spline :: Functions (MATLAB Function Reference) text://0
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MATLAB Function Reference
spline
Cubic spline data interpolation
Syntax
pp = spline(x,Y)
yy = spline(x,Y,xx)
Description
pp = spline(x,Y) returns the piecewise polynomial form of the cubic spline interpolant for later use with ppval and
the spline utility unmkpp. x must be a vector. Y can be a scalar, a vector, or an array of any dimension, subject to the
following conditions:
If Y is a scalar or vector, it must have the same length as x. A scalar value for x or Y is expanded to have the same
length as the other. See Exceptions (1) for an exception to this rule, in which the not-a-knot end conditions are
used.
If Y is an array that is not a vector, the size of Y must have the form [d1,d2,...,dk,n], where n is the length of
x. The interpolation is performed for each d1-by-d2-by-...-dk value in Y. See Exceptions (2) for an exception to
this rule.
yy = spline(x,Y,xx) is the same as yy = ppval(spline(x,Y),xx), thus providing, in yy, the values of the
interpolant at xx. xx can be a scalar, a vector, or a multidimensional array. The sizes of xx and yy are related as follows:
If Y is a scalar or vector, yy has the same size as xx.
If Y is an array that is not a vector,
If xx is a scalar or vector, size(yy) equals [d1, d2, ..., dk, length(xx)].
If xx is an array of size [m1,m2,...,mj], size(yy) equals [d1,d2,...,dk,m1,m2,...,mj].
Exceptions
If Y is a vector that contains two more values than x has entries, the first and last value in Y are used as the
endslopes for the cubic spline. If Y is a vector, this means
f(x) = Y(2:end-1)
df(min(x)) = Y(1)
df(max(x)) = Y(end)
1.
If Y is a matrix or an N-dimensional array with size(Y,N) equal to length(x)+2, the following hold:
f(x(j)) matches the value Y(:,...,:,j+1) for j=1:length(x)
Df(min(x)) matches Y(:,:,...:,1)
Df(max(x)) matches Y(:,:,...:,end)
2.
Note You can also perform spline interpolation using the interp1 function with the command
interp1(x,y,xx,'spline'). Note that while spline performs interpolation on rows of an input matrix,
interp1 performs interpolation on columns of an input matrix.
Examples
Example 1
This generates a sine curve, then samples the spline over a finer mesh.
x = 0:10;
y = sin(x);
xx = 0:.25:10;
yy = spline(x,y,xx);
plot(x,y,'o',xx,yy)
