Start prototyping benchmark

Author: mofeing

perf/lanczos/Project.toml

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+[deps]
+Reactant = "3c362404-f566-11ee-1572-e11a4b42c853"
+
+[sources]
+Reactant = {path = "../.."}

perf/lanczos/README.md

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+# Lanczos benchmark
+
+This benchmark implements the Lanczos algorithm for top-k eigenvalue decomposition of a Hermitian matrix.
+
+> **require** $A, b$
+>
+> $\beta_1 v_1 = b$ s.t. $||v_1|| = 1$
+>
+> **for** $k = 1, 2, \dots$
+>
+> $\quad\alpha_k = v_k^\dagger A v_k$
+>
+> $\quad\beta_{k+1} v_{k+1} = A v_k - \alpha_k v_k - \beta_k^* v_{k-1}$
+>
+> **end**
+
+$A V_k = V_k T_k + \beta_{k+1,k} v_{k+1}e_k^T = V_{k+1}T_{k+1,k}$
+
+$V_k^\dagger V_k = \mathbb{I}_k$

perf/lanczos/main.jl

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+using Reactant
+using LinearAlgebra
+using Random
+
+Random.seed!(0)
+
+A = rand(ComplexF64, 512, 512)
+A = A' * A # make it hermitian
+@assert ishermitian(A)
+
+b = normalize!(rand(ComplexF64, 512))
+
+Are = Reactant.to_rarray(A)
+bre = Reactant.to_rarray(b)