Technical reports

These pages are a collection of findings while working on ComPWA packages such as ampform, qrules, and tensorwaves. Most of these findings were not implemented, but may become relevant later on or could be useful to other frameworks as well.

	TR	Title	Details	Tags	Status
	TR‑000	Square root over arrays with negative values	This notebook investigates how to write a square root function in sympy that computes the positive square root for negative values. The lambdified version of this ‘complex square root’ should have the same behavior for each computational backend.	lambdification sympy	✅ tensorwaves#284
	TR‑001	Custom lambdification	See also SymPy’s tutorial page on the printing modules.	lambdification sympy	✅ ampform#72, tensorwaves#284
	TR‑002	Faster lambdification by splitting expressions	This notebook investigates how to speed up sympy.lambdify by splitting up the expression tree of a complicated expression into components, lambdifying those, and then combining them back again.	lambdification sympy	✅ tensorwaves#281
	TR‑003	Chew-Mandelstam dispersion integrals	This report formulates a symbolic dispersion integral to approach the left-hand cut in the form factor for arbitrary angular momentum. The integral is evaluated with SciPy’s quad_vec.	physics sympy	🚧 ampform#265
	TR‑004	Investigation of analyticity		physics
	TR‑005	Symbolic K-matrix expressions	Implementation of this report is tracked through ampform#67.	physics
	TR‑006	Interactive 3D plots	This report illustrates how to interact with matplotlib 3D plots through Matplotlib sliders and ipywidgets.	tips	✅ ampform#38
	TR‑007	MatrixSymbols	This report is a sequel to TR-005. In that report, the \(\boldsymbol{K}\) was constructed with a sympy.Matrix, but it might be more elegant to work with MatrixSymbols.	sympy
	TR‑008	Indexed free symbols	This report has been implemented in ampform#111. Additionally, tensorwaves#427 makes it possible to lambdify sympy.Expr with Indexed symbols directly.	sympy	✅ ampform#111
	TR‑009	Symbolic expressions for Lorentz-invariant K-matrix	This report is a sequel to TR-005.	physics sympy	✅ ampform#120
	TR‑010	P-vector	This report is a sequel to TR-005 and TR-009.	physics sympy	✅ ampform#131
	TR‑011	Helicity angles as symbolic expressions	This report has been implemented in and ampform#177 and tensorwaves#345. The report contains some bugs which were also addressed in these PRs.	physics sympy	✅ ampform#177, tensorwaves#345
	TR‑012	Extended DataSample performance	ampform#198 makes it easier to generate expressions for kinematic variables that are not contained in the HelicityModel.expression. In TensorWaves, this results in a DataSample with more keys. A question was raised whether this affects the duration of fits. This report shows that this is not the case (see Conclusion).	lambdification sympy
	TR‑013	Spin alignment with data	In this report, we attempt to check the effect of activating spin alignment (ampform#245) and compare it with Figure 2 in [Marangotto, 2020]. See also TR-014 and TR-015.	physics
	TR‑014	Amplitude model with sum notation	See also TR-013 and TR-015.	sympy	✅ ampform#245
	TR‑015	Spin alignment implementation	This report has been implemented through ampform#245. For details on how to use it, see this notebook. See also TR-013 and TR-014.	physics sympy	✅ ampform#245
	TR‑016	Symbolic integral	This report investigates how to formulate a symbolic integral that correctly evaluates to	sympy
	TR‑017	Symbolic phase space boundary for a three-body decay	This reports shows how define the physical phase space region on a Dalitz plot using a Kibble function.	physics sympy	✅ compwa.github.io#139
	TR‑018	Intensity distribution generator with importance sampling	This reports sets out how data generation with TensorWaves works and what would be the best approach to tackle tensorwaves#402.	physics tensorwaves
	TR‑019	Integrating Jupyter notebook with Julia notebooks in MyST-NB	This report shows how to define a Julia kernel for Jupyter notebooks, so that it can be executed and converted to static pages with MyST-NB.	DX tips	✅ compwa.github.io#174
	TR‑020	Amplitude analysis with zfit	This reports builds a simple symbolic amplitude model with qrules and ampform and feeds it to zfit instead of tensorwaves.	physics sympy tensorwaves	✅ compwa.github.io#151
	TR‑021	Polarimeter vector field	Mikhail Mikhasenko @mmikhasenko, Remco de Boer @redeboer This report formulates the polarimeter vector field for in \(\Lambda_c \to p\pi K\) with SymPy and visualizes it as an interactive widget with TensorWaves and ipywidgets.	physics polarimetry polarization	✅ compwa.github.io#129
	TR‑022	Polarimetry: Computing the B-matrix for Λc→pKπ	The \(B\)-matrix forms an extension of the polarimeter vector field \(\vec\alpha\) (arXiv:2301.07010, see also TR-021) that takes the polarization of the proton into account. See arXiv:2302.07665, Eq. (B6).	physics polarimetry polarization	✅ compwa.github.io#196
	TR‑023	Support for Plotly plots in Technical Reports		3d documentation jupyter sphinx	✅ compwa.github.io#206
	TR‑024	Symbolic expressions and model serialization	Investigation into dumping SymPy expressions to human-readable format for model preservation. The notebook was motivated by the COMAP-V workshop on analysis preservation. See also SymPy printing, parsing, and expression manipulation.	documentation	🚧 polarimetry#319
	TR‑025	Rotated square root cut	Investigation of the branch cut in the two Riemann sheets of a square root and what happens if the cut is rotated around \(z=0\).		✅ compwa.github.io#236
	TR‑026	Visualization of the Riemann sheets for the single-channel \(T\) matrix with one resonance pole	This report investigates and reproduces the Riemann sheets shown in Fig. 50.1 and 50.2 of the PDG. The lineshape parametrization is directly derived with the \(K\)-matrix formalism. The transition from the first physical sheet to the second unphysical sheet is derived using analytic continuation.		🚧 ampform#67
	TR‑027	Visualization of the Riemann sheets for the two-channel \(T\)-matrix with one pole	Following TR-026, the Riemann sheets for the amplitude calculated within the \(K\)-matrix formalism for the two-channel case are visualized. The method of transitioning from the first physical sheet to the unphysical sheets is extended to the two dimensional case using Eur. Phys. J. C (2023) 83:850 in order to visualize the third and the fourth unphysical sheet.		🚧 ampform#67

Execution times

Document	Modified	Method	Run Time (s)	Status
report/003	2024-04-06 10:05	cache	27.76	✅
report/004	2024-04-06 10:05	cache	7.09	✅
report/006	2024-04-06 10:05	cache	13.2	✅
report/007	2024-04-06 10:05	cache	12.47	✅
report/016	2024-04-06 10:05	cache	10.87	✅
report/023	2024-04-06 10:05	cache	3.58	✅
report/024	2024-04-06 10:06	cache	43.95	✅
report/025	2024-04-06 10:06	cache	5.66	✅
report/026	2024-04-06 10:06	cache	6.3	✅
report/027	2024-04-06 10:07	cache	31.34	✅
symbolics	2024-04-06 10:07	cache	15.24	✅