ALGORITHM

SimplexNumerica provides the following algorithms:

 

MATH FUNCTIONS SORT

Sort active Graph by X-SampleData

Sort all Graphs by X-SampleData

Sort active Graph by Y-SampleData

Sort all Graphs by Y-SampleData

Sort active Graph by Z-SampleData

Sort all Graphs by Z-SampleData

Sort separate all selected Columns

 

GRAPH TABLE MATH FUNCTIONS FILL

Fill n times

Fill incremental

Fill random

 

GRAPH TABLE MATH FUNCTIONS SWAP

Swap active x/y-SampleData

Swap all x/y-SampleData

Swap two selected Columns

 

GRAPH TABLE MATH FUNCTIONS ROTATE

Rotate active X-SampleData

Rotate active Y-SampleData

Rotate all X-SampleData

Rotate all Y-SampleData

Rotate all selected Columns

 

GRAPH TABLE MATH FUNCTIONS CALCULATE

Calc active X-SampleData

Calc active Y-SampleData

Calc all X-SampleData

Calc all Y-SampleData

Calc all selected Columns

 

GRAPH TABLE MATH FUNCTIONS NORMALIZE

Normalize to Maximum

Normalize to each Z Value

Normalize to Reference Value

Subtract a Reference Value

Set Single Reference Value

Normalize to Reference Array

Subtract a Reference Array

Set Single Reference Column

 

GRAPH TABLE MATH FUNCTIONS ACCUMULATE

Accumulate active Y-SampleData

Accumulate all Y-SampleData

Accumulate each selected Column

 

GRAPH TABLE MATH FUNCTIONS TRANSFORM

Transpose Columns/Rows in Excel file...

dto., but rows form x, y, x, y, x,...

Polar in Cartesian Coordinates

Cartesian in Polar Coordinates

Smith Chart, z-Level in r-Level

Smith Chart, r-Level in z-Level

 

GRAPH TABLE MATH FUNCTIONS DATE/TIME

All x-Axes in Time Span [sec.]

 

SPREADSHEET TABLE FORMAT

Format Cells...

Lookup Cell Format...

Resize all Columns to Fit

Resize all Rows to Fit

Resize selected Rows to Fit

Resize selected Columns to Fit

 

DATABASE REQUERY

Requery Import Database

Requery Chart Label

Requery Chart Label by Date/Time

Requery Text Label

Requery Selected Text Label

Requery Text Label by Date/Time

Jump over inhibited Layers

 

INTERFACE RECALC

Recalc Chart Labels

Recalc All Text Labels

Recalc Selected Text Label(s)

Set Recalc Tag Names equal Shape Names

Set Recalc Tag Names equal Report Names

Set Constants...

Number of Iterations...

Jump over inhibited Layers

Enable Database Storage

 

ALGORITHM FUNCTIONPLOT

Regular Function f(x)...

Parametric Function x(t), y(t)...

Polar Function r(t)...

Relations (Equation/Inequality)...

Add Tangent

Add Normal

Fill Area

Custom Functions Constants...

 

ALGORITHM REGRESSION

Linear Least Squares Statistics

Robust Linear Regression

Levenberg-Marquardt Linear Regression

Segmented Linear Regression

Iteratively reweighted least sq. (IRLS)

Alternative LMEDS

Random Sample Consensus (RANSAC)

Progressive Sample Consensus (PROSAC)

Randomized RANSAC (RRANSAC)

Least Median of Squares (LMEDS)

M-Estimator Sample Consensus (MSAC)

Randomized MSAC (RMSAC)

Maximum LikeLihood Estimation Sample Consensus (MLESAC)

Adapted from Point Cloud Library©

Exponential Least Squares Fit

Logarithmic Least Squares Fit

Power Least Squares Fit

Invers Least Squares Fit

Invers Least Squares Fit2

Power Law Regression

Power Law IRLS Weighted

Exponential Law IRLS Weighted

n-dim. Polynomial

Quadratic Polynomial

Cubic Polynomial

Sine Wave

Line Form

Circle Form

Ellipse Form

Inner Circle Arcs (open)

Inner Circle Arcs (closed)

 

ALGORITHM APPROXIMATION

Downhill Simplex Algorithm

Gauss–Newton Custom Fit

Levenberg-Marquardt Fit

Symbolic partial derivatives (slow)

Numeric partial derivatives (fast)

Bézier Curve

Bezier V2

B-Spline

Smoothing Spline

Auto Smoothing Spline

Penalized Smoothing Spline

Parametric Smoothing Spline

Cyclic Smoothing Spline

Radial Basis Function (RBF)

Gaussian Process Exp. Kernel,

Gaussian Process Matern Kernel

 

MISSING VALUE

Highlight (previous) Missing Data Point Positions (?)

