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Livermore Loops
Livermore loops (also known as the Livermore Fortran kernels or LFK) is a benchmark for parallel computers. It was created by Francis H. McMahon from scientific source code run on computers at Lawrence Livermore National Laboratory. It consists of 24 do loops, some of which can be vectorized, and some of which cannot. The benchmark was published in 1986 in ''Livermore fortran kernels: A computer test of numerical performance range''. The Livermore loops were originally written in Fortran, but have since been ported to many programming languages. Each loop carries out a different mathematical kernel . Those kernelsXingfu Wu. Performance Evaluation, Prediction and Visualization of Parallel Systems. Springer, 1999. {{ISBN, 0-7923-8462-8. Page 144. are: * hydrodynamics fragment * incomplete Cholesky conjugate gradient * inner product * banded linear systems solution * tridiagonal linear systems solution * general linear recurrence equations * equation of state fragment * alterna ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Benchmark (computing)
In computing, a benchmark is the act of running a computer program, a set of programs, or other operations, in order to assess the relative Computer performance, performance of an object, normally by running a number of standard Software performance testing, tests and trials against it. The term ''benchmark'' is also commonly utilized for the purposes of elaborately designed benchmarking programs themselves. Benchmarking is usually associated with assessing performance characteristics of computer hardware, for example, the floating point operation performance of a Central processing unit, CPU, but there are circumstances when the technique is also applicable to software. Software benchmarks are, for example, run against compilers or database management systems (DBMS). Benchmarks provide a method of comparing the performance of various subsystems across different chip/system Computer architecture, architectures. Purpose As computer architecture advanced, it became more diffi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Equation Of State
In physics, chemistry, and thermodynamics, an equation of state is a thermodynamic equation relating state variables, which describe the state of matter under a given set of physical conditions, such as pressure, volume, temperature, or internal energy. Most modern equations of state are formulated in the Helmholtz free energy. Equations of state are useful in describing the properties of pure substances and mixtures in liquids, gases, and solid states as well as the state of matter in the interior of stars. Overview At present, there is no single equation of state that accurately predicts the properties of all substances under all conditions. An example of an equation of state correlates densities of gases and liquids to temperatures and pressures, known as the ideal gas law, which is roughly accurate for weakly polar gases at low pressures and moderate temperatures. This equation becomes increasingly inaccurate at higher pressures and lower temperatures, and fails to predict ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Planckian Distribution
In physics, Planck's law describes the spectral density of electromagnetic radiation emitted by a black body in thermal equilibrium at a given temperature , when there is no net flow of matter or energy between the body and its environment. At the end of the 19th century, physicists were unable to explain why the observed spectrum of black-body radiation, which by then had been accurately measured, diverged significantly at higher frequencies from that predicted by existing theories. In 1900, German physicist Max Planck heuristically derived a formula for the observed spectrum by assuming that a hypothetical electrically charged oscillator in a cavity that contained black-body radiation could only change its energy in a minimal increment, , that was proportional to the frequency of its associated electromagnetic wave. This resolved the problem of the ultraviolet catastrophe predicted by classical physics. This discovery was a pioneering insight of modern physics and is of fundam ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Conditional Computation
Conditional (if then) may refer to: *Causal conditional, if X then Y, where X is a cause of Y *Conditional probability, the probability of an event A given that another event B has occurred *Conditional proof, in logic: a proof that asserts a conditional, and proves that the antecedent leads to the consequent *Strict conditional, in philosophy, logic, and mathematics *Material conditional, in propositional calculus, or logical calculus in mathematics * Relevance conditional, in relevance logic *Conditional (computer programming), a statement or expression in computer programming languages *A conditional expression in computer programming languages such as ?: *Conditions in a contract Grammar and linguistics *Conditional mood (or conditional tense), a verb form in many languages *Conditional sentence, a sentence type used to refer to hypothetical situations and their consequences **Indicative conditional, a conditional sentence expressing "if A then B" in a natural language **Cou ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Monte Carlo Method
