Solutions of Systems of Linear Equations (Real and Complex)

Ax = b

Gauss Jordan, QR Factorization, LU Decomposition, Cholesky Factorization

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Real, solution of equations example        Complex, solution of equations example

There is a symmetrical group of eight classes for the solution of real and complex linear systems. These classes correspond to real and complex versions of Cholesky factorization (LESCholesky, LESXCholesky), LU Decomposition (LESLU, LESXLU), QR Factorization (LESQR, LESXQR) and Gauss-Jordan (LESGJ, LESXGJ). Each class provides for the solution of one right hand side, multiple right hand sides and matrix inverse.

Solving for eigenvalues and eigenvectors (Real and Complex)

AX = λX

QL, QR and LR algorithms

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Real, solution of eigensystems            Complex, solution of eigensystems

The eigensystem problem is divided into three categories real-symmetric, real-unsymmetric, complex symmetric (Hermitian) and complex unsymmetric. The real-symmetric case is handled using the QL algorithm in class EigenQL. The EigenQR and EigenQR2 classes use the QR algorithm to solve the real-unsymmetric case. And the EigenXLR class uses the LR algorithm to solve general complex eigenvalue problems.

Least Squares Regression

Multiple regression, forward, backward, stepwise and split regression

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Multiple Regression

General multiple regression, forward regression, backward regression, stepwise and split regression and regression summary statistics are found in the MulReg, StepwiseMulReg and SplitMulReg classes.

Curve Fitting

Polynomial, exponential, rational polynomial and cubic splines

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Polynomial Curve Fitting

The CurveFit class includes support for polynomial, exponential, rational polynomial, and mixed curve fitting. The CubicSplines class uses a cubic splines algorithm for discrete function evaluation.

Digital Signal Processing

FFTs, Windowing, Power Spectrum

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FFT and Power Spectrum Calculation

The DSP class includes routines for real and complex FFT’s and power spectrum calculations. Auxiliary routines calculate FFT magnitudes, phases and frequencies.

Thermocouple Linearization

NIST ITS-90 standard as published in the NIST Monograph 17

The thermocouple linearization routines will convert from millivolts to temperature and temperature to millivolts, for B, E, J, K, N, R, S, T thermocouple types. Calculations are based on the NIST ITS-90 standard as published in the NIST Monograph 175..

Matrix Viewers

.Net (C# and VB) matrix viewer controls for real and complex matrices

DMatrixViewer displays matrix elements of a DDMat (real) matrix

XMatrixViewer displays matrix elements of a DXMat (complex) matrix

The DMatViewer and XMatViewer classes are UserControl subclasses that display real and complex number matrices, respectively. If the matrix is larger than the size you have created the view, scrollbars give the option of scrolling the rows and columns of the matrix.  The matrix viewers include options to change font characteristics, the numeric format of the matrix element values, and the number of displayed rows and columns. The matrix viewer can be read-only, or it can edited by clicking on a matrix element.