Task View on Numerical Analysis and Differential Equations

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Task View on Numerical Analysis and Differential Equations

Hans W Borchers
I am wondering if it would be time to have a new Task View, this time
for the subject of "Numerical Analysis and Differential Equations".
The list of packages possibly appearing in such a task view is already
quite long and could, for example, include:

Numerical Analysis and Linear Algebra

Bessel        Bessel Functions Computations and Approximations
cubature      Adaptive multivariate integration over hypercubes
elliptic      Elliptic and related functions
expm          Matrix exponential, logarithm, etc.
fdim      Functions for calculating fractal dimension
gaussquad     Collection of functions for Gaussian quadrature
gmp           Multiple precision arithmetic
gsl           Wrapper for the Gnu Scientific Library
hypergeo      The hypergeometric function
irlba         Fast partial SVD by Lanczos bidiagonalization
matlab        MATLAB emulation package
multipol      Multivariate polynomials
numDeriv      Accurate numerical derivatives
onion         Octonions and quaternions
orthogonalsplinebasis  Orthogonal Bspline basis functions
orthopolynom  Functions for orthogonal and orthonormal polynomials
polspline     Polynomial spline routines
polynom       Implement a class for univariate polynomial manipulations
PolynomF      Polynomials in R
pracma        Practical numerical math functions
pspline       Penalized smoothing splines
quaternions   Arithmetics and linear algebra with quaternions
R2Cuba        Multidimensional numerical integration
RcppArmadillo Rcpp integration for Armadillo templated linear algebra library
RcppEigen  Rcpp integration for the Eigen templated linear algebra library
RcppOctave    Rcpp integration of Octave
R.matlab  Read and write of MAT files and R-to-Matlab connectivity
Rmpfr      Multiple precision floating-point reliable
sparseGrid    Sparse grid integration in R
spuRs         Functions and datasets scientific programming and simulation
sspline       Smoothing splines on the sphere
stinepack     Stineman: consistently well behaved method of interpolation
svd           Interfaces to various state-of-art SVD and eigensolvers
voronoi       Methods and applications related to Voronoi tessellations
wavelets...

Simulation and Differential Equations

bvpSolve  Solvers for boundary value problems of ODEs
ddesolve      Solver for Delay Differential Equations
deSolve       General solvers for initial value problems of ordinary
              differential equations (ODE), partial differential equations
              (PDE), differential algebraic equations (DAE), and delay
              differential equations (DDE)
deTestSet  Testset for differential equations
odesolve  Solvers for Ordinary Differential Equations
PBSddesolve  Solver for Delay Differential Equations
rootSolve     Root finding, equilibrium and steady-state analysis of ODEs
sde           Simulation and Inference for Stochastic Differential Equations
Sim.DiffProc  Simulation of diffusion processes
simecol       Simulation of ecological and other dynamic systems

and probably many more in the end. I left out the optimization
packages deliberately, but of course there would be a strong hint to
that task view.

Regards
Hans Werner Borchers

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Re: Task View on Numerical Analysis and Differential Equations

Berend Hasselman

On 08-03-2012, at 12:16, Hans W Borchers wrote:

