spline

spline(x,v,xq) returns the cubic spline interpolated data of function v corresponding to the querying elements in xq. Spline uses the not-a-knot end conditions by default but it can also use the 'clamped' end condition.

x: vector with sample points
v: evaluation of x. It can be a vector or a matrix. If v is a vector the same size as x, the not-a-knot end conditions are use. If v is a vector containing exactly two more elements than x, the 'clamped' end conditions are used. In this case, the first and last elements in v are used as the end-slopes for the cubic spline. The same applies row by row in the case of v being a matrix
xq: coordinates of querying points. It can be a vector or a matrix

Examples

>> x = [1 2 3 4]
y = [5 2 10 9]
xq = 1:0.1:4
yq = spline(x,y,xq)
op = struct('show', false)
overlay({plot(xq,yq,op), scatter(x,y,op)})

>> x = [1 2 3 4]
y = [5 2 10 9; 1 3 -5 7]  % y matrix 
xq = 1:0.1:4
yq = spline(x,y,xq)
op = struct('show', false)
overlay({plot(xq,yq,op), scatter(x,y,op)})

>> x = [0 1 3 4]
y = [0 0 2 2]
xq = 0:0.1:4

% not-a-knot interpolation
yq1 = spline(x,y,xq)

% 'clamped' interpolation: 0 and 1 are used as endslopes
yq2 = spline(x,[0 y 1],xq) 

o = struct('show', false) % options struct for scatter
o.markerStroke = 'black'
o.markerSize = 4
s = scatter(x,y,o)

o = struct('show', false)  % options struct for not-a-knot
o.lineStroke = 'blue'
p1 = plot(xq,yq1,o)

o = struct('show', false) % options struct for clamped
o.lineStroke = '#ff0000'
o.dashArray = '6 8'
o.lineWidth = 2
p2 = plot(xq,yq2,o)

o = struct % initializing global options struct
o.showLegend = true
o.legendLabels = {'data points','not-a-knot', 'clamped'}
o.legendX = 263
o.legendY = 180

overlay({s,p1,p2},o)

References

[1] C. de Boor, "A Practical Guide to Splines", Springer-Verlag, 1978.

spline

Examples

References

See also