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(l 1 :u 1, l 2 :u 2, ‧ ‧ ‧ l k :u k ) :: & list-of-array-names l i :u i The specified lower limit l i through the upper limit u i. The number k of dimensions, called the rank ( 秩 ) of array, is at most seven.

Declaration of Allocatable Array type, DIMENSION(:, :, ‧ ‧ ‧ :), & ALLOCATABLE :: list type, 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 Statement ALLOCATE (list) ALLOCATE (list, STAT = status-variable) where list is a list of array specifications of the form array-name (l 1 :u 1, l 2 :u 2, ‧ ‧ ‧ l k :u k ) 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

Input/Output Using DO Loops INTEGER, DIMENSION (3, 4) :: Table DO Row = 1, 3 DO Col =1, 4 READ *, Table (Row, Col) END DO

Input/Output Using DO Loops INTEGER, DIMENSION (3, 4) :: Table DO Col =1, 4 DO Row = 1, 3 READ *, Table (Row, Col) END DO DO Row = 1, 3 DO Col =1, 4 PRINT *, Table (Row, Col) END DO

Input/Output Using the Array Name INTEGER, DIMENSION (3, 4) :: Table READ *, Table 77, 99, 48, 56, 10, 89 32, 100, 77, 25, 46, 33 PRINT ‘ (1X, 4I5/) ’ Table

Input/Output Using Implied DO Loops INTEGER, DIMENSION (3, 4) :: Table READ *, ((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

Examples Figure 9.3, p.628 Temperature Table Rate is a 3 × 4 array

Examples: p. 630 READ *, N, (Number (I), I =1, N), M, & ((Rate (I,J), J = 1, N), I = 1, M) 4 16, 37, 76, , 7.3, 18.4, , 1.0, 1.0, , 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 _________________________ Row _________________________ Row _________________________

Examples: p. 630 PRINT 6, (J, (Rate (I,J), I = 1, 3), & Number (J), J= 1, 4), “ Total ”, Total 6 FORMAT (4(1X, I4, 5X, 3F6.1, I10/), A, T35, I3) Total 152

9.3 Processing Multidimensional Arrays Array Constants INTEGER, DIMENSION (2, 3) :: A A = RESHAPE ((/ 11, 22, 33, 44, 55, 66 /), (/ 2, 3 /)) or A = RESHAPE ((/ (11*N, N =1, 6) /), (/ 2, 3 /) Reshape (v.) 重塑 Shape (n. v.) 形狀

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.

Array Constants A = RESHAPE ((/11, 22, 33, 44 /), (/ 2, 3 /), & PAD = (/0, 0/), ORDER = (/2, 1)) pad (v.) 填充

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)

Array sections and Subarrays A(2, 1:3:1) or A(2, :) A((/ 2, 1 /), 2:3)

Array Assignment INTEGER, DIMENSION (2, 3) :: A INTEGER, DIMENSION (3, 2) :: B A = 0 B = RESHAPE (A, (/3, 2/))

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

Array Assignment: Example REAL, DIMENSION (2, 3) :: Alpha, Beta WHERE (Alpha /= 0.0) Beta = 1.0 / Alpha ELSEWHERE Beta = 0.0 END WHERE

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