> I am wondering if it would be time to have a new Task View, this time
> for the subject of "Numerical Analysis and Differential Equations".
> The list of packages possibly appearing in such a task view is already
> quite long and could, for example, include:
>
> Numerical Analysis and Linear Algebra
>
> Bessel        Bessel Functions Computations and Approximations
> cubature      Adaptive multivariate integration over hypercubes
> elliptic      Elliptic and related functions
> expm          Matrix exponential, logarithm, etc.
> fdim      Functions for calculating fractal dimension
> gaussquad     Collection of functions for Gaussian quadrature
> gmp           Multiple precision arithmetic
> gsl           Wrapper for the Gnu Scientific Library
> hypergeo      The hypergeometric function
> irlba         Fast partial SVD by Lanczos bidiagonalization
> matlab        MATLAB emulation package
> multipol      Multivariate polynomials
> numDeriv      Accurate numerical derivatives
> onion         Octonions and quaternions
> orthogonalsplinebasis  Orthogonal Bspline basis functions
> orthopolynom  Functions for orthogonal and orthonormal polynomials
> polspline     Polynomial spline routines
> polynom       Implement a class for univariate polynomial manipulations
> PolynomF      Polynomials in R
> pracma        Practical numerical math functions
> pspline       Penalized smoothing splines
> quaternions   Arithmetics and linear algebra with quaternions
> R2Cuba        Multidimensional numerical integration
> RcppArmadillo Rcpp integration for Armadillo templated linear algebra library
> RcppEigen  Rcpp integration for the Eigen templated linear algebra library
> RcppOctave    Rcpp integration of Octave
> R.matlab  Read and write of MAT files and R-to-Matlab connectivity
> Rmpfr      Multiple precision floating-point reliable
> sparseGrid    Sparse grid integration in R
> spuRs         Functions and datasets scientific programming and simulation
> sspline       Smoothing splines on the sphere
> stinepack     Stineman: consistently well behaved method of interpolation
> svd           Interfaces to various state-of-art SVD and eigensolvers
> voronoi       Methods and applications related to Voronoi tessellations
> wavelets...
>
> Simulation and Differential Equations
>
> bvpSolve  Solvers for boundary value problems of ODEs
> ddesolve      Solver for Delay Differential Equations
> deSolve       General solvers for initial value problems of ordinary
>              differential equations (ODE), partial differential equations
>              (PDE), differential algebraic equations (DAE), and delay
>              differential equations (DDE)
> deTestSet  Testset for differential equations
> odesolve  Solvers for Ordinary Differential Equations
> PBSddesolve  Solver for Delay Differential Equations
> rootSolve     Root finding, equilibrium and steady-state analysis of ODEs
> sde           Simulation and Inference for Stochastic Differential Equations
> Sim.DiffProc  Simulation of diffusion processes
> simecol       Simulation of ecological and other dynamic systems
>
> and probably many more in the end. I left out the optimization
> packages deliberately, but of course there would be a strong hint to
> that task view.


If you put pracma in "Numerical Analysis and Linear Algebra", then I feel you should also include  BB and nleqslv under that heading. Both of these do things that can be classified as Numerical Analysis. And both can of course also be used for simulation.

BB  solve  (sparse) systems of non linear equations using spectral gradient methods
nleqslv solve systems of nonlinear equations combining global strategies with a Broyden or Newron method.

Berend

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Re: Task View on Numerical Analysis and Differential Equations

Ravi Varadhan
Dear Hans Werner,

I like the idea overall.  Nothing prevents you from doing this, but you should be committed to getting it up and running and then keeping it updated.

In addition to concurring with Berend's comments, I also would like to mention that numerical analysis (NA) is an extremely broad category.  I am not sure how to restrict that in order to make the taskview manageable.  How about including (i) convergence acceleration of sequences, (ii) fourier transforms/wavelets, (iii) function approximation and special functions of mathematical physics?

Best regards,
Ravi

P.S. I have a package called "eiginv" for solving certain types of inverse eigenvalue problems (e.g., generating a matrix of a specific structure with a given set of eigenvalues)


-----Original Message-----
From: [hidden email] [mailto:[hidden email]] On Behalf Of Berend Hasselman
Sent: Thursday, March 08, 2012 9:59 AM
To: Hans W Borchers
Cc: [hidden email]
Subject: Re: [Rd] Task View on Numerical Analysis and Differential Equations


On 08-03-2012, at 12:16, Hans W Borchers wrote:

