SciPy is an open source scientific computing library for the Python programming language. SciPy 1.0 was released in late 2017, about 16 years after the original version 0.1 release. SciPy has become a de facto standard for leveraging scientific algorithms in the Python programming language, with more than 600 unique code contributors, thousands of dependent packages, over 100,000 dependent repositories, and millions of downloads per year. This includes usage of SciPy in almost half of all machine learning projects on GitHub, and usage by high profile projects including LIGO gravitational wave analysis and creation of the first-ever image of a black hole (M87). The library includes functionality spanning clustering, Fourier transforms, integration, interpolation, file I/O, linear algebra, image processing, orthogonal distance regression, minimization algorithms, signal processing, sparse matrix handling, computational geometry, and statistics. In this work, we provide an overview of the capabilities and development practices of the SciPy library and highlight some recent technical developments.

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SciPy 1.0--Fundamental Algorithms for Scientific Computing in Python

Array programming provides a powerful, compact and expressive syntax for accessing, manipulating and operating on data in vectors, matrices and higher-dimensional arrays. NumPy is the primary array programming library for the Python language. It has an essential role in research analysis pipelines in fields as diverse as physics, chemistry, astronomy, geoscience, biology, psychology, materials science, engineering, finance and economics. For example, in astronomy, NumPy was an important part of the software stack used in the discovery of gravitational waves1 and in the first imaging of a black hole2. Here we review how a few fundamental array concepts lead to a simple and powerful programming paradigm for organizing, exploring and analysing scientific data. NumPy is the foundation upon which the scientific Python ecosystem is constructed. It is so pervasive that several projects, targeting audiences with specialized needs, have developed their own NumPy-like interfaces and array objects. Owing to its central position in the ecosystem, NumPy increasingly acts as an interoperability layer between such array computation libraries and, together with its application programming interface (API), provides a flexible framework to support the next decade of scientific and industrial analysis. NumPy is the primary array programming library for Python; here its fundamental concepts are reviewed and its evolution into a flexible interoperability layer between increasingly specialized computational libraries is discussed.

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Array programming with NumPy

SciPy is an open-source scientific computing library for the Python programming language. Since its initial release in 2001, SciPy has become a de facto standard for leveraging scientific algorithms in Python, with over 600 unique code contributors, thousands of dependent packages, over 100,000 dependent repositories and millions of downloads per year. In this work, we provide an overview of the capabilities and development practices of SciPy 1.0 and highlight some recent technical developments.

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SciPy 1.0: fundamental algorithms for scientific computing in Python.

The status of experimental tests of general relativity and of theoretical frameworks for analyzing them is reviewed and updated. Einstein’s equivalence principle (EEP) is well supported by experiments such as the Eotvos experiment, tests of local Lorentz invariance and clock experiments. Ongoing tests of EEP and of the inverse square law are searching for new interactions arising from unification or quantum gravity. Tests of general relativity at the post-Newtonian level have reached high precision, including the light deflection, the Shapiro time delay, the perihelion advance of Mercury, the Nordtvedt effect in lunar motion, and frame-dragging. Gravitational wave damping has been detected in an amount that agrees with general relativity to better than half a percent using the Hulse-Taylor binary pulsar, and a growing family of other binary pulsar systems is yielding new tests, especially of strong-field effects. Current and future tests of relativity will center on strong gravity and gravitational waves.

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The Confrontation Between General Relativity and Experiment

Many physically motivated extensions to general relativity (GR) predict significant deviations at energies present in massive neutron stars. We report the measurement of a 2.01 $\pm $ 0.04 solar mass (M$_\odot $) pulsar in a 2.46-h orbit around a 0.172 $\pm $ 0.003 M$_\odot $ white dwarf. The high pulsar mass and the compact orbit make this system a sensitive laboratory of a previously untested strong-field gravity regime. Thus far, the observed orbital decay agrees with GR, supporting its validity even for the extreme conditions present in the system. The resulting constraints on deviations support the use of GR-based templates for ground-based gravitational wave detection experiments. Additionally, the system strengthens recent constraints on the properties of dense matter and provides novel insight to binary stellar astrophysics and pulsar recycling.

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A massive pulsar in a compact relativistic binary

The soft gamma-ray repeater (SGR) 1806-20 is associated with the center-brightened nonthermal nebula Gl0.0-0.3, thought to be a plerion. As in other plerions, a steady X-ray source, AX 1805.7-2025, has been detected coincident with the peak of the nebular radio emission. Vasisht et al. have shown that the radio peak has a core-jet appearance and argue that the core marks the true position of the SGR. At optical wavelengths, we detect three objects in the vicinity of the radio core. Only for the star closest to the core, barely visible in the optical but bright in the infrared (K = 8.4 mag), the reddening is consistent with the high extinction (A_v≃30 mag) that has been inferred for AX 1805.7-2025. From the absence of CO band absorption, we infer that the spectral type of this star is earlier than late-G/early-K. The large extinction probably arises in a molecular cloud located at a distance of 6 kpc, which means that the star, just like AX 1805. 7 - 2025, is in or behind this cloud. This implies that the star is a supergiant. Since supergiants are rare, a chance coincidence with the compact radio core is very unlikely. To our knowledge, there are only three other examples of luminous stars embedded in nonthermal radio nebulae: SS 433, Cir X-1, and G70.7+1.2. Given this and the low coincidence probability, we suggest that the bright star is physically associated with SGR 1806- 20, making it the first stellar identification of a high-energy transient.

