Jacobian

Complex step differentiation (CSD) has many advantages in efferency and accuracy over finite difference approaches (central, forward and backward). This code demonstrates how the Jacobian matrix of a given function at the reference point can be calculated using the CSD approach. Platforms: Matlab

A wrap of lsqnonlin to calculate Jacobian using symbolic math toolbox. This is one of applications of symbolic math toolbox for optimization. Due to limitations of the symbolic math toolbox, the objective function must be supported by the symbolic math toolbox. Platforms: Matlab

Three M-Files for a small GUI-based demo on the behaviour of the VanDerPol equation, the solution and the eigenvalues of the Jacobian matrix.There is an explanation in the header of the main file vdpeig.mTested under MATLAB 5.x Platforms: Matlab

Lyapunov exponent calcullation for ODE-system. The alogrithm employed in this m-file for determining Lyapunov exponents was proposed in A. Wolf, J. B. Swift, H. L. Swinney, and J. A. Vastano, "Determining Lyapunov Exponents from a Time Series," Physica D, Vol. 16, pp. 285-317, 1985.For... Platforms: Matlab

Usage: Newton(@funfcn,X0[,Options[,Params]); funfcn is a function script with the following interface: function F = function(X) % ... or a string containing the code as shown below, were F is the vector of the functions, and X the vector of the unknowns which must have the same length. A guess... Platforms: Matlab

Newton's method for solving a system of nonlinear equations, see http://en.wikipedia.org/wiki/Newton's_methodNewton(X,F,X0) solves nonlinear system F(x)=0 by Newton's method, using the given initial approximation X0. The derivative (Jacobian) is evaluated symbolically. The iterations are... Platforms: Matlab

The function LMFsolve.m serves for finding optimal solution of an overdetermined system of nonlinear equations in the least-squares sense. The standard Levenberg- Marquardt algorithm was modified by Fletcher and coded in FORTRAN many years ago. LMFsolve is its essentially shortened version... Platforms: Matlab

It estimates the Newton Raphson optimization procedure for (m) unknowns of (n) non-linear equations. In case no Jacobian vector is presented, then the initial Jacobian vector is estimated by Broyden Method (multivariate secant approach) and it is then updated using the Sherman Morrison... Platforms: Matlab

The function The LMFnlsq.m serves for finding optimal solution of an overdetermined system of nonlinear equations in the least-squares sense. The standard Levenberg- Marquardt algorithm was modified by Fletcher and coded in FORTRAN many years ago (see the Reference). This version of LMFnlsq is... Platforms: Matlab

Extracts the edges of a color image without converting it to grayscale.Changes in color are detected even when the grayscale color of two pixels are the same. The edge strength is typically greater or equal to the magnitude obtained by simply filtering a grayscale image.Optionally, the edge... Platforms: Matlab

Two Econometrics Toolbox functions, lmtest and waldtest, require you to give derivative estimates or covariance estimates as inputs. How are you supposed to calculate those inputs? This demo shows how to calculate them using the Symbolic Math Toolbox jacobian function for gradients and... Platforms: Matlab

Smale horseshoes, curvilinear rectangles and their U-shaped images patterned onSmaled-deOaos famous example, provide a rigorous way to study chaos in dynamicalsystems. This program is written according to the algorithm proposed in thepaper, which has submitted to DDSN d-deDUAn algorithm to... Platforms: Matlab

Two simple models are provided showing the characteristics of basic iterative algorithms for the inversion of kinematics, namely the Jacobian transpose, its pseudo-inverse and the damped least-squares (DLS). The pro's and con's can be compared interactively for a serial two-links and a... Platforms: Matlab

Nonlinear state estimation is a challenge problem. The well-known Kalman Filter is only suitable for linear systems. The Extended Kalman Filter (EKF) has become a standarded formulation for nonlinear state estimation. However, it may cause significant error for highly nonlinear systems because of... Platforms: Matlab

This graphical tutorial is intended to help neuro-imaging researchers from non-mathematical backgrounds to understand the so-called "modulation" process in voxel-based morphometry. This preserves volume (locally and globally) in spatially normalised (warped) images by multiplying the original... Platforms: Matlab

Affine and B-spline grid based registration and data-fitting of two 2D color/grayscale images or 3D volumes or point-data. Registration can be done intensity / pixel based, or landmark / corresponding points based (See OpenSurf), or a combination.Description Pixel-based registration:This function... Platforms: PHP