> I am wondering if it would be time to have a new Task View, this time
> for the subject of "Numerical Analysis and Differential Equations".
> The list of packages possibly appearing in such a task view is already
> quite long and could, for example, include:
>
> Numerical Analysis and Linear Algebra
>
> Bessel        Bessel Functions Computations and Approximations
> cubature      Adaptive multivariate integration over hypercubes
> elliptic      Elliptic and related functions
> expm          Matrix exponential, logarithm, etc.
> fdim      Functions for calculating fractal dimension
> gaussquad     Collection of functions for Gaussian quadrature
> gmp           Multiple precision arithmetic
> gsl           Wrapper for the Gnu Scientific Library
> hypergeo      The hypergeometric function
> irlba         Fast partial SVD by Lanczos bidiagonalization
> matlab        MATLAB emulation package
> multipol      Multivariate polynomials
> numDeriv      Accurate numerical derivatives
> onion         Octonions and quaternions
> orthogonalsplinebasis  Orthogonal Bspline basis functions orthopolynom  
> Functions for orthogonal and orthonormal polynomials
> polspline     Polynomial spline routines
> polynom       Implement a class for univariate polynomial manipulations
> PolynomF      Polynomials in R
> pracma        Practical numerical math functions
> pspline       Penalized smoothing splines
> quaternions   Arithmetics and linear algebra with quaternions
> R2Cuba        Multidimensional numerical integration
> RcppArmadillo Rcpp integration for Armadillo templated linear algebra library
> RcppEigen  Rcpp integration for the Eigen templated linear algebra library
> RcppOctave    Rcpp integration of Octave
> R.matlab  Read and write of MAT files and R-to-Matlab connectivity
> Rmpfr      Multiple precision floating-point reliable
> sparseGrid    Sparse grid integration in R
> spuRs         Functions and datasets scientific programming and simulation
> sspline       Smoothing splines on the sphere
> stinepack     Stineman: consistently well behaved method of interpolation
> svd           Interfaces to various state-of-art SVD and eigensolvers
> voronoi       Methods and applications related to Voronoi tessellations
> wavelets...
>
> Simulation and Differential Equations
>
> bvpSolve  Solvers for boundary value problems of ODEs
> ddesolve      Solver for Delay Differential Equations
> deSolve       General solvers for initial value problems of ordinary
>              differential equations (ODE), partial differential equations
>              (PDE), differential algebraic equations (DAE), and delay
>              differential equations (DDE)
> deTestSet  Testset for differential equations
> odesolve  Solvers for Ordinary Differential Equations
> PBSddesolve  Solver for Delay Differential Equations
> rootSolve     Root finding, equilibrium and steady-state analysis of ODEs
> sde           Simulation and Inference for Stochastic Differential Equations
> Sim.DiffProc  Simulation of diffusion processes
> simecol       Simulation of ecological and other dynamic systems
>
> and probably many more in the end. I left out the optimization
> packages deliberately, but of course there would be a strong hint to
> that task view.


If you put pracma in "Numerical Analysis and Linear Algebra", then I feel you should also include  BB and nleqslv under that heading. Both of these do things that can be classified as Numerical Analysis. And both can of course also be used for simulation.


BB  solve  (sparse) systems of non linear equations using spectral gradient methods nleqslv solve systems of nonlinear equations combining global strategies with a Broyden or Newron method.

Berend

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Re: Task View on Numerical Analysis and Differential Equations

Achim Zeileis-4
Hans,

thanks for the suggestion and sorry for coming so late to the thread. I
have only a little to add to Ravi's comments.

> I like the idea overall.  Nothing prevents you from doing this, but you
> should be committed to getting it up and running and then keeping it
> updated.

Yes completely d'accord with all comments.

If you want to put together a .ctv, please have a look at

vignette("ctv-howto", package = "ctv")

and send me the resulting .ctv.

> In addition to concurring with Berend's comments, I also would like to
> mention that numerical analysis (NA) is an extremely broad category.  I
> am not sure how to restrict that in order to make the taskview
> manageable.

I also completely agree with this. I'm not sure what the best way to focus
the task view is. Maybe differential equations should be in a separate
(relatively small) view? The experience is that very large task views
become harder to maintain in the future because the number of packages
will grow over time.

