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https://github.com/JohnReeves/numerical-recipes-in-fortran

FORTRAN things build in bash; blazingly fast!
https://github.com/JohnReeves/numerical-recipes-in-fortran

Last synced: 2 months ago
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FORTRAN things build in bash; blazingly fast!

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README 

        
#### Directory structure & progress chart



`NB:` repl.it has a bug that erases any templated folders.



* use `run` to execute main.sh;   

* modify `main.sh` to build & add linux features; or    

* use `gfortran sample.f -o ./Results/sample` to build your code.    

* type `./Results/sample` to run your code.    



Section / Title | Progress | Results

---|---|---

*'01 Preliminaries'* | WIP |

'00 Introduction' | WIP | `hello.c`

'01 Program Optimisation and Control Structures' | Not Started  

'02 Some C Conventions for Scientific Computing' | Not Started   

'03 Error, Accuracy and Stability' | Not Started  

*'02 Solutions of Linear Algebraic Equations'* | Not Started  

'00 Introduction' | Not Started  

'01 Gauss-Jordan Elimination' | Not Started  

'02 Gaussian Elimination with Backsubstitution' | Not Started  

'03 LU Decomposition and Its Applications' | Not Started  

'04 Tridiagonal and Band Diagonal Systems of Equations' | Not Started  

'05 Iterative Improvement of a Solution to Linear Equations' | Not Started  

'06 Singular Value Decomposition' | Not Started  

'07 Sparse Linear Systems' | Not Started  

'08 Vandermonde Matrices and Toeplitz Matrices' | Not Started  

'09 Cholesky Decomposition' | Not Started  

'10 QR Decomposition' | Not Started  

'11 Is Matrix Inversion an N**3 Process?' | Not Started  

*'03 Interpolation and Extrapolation'*| Not Started  

'00 Introduction' | Not Started  

'01 Polynomial Interpolation and Extrapolation'| Not Started    

'02 Rational Function Interpolation and Extrapolation' | Not Started    

'03 Cubic Spline Interpolation'| Not Started   

'04 How to search an Ordered Table' | Not Started  

'05 Coefficients of the Interpolating Polynomial' | Not Started  

'06 Interpolation in Two or More Dimensions'| Not Started    

*'04 Integration of Functions'*| Not Started   

'00 Introduction' | Not Started  

'01 Classical Formulas for Equally Spaced Abscissas' | Not Started   

'02 Elementary Algorithms'| Not Started   

'03 Romberg Integration' | Not Started   

'04 Improper Integrals' | Not Started    

'05 Gaussian Quadrature and Orthogonal Polynomials'| Not Started    

'06 Multidimensional Integrals' | Not Started    

*'05 Evaluation of Functions'* | Not Started    

'00 Introduction' | Not Started  

'01 Series and Their Convergence'| Not Started    

'02 Evaluation of Continued Fractions'| Not Started    

'03 Polynomials and Rational Functions' | Not Started    

'04 Complex Arithmetic' | Not Started    

'05 Recurrence Relations and Clenshaw's Recurrence Formula' | Not Started    

'06 Quadratic and Cubic Equations' | Not Started    

'07 Numerical Derivatives' | Not Started    

'08 Chebyshev approximation' | Not Started    

'09 Derivatives or Integrals of a Chebyshev-approximated Function'| Not Started    

'10 Polynomials approximation from Chebyshev Coefficients' | Not Started    

'11 Economisation of Power Series' | Not Started    

'12 Pade Approximants' | Not Started    

'13 Rational Chebyshev approximation' | Not Started    

'14 Evaluation of Functions by Path Integration' | Not Started    

*'06 Special Functions'*| Not Started    

'00 Introduction' | Not Started  

'01 Gamma Function, Beta Function, Factorials, Binomial Coefficients'| Not Started    

'02 Incomplete Gamma Function, Error Function, Chi-Square Probability Function, Cumulative Poisson Function' | Not Started    

'03 Exponential Integrals' | Not Started    

'04 Incomplete Beta Function, Student Distribution, F-Distribution, Cumulative Binomial Distribution' | Not Started    

'05 Bessel Functions of Integer Order' | Not Started    

'06 Modified Bessel Functions of Integer Order' | Not Started   

'07 Bessel Functions of Fractional Order, Airy Functions, Spherical Bessel Functions' | Not Started    

