Title: Interpolation

1 Classes

GSL
- Interp (class)
  - Accel (class)
- Spline (class)

2 GSL::Interp class

2.1 Class methods

GSL::Interp.new(T, n)

GSL::Interp.alloc(T, n)

GSL::Interp.alloc(T, x, y)

GSL::Interp.alloc(x, y)

These methods create an interpolation object of type T for n data-points.

The library provides six types, which are specifiled by an identifier of a constant or a string:

Interp::LINEAR or "linear"

Linear interpolation. This interpolation method does not require any additional memory.
Interp::POLYNOMIAL or "polynomial"

Polynomial interpolation. This method should only be used for interpolating small numbers of points because polynomial interpolation introduces large oscillations, even for well-behaved datasets. The number of terms in the interpolating polynomial is equal to the number of points.
Interp::CSPLINE or "cspline"

Cubic spline with natural boundary conditions.
Interp::CSPLINE_PERIODIC or "gsl_cspline_periodic" or "cspline_periodic"

Cubic spline with periodic boundary conditions
Interp::AKIMA or "akima"

Non-rounded Akima spline with natural boundary conditions. This method uses the non-rounded corner algorithm of Wodicka.
Interp::AKIMA_PERIODIC or "akima_periodic"

Non-rounded Akima spline with periodic boundary conditions. This method uses the non-rounded corner algorithm of Wodicka.
- ex: For cubic spline for 10 points,
```
sp = Interp.new("cspline", 10)
```

GSL::Interp.bsearch(xa, x, index_lo, index_hi)

This returns the index i of the vector xa such that xa[i] <= x < x[i+1]. The index is searched for in the range [index_lo,index_hi].

2.2 Methods

GSL::Interp#init(xa, ya): This method initializes the interpolation object interp for the data (xa,ya) where xa and ya are vectors. The interpolation object (GSL::Interp) does not save the data vectors xa, ya and only stores the static state computed from the data. The xa vector is always assumed to be strictly ordered; the behavior for other arrangements is not defined.
GSL::Interp#name: This returns the name of the interpolation type used by self.
GSL::Interp#min_size: This returns the minimum number of points required by the interpolation type of self. For example, Akima spline interpolation requires a minimum of 5 points.
GSL::Interp#accel: In C level, the library requires a gsl_interp_accel object, but it is hidden in Ruby/GSL. It is automatically allocated when a GSL::Interp object is created, stored in it, and destroyed when the Interp object is cleaned by the Ruby GC. This method is used to access to the Interp::Accel object stored in self.
GSL::Interp#find(xa, x)
GSL::Interp#accel_find(xa, x)
GSL::Interp::Accel#find(xa, x): This method performs a lookup action on the data array xa. This is how lookups are performed during evaluation of an interpolation. The function returns an index i such that xa[i] <= x < xa[i+1].
GSL::Interp#eval(xa, ya, x)
GSL::Interp#eval_e(xa, ya, x): These methods return the interpolated value for a given point x, using the interpolation object self, data vectors xa and ya. The data x can be a Numeric, Vector, Matrix or an NArray.
GSL::Interp#eval_deriv(xa, ya, x)
GSL::Interp#eval_deriv_e(xa, ya, x): These methods return the derivative of an interpolated function for a given point x, using the interpolation object self, data vectors xa and ya.
GSL::Interp#eval_deriv2(xa, ya, x)
GSL::Interp#eval_deriv2_e(xa, ya, x): These methods return the second derivative of an interpolated function for a given point x, using the interpolation object self, data vectors xa and ya.
GSL::Interp#eval_integ(xa, ya, a, b)
GSL::Interp#eval_integ_e(xa, ya, a, b): These methods return the numerical integral result of an interpolated function over the range [a, b], using the interpolation object self, data vectors xa and ya.

3 GSL::Spline class

3.1 Class methods

GSL::Spline.new(T, n)

GSL::Spline.alloc(T, x, y)

GSL::Spline.new(x, y, T)

This creates a GSL::Spline object of type T for n data-points. The type T is the same as GSL::Interp class.

These two are equivalent.

GSL::Spline.alloc and GSL::Spline#init

sp = GSL::Spline.alloc(T, n)
sp.init(x, y)                 # x and y are vectors of length n

GSL::Spline.alloc with two vectors
```
sp = GSL::Spline.alloc(T, x, y)
```

If T is not given, "cspline" is used.

3.2 Methods

GSL::Spline#init(xa, ya)

This initializes a GSL::Spline object self for the data (xa, ya) where xa and ya are Ruby arrays of equal sizes or GSL::Vector.

GSL::Spline#name

This returns the name of the spline type used by self.

GSL::Spline#eval(x)

This returns the interpolated value for a given point x. The data x can be a Numeric, Vector, Matrix or an NArray.

NOTE: In a GSL-C program, a gsl_interp_accel object is required to use the function gsl_spline_eval. In Ruby/GSL, the gsl_interp_accel is hidden, it is automatically allocated when a GSL::Spline object is created, and also destroyed when the Spline object is cleaned by the Ruby GC. The accel object can be accessed via the method GSL::Spline#accel.

GSL::Spline#eval_deriv(x)

This returns the derivative of an interpolated function for a given point x, usingthe data arrays xa and ya set by init.

GSL::Spline#eval_deriv2(x)

This returns the second derivative at x.

GSL::Spline#eval_integ(a, b)

Returns the numerical integral over the range [a, b].

GSL::Spline#find(xa, x)

GSL::Spline#accel_find(xa, x)

This method performs a lookup action on the data array xa. This is how lookups are performed during evaluation of an interpolation. The function returns an index i such that xa[i] <= x < xa[i+1].

See also the GSL manual and the examples in samples/

prev next

Reference index top