Hello, I tried to implement cross_product function as a component of linalg module. And a brief description is presented below. If we can have an agreement on the interface of cross_product, I will create a pull request.

Cross Product

Overview

Cross product is a binary operation on two vectors in space, denoted by . The result of is a vector that is perpendicular to both and . Let , , and being the orthonormal basis vectors in space, and can be represented by the following expressions


Then has a determinant form:

API

interface
 function cross_product(a, b) result(c)
 real, intent(in) :: a(:)
 real, intent(in) :: b(:)
 real :: c(3)
 end function
end interface

error stop when the size of a or b is not equal to 3.

Discussion

I think the vectors a and b should be passed as assumed-shape array. There is no need to explicitly define a and b as fixed-size array, i.e. real, intent(in) :: a(3), b(3). Compilers are not able to check whether the size is reasonable at compile-time since in many cases, allocatable arrays are used. Therefore, the assertion for array size is placed in the body of cross_product function, where error_stop is called. As a result, cross_product is no longer a pure function.

Based on the above discussion and consideration of simplicity, I chose an analogous way to Julia to implement cross_product.

Reference Implementations

• Numpy
• Julia
• C++ (Boost)