XLPack is a set of expansion modules for Excel which is developed for easy numerical calculation of small and medium-size on office / home PCs. It adds the features useful for wide range of scientific fields to Excel.
XLPack consists of a worksheet function library, a solver add-in, and a VBA subroutine library. By using worksheet functions or a solver, numerical calculations can be performed without programming. Also, the VBA subroutine library can be called from Excel VBA so that the numerical calculation programming can be made easier.
(1) The worksheet function library provides worksheet functions that can be entered directly in the Excel worksheet. You can perform calculations such as linear equations, eigenvalues, and special functions simply by entering data in the Excel worksheet.
(2) By using the solver, solutions for nonlinear equations, quadrature and ordinary differential equations can be obtained using the formulas entered in the Excel worksheet by menu operation.
(3) The VBA subroutine library provides subroutines that can be called from Excel VBA. Using the professional numerical computation routines provided by the library, advanced numerical application programs for Excel can be developed easily.
XLPack works with Excel 2013 / 2016 / 2019 / 2021 / 365. No other development tools are required.
The other app "XLPack Basic" must be installed from Microsoft Store to use this app. XLPack Basic allows you to use basic 27 worksheet functions and 138 VBA subroutines/functions.
In addition, you can add more expert functions by installing this app "XLPack Addons" and purchasing additional Modules 1 to 4 with in-app purchase. Then you will be able to use a total of 148 worksheet functions and 902 VBA subroutines.
Online manuals and sample worksheets are provided on the website (https://www.ktech.biz/manual/xlpack-60-manual/).
Major features
(1) Module 1 (linear computation (real)), (2) Module 2 (linear computation (complex))
- Linear computation (LAPACK, BLAS)
- Elementary vector operations, elementary matrix operations
- Solution of systems of linear equations (general matrices, symmetric/Hermitian matrices, band matrices, positive definite matrices, triangular matrices)
- Eigenvalues and eigenvectors (symmetric/Hermitian matrices, general matrices)
- Generalized eigenvalue problems (symmetric/Hermitian matrices, general matrices)
- Singular value decomposition (SVD) (general matrices)
- Generalized singular value decomposition (GSVD) (general matrices)
- Linear least squares method (QR decomposition, SVD), variance covariance matrices
- Constrained linear least squares problems (LSE and GLM problems)
(3) Module 3 (special functions, nonlinear computation)
- Special functions
- Bessel functions, modified Bessel functions, spherical Bessel functions, Airy functions, exponential integrals, logarithmic integrals, cosine and sine integrals, gamma functions, beta functions, incomplete gamma functions, incomplete beta functions, polygamma functions, Riemann zeta function, error functions, Fresnel integrals, hypergeometric functions, Jacobi elliptic functions, elliptic integrals, polynomials
- Nonlinear equations
- Roots of polynomials (Newton method, companion method, DKA method)
- Solution of single general nonlinear equation (Dekker's method)
- Solution of system of nonlinear equations (Powell's hybrid method, Brown's method)
- Nonlinear optimization
- Unconstrained optimization of general univariate function (Brent's method)
- Unconstrained optimization of general multivariate function (quasi-Newton method, trust region method)
- Optimization of general multivariate simply bounded function (trust region method)
- Fast Fourier transform (FFT)
- One-dimensional real fast Fourier transform, one-dimensional complex fast Fourier trans-form, one-dimensional trigonometric fast Fourier transform
- Two-dimensional real fast Fourier transform, two-dimensional complex fast Fourier trans-form
(4) Module 4 (interpolation, quadrature, ordinary differential equations, random numbers)
- Interpolation
- Polynomial interpolation
- Piecewise cubic Hermite interpolation, cubic spline interpolation, B-spline interpolation
- Quadrature involving fitted functions
- Quadrature
- Finite interval quadrature (tabulated integrand) (parabolic approximation)
- Finite interval quadrature (user-defined integrand function) (fixed points) (Gauss-Kronrod rule)
- Finite interval quadrature (user-defined integrand function) (automatic quadrature) (Gauss-Kronrod rule, double exponential (DE) formula)
- Finite interval quadrature (user-defined integrand function) (automatic quadrature) (special integrand functions)
- Semi-infinite or infinite interval quadrature (user-defined integrand function) (automatic quadrature) (Gauss-Kronrod rule, double exponential (DE) formula)
- Initial value problem of ordinary differential equations
- Non-stiff problems (Runge-Kutta-Fehlberg method, Dorman-Prince method, Runge-Kutta-Verner method, Adams method, extrapolation method)
- Stiff problems (BDF method, implicit Runge-Kutta method, Rosenbrock method, extrapolation method)
- Differential algebraic equations (DAEs) (DASSL)
- Nonlinear least squares method
- Unconstrained nonlinear least squares problems (Levenberg-Marquardt method, adaptive algorithm)
- Simply bounded nonlinear least squares problems (adaptive algorithm)
- Random number generation
- Uniform random numbers (Mersenne-Twister, Knuth's method, linear congruential method)
- Normal random numbers, exponential random numbers, gamma random numbers
