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https://github.com/jacobwilliams/bspline-fortran

Multidimensional B-Spline Interpolation of Data on a Regular Grid
https://github.com/jacobwilliams/bspline-fortran

b-spline extrapolation fortran fortran-package-manager interpolation least-squares-curve-fitting quadrature-integration splines

Last synced: 11 days ago
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Multidimensional B-Spline Interpolation of Data on a Regular Grid

Host: GitHub
URL: https://github.com/jacobwilliams/bspline-fortran
Owner: jacobwilliams
License: other
Created: 2015-02-25T05:58:13.000Z (almost 10 years ago)
Default Branch: master
Last Pushed: 2024-01-07T03:23:06.000Z (about 1 year ago)
Last Synced: 2024-11-08T03:09:30.886Z (2 months ago)
Topics: b-spline, extrapolation, fortran, fortran-package-manager, interpolation, least-squares-curve-fitting, quadrature-integration, splines
Language: Fortran
Homepage:
Size: 18.6 MB
Stars: 171
Watchers: 22
Forks: 54
Open Issues: 12
Metadata Files:
- Readme: README.md
- License: LICENSE

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README

        ![bspline-fortran](media/bspline-fortran.png)

============

Multidimensional B-Spline Interpolation of Data on a Regular Grid.

## Status

[![Language](https://img.shields.io/badge/-Fortran-734f96?logo=fortran&logoColor=white)](https://github.com/topics/fortran)

[![GitHub release](https://img.shields.io/github/release/jacobwilliams/bspline-fortran.svg)](https://github.com/jacobwilliams/bspline-fortran/releases/latest)

[![Build Status](https://github.com/jacobwilliams/bspline-fortran/actions/workflows/CI.yml/badge.svg)](https://github.com/jacobwilliams/bspline-fortran/actions)

[![codecov](https://codecov.io/gh/jacobwilliams/bspline-fortran/branch/master/graph/badge.svg)](https://codecov.io/gh/jacobwilliams/bspline-fortran)

[![last-commit](https://img.shields.io/github/last-commit/jacobwilliams/bspline-fortran)](https://github.com/jacobwilliams/bspline-fortran/commits/master)

[![DOI](https://zenodo.org/badge/31299552.svg)](https://zenodo.org/badge/latestdoi/31299552)

## Brief description

The library provides subroutines for 1D-6D interpolation and extrapolation using B-splines. The code is written in modern Fortran (i.e., Fortran 2003+). There are two ways to use the module, via a basic subroutine interface and an object-oriented interface. Both are thread safe.

## Subroutine interface

The core routines for the subroutine interface are:

```fortran

!f(x)

subroutine db1ink(x,nx,fcn,kx,iknot,tx,bcoef,iflag)

subroutine db1val(xval,idx,tx,nx,kx,bcoef,f,iflag,inbvx,w0,extrap)

!f(x,y)

subroutine db2ink(x,nx,y,ny,fcn,kx,ky,iknot,tx,ty,bcoef,iflag)

subroutine db2val(xval,yval,idx,idy,tx,ty,nx,ny,kx,ky,bcoef,f,iflag,inbvx,inbvy,iloy,w1,w0,extrap)

!f(x,y,z)

subroutine db3ink(x,nx,y,ny,z,nz,fcn,kx,ky,kz,iknot,tx,ty,tz,bcoef,iflag)

subroutine db3val(xval,yval,zval,idx,idy,idz,tx,ty,tz,nx,ny,nz,kx,ky,kz,bcoef,f,iflag,inbvx,inbvy,inbvz,iloy,iloz,w2,w1,w0,extrap)

!f(x,y,z,q)

subroutine db4ink(x,nx,y,ny,z,nz,q,nq,fcn,kx,ky,kz,kq,iknot,tx,ty,tz,tq,bcoef,iflag)

subroutine db4val(xval,yval,zval,qval,idx,idy,idz,idq,tx,ty,tz,tq,nx,ny,nz,nq,kx,ky,kz,kq,bcoef,f,iflag,inbvx,inbvy,inbvz,inbvq,iloy,iloz,iloq,w3,w2,w1,w0,extrap)

!f(x,y,z,q,r)

subroutine db5ink(x,nx,y,ny,z,nz,q,nq,r,nr,fcn,kx,ky,kz,kq,kr,iknot,tx,ty,tz,tq,tr,bcoef,iflag)

subroutine db5val(xval,yval,zval,qval,rval,idx,idy,idz,idq,idr,tx,ty,tz,tq,tr,nx,ny,nz,nq,nr,kx,ky,kz,kq,kr,bcoef,f,iflag,inbvx,inbvy,inbvz,inbvq,inbvr,iloy,iloz,iloq,ilor,w4,w3,w2,w1,w0,extrap)

!f(x,y,z,q,r,s)

subroutine db6ink(x,nx,y,ny,z,nz,q,nq,r,nr,s,ns,fcn,kx,ky,kz,kq,kr,ks,iknot,tx,ty,tz,tq,tr,ts,bcoef,iflag)

subroutine db6val(xval,yval,zval,qval,rval,sval,idx,idy,idz,idq,idr,ids,tx,ty,tz,tq,tr,ts,nx,ny,nz,nq,nr,ns,kx,ky,kz,kq,kr,ks,bcoef,f,iflag,inbvx,inbvy,inbvz,inbvq,inbvr,inbvs,iloy,iloz,iloq,ilor,ilos,w5,w4,w3,w2,w1,w0,extrap)