X: Remove Missing Data Pairs

X: Set Average value from previous next cell

Y: Impute using Linear Regression

Y: Approximative Imputation

Y: Interpolative Imputation

Y/Z: Set Mean value from the whole column

Y/Z: Set Median value from the whole column

Y/Z: Set Average value from previous next cell

X/Y: Remove Data Pairs if one is missing

X/Y/Z: Set All Missing Data to Zero

Rollback (Undo) last action

 

ALGORITHM INTERPOLATION

Polygonal Segments

Forwardflat Segments

Backwardflat Segments

Additional Segments

(n-1) Polynomial Interpolation

Lagrange Interpolation

Newton Interpolation

Rationale Interpolation

Aitken/Neville Interpolation

Barycentric Rational Interpolation

Radial basis function (RBF)

Cubic Spline

Modified Cubic Splines

Constrained Spline

Natural Overshooting

Non-overshooting in 1st Derivative

Non-overshooting in 2nd Derivative

Parabolic Interpolation

Fritsch-Butland Interpolation

Akima Interpolation

Kruger Interpolation

Extrapolation Cubic Spline

Extrapolation Cubic Spline (Monotonic)

Steffen Spline

Bessel Spline

Pchip Spline

Quintic Spline

Parametric Spline

Periodic Spline

Cyclic Spline

Straightening Spline

Akima Subspline

Renner Subspline

Hermite Splines

Cubic Hermite Spline

Cubic Hermite Spline (Monotonic)

Catmull-Rom Spline

Kochanek-Bartel Spline

Cardinal Spline

 

ALGORITHM 2D SURFACE INTERPOLATION

Nearest Neighbors Linear Interpolation

Built-in Spline Interpolation

Built-in Bilinear Interpolation

Thin Plate Surface Spline

 

ALGORITHM 3D SURFACE INTERPOLATION

Nearest Neighbors Distance

Nearest Neighbors Around Distance

Thin Plate Surface Spline

Bivariate Cubic Spline

 

ALGORITHM DIGITAL SIGNAL PROCESSING

Spectrum Generator

Generate Signal

Simple Waveforms

Sine Waveform

Sine Waveform with Harmonics

Square Waveform

Triangle Waveform

Sawtooth Waveform

Gaussian Noise

Complex Waveforms

Summation of sine waves

Sawtooth wave by summation

Sawtooth wave by direct calculation

Inverse sawtooth wave

Triangle wave

Square waves

Pulse wave

Frequency modulation FM

Phase modulation PM

Amplitude modulation AM

Ring modulation AM

Pulse wave buzz

Pulse wave buzz2

Dynamic spectrum

Bandwidth limited

Waveshaping

White noise

Envelope Generators

Simple Linear Integration

Convex Exponential Interpolation

Variable Exponential Interpolation

Logarithmic Interpolation

DB Interpolation

Simple State Machine

Multiple Segments ADSR

Multiple Segments State Machine

Constant Rate ADSR

Constant Rate ADSR Transformed

Amplitude Envelope

DFT Approximation

DFT Spectrum

DFT Phase

DFT Real Part

DFT Imaginary Part

FFT Approximation

FFT Spectrum (Simplex FFT)

FFT Spectrum (Complex FFT

FFT Spectrum (Real FFT)

FFT Phase

FFT Real Fourier Analysis

FFT Real Fourier Synthesis

FFT Real Part

FFT Imaginary Part

FFT Interpolation (2:1 ratio)

Window Functions

None Window (Rectangle)

Hamming Window

Hanning Window

Hann Window (Matlab)

Blackman Window

Triangular Window

Sqrt Window

Hann Window (Numerical Recipes)

Blackman-Harris Window

Bartlett Window

Parzen Window

Welch Window

Steeper Window

Kaiser Window

Flat Top Window

Flat Top Window (Stanford)

Goertzel DFT (Filter)

Scaled Magnitude

Tone detection

FIR Filter

FIR Coefficients (Remez Algorithm)

FIR Filter Graph (Remez Algorithm)

FIR Coefficients (Parks McClellan Algorithm)

FIR Filter Graph (Parks McClellan Algorithm)

FIR Coefficients (Iowa Hills Algorithm)

FIR Filter Graph (Iowa Hills Algorithm)

IIR Filter

RBJ Biquad

Butterworth

Chebyshev I

Chebyshev II

Elliptic

Bessel

Legendre

Custom

Time-series Filter

Simple Moving Averages

Simple Moving Averages V2

Exponential Moving Averages

Exponential Moving Averages V2

Hodrick/Prescott Filter

Hodrick/Prescott Filter V2

Baxter/King Bandpass Filter

Christiano/Fitzgerald Filter

Butterworth Filter

Polynomial Trend Filter

Polynomial Trend Filter (Weighted)

Linear Moving Averages

Savitzky-Golay Filter

FIR / IIR Real Filter

 

Audio Signals

Play...

