NMath Suite

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NMath Suite V5.1

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NMath and NMath Stats libraries are now available for use in developing applications on Mono. The Mono versions include all of the same features as the .NET Windows libraries, with native code compiled for Linux and Mac OS X.

What's new in NMath Suite V5.1?

• Added assembly NMathChartMicrosoft.dll containing class NMathChart, which provides static methods for plotting NMath types using the Microsoft Chart Controls for .NET.
• Upgraded to Intel MKL 10.3 Update 6 with resulting performance increases.
• Added classes for solving first order initial value differential equations by the Runge-Kutta method. Class FirstOrderInitialValueProblem encapsulates a first order initial value differential equation, and class RungeKuttaSolver solves them.
• Added static method NMathFunctions.NaNSort() for sorting vectors containing NaN's. NMathFunctions.Sort() no longer supports vectors containing NaN's.
• NMathFunctions.Sort() now does a much faster in-place sort for compact vectors and an out-of-place sort for strided vectors. Previously all sorting was done out-of-place.
• Added method NMathFunctions.Sign() that applies the signum function over real vectors.
• Redesigned method NMathFunctions.Median(), which is now approximately 25X faster.
• Added new Fill() method to vectorized random number generators for filling a DoubleVector.
• Added NMathFunctions.CumulativeProduct() methods.
• Improved performance of NMathFunctions.OuterProduct().
• Added exponential moving average filter weights to class MovingWindowFilter.
• Added MatrixFunctions.Solve() methods for factoring and solving general sparse matrices.
• Added class LevenbergMarquardtMinimizer and deprecated LevenburgMarquardtMinimizer.
• Added static method NMathKernel.Init() for explicitly loading the kernel assembly (for example, on application start-up).
• Modified class TDistribution to accept fractional degrees of freedom. - NMath Stats
• Added class TwoSampleUnpairedUnequalTTest. Unlike TwoSampleUnpairedTTest, a pooled estimate of the variance is not used.- NMath Stats

What's new in NMath Suite V5.0?

NMath

• A new set of random number generator classes based on MKL vectorized random number generators
• Classes for creating independent streams of random numbers using the leapfrop and skip-ahead methods
• Classes for generating quasirandom sequences using Niederreiter and Sobal methods
• Classes for solving quadratic programming (QP) and nonlinear programming (NLP) problems

NMath Stats

• Added a class for performing a Pearson's chi-square hypothesis test.

What's new in NMath Suite V4.0?

NMath Stats

• K-Means Clustering - NMath Stats 3.1 includes a class for k-means clustering, to complement the hierarchical cluster analysis already in the library. The k-means clustering method assigns data points into k groups such that the sum of squares from points to the computed cluster centers is minimized. In general, k-means clustering uses far less memory that constructing a full hierarchical cluster tree.
• Cronbach’s Alpha - NMath Stats 3.1 includes a method for computing Cronbach’s alpha, a measure of reliability (or consistency) in the framework of the domain sampling model. Cronbach’s alpha measures how well a set of items (or variables) measures a single unidimensional latent construct.
• Smoothing Filters - NMath Stats 3.1 will include classes for smoothing data by replacing each data point with a linear combination of the data points immediately to the left and right of the data point. You can provide the coefficients to use in the linear combination, or use provided methods to generate coefficients that implement a moving average filter and a Savitzky-Golay filter. A Savitzky-Golay filter performs a local polynomial regression on the data to determine the smoothed value for each point. This tends to preserve features of the data which are flattened by moving averages, for example, peak finding.

NMath

• Fast Fourier Transforms (FFTs)- NMath 4.0 contains high performance, multi-core aware FFT classes. This set of classes will support all common 1D and 2D FFT computations in a robust easy-to-use object-oriented interface. All classes will efficiently support FFT’s of arbitrary length, with a simple interface for both in-place and out-of-place computations. Additionally, there is a parallel set of classes for single precision computation.
• Levenberg-Marquardt Nonlinear Least Squares - NMath 4.0 includes class LevenbergMarquardtMinimizer for minimizing the L2 norm of a function using the Levenberg-Marquardt algorithm (LMA). LMA is a standard in non-linear optimization, and is widely used for solving generic curve-fitting problems. LMA significantly outperforms gradient descent and conjugate gradient methods for medium sized problems, and complements the Trust Region minimizer already in NMath.
• Linear Spline Interpolation- NMath 4.0 includes a class LinearSpline for representing a function whose values are determined by linear interpolation between tabulated values.
• MKL Version 10.2 - NMath 4.0 now leverages Intel’s MKL Version 10.2. This provides many performance improvements for faster execution and taking advantage of more cores. It now also can take advantage of threading on more cores and more CPUs. These speed improvements generally range from 10% to 25%, and if you have a 24 core machine, the improvement can be as high as 130 times as great.
• AnyCPU configuration - Use AnyCPU configuration to build one application that automatically loads native x86 or x64 code as required.

NMath Suite includes: NMath Core, NMath Analysis, NMath Matrix and NMath Stats.

