interp

cubic spline evaluation function

Calling Sequence

[yp [,yp1 [,yp2 [,yp3]]]]=interp(xp, x, y, d [, out_mode])

Arguments

:xp real vector or matrix : :x,y,d real vectors of the same size defining a cubic spline or sub-

spline function (called s in the following)

: :out_mode (optional) string defining the evaluation of s outside

the [x1,xn] interval

: :yp vector or matrix of same size than xp, elementwise evaluation

of s on xp (yp(i)=s(xp(i) or yp(i,j)=s(xp(i,j))

: :yp1, yp2, yp3 vectors (or matrices) of same size than xp,

elementwise evaluation of the successive derivatives of s on xp

:

Description

Given three vectors (x,y,d) defining a spline or sub-spline function (see `splin`_) with yi=s(xi), di = s’(xi) this function evaluates s (and s’, s’‘, s’‘’ if needed) at xp(i) :

The out_mode parameter set the evaluation rule for extrapolation, i.e. for xp(i) not in [x1,xn] :

:”by_zero” an extrapolation by zero is done : :”by_nan” extrapolation by Nan : :”C0” the extrapolation is defined as follows : : :”natural” the extrapolation is defined as follows ( p_i being the

polynomial defining s on [x_i,x_{i+1}]) :

: :”linear” the extrapolation is defined as follows : : :”periodic” s is extended by periodicity. :

Examples

// see the examples of splin and lsq_splin

// an example showing C2 and C1 continuity of spline and subspline
a = -8; b = 8;
x = `linspace`_(a,b,20)';
y = `sinc`_(x);
dk = `splin`_(x,y);  // not_a_knot
df = `splin`_(x,y, "fast");
xx = `linspace`_(a,b,800)';
[yyk, yy1k, yy2k] = interp(xx, x, y, dk);
[yyf, yy1f, yy2f] = interp(xx, x, y, df);
`clf`_()
`subplot`_(3,1,1)
`plot2d`_(xx, [yyk yyf])
`plot2d`_(x, y, style=-9)
`legends`_(["not_a_knot spline","fast sub-spline","interpolation points"],...
        [1 2 -9], "ur",%f)
`xtitle`_("spline interpolation")
`subplot`_(3,1,2)
`plot2d`_(xx, [yy1k yy1f])
`legends`_(["not_a_knot spline","fast sub-spline"], [1 2], "ur",%f)
`xtitle`_("spline interpolation (derivatives)")
`subplot`_(3,1,3)
`plot2d`_(xx, [yy2k yy2f])
`legends`_(["not_a_knot spline","fast sub-spline"], [1 2], "lr",%f)
`xtitle`_("spline interpolation (second derivatives)")

// here is an example showing the different extrapolation possibilities
x = `linspace`_(0,1,11)';
y = `cosh`_(x-0.5);
d = `splin`_(x,y);
xx = `linspace`_(-0.5,1.5,401)';
yy0 = interp(xx,x,y,d,"C0");
yy1 = interp(xx,x,y,d,"linear");
yy2 = interp(xx,x,y,d,"natural");
yy3 = interp(xx,x,y,d,"periodic");
`clf`_()
`plot2d`_(xx,[yy0 yy1 yy2 yy3],style=2:5,frameflag=2,leg="C0@linear@natural@periodic")
`xtitle`_(" different way to evaluate a spline outside its domain")

See Also

• `splin`_ cubic spline interpolation
• `lsq_splin`_ weighted least squares cubic spline fitting

History

Version Description 5.4.0 previously, imaginary part of input arguments were implicitly ignored. .. _splin: splin.html .. _lsq_splin: lsq_splin.html