NumPal

NumPal provides numerical analysis for both scalar, and complex data structures such as vectors and matrices.
Vectors are collected as single-column data, and are used as Vectors, or as inputs to differential equations, or statistical operations requiring a list of numbers. Computations yielding a Vector as an output can either be saved, printed or simply viewed.
Matrices are collected as multi-column data and are either used as Matrices, or as inputs in ANOVA, stationarity, cointegration tests, Principal Component Analysis, Regression analysis.
NumPal also produces comprehensive working steps for Simple Linear Regression Analysis, Multiple Linear Regression Analysis, several data statistics, Matrix Algebra, including Matrix and Vector Addition, subtraction, multiplication, Matrix and Vector scalar operations, Matrix determinant, minor, cofactor, adjunct, Matrix inverse, Matrix equation, and characteristic polynomials of Matrices for up to 5 by 5 Matrices.
Computations yielding a Matrix as an output can also be saved for further processing. Data can be collected either through direct input, or importation.

Key Features
No internet required.
Step-by-step explanations
Comprehensive Pdf reports
Graphs

Topics Covered

Statistics: significance testing, ANOVA, averages, descriptive statistics, correlation, distance and divergence, distributions, statistical experiment,
kernel density estimation, outliers, random variable, circular statistics.

Matrix Algebra: addition, subtraction, multiplication, scalar operations, determinant, covariance matrix, householder matrix,
matrix equation, minor, transpose, cofactor, adjunct, inverse, direct sum, Kronecker sum, mean deviation, trace, rank sums, means, Frobenius norm, infinity norm, max norm, REF, RREF,
Lu decomposition, Qr decomposition, Crout decomposition, Cholesky decomposition, characteristic polynomials, eigenvalues, eigenvectors, properties, special matrices

Vector Algebra: dot product, perp dot product, l1 norm, l2 norm, addition, subtraction, multiplication, outer product, cross product, projection

Regression Analysis: Simple Linear regression, force point regression, Kendall robust line, Lineweaver–Burk regression, Hanes-Woolf regression, power law regression,
local polynomial regression, augmented Dickey–Fuller test, Johansen Cointegration, multiple regression, principal component analysis

Finance: payment, interest, principle, periods, annual equivalent rate, future value, present value, rate, internal rate of return, payback, profitability index

Probability: combinatorics, discrete distribution, multivariate distribution, z-table, t-table, chi-squared table, continuous distribution

Functions: gamma, beta, error function, hypergeometric, logistic, sigmoid, SoftMax

Calculus: differential calculus, integral calculus

Basic Algebra: factors, prime factors, common divisor, quadratic equation, cubic equation, quartic equation

Numerical Analysis: Interpolation, Differentiation, Integration

Information Theory: Shannon entropy, Shannon Nat entropy, Shannon Hartley entropy, cross entropy, Renyi entropy, perplexity