Pith. sign in

REVIEW 2 major objections 5 minor 31 references

SAXO+, the second-stage adaptive optics for SPHERE: NCPA compensation and dark-hole loop with a pyramid wavefront sensor

T0 review · 2 major / 5 minor · reviewed 2026-07-14 · grok-4.5

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

Pith's one-line read SAXO+ NCPAs are expected at 27 nm RMS and can be largely offloaded to the first-stage mirror, preserving the second-stage stroke for high-speed AO.

desk verdict Solid engineering validation of the SAXO+ NCPA budget and a practical DM1-offload recipe; the Monte-Carlo number is useful but incomplete for the frequencies that matter to dark-hole performance. read the letter →

arxiv 2607.10124 v1 pith:FYM4Y4W5 submitted 2026-07-11 astro-ph.IM

Johan Mazoyer , Charles Goulas , Raphaël Galicher , Axel Potier , Fabrice Vidal , Florian Ferreira , Arnaud Sevin , Clémentine Béchet
show 16 more authors
Isaac Bernardino Dinis Anthony Boccaletti Gael Chauvin Fausto Cortecchia Emiliano Diolaiti Nicolas Galland Caroline Kulcsár Maud Langlois Matteo Lombini Julien Milli Mamadou N'diaye Henri-François Raynaud Laura Schreiber Michel Tallon Arthur Vigan François Wildi
This is my paper
classification astro-ph.IM
keywords adaptiveopticsmulti-stageAOhigh-contrastimagingcoronagraphynon-commonpathaberrationspyramidwavefrontsensorSAXO+SPHERE
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

SAXO+ adds a second-stage near-infrared pyramid wavefront sensor and deformable mirror to SPHERE so that residual atmospheric errors can be corrected at higher speed. For the coronagraph to reach its full contrast, static non-common-path aberrations (NCPAs) that the wavefront sensors never see must also be measured and removed. Using Monte Carlo runs on an updated Zemax model of the instrument, the authors show that those NCPAs should average only 27 nm RMS (about 19 nm without tip-tilt), matching earlier SPHERE measurements and the assumptions used in prior performance forecasts. They also give a three-step calibration sequence that places most of the static correction on the large-stroke first-stage mirror, leaving the second-stage MEMS free for high-bandwidth residual correction. The same framework supports a later dark-hole loop that can suppress residual starlight by another large factor once both adaptive-optics stages are closed.

What carries the argument

Difference of Monte-Carlo optical-path-difference maps: one generated at the pyramid wavefront-sensor focus, the other at the coronagraph focus, under the assumption that the pyramid fully corrects static aberrations in its own channel. That residual map is the predicted NCPA error budget.

What would settle it

Once SAXO+ is installed, measure the residual NCPA map with the Zernike sensor (or with a dark-hole reconstruction) under typical internal-source and on-sky conditions; if the measured RMS systematically exceeds ~40 nm or shows substantially more power above 12 λ/D than the Monte-Carlo ensemble, the optical-model prediction is falsified.

Watch

Extended reading notes

Core claim

Monte Carlo sampling of alignment and figure errors in the SAXO+ optical model predicts NCPAs of 27 ± 8 nm RMS (19 ± 2 nm excluding tip-tilt) at the coronagraph, with 99.5 % of realizations remaining inside the capture range of the daily Zernike wavefront-sensor calibration; these numbers validate the aberration levels previously assumed for end-to-end contrast simulations and confirm that the dual-stage architecture can keep the pyramid sensor inside its linear regime.

Load-bearing premise

That the difference between the two Monte-Carlo wavefront maps, after assuming the pyramid fully corrects its own channel, is a faithful predictor of the real NCPAs that will appear on sky at the coronagraph.

Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

2 major / 5 minor

Summary. This proceeding refines the expected non-common path aberration (NCPA) budget for the SAXO+ second-stage AO upgrade of VLT/SPHERE and outlines calibration procedures for static NCPA compensation and focal-plane dark-hole control with a near-infrared pyramid WFS. Monte Carlo sampling of an updated Zemax optical model (500 OPD maps) yields expected NCPAs of 27±8 nm RMS (19±2 nm excluding tip-tilt) and 135±49 nm P2V at the coronagraph, with 99.5% of realizations below the ZWFS λ/4 capture range. The PSD of the generated maps is shown to agree with prior SPHERE Zelda measurements below ~12 λ/D. The paper also proposes a three-step internal-source calibration sequence that offloads static corrections onto the first-stage HODM so that the low-stroke MEMS second-stage DM retains stroke for high-speed residual correction, and it sketches the corresponding on-sky ZWFS and dark-hole loops that offset the pyramid WFS reference.

