definitions.md

Particular Definitions, Enums

enum Cos : std::size_t { X_AXIS = 0, Y_AXIS, Z_AXIS };

Represents the axis related to a direction cosine. (For example, if you want the direction cosine in respect to the X axis, you'll make a call such as someVector.direction_cosine(MathLibrary::Cos::X_AXIS).

enum class ComplexInnerProduct { ANTILINEAR_FIRST_ARGUMENT, ANTILINEAR_SECOND_ARGUMENT };

This enum class is used for the complex dot product. When you call a function on a complex vector, in most cases you'll be required to pass a template argument ComplexInnerProduct. Otherwise, the default member used will be ComplexInnerProduct::ANTILINEAR_FIRST_ARGUMENT. Commonly, a complex dot product might have two definitions. For each of these definitions, you can pass a ComplexInnerProduct template argument to choose which one you'd like to use.

• $a\cdot b=\sum_i \overline {a_i} b_i$ -> Template argument to pass is MathLbr::ComplexInnerProduct::ANTILINEAR_FIRST_ARGUMENT
• $a\cdot b=\sum_i a_i \overline {b_i}$ -> Template argument to pass is MathLbr::ComplexInnerProduct::ANTILINEAR_SECOND_ARGUMENT

For example:

int main() {
  MathLbr::vector<std::complex<double>> vec{{{2,4},{3,3}}};
  MathLbr::vector<std::complex<double>> sameVec{{{2,4},{3,3}}};
  MathLbr::Vector::inner_product<MathLbr::ComplexInnerProduct::ANTILINEAR_SECOND_ARGUMENT>(vec, sameVec);