Nonnegative

Given a nonnegative integer n, return the nth Lucas number. Return an error message if the argument is not an integer.

For fixed integers a and b such that D = a^2 + 4*b is nonnegative, the sequence V_n = GeneralizedLucas(n,a,b) satisfies the recurrenceV_n = V_{n-1} + V_{n-2} and the initial conditions V_0 = 2 and V_1 = a. When a=b=1, this is the Lucas sequence.

This m-file gives the expansion of powers of sums of any real or complex numbers x and y, and any nonnegative integer n. It is also known as the Newton's binomial. From it emerges the discrete binomial (positive) distribution.Syntax: function bintheor(x,y,n) Input:x,y - pair of interested terms...


Platforms: Matlab

Solves the linear least squares problem with nonnegative variables using the newton's algorithm in:Portugal, Judice and Vicente, A comparison of block pivoting and interior point algorithms for linear least squares problems with nonnegative variables, Mathematics of Computation, 63(1994), pp....


Platforms: Matlab

Solves the linear least squares problem with nonnegative variables using the predictor-corrector algorithm in:Portugal, Judice and Vicente, A comparison of block pivoting and interior point algorithms for linear least squares problems with nonnegative variables, Mathematics of Computation,...


Platforms: Matlab

Given a nonnegative integer n, tau(n) is the Ramanujan tau function of n, defined as the coefficient of x^n in the Taylor expansion ofx * prod_{k>=0}(1 - x^k)^24. This is an integer function with fascinating number theoretic properties. For instance, it's multiplicative, meaning tau(m*n) =...


Platforms: Matlab

NMath Stats is a .NET statistics library that provides functions for statistical computation and biostatistics, including descriptive statistics, probability distributions, combinatorial functions, multiple linear regression, hypothesis testing, analysis of variance, multivariate statistics,...


Platforms: Windows

Consider the digraph with N vertices and M arcsN Vertices of the graph is expressed by the numbers 1,d-deTZ,N.Given the capacities of arcs, the demand functions of vertices and the cost functions of the arcs, then define the flow network of the given flow network.This function computes the...


Platforms: Matlab

I need to thank Duane Hanselman for suggesting this great idea.Fminspleas is a simple nonlinear least squares tool that fits regression models of the formY = a1*f1(X,C) + a2*f2(X,C) + ... + an*fn(X,C)X can be any array, so it works on multidimensionalproblems, and C is the set of only...


Platforms: Matlab

Matlab Toolbox for Submodular Function Optimization (v 2.0)By Andreas Krause (krausea@gmail.com).Slides, videos and detailed references available at http://www.submodularity.orgTested in MATLAB 7.0.1 (R14), 7.2.0 (R2006a), 7.4.0 (R2007a, MAC), 7.9.0 (MAC)This toolbox provides functions for...


Platforms: Matlab

LaguerreGen calculates the generalized Laguerre polynomial L{n, alpha}This function computes the generalized Laguerre polynomial L{n,alpha}.If no alpha is supplied, alpha is set to zero and this function calculates the "normal" Laguerre polynomial.Input: - n = nonnegative integer as degree level...


Platforms: Matlab

R = RCR(S) computes the semi-edge-length of the mean-centered hypercube with 95% probability given S, which is either a covariance matrix or a vector of standard deviations from a multivariate normal distribution. If S is a real, nonnegative vector, RCR(S) is equivalent to RCR(DIAG(S.^2)). Scalar...


Platforms: Matlab

This function uses rectangle command to plot a circle. The center is to be given in a vector form and radius is a non-negative number.


Platforms: Matlab

Henze and Zirkler (1990) introduce a multivariate version of the univariate There are many tests for assessing the multivariate normality in the statistical literature (Mecklin and Mundfrom, 2003). Unfortunately, there is no known uniformly most powerful test and it is recommended to perform...


Platforms: Matlab

This m-file returns the multinomial coefficient with parameter N at the values in X. Let {X1, X2, . . . , Xk}, k > 1, be a set of random variables, each of which can take the values 0, 1, . . . , n; such that for every set of k nonnegative integers {n1, . . . , nk} whose sum is n, the multinomial...


Platforms: Matlab

This m-file returns the multinomial probability density function value with parameters N and P at the values in X. Note that the density function is zero unless X is an integer.Let {X1, X2, . . . , Xk}, k > 1, be a set of random variables, each of which can take the values 0, 1, . . . , n....


Platforms: Matlab

The function performs a nonlinear, constrained optimization to find a positive semi-definite matrix that is closest (2-norm) to a symmetric matrix that is not positive semi-definite which the user provides to the function. The optimization is subject to the constraint that the output matrix'...


Platforms: Matlab

To enhance the efficiency and accuracy of Kalman filter computations, in particular the time and measurement updates, UDU factorization is employed. An interesting feature of the current implementation is the extension to semi-positive (nonnegative) matrices and systems with a time-varying state...


Platforms: Matlab

UNINIT is very similar to the ZEROS function, except that UNINIT returns an uninitialized array instead of a zero-filled array. Thus, UNINIT is faster than the ZEROS function for large size arrays. Since the return variable is uninitialized, the user must take care to assign values to the...


Platforms: Matlab

ASA solves bound constrained problems; the user provides routines to calculate the function and gradASA (Active-Set Algorithm) is a bound constrained optimization program developed W. W. Hager and H. Zhang. In recent academic tests (e.g. "Evaluating bound-constrained minimization software" by E....


Platforms: Matlab