Search NASA⌕ Search

SEARCH · Search NASA

Results for “LINEAR TRANSFORMATION”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 19 records
All sourcesNASA NTRSDOE OSTI
NASA NTRS1977

Computations and applications of linear hypergeometric transformations

Linear transformations are well-known in the theory of hypergeometric functions. In this note, it is indicated, both by analyses and by supporting numerical experiments, how these transformations can be applied to the computation of Legendre's functions, the incomplete Beta function, and the variance-ratio probability distribution function. It is shown that a simple transformation can in many cases cause dramatic improvement in computation.

Ng, E. W.↗
DOE OSTI2025

Spatially Aware Linear Transformer (SAL-T) for Particle Jet Tagging

Transformers are very effective in capturing both global and local correlations within high-energy particle collisions, but they present deployment challenges in high-data-throughput environments, such as the CERN LHC. The quadratic complexity of transformer models demands substantial resources and increases latency during inference. In order to address these issues, we introduce the Spatially Aware Linear Transformer (SAL-T), a physics-inspired enhancement of the linformer architecture that maintains linear attention. Our method incorporates spatially aware partitioning of particles based on kinematic features, thereby computing attention between regions of physical significance. Additionally, we employ convolutional layers to capture local correlations, informed by insights from jet physics. In addition to outperforming the standard linformer in jet classification tasks, SAL-T also achieves classification results comparable to full-attention transformers, while using considerably fewer resources with lower latency during inference. Experiments on a generic point cloud classification dataset (ModelNet10) further confirm this trend. Our code is available at https://github.com/aaronw5/SAL-T4HEP.

Wang, Aaron [Illinois U., Chicago] (ORCID:00000003↗
NASA NTRS2017

Linear Transformer Drivers for Z-pinch Based Propulsion

The MSFC/UAH team has been developing of a novel power management and distribution system called a Linear Transformer Driver (LTD). LTD's hold the promise of dramatically reducing the required mass to drive a z-pinch by replacing the capacitor banks which constitute half the mass of the entire system. The MSFC?UAH tea, is developing this technology in hope of integrating it with the Pulsed Fission Fusion (PuFF) propulsion concept. High-Voltage pulsed power systems used for Z-Pinch experimentation have in the past largely been based on Marx Generators. Marx generators deliver the voltage and current required for the Z-Pinch, but suffer from two significant drawbacks when applied to a flight system: they are very massive, consisting of high-voltage capacitor banks insulated in oil-filled tanks and they do not lend themselves to rapid pulsing. The overall goal of Phase 2 is to demonstrate the construction of a higher voltage stack from a number of cavities each of the design proven in Phase 1 and to characterize and understand the techniques for designing the stack. The overall goal of Phase 3 is to demonstrate the feasibility of constructing a higher energy cavity from a number of smaller LTD stacks, to characterize and understand the way in which the constituent stacks combine, and to extend this demonstration LTD to serve as the basis for a 64 kJ pulse generator for Z-Pinch experiments.

Adams, Robert↗
NASA NTRS1985

Evaluation of the Radiometric Quality of the TM Data Using Clustering, Linear Transformations and Multispectral Distance Measures

The radiometric quality of LANDSAT 4 TM data for the classification and identification of Earth surface features was evaluated. Techniques employed in the evaluation included clustering, data compression (linear transformations), multispectral distance measures, and hierarchical classification methods. TM and MSS data for the Chicago, Illinois test site were studied. In order to determine the radiometric quality of the TM thermal data for temperature mapping of surface water, a test site was selected within the area covered by the TM scene (Scene ID: 40101-16025) gathered over Illinois. This site was chosen because it includes a surface water body with a large range of temperatures, i.e., a cooling pond for the Dresden nuclear power plant and the junction of two rivers.

Bartolucci, L. A.↗
NASA NTRS1991

Application and flight test of linearizing transformations using measurement feedback to the nonlinear control problem

The design of nonlinear controllers has relied on the use of detailed aerodynamic and engine models that must be associated with the control law in the flight system implementation. Many of these controllers were applied to vehicle flight path control problems and have attempted to combine both inner- and outer-loop control functions in a single controller. An approach to the nonlinear trajectory control problem is presented. This approach uses linearizing transformations with measurement feedback to eliminate the need for detailed aircraft models in outer-loop control applications. By applying this approach and separating the inner-loop and outer-loop functions two things were achieved: (1) the need for incorporating detailed aerodynamic models in the controller is obviated; and (2) the controller is more easily incorporated into existing aircraft flight control systems. An implementation of the controller is discussed, and this controller is tested on a six degree-of-freedom F-15 simulation and in flight on an F-15 aircraft. Simulation data are presented which validates this approach over a large portion of the F-15 flight envelope. Proof of this concept is provided by flight-test data that closely matches simulation results. Flight-test data are also presented.

