CHAPTER 9 MUTIDIMENSIONAL ARRAYS

Introduction to multidimensional Arrays and Multiply subscripted variables

Compile-Time Arrays & Run-Time Arrays

Compile-Time Arrays: The size is fixed before execution begins.Run-Time (or Allocatable 可分配的 ) Arrays: The memory is allocated ( 分配 ) during execution, making it possible to allocate an array of appropriate size.

Compile-Time Arrays

REAL, DIMENSION(4, 3)::Temperature REAL, DIMENSION(1:4, 1:3):: Temperature Temperature (2, 3 ) 64.5 Temperature (I, J)

REAL, DIMENSION(4, 3, 7):: TemperatureArray REAL, DIMENSION(1:4, 1:3, 1:7)::TemperatureArray TemperatureArray (1, 3, 2) → 64.3 TemperatureArray (Time, Location, Day)

→

Compile-Time Arrays

REAL, DIMENSION(1:2, -1:3)::Gamma Gamma(1, -1), Gamma(1,0),

Gamma(1,1), Gamma(1, 2), Gamma(1,3), Gamma(2, -1), Gamma(2,0), Gamma(2,1), Gamma(2, 2), Gamma(2,3)

REAL, DIMENSION (0:2, 0:3, 1:2) :: Beta INTEGER, DIMENSION(5:12) :: Kappa

Declaration of Compile-Time Array

type, DIMENSION(l1:u1, l2:u2 , ‧ ‧ ‧ lk:uk) :: & list-of-array-names

li:ui

The specified lower limit li through the upper limit ui.

The number k of dimensions, called the rank ( 秩 ) of array, is at most seven.

Declaration of Allocatable Array

type, DIMENSION(:, : , ‧ ‧ ‧ :), &

ALLOCATABLE :: listtype, DIMENSION(:, : , ‧ ‧ ‧ :) :: list

ALLOCATABLE :: list

The rank k of the array (the number of dimensions) is at most seven.

Allocatable Array ( 可分配的 ) / Run-Time Arrays

REAL, DIMENSION(:, :, :), ALLOCATABLE :: &

Beta

REAL, DIMENSION(:, :), ALLOCATABLE :: & Gamma

ALLOCATE StatementALLOCA TE (list)ALLOCATE (list, STAT = status-variable)

where list is a list of array specifications of the form array-name (l1:u1, l2:u2 , ‧ ‧ ‧ lk:uk)

ALLOCATE (Beta(0:2, 0:3, 1:2), Gamma & (1:N, -1:3), STAT = AllocateSatus)

DEALLOCATE(***)

Input/Output of Multidimensional Arrays

Element-wise Processing row ( 列 ) × column ( 行 )

Two natural orders for processing the elements of a two-dimensional array: row-wise and column-wise.In most cases, a programmer can select one of these orderings by controlling the way the subscripts ( 下標 ) vary. If this is not done, the Fortran convention is that two-dimensional arrays will be processed column-wise.

(a) Row-wise Processing (b) Column-wise Processing

Processing a Three-Dimensional Array

(2×4×3)

Input/Output of Array Elements

Using a DO loop Using the array name Using an implied DO loop Using an array section

INTEGER, DIMENSION (3, 4) :: Table

33

46

25

77

100

32

89

10

56

48

99

77

Input/Output Using DO Loops

INTEGER, DIMENSION (3, 4) :: TableDO Row = 1, 3

DO Col =1, 4READ *, Table (Row, Col)

END DO END DO

Input/Output Using DO LoopsINTEGER, DIMENSION (3, 4) :: Table

DO Col =1, 4DO Row = 1, 3

READ *, Table (Row, Col)END DO

END DO

DO Row = 1, 3DO Col =1, 4

PRINT *, Table (Row, Col)END DO

END DO

Input/Output Using the Array Name

INTEGER, DIMENSION (3, 4) :: Table READ *, Table

77, 99, 48, 56, 10, 8932, 100, 77, 25, 46, 33

PRINT ‘(1X, 4I5/)’ Table

33

46

25

77

100

32

89

10

56

48

99

77

Input/Output Using Implied DO Loops

INTEGER, DIMENSION (3, 4) :: TableREAD *, ((Table (Row, Col), Col =1, 4 ), & Row = 1, 3)

READ *, (Table (Row,1), Table (Row,2), & Table (Row,3), Table (Row,4), & Row = 1, 3)

Input/Output Using Implied DO Loops

READ *, ((Table (Row, Col), Row = 1, 3) ), &

Col =1, 4)

READ *, (((B(I, J, K), I = 1, 2), J =1, 4), & K = 1, 3)