Significance. If the NCPA budget and off-load strategy hold, the work supplies a concrete, instrument-specific calibration framework that is required for SAXO+ to reach the contrast gains already claimed in the companion end-to-end study (Goulas et al. 2026). The quantitative Monte Carlo comparison to existing Zelda data and the explicit stroke-management procedure are useful engineering results for any multi-stage AO system that pairs a high-stroke first stage with a low-stroke MEMS second stage. The manuscript is primarily a conference proceeding that consolidates optical-model validation and operational procedures rather than a new performance demonstration; its value is therefore practical and timely for the SAXO+ project.

major comments (2)
  1. Section 3: the central NCPA figure (27±8 nm RMS) is obtained by subtracting Monte-Carlo OPD maps under the explicit assumption that “the PyWFS corrects completely the static aberrations introduced in its channel.” That assumption is not tested against residual turbulence, optical-gain variation, or the limited linear range of a pyramid sensor. Because residual mid-to-high-frequency content after both loops close is precisely what the dark-hole and on-sky ZWFS procedures of Section 4 must correct, and because residual stroke on DM2 is the quantity the off-load strategy is designed to protect, the reported budget is not yet a faithful predictor of the residual that will appear at the coronagraph. A short sensitivity test (or an explicit statement of residual after realistic closed-loop correction) is needed to close this claim.
  2. Section 3 and Figure 3: the same Monte-Carlo analysis omits surface roughness (producing the under-prediction of power above ~12 λ/D relative to Zelda) and high-frequency DM figure errors beyond the actuator cut-offs. These terms dominate residual stroke and dark-hole performance. The paper correctly notes the omission, but the quantitative claim that the model “validates our assumption that the level of aberrations and frequency content after SAXO+ will be comparable” therefore holds only below the DM cut-offs. The text should either bound the missing high-frequency contribution or restrict the validation statement accordingly.
minor comments (5)
  1. Figure 2 caption and body text: the P2V standard deviation is given as 49 nm in the figure label but as 9 nm in the accompanying sentence; the RMS and tip-tilt-excluded numbers also need consistent reporting so that the 99.5% capture-range claim can be verified.
  2. Section 4, Step 2 description: “offested” appears twice and should be corrected to “offset.”
  3. Section 2: the actuator count update (26 → 28.1 across the pupil) is noted but the simulations themselves have not yet been re-run; a one-sentence statement of the expected impact (or lack thereof) on the NCPA budget would strengthen the claim that results are unchanged.
  4. Figure 1 and the calibration schematic (Figure 4) use overlapping but not identical notation for the two DMs (DM1/HODM vs. DM2/XPDM); a single consistent nomenclature would improve readability.
  5. Several typographical inconsistencies remain (“SAXO+upgrade” missing space, “isa priorimuch harder”, “Y or YJ bands” layout, “DDTS” vs. “DTTS”). A careful copy-edit pass is warranted.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: NCPA budget is generated from an independent Zemax Monte-Carlo model and only afterwards compared to prior Zelda data and earlier assumptions.

full rationale

The paper’s central quantitative claim (Section 3, Fig. 2: 27 ± 8 nm RMS NCPA) is obtained by differencing Monte-Carlo OPD maps produced from an updated Zemax optical model under stated alignment and figure tolerances; the result is not fitted to, nor defined in terms of, the SPHERE Zelda measurements or the Goulas et al. (2026) performance assumptions that it later cites for comparison. Those self-citations supply historical context and the performance-study baseline that the new model is intended to validate; they do not enter the Monte-Carlo generation itself. The calibration off-load procedure of Section 4 is a proposed operational sequence, not a derived prediction. No free parameter is fitted and then re-presented as a forecast, no uniqueness theorem is imported from the authors’ prior work to force the result, and no ansatz is smuggled via citation. The derivation chain is therefore self-contained against external optical-model inputs and does not reduce by construction to its own premises.

