Error function of complex numbers

Extend the error function to the complex plane.

. ERFZ enhances ERF to evaluate the error function of complex numbers too. If called with real numbers, it is identical to ERF and equally fast. ERFZ can replace ERF if no error message is required when

Faddeeva Package: complex error functions

C++ MEX plugins to compute error functions (erf, erfc, erfi, erfcx, Faddeeva, ...) of complex args

| [similar to G. P. M. Poppe and C. M. J. Wijers, "More efficient computation of the complex error function," ACM Trans. Math. Soft. 16 (1), pp. 38–46 (1990)], and a completely different algorithm for smaller

Computing of Voigt/complex error function with small y

This program file is presented for highly accurate approximation of the Voigt/complex error function with small imaginary argument y ≤ 0.1.

[Kxy,Lxy]=cedawSeu(x,y).This program file computes the complex error function with small imaginary argument 0≤y≤ 0.1. In the real and imaginary parts this program provides average accuracy exceeding

Complex Erf (Error Function), Fresnel Integrals

complex erf function

This file is similar to the built-in MATLAB erf function, but accepts complex arguments. An included application example uses erf_ to compute the Fresnel integral functions and plot a Cornu spiral

The Voigt/complex error function (second version)

The function file fadf.m computes the Voigt/complex error function with high accuracy

This program file computes the complex error function, also known as the Faddeeva function. The algorithmic implementation utilizes the approximations based on the Fourier expansion [1, 2] and the

Complex scaled complementary error function

Function computes the complex scaled complementary error function.

Matlab provides the function erfcx which computes a scaled error function. However, the input argument must be real. This function computes the values of the Fadeeva function for complex inputs. Note

Deconvolution Mordenite Zeolite

The program deconvolutes IR spectra of mordenites

maximum intensity of 1, defined width and position- complexErrorFunction.m and complexErrorFunction.m calculate comples error function and Voigt profile as kindly provided by Dr. F. Schreier. See doi

The Voigt/complex error function by vectorized interpolation

Program-shell that accelerates computation of the Voigt and complex error functions for the HITRAN applications.

This function file computes the Voigt and complex error functions (also known as the Faddeeva function) in a rapid algorithm by vectorized interpolation. The program is particularly efficient for

A sampling-based algorithm for the Voigt/complex error function

A function file to compute the complex error function with high-accuracy.

This function file computes the complex error function (also known as the Faddeeva function) by using a new method of sampling based on incomplete cosine expansion of the sinc function [1, 2

cxroot - Complex root of complex function

The function solves a problem of complex root of a complex user-defined function.

The function finds a complex root of a complex function FUN by solving a system of two nonlinear real equations real(FUN(x)) = 0; imag(FUN(x)) = 0; of a complex variable x = complex

Phase Plots of Complex Functions

Routines for creating color representations of complex functions (phase plots)

The ZIP-file provides several routines for creating color representations of complex (in particular analytic and meromorphic) functions. Basically the argument (phase) of the function is encoded by a

Complex Function Visualization (amplitude, phase)

Imaging Complex Functions with a color map

This function provides a visualization tool of complex functions and 2D-real vector field.IMAGECF(Z) IMAGECF(Z,Zmax) IMAGECF(X+iY,Z) IMAGECF(X+iY,Z,Zmax) IMAGECF(ax,___) IMAGECF(___, option

Complex Function Explorer

Routines and user interface to depict and explore complex functions using color representations

The submission provides routines for visual exploration of complex (in particular analytic and meromorphic) functions. Basically the function values are color-coded and displayed as images either

erfz

Compute the error function for complex inputs.

Compute the erf or error function for complex inputs. Valid over the entire complex plane.

soapSnake - understanding complex functions

Didactic tool to understand complex functions over the real domain.

function plots any complex function you like: f(x) = exp(ix);f(x) = x.^x;f(x) = log(x);f(x) = sin(i*x);A couple of examples are added in the demo file. NB: It is also possible to show the complex spectrum of

Silly Badger error function

Lighthearted custom error function.

Displays a judgemental badger when your code errors out, and googles the error message for you.When testing code, use try - catch to implement custom error function. For example:%try S = N;catch

Bessel Function of Complex Order and Argument

Bessel function of complex order and argument

As so many people have asked me the C++ code for calculating besel functions of complex order and complex arguemnt, I now submit them to benifit more people ...

Complex Mode Indicator Function (CMIF)

This is a robust complex mode indicator function, which can be used to identify Eigen values. A simple example is provided.

