Automatic Differentiation for Complex Valued SVD

Automatic differentiation(AD) evaluates derivatives or gradients of any functions specified by computer programs[ 1 ]. It is implemented by propagating derivatives of primitive operations v ia chain rules. Such approach is different from classical symbolic or numerical differentiations. Symbolic differentiat ion faces the challenge of converting a complicated computer program into expressions, while numerical differentiation faces the difficulty of numerical errors in the discretization. Besides, both symbolic and numerical methods have problems in calculating higher order derivatives and are also slow at computing gradients with respect to lots of input s variables, e.g. in the case for gradient-based optimization algorithms.