Operations and Functions that manipulate arrays

Prelude: Conformable arrays
- Conformable Arrays
- Many functions and operations that manipulate arrays in Fortran operates only on conformable arrays

Operations on array operands

The operands:

+ - * / **

can be applied to conformable arrays

Effect:

A op B <=> perform the operation op on each pair of values in A and B op = +, -, *, /, **

Examples:

REAL, DIMENSION(3,3) :: A1 REAL, DIMENSION(3,3) :: A2 REAL, DIMENSION(3,3) :: B B = A2 + A1

is the same as:

REAL, DIMENSION(3,3) :: A1 REAL, DIMENSION(3,3) :: A2 REAL, DIMENSION(3,3) :: B integer i, j; DO i = 1, 3 DO j = 1, 3 B(i,j) = A2(i,j) + A1(i,j) END DO END DO

Example Program: (Demo above code)

Prog file: click here

NOTE:

The array multiplication operation:
is NOT the same as the matrix * matrix multiplication operation that we have defined in C++
The array multiplication * is not a row-column inner product operation, but multiplies the corresponding elements

Example:

+- -+ +- -+ +- -+ | 1 2 | | -1 2 | | 1*-1 2*2 | | | * | | = | | | 3 4 | | -3 4 | | 3*-3 4*4 | +- -+ +- -+ +- -+

Example Program: (Demo above code)
- Prog file: click here

Function applied to arrays

When an intrinsic function is applied on an array variable , then the function is applied to every element in the array

Example:

REAL, DIMENSION(2,2) :: A REAL, DIMENSION(2,2) :: B B = SQRT(A) !! Square root
Same effect as: DO i = 1, 2 DO j = 1, 2 B(i,j) = SQRT(A(i,j)) END DO END DO

Example Program: (Demo above code)
- Prog file: click here

Array and scalar "inter"-operation

Arrays and scalars (numbers) can also be mixed in operations :

When array variables and scalars are used in an arithmetic expression , the scalar is first converted into an array of the same shape

and then the corresponding array operation is applied.

Example:

REAL, DIMENSION(3,3) :: A REAL, DIMENSION(3,3) :: B B = A + 10 or: B = 10 + A
Effect: DO i = 1, 3 DO j = 1, 3 B(i,j) = A(i,j) + 10 END DO END DO

Example Program: (Demo above code)
- Prog file: click here

Masked array assignments

A masked array assignment is used to selectively update elements in an array.

Syntax of a masked array assigment:

WHERE (array-logical-expression) array = array-expression ... [ ELSEWHERE array = array-expression ... ] END WHERE

Meaning:

The array logical expression is evaluated for each pair of values in the corresponding arrays
The array logical expression is called a "mask"
It controls the selection of array elements that will be altered.
If the array logical expression for some pair is true, the then part is executed.
Otherwise, if the ELSEWHERE part is specified, the else part is executed.

Example:

+- -+ | 1 2 | A = | | | 3 4 | +- -+ +- -+ | 4 1 | B = | | | 7 1 | +- -+ WHERE (A > B) A = 1 B = 0 ELSEWHERE B = 1 A = 0 END WHERE
Result: +- -+ | 0 1 | A = | | | 0 1 | +- -+ +- -+ | 1 0 | B = | | | 1 0 | +- -+

Example Program: (Demo above code)
- Prog file: click here

Matrix and Vector operations in Fortran

Fortran 90 does provide some commonly used matrix and vector operations, but in the form of intrinsic function

Matrix/vector related intrinsic function in F90:

SUM(v): sum al elements in v (vector or matrix) DOT_PRODUCT(v1, v2): compute the vector dot-product of v1 and v2 MATMUL(A1, A2): (real) matrix multiplication

Summing an array

Example:

REAL, DIMENSION(2,2) :: A REAL, DIMENSION(3) :: v REAL :: x x = SUM(v) x = SUM(A)
Result: x = v(1) + v(2) + v(3) x = A(1,1) + A(1,2) + A(2,1) + A(2,2)

Example Program: (Demo above code)
- Prog file: click here

Vector dot-product

Example:

REAL, DIMENSION(3) :: v1, v2 REAL :: x x = DOT_PRODUCT(v1, v2)
Result: x = v1(1)*v2(1) + v1(2)*v2(2) + v1(3)*v2(3)

Example Program: (Demo above code)
- Prog file: click here

Matrix multiplication

Example:

REAL A(2,3) REAL B(3,2) REAL C(2,2) ! Output matrices REAL D(3,3) C = MATMUL(A, B) D = MATMUL(B, A)

Example Program: (Demo above code)
- Prog file: click here