Complex Matrix Product Calculation With Real-Imaginary i-Swap
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Solution Overview
Problem
The method of replacing a complex matrix product with a real matrix product increases costs due to numerous rearrangements and additional memory requirements.
Innovation Solution
A matrix product calculator that separates the complex number into a real part and an imaginary part, performs specific multiplications and additions, and uses an i-swap to swap the imaginary part with the real part, reducing the need for rearrangements and memory usage.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Adaptability or versatility
If complex matrix product is replaced with real matrix product, then complex matrix calculation capability is achieved, but memory requirements and rearrangement operations increase
Solution Approach 1:
The complex matrix B is segmented into its real part (Re(B)) and imaginary part (Im(B)), allowing the complex matrix multiplication to be decomposed into separate real matrix multiplication operations. This segmentation enables the use of existing real matrix product calculators while reducing memory requirements compared to storing and manipulating full complex matrices.
Solution Approach 2:
The invention changes the parameter representation from full complex numbers to separate real and imaginary components. By loading Re(B) and Im(B) separately into calculator elements and performing distinct multiplication operations, the system achieves complex matrix calculation capability while optimizing memory usage and avoiding unnecessary rearrangement operations.
2Adaptability or versatility
If complex matrix product is replaced with real matrix product, then complex matrix calculation capability is achieved, but rearrangement operations increase
Solution Approach 1:
By segmenting the complex matrix B into Re(B) and Im(B) before the calculation process, the invention eliminates the need for complex rearrangement operations that would otherwise be required to handle imaginary unit multiplications. The segmentation allows direct use of real matrix product calculators with simplified data flow.
Solution Approach 2:
The real and imaginary parts of matrix B are separated and prepared in advance before being loaded into the calculator elements. This preliminary action of decomposition prevents the need for rearrangement operations during the actual matrix multiplication process, reducing overall computational complexity.
3Productivity
If imaginary part is swapped with real part in first complex matrix, then second multiplication is enabled, but additional processing steps are required
Solution Approach 1:
The invention applies inversion by swapping the real and imaginary parts of matrix A to enable the second multiplication operation. Instead of performing complex conjugate operations or other complex transformations, the simple swap of real and imaginary components achieves the mathematical equivalent, reducing processing complexity while maintaining productivity.
Data Source
AI summary
A matrix product calculator performs: in calculation of a matrix product using a first complex matrix, a second complex matrix, and a third complex matrix, separating a complex number included in the second complex matrix into a real part and an imaginary part, loading the real part and the imaginary part of the complex number into a plurality of calculator elements, performing first multiplication that multiplies the first complex matrix and the real part of the second complex matrix, and adding the third complex matrix to a result of the first multiplication, swapping the imaginary part with the real part in each complex number of the first complex matrix, and performing second multiplication that multiplies the imaginary part of the second complex matrix and the first complex matrix with the swapped parts, and adding the third complex matrix to a result of the second multiplication.