GRASS GIS: A multi-purpose open source GIS

Abstract

a b s t r a c tLet f be a univariate polynomial with real coefficients, f ∈ R[X ].Subdivision algorithms based on algebraic techniques (e.g., Sturm or Descartes methods) are widely used for isolating the real roots of f in a given interval. In this paper, we consider a simple subdivision algorithm whose primitives are purely numerical (e.g., function evaluation). The complexity of this algorithm is adaptive because the algorithm makes decisions based on local data. The complexity analysis of adaptive algorithms (and this algorithm in particular) is a new challenge for computer science. In this paper, we compute the size of the subdivision tree for the SqFreeEVAL algorithm.The SqFreeEVAL algorithm is an evaluation-based numerical algorithm which is well-known in several communities. The algorithm itself is simple, but prior attempts to compute its complexity have proven to be quite technical and have yielded sub-optimal results. Our main result is a simple O(d (L +ln d)) bound on the size of the subdivision tree for the SqFreeEVAL algorithm on the benchmark problem of isolating all real roots of an integer polynomial f of degree d and whose coefficients can be written with at most L bits. Our proof uses two amortization-based techniques: first, we use the algebraic amortization technique of the standard Mahler-Davenport root bounds to interpret the integral in terms of d and L. Second, we use a continuous amortization technique based on an integral to bound the size of the subdivision tree. This paper is the first to use the novel analysis technique of continuous amortization to derive state of the art complexity bounds.

Surface Temperatures at the Continental Scale: Tracking Changes with Remote Sensing at Unprecedented Detail

“…Therefore, we automated the complete workflow to process the dataset parallelized on our HPC system. All calculations were done in GRASS GIS version 7 [30], with the exception of the initial MODIS LST mosaicking and reprojection, which was done with the MODIS Reprojection Tool (MRT 4.1, https://lpdaac.usgs.gov/tools/modis_reprojection_tool) using pyMODIS as the download library (http://pymodis.fem-environment.eu/). Since common statistical software is not able to process the six input grids (LST, altitude, solar angle, two principal components, ocean mask) with about 400 million grid cells each, we used a pure GIS environment optimized for handling large spatial datasets in the billions of pixel range.…”

Overland Flow Analysis Using Time Series of Suas-Derived Elevation Models

“…Overland flow was then simulated for a given design storm using path sampling method for solution of bivariate shallow water flow equations. The processing of sUAS imagery was performed in PhotoScan Professional by Agisoft (Agisoft, 2013), computation of DSMs and flow analysis was carried out using GRASS GIS (Neteler et al, 2012).…”

Dynamic Data Driven Ensemble for Wildfire Behaviour Assessment: A Case Study

“…FireSim is a deterministic parametric and discrete event type simulator structured as a sequential set of D-TMs with a pipeline structure of four stages. -The second simulator is implemented in GRASS GIS [50]. The spread function is based on the least cost path algorithm and simulates the elliptically anisotropic spread.…”