NMath Core

NMath Core is part of CenterSpace Software’s NMath product suite, which provides object-oriented components for math, engineering, scientific, and financial applications on the .NET platform. NMath Core is the foundational library in the suite, and provides basic numerical building blocks such as vector and matrix classes, complex number classes, and random number generators. For most computations, NMath Core uses machine-specific, highly-optimized versions of the C and FORTRAN public domain computing packages known as the BLAS (Basic Linear Algebra Subroutines) and LAPACK (Linear Algebra PACKage). This gives NMath Core classes performance levels comparable to C, and often results in performance an order of magnitude faster than non-platformoptimized implementations.

Fully compliant with the Microsoft Common Language Specification, all NMath Core routines are callable from any .NET language, including C#, Visual Basic.NET, and Managed C++.

NMath Core Product features include:

• Single- and double-precision complex number classes
• Full-featured vector and matrix classes for single- and double-precision floating point numbers and single- and double-precision complex numbers
• Flexible indexing using slices and ranges
• Cubic spline interpolation
• Extension of standard mathematical functions, such as Cos(), Sqrt(), and Exp(), to work with vectors, matrices, and complex number classes
• LU factorization for a matrix, as well as functions for solving linear systems, computing determinants, inverses, and condition numbers
• Least squares solutions
• Random number generation from various probability distributions, including the uniform, normal, Poisson, gamma, binomial, exponential, Pareto, and log normal distributions
• Classes for encapsulating functions of one variable, with support for numerical integration (Romberg and Gauss-Kronrod methods), differentiation (Ridders' method), and algebraic manipulation of functions
• Polynomial encapsulation, interpolation, and exact differentiation and integration.
• Source code version available
• Prebuilt 64-bit assemblies are included

NMath Analysis

NMath Analysis contains classes for function minimization, root-finding, and linear programming.

NMath Analysis Product features include:

• Classes for minimizing univariate functions using golden section search and Brent's method.
• Classes for minimizing multivariate functions using the downhill simplex method, Powell's direction set method, the conjugate gradient method, and the variable metric (or quasi-Newton) method.
• Simulated annealing.
• Linear programming using the simplex method.
• Least squares polynomial fitting.
• Classes for finding roots of univariate functions using the secant method, Ridders' method, and the Newton-Raphson method.
• Numerical methods for double integration of functions of two variables.

NMath Matrix

NMath Matrix is part of CenterSpace Software’s NMath product suite, which provides object-oriented components for mathematical, engineering, scientific, and financial applications on the .NET platform. NMath Matrix extends the foundational library NMath Core to include structured sparse matrix classes and factorizations, general matrix decompositions, advanced least squares solutions, and solutions to eigenvalue problems.

Like NMath Core, NMath Matrix uses machine-specific, highly-optimized versions of the BLAS and LAPACK for most computations. This gives NMath Matrix classes performance levels comparable to C or Fortran.  NMath Matrix is an advanced matrix manipulation library that extends NMath Core to include structured sparse matrix classes (triangular, symmetric, Hermitian, banded, tridiagonal, symmetric banded, and Hermitian banded), factorizations (LU, Bunch-Kaufman, and Cholesky), orthogonal decompositions (QR and SVD), advanced least squares classes (Cholesky, QR, and SVD), and solutions to symmetric, Hermitian, and nonsymmetric eigenvalue problems.

Fully compliant with the Microsoft Common Language Specification, all NMath routines are callable from any .NET language, including C# and Visual Basic.NET. For most computations, NMath libraries use proven, highly optimized versions of public domain linear algebra subroutine libraries, such as the BLAS and LAPACK. This gives NMath routines accuracy you can trust, and performance levels comparable to C or Fortran, combined with state of the art, object-oriented interfaces that leverage the full power of the .NET platform. 

NMath Stats

NMath Stats Features

• NMath Stats contains a data table class with functions for computing descriptive statistics, such as mean, variance, standard deviation, percentile, median, quartiles, geometric mean, harmonic mean, RMS, kurtosis, skewness, and many more
• PDF, CDF, inverse CDF, and random variable moments for a variety of probability distributions, including normal (Gaussian), Poisson, chi-square, gamma, beta, Student's t, F, binomial, and negative binomial
• Combinatorial functions, such as factorial, log factorial, binomial coefficient, and log binomial; Multiple linear regression
• Basic hypothesis tests, such as z-test, t-test, and F-test, with calculation of p-values, critical values, and confidence intervals
• One-way and two-way analysis of variance (ANOVA) and analysis of variance with repeated measures (RANOVA); Partial least squares (PLS) with cross validation and the NIPALS and SIMPLS algorithms
• Non-negative matrix factorization (NNMF); Multivariate statistical analyses, including principal component analysis and hierarchical cluster analysis. 

NMath Stats is part of CenterSpace Software’s NMath product suite, which provides object-oriented components for mathematical, engineering, scientific, and financial applications on the .NET platform. NMath Stats provides functions for statistical computation, including descriptive statistics, probability distributions, combinatorial functions, multiple linear regression, hypothesis testing, and analysis of variance.

Fully compliant with the Microsoft Common Language Specification, all NMath Stats routines are callable from any .NET language, including C#, Visual Basic.NET, and Managed C++.