Antoniewicz, Robert F.↗
NASA NTRS1990

Flight test of a trajectory controller using linearizing transformations with measurement feedback

The design of nonlinear controllers has relied on the use of detailed aerodynamic and engine models that must be associated with the control law in the flight system implementation. Many of these controllers have been applied to vehicle flightpath control problems and have attempted to combine both inner- and outer-loop control functions in a single controller. This paper presents an alternate approach to the design of outer-loop controllers. The approach simplifies the outer-loop design problem by separating the inner-loop (stabilization and control) from the outer-loop (guidance and navigation) functions. Linearizing transformations are applied using measurement feedback to eliminate the need for detailed aircraft models in outer-loop control applications. Also discussed is an implementation of the controller. This implementation was tested on a six-degree-of-freedom F-15 simulation and in flight on an F-15 aircraft. Proof of the concept is provided by flight test data which is presented and discussed.

Antoniewicz, Robert F.↗
NASA NTRS2010

Optical See-Through Head Mounted Display Direct Linear Transformation Calibration Robustness in the Presence of User Alignment Noise

Augmented Reality (AR) is a technique by which computer generated signals synthesize impressions that are made to coexist with the surrounding real world as perceived by the user. Human smell, taste, touch and hearing can all be augmented, but most commonly AR refers to the human vision being overlaid with information otherwise not readily available to the user. A correct calibration is important on an application level, ensuring that e.g. data labels are presented at correct locations, but also on a system level to enable display techniques such as stereoscopy to function properly [SOURCE]. Thus, vital to AR, calibration methodology is an important research area. While great achievements already have been made, there are some properties in current calibration methods for augmenting vision which do not translate from its traditional use in automated cameras calibration to its use with a human operator. This paper uses a Monte Carlo simulation of a standard direct linear transformation camera calibration to investigate how user introduced head orientation noise affects the parameter estimation during a calibration procedure of an optical see-through head mounted display.

Axholt, Magnus↗
NASA NTRS1982

Design of a helicopter autopilot by means of linearizing transformations

An automatic flight control systems design methods for aircraft that have complex characteristics and operational requirements, such as the powered lift STOL and V/STOL configurations are discussed. The method is effective for a large class of dynamic systems that require multiaxis control and that have highly coupled nonlinearities, redundant controls, and complex multidimensional operational envelopes. The method exploits the possibility of linearizing the system over its operational envelope by transforming the state and control. The linear canonical forms used in the design are described, and necessary and sufficient conditions for linearizability are stated. The control logic has the structure of an exact model follower with linear decoupled model dynamics and possibly nonlinear plant dynamics. The design method is illustrated with an application to a helicopter autopilot design.

Meyer, G.↗
DOE OSTI2026

Laplace Transform–Based Quantum Eigenvalue Transformation via Linear Combination of Hamiltonian Simulation

Eigenvalue transformations, which include solving time-dependent differential equations as a special case, have a wide range of applications in scientific and engineering computation. While quantum algorithms for singular value transformations are well studied, eigenvalue transformations are distinct, especially for nonnormal matrices. Here, we propose an efficient quantum algorithm for performing a class of eigenvalue transformations that can be expressed as a certain type of matrix Laplace transformation. This allows us to significantly extend the recently developed linear combination of Hamiltonian simulation method [D. An, J.-P. Liu, and L. Lin, Phys. Rev. Lett., 131 (2023), 150603; D. An, A. M. Childs, and L. Lin, Commun. Math. Phys. 407, 19 (2026)] to represent a wider class of eigenvalue transformations, such as powers of the matrix inverse, 𝐴 −𝑘 , and the exponential of the matrix inverse, 𝑒 −𝐴 −1 . The latter can be interpreted as the solution of a mass-matrix differential equation of the form form 𝐴⁢𝑢′⁡⁡(𝑡) =−𝑢⁡(𝑡). We demonstrate that our eigenvalue transformation approach can solve this problem without explicitly inverting 𝐴, thereby reducing the computational complexity.

Laplace transform↗
NASA NTRS1988

Linear canonical transformations of coherent and squeezed states in the Wigner phase space

It is shown that classical linear canonical transformations are possible in the Wigner phase space. Coherent and squeezed states are shown to be linear canonical transforms of the ground-state harmonic oscillator. It is therefore possible to evaluate the Wigner functions for coherent and squeezed states from that for the harmonic oscillator. Since the group of linear canonical transformations has a subgroup whose algebraic property is the same as that of the (2+1)-dimensional Lorentz group, it may be possible to test certain properties of the Lorentz group using optical devices. A possible experiment to measure the Wigner rotation angle is discussed.

Han, D.↗