Promote op and preallocating result of linear operators

When working with linear operators in Julia, it is often beneficial to promote the operands and preallocate the result to improve performance. In this article, we will explore three different ways to achieve this.

Option 1: Using the promote_rule function

Julia provides the promote_rule function, which allows us to define how two operands should be promoted before performing a linear operation. We can use this function to promote the operands and preallocate the result.


function promote_and_preallocate(op1, op2)
    promoted_op1, promoted_op2 = promote_rule(op1, op2)
    result = similar(promoted_op1)
    return promoted_op1, promoted_op2, result
end

op1 = [1, 2, 3]
op2 = [4, 5, 6]

promoted_op1, promoted_op2, result = promote_and_preallocate(op1, op2)
result .= promoted_op1 .+ promoted_op2

This approach uses the promote_rule function to promote the operands op1 and op2, and then creates a result array of the same type as the promoted operands. The result array is preallocated using the similar function. Finally, the linear operation is performed by broadcasting the addition operator .+ over the promoted operands and storing the result in the preallocated array.

Option 2: Using the promote_type function

Another approach is to use the promote_type function, which returns the common type of two operands. We can then use this common type to promote the operands and preallocate the result.


function promote_and_preallocate(op1, op2)
    common_type = promote_type(op1, op2)
    promoted_op1 = convert(common_type, op1)
    promoted_op2 = convert(common_type, op2)
    result = similar(promoted_op1)
    return promoted_op1, promoted_op2, result
end

op1 = [1, 2, 3]
op2 = [4, 5, 6]

promoted_op1, promoted_op2, result = promote_and_preallocate(op1, op2)
result .= promoted_op1 .+ promoted_op2

In this approach, we use the promote_type function to determine the common type of the operands op1 and op2. We then convert the operands to this common type using the convert function. The result array is preallocated in the same way as in the previous option, and the linear operation is performed using broadcasting.

Option 3: Using the promote_type and promote_rule functions together

A third option is to combine the promote_type and promote_rule functions to promote the operands and preallocate the result.


function promote_and_preallocate(op1, op2)
    common_type = promote_type(op1, op2)
    promoted_op1, promoted_op2 = promote_rule(convert(common_type, op1), convert(common_type, op2))
    result = similar(promoted_op1)
    return promoted_op1, promoted_op2, result
end

op1 = [1, 2, 3]
op2 = [4, 5, 6]

promoted_op1, promoted_op2, result = promote_and_preallocate(op1, op2)
result .= promoted_op1 .+ promoted_op2

In this approach, we first determine the common type of the operands using the promote_type function. We then convert the operands to this common type and use the promote_rule function to further promote them if necessary. The result array is preallocated as before, and the linear operation is performed using broadcasting.

After comparing these three options, it is clear that Option 1, which uses the promote_rule function, is the most concise and efficient solution. It directly promotes the operands and preallocates the result without the need for additional conversions. Therefore, Option 1 is the recommended approach for promoting operands and preallocating the result of linear operators in Julia.

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