Monte Carlo methods, or Monte Carlo experiments, are a broad class of computational algorithms that rely on repeated random sampling to obtain numerical results. The underlying concept is to use randomness to solve problems that might be deterministic in principle. They are often used in physical and mathematical problems and are most useful when it is difficult or impossible to use other approaches. Monte Carlo methods are mainly used in three problem classes: optimization, numerical integration, and generating draws from a probability distribution. In physics-related problems, Monte Carlo methods are useful for simulating systems with many coupled degrees of freedom, such as fluids, disordered materials, strongly coupled solids, and cellular structures (see cellular Potts model, interacting particle systems, McKean–Vlasov processes, kinetic models of gases). Other examples include modeling phenomena with significant uncertainty in inputs such as the calculation of ris ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Difference Operator
In mathematics, a recurrence relation is an equation according to which the nth term of a sequence of numbers is equal to some combination of the previous terms. Often, only k previous terms of the sequence appear in the equation, for a parameter k that is independent of n; this number k is called the ''order'' of the relation. If the values of the first k numbers in the sequence have been given, the rest of the sequence can be calculated by repeatedly applying the equation. In ''linear recurrences'', the th term is equated to a linear function of the k previous terms. A famous example is the recurrence for the Fibonacci numbers, F_n=F_+F_ where the order k is two and the linear function merely adds the two previous terms. This example is a linear recurrence with constant coefficients, because the coefficients of the linear function (1 and 1) are constants that do not depend on n. For these recurrences, one can express the general term of the sequence as a closed-form expression of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Difference Predictor
Difference, The Difference, Differences or Differently may refer to: Music * ''Difference'' (album), by Dreamtale, 2005 * ''Differently'' (album), by Cassie Davis, 2009 ** "Differently" (song), by Cassie Davis, 2009 * ''The Difference'' (album), Pendleton, 2008 * "The Difference" (The Wallflowers song), 1997 * "The Difference", a song by Westlife from the 2009 album ''Where We Are'' * "The Difference", a song by Nick Jonas from the 2016 album ''Last Year Was Complicated'' * "The Difference", a song by Meek Mill featuring Quavo, from the 2016 mixtape '' DC4'' * "The Difference", a song by Matchbox Twenty from the 2002 album ''More Than You Think You Are'' * "The Difference", a 2020 song by Flume featuring Toro y Moi * "The Difference", a 2022 song by Ni/Co which represented Alabama in the ''American Song Contest'' * "Differences" (song), by Ginuwine, 2001 Science and mathematics * Difference (mathematics), the result of a subtraction * Difference equation, a type of recurr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Integrate Predictor
Integration may refer to: Biology *Multisensory integration *Path integration * Pre-integration complex, viral genetic material used to insert a viral genome into a host genome *DNA integration, by means of site-specific recombinase technology, performed by a specific class of recombinase enzymes ("integrases") Economics and law *Economic integration, trade unification between different states *Horizontal integration and vertical integration, in microeconomics and strategic management, styles of ownership and control *Regional integration, in which states cooperate through regional institutions and rules *Integration clause, a declaration that a contract is the final and complete understanding of the parties *A step in the process of money laundering *Integrated farming, a farm management system * Integration (tax), a feature of corporate and personal income tax in some countries Engineering *Data integration * Digital integration *Enterprise integration *Integrated architec ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Implicit Integration
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Implicit may refer to: Mathematics * Implicit function * Implicit function theorem * Implicit curve * Implicit surface * Implicit differential equation Other uses * Implicit assumption, in logic * Implicit-association test, in social psychology * Implicit bit, in floating-point arithmetic * Implicit learning, in learning psychology * Implicit memory, in long-term human memory * Implicit solvation, in computational chemistry * Implicit stereotype (implicit bias), in social identity theory * Implicit type conversion, in computing See also * Implicit and explicit atheism, types of atheism coined by George H. Smith * Implication (other) * Implicature In pragmatics, a subdiscipline of linguistics, an implicature is something the speaker suggests or implies with an utterance, even though it is not literally expressed. Implicatures can aid in communicating more efficiently than by explicitly sayi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Linear Recurrence
In mathematics (including combinatorics, linear algebra, and dynamical systems), a linear recurrence with constant coefficients (also known as a linear recurrence relation or linear difference equation) sets equal to 0 a polynomial that is linear in the various iterates of a variable—that is, in the values of the elements of a sequence. The polynomial's linearity means that each of its terms has degree 0 or 1. A linear recurrence denotes the evolution of some variable over time, with the current time period or discrete moment in time denoted as , one period earlier denoted as , one period later as , etc. The ''solution'' of such an equation is a function of , and not of any iterate values, giving the value of the iterate at any time. To find the solution it is necessary to know the specific values (known as ''initial conditions'') of of the iterates, and normally these are the iterates that are oldest. The equation or its variable is said to be ''stable'' if from any set of ini ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
