# Fortran Arrays Array operations

## Example

Due to its computational goals, mathematical operations on arrays are straight forward in Fortran.

Operations on arrays of the same shape and size are very similar to matrix algebra. Instead of running through all the indices with loops, one can write addition (and subtraction):

``````real, dimension(2,3) :: A, B, C
real, dimension(5,6,3) :: D
A    = 3.    ! Assigning single value to the whole array
B    = 5.    ! Equivalent writing for assignment
C    = A + B ! All elements of C now have value 8.
D    = A + B ! Compiler will raise an error. The shapes and dimensions are not the same
``````

Arrays from slicing are also valid:

``````integer :: i, j
real, dimension(3,2) :: Mat = 0.
real, dimension(3)   :: Vec1 = 0., Vec2 = 0., Vec3 = 0.
i = 0
j = 0
do i = 1,3
do j = 1,2
Mat(i,j) = i+j
enddo
enddo
Vec1 = Mat(:,1)
Vec2 = Mat(:,2)
Vec3 = Mat(1:2,1) + Mat(2:3,2)
``````

## Function

In the same way, most intrinsic functions can be used implicitly assuming component-wise operation (though this is not systematic):

``````real, dimension(2) :: A, B
A(1) = 6
A(2) = 44 ! Random values
B    = sin(A) ! Identical to B(1) = sin(6), B(2) = sin(44).
``````

## Multiplication and division

Care must be taken with product and division: intrinsic operations using `*` and `/` symbols are element-wise:

``````real, dimension(2) :: A, B, C
A(1) = 2
A(2) = 4
B(1) = 1
B(2) = 3
C = A*B ! Returns C(1) = 2*1 and C(2) = 4*3
``````

This must not be mistaken with matrix operations (see below).

## Matrix operations

Matrix operations are intrinsic procedures. For example, the matrix product of the arrays of the previous section is written as follows:

``````real, dimension(2,1) :: A, B
real, dimension(1,1) :: C
A(1) = 2
A(2) = 4
B(1) = 1
B(2) = 3
C = matmul(transpose(A),B) ! Returns the scalar product of vectors A and B
``````

Complex operations allow encapsulated of functions by creating temporary arrays. While allowed by some compilers and compilation options, this is not recommanded. For example, a product including a matrix transpose can be written:

``````real, dimension(3,3) :: A, B, C
A(:) = 4
B(:) = 5
C = matmul(transpose(A),matmul(B,matmul(A,transpose(B)))) ! Equivalent to A^t.B.A.B^T
`````` PDF - Download Fortran for free