XLPack
XLPack is a set of expansion modules of Excel for numerical calculation which is developed for easy calculations on office/home PCs. It adds the features useful for wide range of scientific fields to Excel.
Excel is a widely used spreadsheet software. It is possible to program with VBA* and display the result in understandable visual form by graph functions. It can become an easytouse and powerful numerical calculation tool by enhancing the numerical calculation functions. (* Visual Basic for Applications: Builtin macro language of Excel)
XLPack consists of worksheet function library, solver and VBA subroutine/function library. These can be divided into two types: tools for numerical calculations without programming and tools that support programming.
 Numerical calculation without programming

 Worksheet function library: These functions can be entered directly in the Excel worksheet. Just by inputting the data into a worksheet, you can you can calculate linear equations, eigenvalues, special functions, etc.
 Worksheet function library: These functions can be entered directly in the Excel worksheet. Just by inputting the data into a worksheet, you can you can calculate linear equations, eigenvalues, special functions, etc.

 Solver addin: Using the formulas entered in the Excel worksheet, solutions for nonlinear equations, quadrature and ordinary differential equations can be obtained by menu operation.
 Solver addin: Using the formulas entered in the Excel worksheet, solutions for nonlinear equations, quadrature and ordinary differential equations can be obtained by menu operation.
 Supporting VBA numerical programming

 VBA subroutine/function library: A variety of subroutines and functions which can be called from Excel VBA are provided. By using these subroutines and functions, advanced numerical application programs can be developed in a short development period. Professional knowledge on numerical calculation is not required.
 Fast calculation
XLPack calculates faster than the equivalent VBA program. The next figure shows the measurements of CPU time to solve systems of linear equations. In this example case, XLPack is more than 100 times faster than the VBA program.
 Efficient algorithms
XLPack employs the latest efficient algorithms. The following figure shows the example of an initial value problem of ODE (ordinary differential equation). The (logarithm of) number of function evaluations is plotted against the relative error of the solution. The number of function evaluations required by the algorithms used in XLPack are less than those required by commonly used Euler method and 4th order RungeKutta method.
 Calculation tool for researchers and engineers
 Provides easy and practically fast numerical calculations for medium and small scale problems
 Researchers and engineers can concentrate on their main job without spending time for the details of calculation
 Development support tool
 Used for prototyping and onetime programs
 Platform in education fields
 Used for study and training of numerical calculation
XLPack can easily be introduced if you just have a personal computer running Excel.
 To support introduction, XLPack Lite is provided. It can be used for the compatibility testing with your PC environment before purchasing product.
 The product is provided as four separate feature modules so that you can purchase only the necessary modules.
XLPack Version 5.4
 Windows version
 Windows 10, Windows 8.1 Update or Windows 7 SP1
 Office 365 Excel, Excel 2019, Excel 2016, Excel 2013 SP1 or Excel 2010 SP2
 macOS version
 macOS Mojave (10.14), macOS Catalina (10.15) or macOS Big Sur (Intel) (11.0)
 Excel for Mac (Office 365 (Subscription) or Office 2019 for Mac (Onetime purchase))
 The latest versions are recommended. Office 2016 for Mac (Onetime purchase) is not supported.
 XLPack
 Divided into four modules. Modules 1, 2, 3 and 4 single products and all bundled product are lined up: M1: Linear computation (real), M2: Linear computation (complex), M3: Special functions, nonlinear computation, M4: Interpolation, differential/integral equations, random numbers
 VBA subroutine/function library routines: 841 (total)
 Worksheet function library routines: 154 (total)
 Solver addin (for M3 and M4)
 1,500 page PDF manuals
 Sample worksheets
 XLPack Lite
Subset version with major features. Same software requirements and performance as product version. For evaluation and compatibility testing before purchasing product
 Individual users can continue to use for noncommercial and nonorganizational purposes
The program and sample worksheets can be downloaded from Web site. Online manual and tutorial are also available.
 Major features:
 Module 1 (linear computation (real)), 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)
 Linear computation (LAPACK, BLAS)
 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 (quasiNewton method, trust region method)
 Optimization of general multivariate simply bounded function (trust region method)
 Fast Fourier transform (FFT)
 Onedimensional real fast Fourier transform, onedimensional complex fast Fourier transform, onedimensional trigonometric fast Fourier transform
 Twodimensional real fast Fourier transform, twodimensional complex fast Fourier transform
 Special functions
 Module 4 (interpolation, quadrature, ordinary differential equations, random numbers)
 Interpolation
 Polynomial interpolation
 Piecewise cubic Hermite interpolation, cubic spline interpolation, Bspline interpolation
 Quadrature involving fitted functions
 Quadrature
 Finite interval quadrature (tabulated integrand) (parabolic approximation)
 Finite interval quadrature (userdefined integrand function) (fixed points) (GaussKronrod rule)
 Finite interval quadrature (userdefined integrand function) (automatic quadrature) (GaussKronrod rule, double exponential (DE) formula)
 Finite interval quadrature (userdefined integrand function) (automatic quadrature) (special integrand functions)
 Semiinfinite or infinite interval quadrature (userdefined integrand function) (automatic quadrature) (GaussKronrod rule, double exponential (DE) formula)
 Initial value problem of ordinary differential equations
 Nonstiff problems (RungeKuttaFehlberg method, DormanPrince method, RungeKuttaVerner method, Adams method, extrapolation method)
 Stiff problems (BDF method, implicit RungeKutta method, Rosenbrock method, extrapolation method)
 Differential algebraic equations (DAEs) (DASSL)
 Nonlinear least squares method
 Unconstrained nonlinear least squares problems (LevenbergMarquardt method, adaptive algorithm)
 Simply bounded nonlinear least squares problems (adaptive algorithm)
 Random number generation
 Uniform random numbers (MersenneTwister, Knuth’s method, linear congruential method)
 Normal random numbers, exponential random numbers, gamma random numbers
 Interpolation
 Module 1 (linear computation (real)), Module 2 (linear computation (complex))
 Detail function list: Open in a separate tab
Calculation modules can be called as the numerical library from other languages such as C/C++, Python, Julia, C#, F#, VB.Net and Pascal(Delphi).
Refer to here for more details.
Related links
 XLPack sample worksheets: Go to download page
 XLPack Lite program and sample worksheets: Go to download page
 Brochure: Download
 Tutorial is available for those who are first to XLPack or who want to look at the usage examples.