```

The ```ink``` routines compute the interpolant coefficients, and the ```val``` routines evalute the interpolant at the specified value of each coordinate. The 2D and 3D routines are extensively refactored versions of the original routines from the [NIST Core Math Library](http://www.nist.gov/itl/math/mcsd-software.cfm).  The others are new, and are simply extensions of the same algorithm into the other dimensions.

## Object-oriented interface

In addition to the main subroutines, an object-oriented interface is also provided. For example, for the 3D case:

```Fortran

type(bspline_3d) :: s

call s%initialize(x,y,z,fcn,kx,ky,kz,iflag,extrap)

call s%evaluate(xval,yval,zval,idx,idy,idz,f,iflag)

call s%destroy()

```

Which uses the default "not-a-knot" end conditions. You can also specify the knot vectors (in this case, `tx`, `ty`, and `tz`) manually during class initialization:

```Fortran

call s%initialize(x,y,z,fcn,kx,ky,kz,tx,ty,tz,iflag,extrap)

```

The various bspline classes can also be initialized using constructors, which have similar interfaces as the `initialize` methods. For example:

```Fortran

type(bspline_3d) :: s

s = bspline_3d(x,y,z,fcn,kx,ky,kz,iflag,extrap)

```

## Spline order

The various `k` inputs (i.e., `kx`, `ky`, etc.) specify the spline order for each dimension. The order is the polynomial degree + 1. For example:

* `k=2` : Linear

* `k=3` : Quadratic

* `k=4` : Cubic

* etc.

## Extrapolation

The library optionally supports extrapolation for points outside the range of the coefficients. This is disabled by default (in which case an error code is returned for points outside the bounds). To enable extrapolation, use the optional `extrap` input to the various `db*val` subroutines or the `initialize` methods from the object-oriented interface.

## Integration

The library also contains routines for computing definite integrals of bsplines. There are two methods (currently only for 1D):

* Basic version: `db1sqad` (`integral` in the object-oriented interface) -- Computes the integral on `(x1,x2)` of a b-spline by applying a 2, 6, or 10 point Gauss formula on subintervals of `(x1,x2)`. This is only valid for orders <= 20.

* More general version: `db1fqad` (`fintegral` in the object-oriented interface) -- Computes the integral on `(x1,x2)` of a product of a user-defined function `fun(x)` and the ith derivative of a b-spline with an adaptive 8-point Legendre-Gauss algorithm.

Note that extrapolation is not currently supported for these.

## Least squares fitting

The BSpline-Fortran library also exports the `defc` subroutine, which can be used to fit B-spline polynomials to 1D data using a weighted least squares method. The `dfc` subroutine also allows for equality and inequality constraints to be imposed on the fitted curve. These procedures are not yet available in the object oriented interface.