COMPLEX MODE INDICATOR FUNCTION (SINGULAR VALUE DECOMPOSITION)CMIF is defined as the Eigen values solved from the normal matrix, which is formed from frequency response function (FRF) matrix. CMIF

handleError - generic error-handling function

A general-purpose error-handling function with an ability to register automatic cleanup actions

handleError is a general-purpose error-handling function. The user can register cleanup actions that will automatically be activated in case of error. If an error occurred and handleError is called

erfz(z)

erfz(z) returns the error function of complex argument

% erfz(z) returns the error function of complex argument using the method% specificied in Abrahamowitz and Stegun 7.1.29

Error propagation through a function

Calculates the error propagation through a function NEEDS : Symbolic Math Toolbox

function at (IMPORTANT : must be in the same order as the variables in 2))4) A 1*n matrix of the values of the errors of the variables at the point given in 3) (IMPORTANT : must be in the same order as the

Randomness Properties

5 Randomness tests

The following 5 tests are implemented:1. Linear Complexity2. Probability LC Finite3. LC Periodic Infinite4. Topology Binary Test5. K-Error LC FiniteThe help is also provided to explain each test.

Fractional variable order closed loop systems toolbox

The toolbox allows to simulate and tune parameters of closed-loop systems with a fractional-variable-order digital PID (FVOPID) controller.

implementation if necessary.In the future versions of the toolbox the controller blocks implemented as C-MEX S-functions will be added to improve the performance of calculation of FVOPIDs for long simulations or

Adjust error bar width

Adjust error bars width in an errorbar plot to a ratio of the x-axis or a length (x-axis units).

function errorbar_tick(h,w,xtype)ERRORBAR_TICK Adjust the width of errorbarsERRORBAR_TICK(H) adjust the width of error bars with handle H. Error bars width is given as a ratio of X axis lenght

Complex step Jacobian

Calculate Jacobian using complex step differentiation

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

Complex Zeros of Functions

Complex zeros of a function of z=x+i*y are computed using graphics and Muller's method.

plane muller.m - a function based on Muller's method employing quadratic interpolation and deflation to computeone or several roots of a general complex valued functionerfs.m - Error

Complex-step-compatible atan2()

atan2() or arctan2() function that is compatible with complex-step derivative operations.

The function atan2(Y,X) [or arctan2(Y,X)] is the four quadrant arctangent of the elements of X and Y such that -pi <= atan2(Y,X) <= pi.MATLAB atan2() reports an error when inputs are complex

Complex step Hessian

Calculate Hessian using complex step differentiation

Hessian is the second order derivative of a scalar function. It is relatively difficult using finite difference to get accurate Hessian due to the approximation error if the differentiation step is

fastRPCA

Code for Robust PCA

Matlab code for all variants of robust PCA and SPCP

barwitherr(errors,varargin)

This is a very simple extension of MatLab's bar function to add error bars.

Special Functions math library

Collection of Special Functions programs.

A collection of special function programs valid in the entire complex plane. Includes Gamma, loggamma, psi, polygamma, error, zeta, and others.Editor's Note: Please note that these files have the

Taylor series in the complex plane

2D plot of complex functions using color wheel, and animates their Taylor series convergence

Running the code taylor will show you several examples of visualizing functions on the complex plane, and animating their n-term Taylor series as n increased from 1 to say 20. This provides an

Chebfun V4 - old version; please download current version instead

Numerical computation with functions

Old version of Chebfun. To download latest version see www.chebfun.org, www.github.com/chebfun, or the Matlab File Exchange www.mathworks.com/matlabcentral/fileexchange.

lpc frame

This exercise shows how the method of linear predictive coding (LPC) models a speech frame.

This MATLAB exercise computes the log magnitude of the STFT of a specified frame of speech. Then, using the same frame of speech, the exercise computes LPC log spectral matches to the speech frame

p Tube Vocal Tract

This exercise computes the frequency response of a p-tube model of a human vocal tract.

This MATLAB exercise computes and plots the impulse response and the log magnitude spectrum (along with the locations of the formants) for a uniform length p-tube model of the vocal tract by

VUS-Voiced/Unvoiced/Silence_Training

This exercise utilizes four programs to train a Bayesian classifier and classify frames of signals.

delay, 4. first predictor coefficient of p = 12 pole LPC analysis, 5. normalized log prediction error of p = 12 LPC analysis

Complex Method of Optimization

Implements the Complex Method of Constrained Optimization

Implements the Complex Method of Constrained Optimization, as proposed by Box (1965), improved by Guin (1968) and Krus (1992), and following the method in Andresson (2001). This is capable of

Root of complex function

simple routine which search complex root of complex valued function

Let MyFunction(z) to be a complex valued function of the complex argument z.Let z0 to be the initial point from which the search procedure starts.by doing a projection on the hyperspace (a line in

Transfer Function Analysis of Dynamic Systems

Interactive courseware module that introduces transfer function analysis taught in system dynamics and controls courses.

# Transfer Function Analysis of Dynamic Systems[![View on File

erfi function

Imaginary error function (could be complex) using matlab's incomplete gamma function gammainc

Imaginary error function, as it is defined in Mathematica erfi(z)==erf(iz)/i (z could be complex) using the incomplete gamma function in matlab: gammainc

SNR Vs. Probability of Error

The command plots the graph of SNR Versus the Probability of Error using random signal (noise).

This graph represents the error in the transmission process of a communication system.

