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ModuleBase::Vector3 should support manipulation between int and double. #5756

@ErjieWu

Description

@ErjieWu

Background

Currently, when multiplying two vector with type ModuleBase::Vector3 and ModuleBase::Vector3, it will throw an error like

error: invalid operands to binary expression ('const value_type' (aka 'const ModuleBase::Vector3<double>') and 'Vector3<int>')

However, int type should be allowed to make calculations with double type data and return double results.

Describe the solution you'd like

Add support for some basic calculations between ModuleBase::Vector3 and ModuleBase::Vector3.

Task list only for developers

  • Notice possible changes of behavior
  • Explain the changes of codes in core modules of ESolver, HSolver, ElecState, Hamilt, Operator or Psi

Notice Possible Changes of Behavior (Reminder only for developers)

No response

Notice any changes of core modules (Reminder only for developers)

No response

Notice Possible Changes of Core Modules (Reminder only for developers)

No response

Additional Context

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Task list for Issue attackers (only for developers)

  • Review and understand the proposed feature and its importance.
  • Research on the existing solutions and relevant research articles/resources.
  • Discuss with the team to evaluate the feasibility of implementing the feature.
  • Create a design document outlining the proposed solution and implementation details.
  • Get feedback from the team on the design document.
  • Develop the feature following the agreed design.
  • Write unit tests and integration tests for the feature.
  • Update the documentation to include the new feature.
  • Perform code review and address any issues.
  • Merge the feature into the main branch.
  • Monitor for any issues or bugs reported by users after the feature is released.
  • Address any issues or bugs reported by users and continuously improve the feature.

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