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Optical and Infrared Observations of SGR 1806-20

We report on Keck and Hubble Space Telescope observations of the binary millisecond pulsar PSR B1855+09. We detect its white dwarf companion and measure mF555W=25.90+/-0.12 and mF814W=24.19+/-0.11 (Vega system). From the reddening-corrected color, (mF555W-mF814Wp0=1.06+/-0.21, we infer a temperature Teff=4800+/-800 K. The white dwarf mass is known accurately from measurements of the Shapiro delay of the pulsar signal, MC=0.258+0.028-0.016 M middle dot in circle. Hence, given a cooling model, one can use the measured temperature to determine the cooling age. The main uncertainty in the cooling models for such low-mass white dwarfs is the amount of residual nuclear burning, which is set by the thickness of the hydrogen layer surrounding the helium core. From the properties of similar systems, it has been inferred that helium white dwarfs form with thick hydrogen layers, with mass greater, similar3x10-3 M middle dot in circle, which leads to significant additional heating. This is consistent with expectations from simple evolutionary models of the preceding binary evolution. For PSR B1855+09, though, such models lead to a cooling age of approximately 10 Gyr, which is twice the spin-down age of the pulsar. It could be that the spin-down age were incorrect, which would call the standard vacuum dipole braking model into question. For two other pulsar companions, however, ages well over 10 Gyr are inferred, indicating that the problem may lie with the cooling models. There is no age discrepancy for models in which the white dwarfs are formed with thinner hydrogen layers ( less, similar3x10-4 M middle dot in circle).

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The Temperature and Cooling Age of the White Dwarf Companion to the Millisecond Pulsar PSR B1855+09.

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A 1500-MHz survey for pulsars near the Galactic Centre

We present a detailed analysis of time-resolved optical spectra of the ZZ Ceti white dwarf, HS 0507+0434B. Using the wavelength dependence of observed mode amplitudes, we deduce the spherical degree, , of the modes, most of which have . The presence of a large number of combination frequencies (linear sums or differences of the real modes) enabled us not only to test theoretical predictions but also to indirectly infer spherical and azimuthal degrees of real modes that had no observed splittings. In addition to the above, we measure line-of-sight velocities from our spectra. We find only marginal evidence for periodic modulation associated with the pulsation modes: at the frequency of the strongest mode in the lightcurve, we measure an amplitude of km s -1, which has a probability of 2% of being due to chance; for the other modes, we find lower values. Our velocity amplitudes and upper limits are smaller by a factor of two compared to the amplitudes found in ZZ Psc. We find that this is consistent with expectations based on the position of HS 0507+0434B in the instability strip. Combining all the available information from data such as ours is a first step towards constraining atmospheric properties in a convectionally unstable environment from an observational perspective. (Less)

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Time-resolved optical spectroscopy of the pulsating DA white dwarf HS 0507+0434B : New constraints on mode identification and pulsation properties

We report on Keck and {\em Hubble Space Telescope} observations of the binary millisecond pulsar PSR B1855+09. We detect its white-dwarf companion and measure $\mv=25.90\pm0.12$ and $\mi=24.19\pm0.11$ (Vega system). From the reddening-corrected color, $(\mv-\mi)_0=1.06\pm0.21$, we infer a temperature $\Teff=4800\pm800 $K. The white-dwarf mass is known accurately from measurements of the Shapiro delay of the pulsar signal, $\Mcomp=0.258^{+0.028}_{-0.016} \Msun$. Hence, given a cooling model, one can use the measured temperature to determine the cooling age. The main uncertainty in the cooling models for such low-mass white dwarfs is the amount of residual nuclear burning, which is set by the thickness of the hydrogen layer surrounding the helium core. From the properties of similar systems, it has been inferred that helium white dwarfs form with thick hydrogen layers, with mass $\simgt3\times10^{-3} \Msun$, which leads to significant additional heating. This is consistent with expectations from simple evolutionary models of the preceding binary evolution. For PSR B1855+09, though, such models lead to a cooling age of $\sim10 $Gyr, which is twice the spin-down age of the pulsar. It could be that the spin-down age were incorrect, which would call the standard vacuum dipole braking model into question. For two other pulsar companions, however, ages well over 10 Gyr are inferred, indicating that the problem may lie with the cooling models. There is no age discrepancy for models in which the white dwarfs are formed with thinner hydrogen layers ($\simlt3\times10^{-4} \Msun$).

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M. H. van Kerkwijk

Papers

Optical and Infrared Observations of SGR 1806-20

The Temperature and Cooling Age of the White Dwarf Companion to the Millisecond Pulsar PSR B1855+09.

A 1500-MHz survey for pulsars near the Galactic Centre

Time-resolved optical spectroscopy of the pulsating DA white dwarf HS 0507+0434B : New constraints on mode identification and pulsation properties

The Temperature and Cooling Age of the White-Dwarf Companion to the Millisecond Pulsar PSR B1855+09