work (3) ! or print *, work ( 1 : 3 ) ! or print *, work ( : : 1 ) ! or integer : : i do i = 1, 3, 1 print *, work (i) end do ! or another example print *,sum ( work (1: 3) ) ! or another example print *,sum ( work (1: 3 : 2) )

  28. Type of INPUT of sub-arrays integer, dimension ( 10 ) : : a integer, dimension ( 3 ) : : b . b = a ( 4 : 6 ) ! b (1 ) = a (4) ! b (2 ) = a (5) ! b (3 ) = a (6)   . a ( 1 : 3 ) = 0 ! a(1) = a(2) = a(3) = 0 a ( 1 : : 2 ) = 1 ! a(1) = a(3) =…….= a(9) = 1 a ( 1 : : 2 ) = a ( 2 : : 2 ) + 1 ! a(1) = a(2) +1 ! a(3) = a(4) +1 ! a(5) = a(6) +1 ! etc.

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