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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
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