Linear

A Linear operator computes a linear combination of synchronized input values using predefined coefficients. It extends Join to ensure input synchronization before computing the combination.

Coefficients

Coefficients are specified during construction and define the linear combination:

• Minimum of 2 coefficients required
• Each coefficient corresponds to one input port
• Output = c₁x₁ + c₂x₂ + ... + cₙxₙ where cᵢ are coefficients and xᵢ are inputs

Ports

• Input ports: One per coefficient, all NumberData type
• Output port: One NumberData port containing linear combination

Operation

1. Inherits Join synchronization behavior
2. When inputs are synchronized:
   • Computes linear combination
   • Outputs result on first port
   • Clears other output ports

Example

// Create linear combination: 2x - y
auto linear = make_linear("linear1", {2.0, -1.0});

// Process synchronized inputs
linear->receive_data(create_message<NumberData>(1, NumberData{3.0}), 0); // x = 3
linear->receive_data(create_message<NumberData>(1, NumberData{1.0}), 1); // y = 1
linear->execute();
// Output: 5.0 (2*3 - 1)

Error Handling

Throws exceptions for:

• Fewer than 2 coefficients
• Invalid message types
• Port index out of range

Performance Considerations

• O(n) computation where n is number of coefficients
• Memory usage proportional to coefficient count
• Numerical stability maintained for large coefficients