Assumptions & free parameters 0 free parameters · 4 assumptions · 0 invented entities

The central NCPA claim rests on standard optical-modeling practice (Zemax Monte-Carlo of alignment and figure errors) plus domain assumptions about which optics contribute and that the PyWFS fully corrects its own channel. No free parameters are fitted to science data; the 27 nm figure is a simulation output. No new physical entities are postulated. The main load-bearing modeling choices are the omission of surface roughness and the DTTS beamsplitter and the assumption that internal-source calibration transfers sufficiently to on-sky conditions.

assumptions (4)
  • domain assumption Difference of Monte-Carlo OPDs at PyWFS focus and at SAXO+ exit focus, after assuming PyWFS fully corrects statics in its channel, equals the NCPA seen by the coronagraph.
    Section 3; standard AO NCPA definition but not re-validated on the as-built hardware.
  • ad hoc to paper Surface roughness, DTTS beamsplitter, and high-frequency DM figure errors can be neglected for the NCPA budget comparison below the DM cutoffs.
    Explicitly stated omissions in Section 3; the PSD comparison shows under-prediction above ~12 λ/D.
  • domain assumption Internal-source ZWFS and dark-hole calibrations remain useful starting points for on-sky operation once both AO loops are closed.
    Section 4; authors note ~20 nm RMS differences reported by Vigan et al. 2019 and plan on-sky loops, but the offload recipe is still built around internal-source steps.
  • domain assumption First-stage SAXO loop can absorb the bulk of static NCPA stroke without compromising its atmospheric correction role under the bright-star, good-seeing regime where NCPA matter most.
    Section 4 and Figure 4; justified by stroke disparity between HODM and MEMS but not quantified for worst-case red-star cases.

how reviews work

0 comments
Cite this review

Pith. "Pith review of SAXO+, the second-stage adaptive optics for SPHERE: NCPA compensation and dark-hole loop with a pyramid wavefront sensor." pith.science (2026). https://pith.science/paper/FYM4Y4W5

@misc{pith2026260710124,
  author       = {Pith},
  title        = {Pith review of: SAXO+, the second-stage adaptive optics for SPHERE: NCPA compensation and dark-hole loop with a pyramid wavefront sensor},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/FYM4Y4W5}},
  note         = {Machine review of arXiv:2607.10124}
}
read the original abstract

The SAXO+ upgrade of the VLT/SPHERE adaptive optics system introduces a second-stage near-infrared pyramid wavefront sensor to improve high-contrast imaging, making accurate calibration of non-common path aberrations (NCPAs) essential to fully exploit its performance. This work refines the expected level of NCPAs in SAXO+ and presents the calibration procedures developed for static NCPA compensation and focal-plane dark-hole control. Monte Carlo simulations based on an updated Zemax optical model were used to estimate the NCPA error budget. These simulations are in good agreement with previous measurements on SPHERE and with the assumptions adopted in earlier performance studies. We also propose a calibration strategy that offloads most static aberration correction to the first-stage deformable mirror while preserving the second-stage mirror stroke for high-speed adaptive optics correction. These results validate the expected SAXO+ optical quality and establish the calibration framework required for efficient NCPA compensation and focal-plane wavefront control during future on-sky operations.

Figures

Figures reproduced from arXiv: 2607.10124 by the authors.

Figure 1
Figure 1. SAXO+ outline. In blue: current SAXO system. In red: second loop of SAXO+. In green: NCPA correction (adapted from Goulas et al. 20267 ). For bright targets under favorable conditions (when atmospheric turbulence is well-compensated by the AO system), SPHERE coronagraph images are generally dominated by NCPA-induced speckles and methods have been developed to actively correct these speckles during observations.8, 9 … view at source ↗
Figure 2
Figure 2. Distribution of NCPA level in RMS (left) and peak-2-valley (right) randomly generated with SAXO [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Power spectral density of generated NCPA OPD maps (in grey) compared to current level measured in SAXO [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗

Discussion (0). Sign in to comment.

