In this complete introduction to the theory of finding derivatives of scalar-, vector- and matrix-valued functions with respect to complex matrix variables, Hjorungnes describes an essential set of mathematical tools for solving research problems where unknown parameters are contained in complex-valued...
Complex-Valued Matrix DerivativesIn this complete introduction to the theory of finding derivatives of scalar-, vector-,and matrix-valued functions in..
We have introduced complex-valued matrix element to represent apertures, thus having diffraction properties inherent in the description. We have extended the treatments of Baues and Collins to include partially coherent light sources, optical elements of finite size, and distributed random inhomogeneity ...
Patterned Complex-Valued Matrix Derivatives A systematic and simple method is proposed for how to find the derivative of complex-valued matrix functions which depend on matrix arguments that contain ... A Hjørungnes,DP Palomar - IEEE 被引量: 18发表: 2008年 Finding Patterned Complex-Valued Matr...
Frontiers of Optoelectronics, 2022年6月15日 6月15日,华中科技大学光学与电子信息学院张新亮教授,董建绩教授带领的团队,在期刊 Frontiers of Optoelectronics 发表题为 A small microring array that performs large complex-valued matrix-vector multiplication 的论文。
In this chapter, we present a Riemannian geometry approach for optimization of a real-valued ICA cost function J J mathContainer Loading Mathjax of complex-valued matrix argument W , under the constraint that W is an n 脳 n unitary matrix. We present a steepest descent algorithm on the Lie...
The algorithm can be applied to the estimation of complex-valued mixing matrix based on L-shaped arrays and uniform circular arrays. Then, to overcome the limitation that the clustering performance of traditional algorithms is affected by noise, data cleansing detection is introduced to reselect the...
Specifically, we mostly perform complex matrix-matrix multiplications and utilize various linear algebra routines like eigh, expm and schur. We are in the process of switching from PyTorch to JAX and the support of complex numbers on Apple Silicon for JAX would be a huge plus. Most simulation ...
5). The decomposition of a complex-valued matrix follows the MZI arrangement as shown in Fig. 1b, and each MZI is described by Eq. (1). Also refer to Supplementary Notes 4–6, including the input encoding process, the decomposition and implementation of the weight matrices on chip. ...
The weights part can realize an arbitrary complex-valued matrix through singular value decomposition, 𝑀=𝑈𝛴𝑉∗.M=UΣV*. (1) The complex-valued matrix 𝑀M is decomposed into the product of two unitary matrices 𝑈U, 𝑉∗V* and a diagonal matrix 𝛴Σ. The unitary ...