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Array Processing

Array processing

Topics

• Terminology

• Specifications

• Whole array operations

• WHERE statement and construct

• Elemental intrinsic procedures

• Array sections

• Element renumbering

• Zero-sized arrays

• Array assignment

• Array constructors

• Allocatable arrays

• Automatic arrays

• Assumed shape arrays

• Array intrinsic procedures

Terminology

• Rank
  
  Number of dimensions

• Extent
  
  Number of elements in a dimension

• Shape
  
  Vector of extents

• Size
  
  Product of extents

• Conformance
  
  Same shape

Example

• a has
  • rank 2

  • extents 8 and 7

  • shape (/ 8, 7 /)

  • size 56

• a is conformable with b & c, but not with d

Specifications

where:

• type - INTRINSIC or derived type

• DIMENSION - Optional, but required to define default dimensions

• (extent-list) - Gives array dimension:
  • Integer constant

  • integer expression using dummy arguments or constants.

  • : if array is allocatable or assumed shape.

• attribute - as given earlier

• entity-list - list of array names optionally with dimensions and initial values.

Example

• Two dimensions:

• Initialisation:

• Automatic arrays:

• These are all explicit shape arrays

• Allocatable arrays (deferred shape):

• Assumed shape arrays:

Whole array operations

• Arrays for whole array operation must be conformable

• Evaluate element by element, i.e., expressions evaluated before assignment

• Scalars broadcast

• Functions may be array valued

Example

• Fortran 77:

• Fortran 90:

• Fortran 77:

• Fortran 90:

Example

• Fortran 77 requires triple DO loop and IF statements

• Fortran 90:

• Fortran 77 requires DO loops and IF
  statements

• Fortran 90:

Elemental intrinsic
procedures

• Elemental procedures specified for scalar arguments
  • May also be applied to conforming array arguments

  • As if applied to each element separately.

• Example

WHERE statement

• Assignment if logical condition is true

• Note mask (rb > 0.0) must conform with LHS ra

WHERE construct

(Block WHERE)

Array sections

• A simple subscript

• A subscript triplet
  • [lower bound]:[upper bound] [:stride]

  • defaults to declared bounds and stride 1

• A vector subscript

Example

Example

Vector subscripts

• 1D integer array used as array subscript

• Example

• Vector subscript can be on LHS of expression

• Must not repeat values of elements on LHS (many to one)

Array assignment

• Operands must be conformable

• Example

Beware of recursion

DO i=2,n
x(i) = x(i) + x(i-1) (1)
END DO

is not the same as:

x(2:n) = x(2:n) + x(1:n-1) (2)

• In (1):

• Fortran 90 equivalent:

Element renumbering

REAL, DIMENSION (1:8) :: ra
REAL, DIMENSION (-3:4) :: rb
INTEGER, DIMENSION (1) :: locmax1, locmax2
REAL :: max1, max2
ra = (/ 1.2, 3.4, 5.4, 11.2, 1.0, 3.7, 1.0, 1.0/)
rb = ra

! To find the location of max value
locmax1 = MAXLOC(ra) ! = (/ 4 /)
locmax2 = MAXLOC(rb) ! = (/ 4 /)

! To find maximum value from the location
max1 = ra(locmax1(1))
! OK, because ra defined with 1 as lower bound

max2 = rb(LBOUND(rb) + locmax2(1) - 1)
! general form required when lower bound xb9 1

Zero-sized arrays

• When lower bound exceeds upper bound, array has size zero

• Valid providing normal rules are followed

• In particular, must be conformable (if one is zero-sized, all must be)

• Useful at boundaries - code does not need to treat boundaries in a special way:

Array constructor

• Construction of rank 1 array:

• (/ 1.2, 3.4, 3.0, 11.2, 1.0, 3.7 /)

• (/ b(i,2:4), b(1:5:2, i+3) /)
  ! = (/ b(i,2),b(i,3),b(i,4),b(1,i+3),b(3,i+3), b(5,i+3) /)

• (/ (1.0 / REAL(i), i = 1, 6) /)
  !=(/1.0/1.0,1.0/2.0,1.0/3.0,1.0/4.0, 1.0/5.0,1.0/6.0/)

• (/ ((i + j, i = 1, 3), j = 1, 2) /)
  ! = (/ 2, 3, 4, 3, 4, 5 /)

• Transfer to rank > 1 array via RESHAPE function:

• Note that the size of SHAPE must be a constant

• Example:

Array arguments 1

Fortran 77 (wrong)

Array arguments 2

Fortran 77 (right)

Dynamic arrays

• Fortran 77
  • static (fixed) memory allocation

• Fortran 90
  • allocate and deallocate storage as required via allocatable arrays

  • allow local arrays in a procedure to have different size and shape every time the procedure is invoked via automatic arrays

  • reduce overall storage requirement

  • simplify subroutine arguments

Allocatable arrays

• A deferred shape array which is declared with the ALLOCATABLE attribute

• Example:

Automatic arrays

• An explicit shape array in a procedure, whose bounds are provided when the procedure is invoked via:
  • dummy arguments

  • variables defined by use or host associations

• Automatic array must not appear in SAVE or NAMELIST statement, nor be initialised in type declaration

• Example - array bounds depend on dummy arguments

Example

Array arguments 3

Fortran 90 dynamic arrays

Assumed shape arrays

• Shape of actual and dummy arguments must agree

• Fortran 77: pass array dimensions as arguments

• Fortran 90: not necessary to pass array dimensions
  • Assumed shape array uses dimension of actual arguments

  • Can specify lower bound

  • Explicit interface required, so must provide an INTERFACE block if using an external procedure

Example

Array arguments 4

Fortran 90: allocatable, automatic, and assumed shape

Array intrinsic functions

• Reduction:
  
  

• Inquiry:
  
  

• Construction:
  
  

• Reshape:
  
  

• Array Location:
  
  

• Array manipulation:
  
  

• Vector and matrix arithmetic:
  
  

Example

85 76 90 60
score(1:3,1:4) = 71 45 50 80
66 45 21 55

• Largest score:

• Largest score for each student:

• Student with largest score:

• Average score:

• Number of scores above average:

• Pack all scores above the average:

• Did any student always score above the average?

• Did all students score above the average on any of the tests?

Array example

Conjugate gradient algorithm