Computational Methods for Numerical Analysis

Provides the source and examples for James P. Howard, II, "Computational Methods for Numerical Analysis with R," < https://jameshoward.us/cmna>, a forthcoming 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)

Dependencies

• testthat
• roxygen2

Contribution guidelines

• Use Git Flow
• Write unit tests using testthat
• Document functions using roxygen2
• Use ZenHub for project management on GitHub

For more information

• Website for CMNA
• James P. Howard, II <[email protected]>