This chapter describes functions for performing interpolation. The library provides a variety of interpolation methods, including Cubic splines and Akima splines. The interpolation types are interchangeable, allowing different methods to be used without recompiling. Interpolations can be defined for both normal and periodic boundary conditions. Additional functions are available for computing derivatives and integrals of interpolating functions.
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.alloc("cspline", 10)GSL::Interp#init(xa, ya)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#nameGSL::Interp#min_sizeGSL::Interp.bsearch(xa, x, index_lo, index_hi)xa[i] <= x < x[i+1]. The index is searched for in the range
[index_lo,index_hi].GSL::Interp#accelgsl_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)i such that
xa[i] <= x < xa[i+1].GSL::Interp#eval(xa, ya, x)GSL::Interp#eval_e(xa, ya, x)Numeric, Vector, Matrix or an NArray.GSL::Interp#eval_deriv(xa, ya, x)GSL::Interp#eval_deriv_e(xa, ya, x)GSL::Interp#eval_deriv2(xa, ya, x)GSL::Interp#eval_deriv2_e(xa, ya, x)GSL::Interp#eval_integ(xa, ya, a, b)GSL::Interp#eval_integ_e(xa, ya, a, b)GSL::Spline.alloc(T, n)GSL::Spline.alloc(T, x, y)GSL::Spline.alloc(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.
GSL::Spline#init(xa, ya)GSL::Spline object self for the data
(xa, ya) where xa and ya are Ruby arrays of equal sizes
or GSL::Vector.GSL::Spline#nameGSL::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)GSL::Spline#eval_deriv2(x)GSL::Spline#eval_integ(a, b)GSL::Spline#find(xa, x)GSL::Spline#accel_find(xa, x)i such that
xa[i] <= x < xa[i+1].See also the GSL manual and the examples in examples/