Input/Output Using Implied DO Loops

DO Row = 1, 3 PRINT ‘(1X, 4I5)’ , (Table (Row, Col), Col

=1, 4)END DO

33

46

25

77

100

32

89

10

56

48

99

77

Examples Figure 9.3, p.628

Temperature TableRate is a 3 × 4 array

0.0

5.3

5.6

0.0

0.1

4.18

9.16

0.1

3.7

2.18

0.0

1.16

Examples: p. 630READ *, N, (Number (I), I =1, N), M, &

((Rate (I,J), J = 1, N), I = 1, M)

4 16, 37, 76, 23 3 16.1, 7.3, 18.4, 6.5 0.0, 1.0, 1.0, 3.5 18.2, 16.9, 0.0, 0.0

Examples: p. 630

PRINT 5, (“Row”, I, (Rate (I,J), J= 1, 4), I = 1, 3)

5 FORMAT (1X, A, I2, “--”, 4F6.1/)

Row 1-- 16.1 7.3 18.4 6.5_________________________Row 2-- 0.0 1.0 1.0 3.5_________________________Row 3-- 18.2 16.9 0.0 0.0_________________________

Examples: p. 630PRINT 6, (J, (Rate (I,J), I = 1, 3), & Number (J), J= 1, 4), “Total”, Total6 FORMAT (4(1X, I4, 5X, 3F6.1, I10/), A, T35,

I3)

1 16.1 0.0 18.2 16 2 7.3 1.0 16.9 37 3 18.4 1.0 0.0 76 4 6.5 3.5 0.0 23Total 152

9.3 Processing Multidimensional Arrays

Array ConstantsINTEGER, DIMENSION (2, 3) :: AA = RESHAPE ((/ 11, 22, 33, 44, 55, 66 /), (/ 2, 3 /))orA = RESHAPE ((/ (11*N, N =1, 6) /), (/ 2, 3 /) Reshape (v.) 重塑 Shape (n. v.) 形狀

66

55

44

33

22

11

Array Constants

A = RESHAPE ((/11, 22, 33, 44, 55, 66 /), & (/ 2, 3 /), ORDER = (/2, 1/))

The order (/2, 1/) specifies that the second subscript ( 下標 ) is to be varied before the first, which causes the array to be filled row-wise.

66

33

55

22

44

11

Array Constants

A = RESHAPE ((/11, 22, 33, 44 /), (/ 2, 3 /), & PAD = (/0, 0/), ORDER = (/2, 1))

pad (v.) 填充

0

33

0

22

44

11

Array Constants

The intrinsic function SHAPE can be used to determine the shape of an array, which consists of number of dimensions for array and the extent (the number of subscripts 下標之大小程度 ) in each dimension.For example, SHAPE (A) will return (2, 3).

Shape 形狀 (n.); 塑造 (v.)

Array Expressions (p. 636) &Array sections and Subarrays

INTEGER, DIMENSION (2, 3) :: A

A(1:2:1, 2:3:1) or A(:, 2:3)

66

33

55

22

66

33

55

22

44

11A

Array sections and Subarrays

A(2, 1:3:1) or A(2, :)

A((/ 2, 1 /), 2:3)

665544

33

66

22

55

66

33

55

22

44

11A

Array Assignment

INTEGER, DIMENSION (2, 3) :: AINTEGER, DIMENSION (3, 2) :: B

A = 0B = RESHAPE (A, (/3, 2/))

0

0

0

0

0

0A

0

0

0

0

0

0

B

Array Assignment

A(:, 2:3) = RESHAPE ((/ (I**2, I = 1, 4) /), & (/2, 3/))

16

9

4

1

0

0A

Array Assignment: Example

REAL, DIMENSION (2, 3) :: Alpha, BetaWHERE (Alpha /= 0.0)

Beta = 1.0 / AlphaELSEWHERE

Beta = 0.0

END WHERE

0.5

0.0

0.10

0.2

0.0

0.1Alpha

2.0

0.0

1.0

5.0

0.0

0.1Beta

Intrinsic Array-Processing Subprograms

Matrix Processing (Sec. 9.6) &Intrinsic Array-Processing Subprograms

MATMUL (A, B) --- The product AB

TRANSPOSE (A)

Application: Pollution Tables

In a certain city, the air pollution is measured at a two-hour intervals, beginning at midnight. These measurements are recorded for a one-week period and stored in a file, the first line of which contains the pollution level for day 1, the second line for day 2, and so on.A program must be written to produce a weekly report that displays the pollution levels in a table of the form:

Monitoring Air Pollution