## Examples

See the [examples](https://github.com/jacobwilliams/bspline-fortran/tree/master/test) for more details. Note that, to compile and run some of the test programs, the [pyplot-fortran](https://github.com/jacobwilliams/pyplot-fortran) library  (which is used to generate plots) is required. This will automatically be downloaded by `FPM`.

## Compiling

The library can be compiled with recent versions the Intel Fortran Compiler and GFortran (and presumably any other Fortran compiler that supports modern standards).

### FPM

A `fpm.toml` file is provided for compiling bspline-fortran with the [Fortran Package Manager](https://github.com/fortran-lang/fpm). For example, to build:

```

fpm build --profile release

```

By default, the library is built with double precision (`real64`) real values and single precision (`int32`) integer values. Explicitly specifying the real or integer kinds can be done using the following processor flags:

Preprocessor flag | Kind  | Number of bytes

----------------- | ----- | ---------------

`REAL32`  | `real(kind=real32)`  | 4

`REAL64`  | `real(kind=real64)`  | 8

`REAL128` | `real(kind=real128)` | 16

Preprocessor flag | Kind  | Number of bytes

----------------- | ----- | ---------------

`INT8`  | `integer(kind=int8)`  | 1

`INT16`  | `integer(kind=int16)`  | 2

`INT32` | `integer(kind=int32)` | 4

`INT64` | `integer(kind=int64)` | 8

For example, to build a single precision version of the library, use:

```

fpm build --profile release --flag "-DREAL32"

```

To run the unit tests:

```

fpm test --profile release

```

To use `bspline-fortran` within your fpm project, add the following to your `fpm.toml` file:

```toml

[dependencies]

bspline-fortran = { git="https://github.com/jacobwilliams/bspline-fortran.git" }

```

or, to use a specific version:

```toml

[dependencies]

bspline-fortran = { git="https://github.com/jacobwilliams/bspline-fortran.git", tag = "7.3.0"  }

```

### CMake

A basic CMake configuration file is also included. For example, to build a static library:

```bash

 mkdir build

 cd build

 cmake ..

 make

```

Or, to build a shared library:

```bash

 cmake -DBUILD_SHARED_LIBS=ON ..

```

For a debug build:

```bash

 cmake -DCMAKE_BUILD_TYPE=DEBUG ..

```

## Dependencies

The library requires some [BLAS](https://netlib.org/blas/) routines, which are included. However, the user may also choose to link to an external BLAS library. This can be done by using the `HAS_BLAS` compiler directive. For example:

```

fpm build --compiler gfortran --flag "-DHAS_BLAS -lblas"

```

However, note that an external BLAS can only be used if the library is compiled with double precision (`real64`) reals.

## Documentation

The latest API documentation can be found [here](https://jacobwilliams.github.io/bspline-fortran/). This was generated from the source code using [FORD](https://github.com/Fortran-FOSS-Programmers/ford) (i.e. by running `ford ford.md`).

## License

The bspline-fortran source code and related files and documentation are distributed under a permissive free software [license](https://github.com/jacobwilliams/bspline-fortran/blob/master/LICENSE) (BSD-style).

### Keywords

* Bspline, spline, interpolation, data fitting, multivariate interpolation, multidimensional interpolation, integration

## See also

 * This library includes the public domain DBSPLIN and DTENSBS code from the [NIST Core Math Library](http://www.nist.gov/itl/math/mcsd-software.cfm) (CMLIB).

 * [SPLPAK](https://github.com/jacobwilliams/splpak) Multidimensional least-squares cubic spline fitting

 * [FINTERP](https://github.com/jacobwilliams/finterp) Multidimensional Linear Interpolation with Modern Fortran

 * [PCHIP](https://github.com/jacobwilliams/PCHIP) Piecewise Cubic Hermite Interpolation.

 * [Regridpack](https://github.com/jacobwilliams/regridpack) Linear or cubic interpolation for 1D-4D grids.