'08 Spherical Harmonics' | Not Started   

'09 Fresnel Integrals, Cosine and Sine Integrals' | Not Started    

'10 Dawson's Integrals' | Not Started   

'11 Elliptic Integrals and Jacobian Elliptic Functions' | Not Started    

'12 Hypergeometric Functions' | Not Started   

*'07 Random Numbers'* | Not Started    

'00 Introduction' | Not Started  

'01 Uniform Deviates' | Not Started   

'02 Transformation Method: Exponetial and Normal Deviates' | Not Started    

'03 Rejection Method: Gamma, Poisson, Binomial Deviates' | Not Started    

'04 Generation of Random Bits' | Not Started    

'05 Random Sequencies Based on Data Encryption' | Not Started    

'06 Simple Monte Carlo Integration' | Not Started   

'07 Quasi-(that is, Sub-) Random Sequencies' | Not Started    

'08 Adaptive and Recursive Monte-Carlo Methods' | Not Started    

*'08 Sorting'*| Not Started    

'00 Introduction' | Not Started  

'01 Straight Insertion and Shell's Method' | Not Started    

'02 Quicksort' | Not Started    

'03 Heapsort' | Not Started    

'04 Indexing and Ranking' | Not Started    

'05 Selecting the Mth Largest' | Not Started    

'06 Determination of Equivalence Classes' | Not Started   

*'09 Root Finding and Nonlinear Sets of Equations'*| Not Started    

'00 Introduction' | Not Started  

'01 Bracketing and Bisection' | Not Started    

'02 Secant Method, False Position Method, and Ridders' Method' | Not Started    

'03 Van Wijngaarden-Dekker-Brent Method' | Not Started    

'04 Newton-Raphson Method Using Derivatives' | Not Started    

'05 Roots of Polynomials' | Not Started    

'06 Newton-Raphson Method for Nonlinear Systems of Equations' | Not Started   

'07 Globally Convergent Methods for Nonlinear Systems of Equations' | Not Started   

*'10 Minimization or Maximumization of Functions'*| Not Started    

'00 Introduction' | Not Started  

'01 Golden Section Search in One Dimension' | Not Started    

'02 Parabolic Interpolation and Brent's Method in ONe Dimension' | Not Started    

'03 One Dimensional Search with First Derivatives' | Not Started    

'04 Downhill Simplex Method in Multidimensions' | Not Started    

'05 Direction Set (Powell's) Methods in Multidimensions' | Not Started    

'06 Conjugate Gradient Methods in Multidimensions' | Not Started   

'07 Variable Metric Methods in Multidimensions' | Not Started   

'08 Linear Programming and the Simplex Method' | Not Started   

'09 Simulated Annealing Methods' | Not Started   

*'11 Eigensystems'*| Not Started    

'00 Introduction' | Not Started  

'01 Jacobi Transformation of a Symmetric Matrix' | Not Started    

'02 Reduction of a Symmetric Matrix to a Tridiagonal Form: Givens and Householder Reductions' | Not Started    

'03 Eigenvalues and EigenVectors of a Tridiagonal Matrix' | Not Started    

'04 Hermitian Matrices' | Not Started    

'05 Reduction of a General Matrix to Hessenberg Form' | Not Started    

'06 The QR Algorithm for Real Hessenberg Matrices' | Not Started   

'07 Improving Eigenvalues and/or Finding Eigenvectors by Inverse Iteration' | Not Started   

*'12 Fast Fourier Transforms'*| Not Started    

'00 Introduction' | Not Started  

'01 Fourier Transform of Discretely Sampled Data' | Not Started    

'02 Fast Fourer Transform' | Not Started    

'03 FFT of Real Functions, Sine and Cosine Transforms' | Not Started    

'04 FFT in Two or More Dimensions' | Not Started    

'05 Fourier Transform of Real Data in Two and Three Dinesions' | Not Started    

'06 External Storage or Memory-Local FFTs' | Not Started   

*'13 Fourier and Spectral Applications'*| Not Started    

'00 Introduction' | Not Started  

'01 Convolution and Deconvolution using the FFT' | Not Started    

'02 Correlation and Autocorrelation using the FFT' | Not Started    

'03 Optimal (Wiener) Filtering using the FFT' | Not Started    

'04 Power Spectrum Estimation using the FFT' | Not Started    

'05 Digital Filtering in the Time Domain' | Not Started    

'06 Linear Prediction and Linear Predictive Coding' | Not Started   

'07 Power Sprectrum Estimation by the Maximum Entropy (All Poles) Method' | Not Started   

