google/tf-quant-finance ? reverse-engineered prompt

Build me a TensorFlow based quantitative finance library that helps with the core math and pricing tools people use in trading and risk work.

I want it to include the basics like optimization, interpolation, root finding, linear algebra, and random number generation, then move up to things like Monte Carlo path simulation, ODE and PDE solvers, and copula sampling. It should also have practical pricing tools for common models like Black Scholes, Hull White, Heston, SABR, and local volatility, plus calibration helpers and rate curve fitting. Make sure it can run fast with TensorFlow, use automatic differentiation, and work well on modern hardware.

Please include a few clear examples or notebooks that show how to price an option, run a simulation, fit a curve, and compute implied volatility. If anything is unclear, look up current TensorFlow docs online and keep the code clean and easy to extend.