Change Sound Tempo

Change Sound Pitch

Change Sound Rate

Adjust Tempo to BPM

 

ALGORITHM MATH OPERATIONS

Add Number

Sub Array

Sub Number

Mul Array

Mul Number

Div Array

Div Number

Append Array

Append Array plus last x

 

ALGORITHM MATH FUNCTIONS

Use Formula Parser...

Bernstein Polynomial [0,1]

Bernstein Polynomial [a,b]

Bernoulli Polynom of order N

Euler Beta Function (Euler's Integral)

Gaus Error Function

Gaus Error Function Inverse

Legendre Polynomial

Hermite Polynomial

 

Bessel Functions

Bessel Function of the first kind

Bessel Function of the second kind

Modified Bessel Function of the first kind

Modified Bessel Function of the second kind

Spherical Bessel Function of the first kind

Spherical Bessel Function of the second kind

 

Airy Functions

Airy function Ai

Airy function Bi

Airy function Ai'

Airy function Bi'

 

Elliptic Integrals

Carlson's elliptic integral RC

Legendre's complete elliptic integral of the first kind

Legendre's complete elliptic integral of the second kind

Legendre's complete elliptic integral of the third kind

 

Jacobi Elliptic Functions

Function cd

Function cn

Function cs

Function dc

Function dn

Function ds

Function nc

Function nd

Function ns

Function sc

Function sd

Function sn

 

Riemann Zeta Function (left)

Riemann Zeta Function (right)

 

ALGORITHM PEAK DETECTION

Summit(s) Trough Finder

Smoothed Z-Score Peak Finder

Smoothed Z-Score (reverse)

Emission Peak(s) Finder

Absorption Peak(s) Finder

Highest Peak

 

Fit 'Spectral Line Shapes'

Gaussian (symmetric)

Gaussian (asymmetric)

Cauchy–Lorentz Distribution

Pearson VII Distribution (symmetric)

Pearson VII Distribution (asymmetric)

Pseudo-Voigt Approximation

Voigt Profile

 

ALGORITHM OUTLIER TEST

Auto Detection

Dean-Dixon Outlier Test

Nalimov Outlier Test

Grubbs Outlier Test

Significance of extreme values

Adjust Cursor Line from Outliers

Show Outliers in Output Window

Show Outliers in GraphTable

Acoustics Alarm if any Outlier

 

ALGORITHM DATA REDUCTION

Routine from MIR (Russian Space Station)

Band Slope Method

Scherenschnitt Method

Removing nth Data Points

Radial Vertex Reduction

Perpendicular Vertex Reduction

Retake Perpendicular Vertex Reduction

Reumann/Witkam Reduction

Ramer/Douglas/Peucker Reduction

Optimized Ramer/Douglas/Peucker Reduction

Opheim Simplification

Lang Simplification

Adapted from Elmar de Koning©

 

ALGORITHM CONVEX HULL

Hull Edge Points

Hull Polygon

Hull Curve

 

DATA CLUSTERING

k-means (Manhattan Metric)

k-means (Euclidean Metric)

Segmented Regression Cluster

 

GRAPH LASSO

Draw Lasso and delete Data Points

Draw and select Lasso, then...

Delete Data Points

Mark Data Points in Table

Show Data Points in Output

Use for Exclude Data Points

Remove last Lasso

 

GRAPH LABELS

Show No Data Points

Show All X Data Points

Show All Y Data Points

Show ArrayEditor Legend

Show X Values pass the Limit

Show Y Values pass the Limit

Show Z Values pass the Limit

Set Exclusive Data Points...

Use Exclude Data Points

Show Label Box

Label Decimal Places

 

SPREADSHEET FORMULAS

Re-calculate Grid

Constraint Check

Named Ranges...

Show Formula in Cells

 

SPREADSHEET CHART

New Chart

Overwrite Chart Data

Append Data to Chart

 

Overwrite Graph(s)

3D Data Structure | x | y | z | x | y | z | x...

2D Data Structure | x | y | x | y | x...

2D Data Structure | x | y | y | y...

2D Data Business | Legend || y | y | y...

1D Data Structure | y | y | y...

 

Append Graph(s)

3D Data Structure | x | y | z | x | y | z | x...

2D Data Structure | x | y | x | y | x...

2D Data Structure | x | y | y | y...

2D Data Business | Legend || y | y | y...

1D Data Structure | y | y | y...