'08 Spectral Analysis of Unevenly Sampled Data' | Not Started    

'09 Computing Fourier Integrals using the FFT' | Not Started    

'10 Wavelet Tranforms' | Not Started   

'11 Numerical Use of the Sampling Theorem' | Not Started   

*'14 Statistical Description of Data'*| Not Started    

'00 Introduction' | Not Started  

'01 Moments of a Distribution: Mean, Variance, Skewness, and So Forth' | Not Started    

'02 Do Two Distributions Have the Same Means or Variances?' | Not Started    

'03 Are Two Distributions Different?' | Not Started    

'04 Contingency Table Analysis of Two Distributions' | Not Started    

'05 Linear Correlation' | Not Started    

'06 Nonparametric or Rank Correlation' | Not Started   

'07 Do Two-Dimensional Distributions Differ?' | Not Started   

'08 Savitsky-Golay Soothing Filters' | Not Started   

*'15 Modelling of Data'*| Not Started    

'00 Introduction' | Not Started  

'01 Least Squares as a Maximum Likelihood Estimator' | Not Started    

'02 Fitting Data to a Straight Line' | Not Started    

'03 Straight-Line Data with Errors in Both Coordinates' | Not Started    

'04 General Linear Least Squares' | Not Started    

'05 Nonlinear Models' | Not Started    

'06 Confidence Limits on Estimated Model Parameters' | Not Started   

'07 Robust Estimation' | Not Started   

*'16 Integration of Ordinary Differential Equations'*| Not Started    

'00 Introduction' | Not Started  

'01 Runge-Kutta Method' | Not Started    

'02 Adaptive Stepsize Control for Runge-Kutta' | Not Started    

'03 Modified Midpoint Method' | Not Started    

'04 Richardson Extrapolation and the Bulirsch-Stoer Method' | Not Started    

'05 Second Order Conservative Equations' | Not Started    

'06 Stiff Sets of Equations' | Not Started   

'07 Multistep, Multivalue, and Predictor-Corrector Methods' | Not Started   

*'17 Two Point Boundary Value Problems'*| Not Started    

'00 Introduction' | Not Started  

'01 The Shooting Method' | Not Started    

'02 Shooting to a Fitting Point' | Not Started    

'03 Relaxation Methods' | Not Started    

'04 Worked Example: Spheroidal Harmonics' | Not Started    

'05 Automate Allocation of Mesh Points' | Not Started    

'06 Handling Internal Boundary Conditions or Singular Points' | Not Started   

*'18 Integral Equations and Inverse Theory'*| Not Started    

'00 Introduction' | Not Started  

'01 Fredholm Equations of the Second Kind' | Not Started    

'02 Volterra Equations' | Not Started    

'03 Integral Equations with Singular Kernels' | Not Started    

'04 Inverse Problems and the Use of a Priori Information' | Not Started    

'05 Linear Regularization Methods' | Not Started    

'06 Bakkus-Gilbert Method' | Not Started   

'07 Maximum Entropy Image Restoration' | Not Started   

*'19 Partial Differential Equations'*| Not Started    

'00 Introduction' | Not Started  

'01 Flux-Conservative Initial Value Problems' | Not Started    

'02 Diffusive Initial Value Problems' | Not Started    

'03 Initial Value Problems in Multidimensions' | Not Started    

'04 Fourier and Cyclic Reduction Methods for Boundary Value Problems' | Not Started    

'05 Relaxation Methods for Boundary Value Problems' | Not Started    

'06 Multigrid Methods for Boundary Value Problems' | Not Started   

*'20 Less-Numerical Algorithms'*| Not Started    

'00 Introduction' | Not Started  

'01 Diagnosing Machine Parameters' | Not Started    

'02 Gray Codes' | Not Started    

'03 Cyclic Redundancy and Other Checksums' | Not Started    

'04 Huffman Coding and Compression of Data' | Not Started    

'05 Arithmetic Coding' | Not Started    

'06 Arithmetic at Arbitrary Precision' | Not Started   



Results .