Reference graph

Works this paper leans on

31 extracted references · 2 linked inside Pith

  1. [1]

    Imaging exoplanets with coronagraphic instruments,

    Galicher, R. and Mazoyer, J., “Imaging exoplanets with coronagraphic instruments,”Comptes Rendus Physique24, 133 (jan 2024). ADS Bibcode: 2024CRPhy..24S.133G

    2024

  2. [2]

    SPHERE: The exoplanet imager for the Very Large Telescope,

    Beuzit, J.-L., Vigan, A., Mouillet, D., et al., “SPHERE: The exoplanet imager for the Very Large Telescope,” Astronomy and Astrophysics631, A155 (Nov. 2019)

    2019

  3. [3]

    First light of the Gemini Planet Imager,

    Macintosh, B., Graham, J. R., Ingraham, P., et al., “First light of the Gemini Planet Imager,”Proceedings of the National Academy of Sciences111, 12661–12666 (Sept. 2014)

    2014

  4. [4]

    Status of the SCExAO instrument: Recent technology upgrades and path to a system-level demonstrator for PSI,

    Lozi, J., Guyon, O., Vievard, S., et al., “Status of the SCExAO instrument: Recent technology upgrades and path to a system-level demonstrator for PSI,” in [Proceedings of the SPIE],11448, 110–121, SPIE (Dec. 2020)

    2020

  5. [5]

    MagAO-X: project status and first laboratory results,

    Males, J. R., Close, L. M., et al., “MagAO-X: project status and first laboratory results,” in [Adaptive Optics Systems VI], Close, L. M., Schreiber, L., and Schmidt, D., eds.,Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series10703, 1070309 (July 2018)

    2018

  6. [6]

    The SPHERE infrared survey for exoplanets (SHINE) V. Full sample characterization,

    Squicciarini, V., Desidera, S., Chauvin, G., et al., “The SPHERE infrared survey for exoplanets (SHINE) V. Full sample characterization,”arXiv e-printsa, arXiv:2605.27247 (May 2026)

    arXiv 2026

  7. [7]

    Non-common path aberration compensation and a dark hole loop with a pyramid adaptive optics system: Application to SAXO+,

    Goulas, C., Galicher, R., Vidal, F., Mazoyer, J., Ferreira, F., Sevin, A., Potier, A., Boccaletti, A., Gendron, E., B´ echet, C., Tallon, M., Langlois, M., Kulcs´ ar, C., Raynaud, H.-F., Galland, N., Schreiber, L., Dinis, I. B., Wildi, F., and Chauvin, G., “Non-common path aberration compensation and a dark hole loop with a pyramid adaptive optics system:...

    2026

  8. [8]

    Calibration of quasi- static aberrations in exoplanet direct-imaging instruments with a Zernike phase-mask sensor. III. On-sky validation in VLT/SPHERE,

    Vigan, A., N’Diaye, M., Dohlen, K., Sauvage, J.-F., Milli, J., Zins, G., Petit, C., Wahhaj, Z., Cantalloube, F., Caillat, A., Costille, A., Le Merrer, J., Carlotti, A., Beuzit, J.-L., and Mouillet, D., “Calibration of quasi- static aberrations in exoplanet direct-imaging instruments with a Zernike phase-mask sensor. III. On-sky validation in VLT/SPHERE,”A...

    2019

Show all 31 references
  1. [9]

    Increasing the raw contrast of VLT/SPHERE with the dark hole technique. II. on-sky wavefront correction and coherent differential imaging,

    Potier, A., Mazoyer, J., Wahhaj, Z., Baudoz, P., Chauvin, G., Galicher, R., and Ruane, G., “Increasing the raw contrast of VLT/SPHERE with the dark hole technique. II. on-sky wavefront correction and coherent differential imaging,”Astronomy and Astrophysics665, A136 (sep 2022)

    2022

  2. [10]

    Peering through SPHERE images: A glance at contrast limitations,

    Cantalloube, F., Dohlen, K., Milli, J., Brandner, W., and Vigan, A., “Peering through SPHERE images: A glance at contrast limitations,”The Messenger176, 25–31 (2019)

    2019

  3. [11]

    SPHERE+: Imaging young jupiters down to the snowline,

    Boccaletti, A., Chauvin, G., Mouillet, D., et al., “SPHERE+: Imaging young jupiters down to the snowline,” arXiv e-prints2003, arXiv:2003.05714 (2020)

