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Higher order partial derivatives computation with respect to one or several tensor-like variables. Taylor series function approximation (derivative table and series function representation). Parametric fixed point computation.

Examples:

• Example-01: Derivative
• Example-02: Derivative table representation
• Example-03: Derivative table propagation
• Example-04: Jet class
• Example-05: Nonlinear mapping approximation
• Example-06: Fixed point
• Example-07: Parametric fixed point
• Example-08: Fixed point manipulation (collision)
• Example-09: Fixed point manipulation (change point type)
• Example-10: Alignment indices chaos indicators
• Example-11: Closed orbit (dispersion)
• Example-12: Closed orbit (quadrupole shift)
• Example-13: Closed orbit (sextupole shift)
• Example-14: Closed orbit (responce matrix & correction)
• Example-15: Tune (chromaticity)
• Example-16: Tune (responce matrix & correction)
• Example-17: Tune (spread)
• Example-18: Parametric twiss
• Example-19: Parametric phase advance
• Example-20: Poisson bracket
• Example-21: Taylor integrator
• Example-22: Yoshida integrator
• Example-23: Direct invariant
• Example-24: Direct invariant (parametric)
• Example-25: Composition
• Example-26: Composition (closed orbit)
• Example-27: Inverse
• Example-28: Inverse (closed orbit)
• Example-29: Momenta generator
• Example-30: Factorization (kick)
• Example-31: Factorization (fodo)
• Example-32: Factorization (factorize)
• Example-33: Nonlinear mapping approximation (gradient)
• Example-34: ORM optics correction
• Example-35: ORM optics correction (training loop)
• Example-36: ORM optics correction (training loop + elementwise computation)
• Example-37: Normalized dispersion
• Example-38: Coupling (minimal tune distance)
• Example-39: Coupling (minimal tune distance correction)
• Example-40: Coupling (amplitude ratio correction)

API:

• Util
• curry_apply()
• first()
• flatten()
• last()
• most()
• multinomial()
• nest()
• orthogonal()
• rest()
• symplectic()
• tolist()
• Derivative
• derivative()
• Gradient
• derivative()
• evaluate()
• factor()
• group()
• hessian()
• index()
• jacobian()
• naught()
• reduce()
• scalar()
• select()
• series()
• signature()
• split()
• Complex
• Signature
• apply()
• chop()
• get()
• set()
• signature()
• to()
• Index
• build()
• index()
• reduce()
• Series
• clean()
• fetch()
• merge()
• series()
• split()
• Evaluate
• compare()
• evaluate()
• table()
• Propagate
• identity()
• propagate()
• Parametric fixed point
• chain_point()
• check_point()
• clean_point()
• fixed_point()
• matrix()
• newton()
• parametric_fixed_point()
• Bracket
• bracket()
• Taylor
• taylor()
• Yoshida
• coefficients()
• yoshida()
• Invariant
• invariant()
• Inverse
• inverse()
• Momenta
• momenta()
• Factorization
• factorize()
• hamiltonian()
• hamiltonian_inverse()
• solution()
• Jet
• Jet

Indices and tables

• Index

• Module Index

• Search Page