Monte Carlo Error Propagation

Error propagation method for an arbitrary analytic function with different error types

distributions that a gaussian distribution (e.g. binomial)c) for complex functions the calculation of partial derivatives can be tedious We wrote a simple Monte Carlo based error propagation, which allows to

Standard error of the mean, ignores NaNs

Calculates s.e.m., ignoring NaN values

s.e.m. = std(vector_data)/sqrt(length(vector_data));Given a vector_data, calculates the standard deviation and length of vector_data without taking NaNs into account.

Calculate Complex Hurst

This Matlab example M-file is to calculate the Complex Hurst for Data like Stock Market.

The Complex Hurst is defined on top of Complex Index of Dispersion for Count, which is based on 1.5th, 2nd and 2.5th order center moment, related to Fractal dimension of fractional Brownian motion

Complex ALU

A Simulator of Complex ALU

This is a simulator of Complex ALU. For documentation http://www.dicecca.net/public/unina/Laboratorio_Architettura/

Complex Roots Finder

Computes the n n-th complex roots of a given complex number

This very simple function computes the n n-th roots of a given complex number. The attained complex roots can be plotted on a polar diagram.It is more performante then roots([1, zeros(1,n-1

Suite of functions to perform uniform sampling of a sphere

Toolbox for generating uniform sampling patterns and decompositions of a unit sphere

, andmedical imaging (e.g., HARDI). The purpose of this submission is to provide Matlab users with a set of functions forgenerating uniform sampling patterns and decompositions of a unit sphere.Summary of Main

Computation of Special Functions

MATLAB translation (via f2matlab) of the original FORTRAN of "Computation of Special Functions."

functions.angular spheroidal wave functionsradial spheroidal wave functionserror function.Fresnel Integrals.modified Fresnel integrals.complex zeros of the error function.complex zeros of the Fresnel Integrals.cosine

LRSLibrary

Low-Rank and Sparse Tools for Background Modeling and Subtraction in Videos

error_ellipse

Plot an error ellipse depicting confidence interval given a covariance matrix.

returns a graphics handle% of the ellipse that was drawn.%% ERROR_ELLIPSE(C33) - Given a 3x3 covariance matrix, plot the% associated error ellipsoid, at the origin, as well as its projections

terrorbar.m: Error bars with controlled widths post-R2014b

Draws error bars (as line objects), allowing you to specify the width of the horizontal bars

; h=terrorbar(xvalues,yvalues,lowererrorrbarheight,uppererrorbarheight,errorbarwidth,widthunits);...and sensible variants of this also work (e.g. omitting the uppererrorbarheight gets you symmetric error bars).NB This function doesn't draw a line through the points, nor bars for a bar chart. Use your

Generation of Random Variates

generates random variates from over 870 univariate distributions

This code package provides a framework for generating random samples of univariate distribution functions. It has an Excel database that currently lists over 870 distributions, their parameters as

Complex Polygon Area

Simply routine for calculating area of complex, self-intersecting polygon

points.This method computes the area of a complex shape consistent with the MATLAB 'inpolygon' function.

B-spline Grid, Image and Point based Registration

B-spline registration of two 2D / 3D images or corrsp. points, affine and with smooth b-spline grid.

corresponding points based (See OpenSurf), or a combination.Description Pixel-based registration:This function is an (enhanced) implementation of the b-spline registration algorithm in D. Rueckert et al

raacampbell/shadedErrorBar

Creates an attractive shaded error region rather than discrete bars.

shadedErrorBar shadedErrorBar is a MATLAB function that creates a continuous shaded error region around a line rather than discrete bars.The error region can either be specified explicitly or

Create Healthy Looking Error Bars

Plots nice error bars as the default. Can also top group plots with error bars.

(x,y,'k','linewidth',2); hold on;errorb(x,y,e) group plot:values=abs(rand(2,3))+1; errors=rand(2,3)/1.5+0;errorb(values,errors,'top');% motivation for the functionIt is possible to plot nice error bars on top of a bar

Image Error Measurements

Measures the differences between 2 images, and measurement of image quality.

main executing reference usage: usage_errorMeasurementsOfImages.m-----------------------------------------------------------------------------The objective is to measure the differences between 2

multimodality non-rigid demon algorithm image registration

non-rigid 2D and 3D image registration with demon (fluid) algorithm, extended with modality transf.

This function will perform demon registration which is an type of fast non-rigid fluid like registration between two 2D or 3D images. Registration between different (MRI) modalities is also

Analytical plot of Dielectric function of Lorentz medium

This code plots complex dielectric function of a Lorentz medium using its analytical formula.

Given the resonant frequency, damping term and frequency axis, this code calculates complex dielectric function of a Lorentz medium using its analytical formula given in many elementary

Viewer3D

MIP, Color, Slice and Shaded 3D (shearwarp) Volume Rendering, interactive 3D view/measurement GUI

This function can be used to interactively view any kind of 2D,3D and 4D image volumes like CT and MRI. Allowing segmentation and distance measurements or ROI selection in 2D slices.It includes