Concepts inA differentiation-enabled Fortran 95 compiler
Fortran
Fortran (previously FORTRAN) is a general-purpose, procedural, imperative programming language that is especially suited to numeric computation and scientific computing.
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Compiler
A compiler is a computer program (or set of programs) that transforms source code written in a programming language (the source language) into another computer language (the target language, often having a binary form known as object code). The most common reason for wanting to transform source code is to create an executable program. The name "compiler" is primarily used for programs that translate source code from a high-level programming language to a lower level language.
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Levenberg¿Marquardt algorithm
In mathematics and computing, the Levenberg¿Marquardt algorithm (LMA), also known as the damped least-squares (DLS) method, provides a numerical solution to the problem of minimizing a function, generally nonlinear, over a space of parameters of the function. These minimization problems arise especially in least squares curve fitting and nonlinear programming. The LMA interpolates between the Gauss¿Newton algorithm (GNA) and the method of gradient descent.
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Automatic differentiation
In mathematics and computer algebra, automatic differentiation (AD), sometimes alternatively called algorithmic differentiation, is a set of techniques to numerically evaluate the derivative of a function specified by a computer program. AD exploits the fact that every computer program, no matter how complicated, executes a sequence of elementary arithmetic operations (addition, subtraction, multiplication, division, etc. ) and elementary functions (exp, log, sin, cos, etc.).
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Vector-valued function
A vector-valued function also referred to as a vector function is a mathematical function of one or more variables whose range is a set of multidimensional vectors or infinite-dimensional vectors. The input of a vector-valued function could be a scalar or a vector. The dimension of the domain is not defined by the dimension of the range.
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Jacobian matrix and determinant
In vector calculus, the Jacobian matrix is the matrix of all first-order partial derivatives of a vector- or scalar-valued function with respect to another vector. Suppose F : R ¿ R is a function from Euclidean n-space to Euclidean m-space. Such a function is given by m real-valued component functions, F1(x1,... ,xn), ... , Fm(x1,... ,xn).
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Gradient
In vector calculus, the gradient of a scalar field is a vector field that points in the direction of the greatest rate of increase of the scalar field, and whose magnitude is that rate of increase. A generalization of the gradient for functions on a Euclidean space that have values in another Euclidean space is the Jacobian. A further generalization for a function from one Banach space to another is the Fréchet derivative.
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Algorithmic efficiency
In computer science, efficiency is used to describe properties of an algorithm relating to how much of various types of resources it consumes. Algorithmic efficiency can be thought of as analogous to engineering productivity for a repeating or continuous process, where the goal is to reduce resource consumption, including time to completion, to some acceptable, optimal level.
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