    2003 arXiv

  4. [12]

    Pupil plane wavefront sensing with an oscillating prism,

    Ragazzoni, R., “Pupil plane wavefront sensing with an oscillating prism,”Journal of Modern Optics43, 289–293 (Feb. 1996)

    1996

  5. [13]

    Improving the performance of a pyramid wavefront sensor with modal sensitivity compensation,

    Korkiakoski, V., V´ erinaud, C., and Louarn, M. L., “Improving the performance of a pyramid wavefront sensor with modal sensitivity compensation,”Applied Optics47, 79 (Jan. 2008)

    2008

  6. [14]

    A telescope-ready approach for modal compensation of pyramid wavefront sensor optical gain,

    Deo, V., Gendron, ´E., Rousset, G., Vidal, F., Sevin, A., Ferreira, F., Gratadour, D., and Buey, T., “A telescope-ready approach for modal compensation of pyramid wavefront sensor optical gain,”Astronomy & Astrophysics629, A107 (Sept. 2019)

    2019

  7. [15]

    On- sky correction of non-common path aberration with the pyramid wavefront sensor,

    Esposito, S., Puglisi, A., Pinna, E., Agapito, G., Quir´ os-Pacheco, F., V´ eran, J. P., and Herriot, G., “On- sky correction of non-common path aberration with the pyramid wavefront sensor,”Astronomy & Astro- physics636, A88 (Apr. 2020)

    2020

  8. [16]

    Pyramid wavefront sensor optical gains compensation using a convolutional model,

    Chambouleyron, V., Fauvarque, O., Janin-Potiron, P., Correia, C., Sauvage, J.-F., Schwartz, N., Neichel, B., and Fusco, T., “Pyramid wavefront sensor optical gains compensation using a convolutional model,” Astronomy & Astrophysics644, A6 (Dec. 2020)

    2020

  9. [17]

    Apodized Pupil Lyot Coronagraphs for Arbitrary Apertures. V. Hybrid Shaped Pupil Designs for Imaging Earth-like planets with Future Space Observatories,

    N’Diaye, M., Soummer, R., Pueyo, L., Carlotti, A., Stark, C. C., and Perrin, M. D., “Apodized Pupil Lyot Coronagraphs for Arbitrary Apertures. V. Hybrid Shaped Pupil Designs for Imaging Earth-like planets with Future Space Observatories,”The Astrophysical Journal818, 163 (Feb. 2016)

    2016

  10. [18]

    Calibration of quasi- static aberrations in exoplanet direct-imaging instruments with a Zernike phase-mask sensor. III. On-sky validation in VLT/SPHERE,

    Vigan, A., N’Diaye, M., Dohlen, K., Sauvage, J. F., Milli, J., Zins, G., Petit, C., Wahhaj, Z., Cantalloube, F., Caillat, A., Costille, A., Le Merrer, J., Carlotti, A., Beuzit, J. L., and Mouillet, D., “Calibration of quasi- static aberrations in exoplanet direct-imaging instr...

    2019

  11. [19]

    Closed loop, DM diversity-based, wavefront cor- rection algorithm for high contrast imaging systems,

    Give’on, A., Belikov, R., Shaklan, S., and Kasdin, J., “Closed loop, DM diversity-based, wavefront cor- rection algorithm for high contrast imaging systems,”Optics Express15, 12338 (09 2007). ADS Bibcode: 2007OExpr..1512338G

    2007

  12. [20]

    Vigan, A., Dohlen, K., N’Diaye, M., Cantalloube, F., Girard, J. H., Milli, J., Sauvage, J.-F., Wahhaj, Z., Zins, G., Beuzit, J.-L., Caillat, A., Costille, A., Le Merrer, J., Mouillet, D., and Tourenq, S., “Calibration of quasi-static aberrations in exoplanet direct-imaging ins...

    2022

  13. [21]

    Upgrading SPHERE with the second stage AO system SAXO+: non- common path aberrations estimation and correction,

    Mazoyer, J., Goulas, C., Vidal, F., Dinis, I. B., Milli, J., Tallon, M., Galicher, R., Absil, O., Bechet, C., Boccaletti, A., Ferreira, F., Langlois, M., Martinez, P., Mugnier, L., N’diaye, M., Xivry, G. O. d., Potier, A., Tallon-Bosc, I., and Vigan, A., “Upgrading SPHERE with...