In any case, I look forward to seeing a new task view.
Thanks & best regards,
Z

> How about including (i) convergence acceleration of sequences, (ii)
> fourier transforms/wavelets, (iii) function approximation and special
> functions of mathematical physics?
>
> Best regards,
> Ravi
>
> P.S. I have a package called "eiginv" for solving certain types of inverse eigenvalue problems (e.g., generating a matrix of a specific structure with a given set of eigenvalues)
>
>
> -----Original Message-----
> From: [hidden email] [mailto:[hidden email]] On Behalf Of Berend Hasselman
> Sent: Thursday, March 08, 2012 9:59 AM
> To: Hans W Borchers
> Cc: [hidden email]
> Subject: Re: [Rd] Task View on Numerical Analysis and Differential Equations
>
>
> On 08-03-2012, at 12:16, Hans W Borchers wrote:
>
>> I am wondering if it would be time to have a new Task View, this time
>> for the subject of "Numerical Analysis and Differential Equations".
>> The list of packages possibly appearing in such a task view is already
>> quite long and could, for example, include:
>>
>> Numerical Analysis and Linear Algebra
>>
>> Bessel        Bessel Functions Computations and Approximations
>> cubature      Adaptive multivariate integration over hypercubes
>> elliptic      Elliptic and related functions
>> expm          Matrix exponential, logarithm, etc.
>> fdim      Functions for calculating fractal dimension
>> gaussquad     Collection of functions for Gaussian quadrature
>> gmp           Multiple precision arithmetic
>> gsl           Wrapper for the Gnu Scientific Library
>> hypergeo      The hypergeometric function
>> irlba         Fast partial SVD by Lanczos bidiagonalization
>> matlab        MATLAB emulation package
>> multipol      Multivariate polynomials
>> numDeriv      Accurate numerical derivatives
>> onion         Octonions and quaternions
>> orthogonalsplinebasis  Orthogonal Bspline basis functions orthopolynom
>> Functions for orthogonal and orthonormal polynomials
>> polspline     Polynomial spline routines
>> polynom       Implement a class for univariate polynomial manipulations
>> PolynomF      Polynomials in R
>> pracma        Practical numerical math functions
>> pspline       Penalized smoothing splines
>> quaternions   Arithmetics and linear algebra with quaternions
>> R2Cuba        Multidimensional numerical integration
>> RcppArmadillo Rcpp integration for Armadillo templated linear algebra library
>> RcppEigen  Rcpp integration for the Eigen templated linear algebra library
>> RcppOctave    Rcpp integration of Octave
>> R.matlab  Read and write of MAT files and R-to-Matlab connectivity
>> Rmpfr      Multiple precision floating-point reliable
>> sparseGrid    Sparse grid integration in R
>> spuRs         Functions and datasets scientific programming and simulation
>> sspline       Smoothing splines on the sphere
>> stinepack     Stineman: consistently well behaved method of interpolation
>> svd           Interfaces to various state-of-art SVD and eigensolvers
>> voronoi       Methods and applications related to Voronoi tessellations
>> wavelets...
>>
>> Simulation and Differential Equations
>>
>> bvpSolve  Solvers for boundary value problems of ODEs
>> ddesolve      Solver for Delay Differential Equations
>> deSolve       General solvers for initial value problems of ordinary
>>              differential equations (ODE), partial differential equations
>>              (PDE), differential algebraic equations (DAE), and delay
>>              differential equations (DDE)
>> deTestSet  Testset for differential equations
>> odesolve  Solvers for Ordinary Differential Equations
>> PBSddesolve  Solver for Delay Differential Equations
>> rootSolve     Root finding, equilibrium and steady-state analysis of ODEs
>> sde           Simulation and Inference for Stochastic Differential Equations
>> Sim.DiffProc  Simulation of diffusion processes
>> simecol       Simulation of ecological and other dynamic systems
>>
>> and probably many more in the end. I left out the optimization
>> packages deliberately, but of course there would be a strong hint to
>> that task view.
>
>
> If you put pracma in "Numerical Analysis and Linear Algebra", then I feel you should also include  BB and nleqslv under that heading. Both of these do things that can be classified as Numerical Analysis. And both can of course also be used for simulation.
>
>
> BB  solve  (sparse) systems of non linear equations using spectral gradient methods nleqslv solve systems of nonlinear equations combining global strategies with a Broyden or Newron method.
>
> Berend
>
> ______________________________________________
> [hidden email] mailing list
> https://stat.ethz.ch/mailman/listinfo/r-devel
>
> ______________________________________________
> [hidden email] mailing list
> https://stat.ethz.ch/mailman/listinfo/r-devel
>

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