Provides the source and examples for James P. Howard, II,
"Computational Methods for Numerical Analysis with R,"
< https://jameshoward.us/cmna>, a book on numerical
methods in R.
This is the R package to support Computational Methods for Numerical
Analysis with R by James P. Howard, II. This book is scheduled for
publication in 2016 and will include a variety of implementations of
numerical analysis algorithms in pure R.
Algorithms included
Elementary and Example Algorithms
Polynomial Expansion
Naive (naivepoly)
Cached Naive (betterpoly)
Horner's Method (horner, rhorner)
Summation
Naive Summation (naivesum)
Kahan Summation (kahansum)
Division
Naive Division (naivediv)
Long Division (longdiv)
Miscellaneous
Naive Primality tester (isPrime)
Nth Root (nthroot)
Quadratic Formula (quadratic, quadratic2)
Samples
Fibbonaci (fibonacci)
Wilinson's Polynomial (wilkinson)
Himmelblau (himmelblau)
Linear Algebra
Row/Vector Operations
Row Replacement (replacerow)
Scale Row (scalerow)
Swap Rows (swaprows)
Norm of a Vector (vecnorm)
Elementary Functions
Determinant (detmatrix)
Matrix Inverse (invmatrix)
Row-Echelon Form (refmatrix)
Reduced Row-Echelon Form (rrefmatrix)
Solve a Matrix, Using Row Reduction (solvematrix)
Decompositions
Cholesky Decomposition (choleskymatrix)
LU Decomposition (lumatrix)
Iterative Methods
Conjugate Gradient (cgmmatrix)
Gauss Seidel (gaussseidel)
Jacobi (jacobi)
Specialty Methods
Tridiagonal Matrix Solver (tridiagmatrix)
Interpolation and Extrapolation
Polynomial Interpolation
Liner Interpolation (linterp)
Polynomial Interpolation (polyinterp)
Splines
Piecewise Linear (pwiselinterp)
Cubic Spline (cubicspline)
Bezier
Quadratic Bezier (qbezier)
Cubic Bezier (cbezier)
Multidimensional Interpolaters
Bilinear (bilinear)
Nearest Neighbor (nn)
Applications
Image Resizing (resizeImageNN, resizeImageBL)
Differentiation
Finite Differences
One-Step (findiff)
More Differentiators (symdiff, rdiff)
Second Derivative (findiff2)
Numerical Integration
Newton-Cotes
Midpoint Method (midpt)
Trapezoid Method (trap)
Simpson's Rule (simp)
Simpson's 3/8s Rule (simp38)
Gaussian Integration
Driver (gaussint)
Specific forms (gauss.hermite, gauss.laguerre, gauss.legendre)
Adaptive Integrators
Recursive Adaptive (adaptint)
Romberg (romberg)
Monte Carlo
Monte Carlo Integration, 1D (mcint)
Monte Carlo Integration, 2D (mcint2)
Applications
Shell Method for Revolved Volume (shellmethod)
Disc Method for Revolved Volume (discmethod)
Gini Coefficient (giniquintile)
Root Finding
Bisection Method (bisection)
Newton's Method (newton)
Secant Method (secant)
Optimization
Continuous
Golden Section (goldsectmax, goldsectmin)
Gradient Descent (gd, gdls, gradasc, graddsc)
Hill Climbing (hillclimbing)
Simulated Annealing (sa)
Discrete
Traveling Salesperson Problem (tspsa)
Differential Equations
Initial Value Problems
Euler Method (euler)
Midpoint Method (midptivp)
Fouth-Order Runge-Kutta (rungekutta4)
Adams-Bashforth (adamsbashforth)
Systems of Differential Equations
Euler Method (eulersys)
Partial Differential Equations
Heat Equation, 1D (heat)
Wave Equation, 1D (wave)
Applications
Boundary Value Problems (bvpexample, bvpexample10)