    2024

  14. [22]

    Saxo+, the second-stage adaptive optics for sphere: high contrast performance analysis,

    Langlois, M., B´ echet, C., Schreiber, L., Tallon, M., Ferreira, F., Milli, J., Loupias, M., Dinis, I., Diolaiti, E., Feldt, M., Galicher, R., Kulcs´ ar, C., Mazoyer, J., N’Diaye, M., Raynaud, H.-F., Goulas, C., Stadler, E., Tallon-Bosc, I., Boccaletti, A., Chauvin, G., Gallan...

    2026

  15. [23]

    Saxo+, the second-stage adaptive optics for sphere: a review of six selected control algorithms and the results achieved to date,

    Tallon, M., B´ echet, C., Dinis, I., Ferreira, F., Fontanillas, P., Galland, N., Goulas, C., Kasper, M., Kulcs’ar, C., Nousiainen, J., Raynaud, H.-F., Tallon-Bosc, I., Thi´ ebaut, E., Langlois, M., Boccaletti, A., Diolaiti, E., Galicher, R., Lelouarn, M., Loupias, M., Mazoyer,...

    2026

  16. [24]

    Improving VLT/SPHERE without additional hardware: comparing quasi-static correction strategies,

    Potier, A., Wahhaj, Z., Galicher, R., Mazoyer, J., Baudoz, P., Chauvin, G., and Ruane, G., “Improving VLT/SPHERE without additional hardware: comparing quasi-static correction strategies,” in [Adaptive Optics Systems VIII], Schreiber, L., Schmidt, D., and Vernet, E., eds.,Soci...

    2022

  17. [25]

    Asterix: Simulate your high-contrast instruments,

    Mazoyer, J., Potier, A., Laginja, I., and Galicher, R., “Asterix: Simulate your high-contrast instruments,” (2019).https://asterix-hci.readthedocs.io/

    2019

  18. [26]

    The astropy project: Sustaining and growing a community-oriented open- source project and the latest major release (v5.0) of the core package,

    Astropy Collaboration et al., “The astropy project: Sustaining and growing a community-oriented open- source project and the latest major release (v5.0) of the core package,”The Astrophysical Journal935, 167 (08 2022)

    2022

  19. [27]

    COMPASS: Status update and long term development plan,

    Gratadour, D., Ferreira, F., Sevin, A., Doucet, N., Cl´ enet, Y., Gendron, E., Lain´ e, M., Vidal, F., Brul´ e, J., Puech, M., V´ erinaud, C., and Carlotti, A., “COMPASS: Status update and long term development plan,” in [Adaptive Optics Systems V],9909, 2057–2063, SPIE (July 2016)

  20. [28]

    Matplotlib: A 2d graphics environment,

    Hunter, J. D., “Matplotlib: A 2d graphics environment,”Computing in Science & Engineering9(3), 90–95 (2007)

    2007

  21. [29]

    Array programming with NumPy,

    Harris, C. R., Millman, K. J., van der Walt, S. J., Gommers, R., Virtanen, P., Cournapeau, D., Wieser, E., Taylor, J., Berg, S., Smith, N. J., Kern, R., Picus, M., Hoyer, S., van Kerkwijk, M. H., et al., “Array programming with NumPy,”Nature585(7825), 357–362 (2020)

    2020

  22. [30]

    pyZELDA: Python code for Zernike wavefront sensors

    Vigan, A. and N’Diaye, M., “pyZELDA: Python code for Zernike wavefront sensors.” Astrophysics Source Code Library, record ascl:1806.003 (June 2018)

    2018

  23. [31]

    Scipy 1.0: Fundamental algorithms for scientific computing in python,

    Virtanen, P., Gommers, R., Oliphant, T. E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S. J., Brett, M., Wilson, J., Millman, K. J., et al., “Scipy 1.0: Fundamental algorithms for scientific computing in pytho...

    2020

Pith tools

Reviewed July 14, 2026 · model on record in the stance chip above.