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Scilab help >> Interpolation > interp1

# interp1

one_dimension interpolation function

### Calling Sequence

`[yp]=interp1(x, y,xp [, method,[extrapolation]])`

### Arguments

xp

reals scalar, vector or matrix (or hypermatrix)

x

reals vector

method

(optional) string defining the interpolation method

extrapolation

(optional) string, or real value defining the yp(j) components for xp(j) values outside [x1,xn] interval.

yp

vector, or matrix (or hypermatrix)

### Description

Given `(x,y,xp)`, this function performs the yp components corresponding to xp by the interpolation(linear by default) defined by x and y.

If `yp` is a vector then the length of xp is equal to the length of `yp,` if `yp` is a matrix then `xp` have the same length than the length of each columns of yp, if `yp` is a hypermatrix then the length of `xp` have the same length than the first dimension of `yp.`

If size(y)=[C,M1,M2,M3,...,Mj] and size(xp)=[N1,N2,N3,...,Nk] then size(yp)=[N1,N2,..,Nk,M1,M2,...Mj] and length of x must be equal to size(y,1)

The `method` parameter sets the evaluation rule for interpolation

"linear"

the interpolation is defined by linear method (see interpln)

"spline"

the interpolation is defined by cubic spline interpolation ( see splin , interp)

"nearest"

for each value xp(j), yp(j) takes the value or y(i) corresponding to x(i) the nearest neighbor of xp(j)

The `extrapolation` parameter sets the evaluation rule for extrapolation, i.e for `xp(i)`not in [x1,xn] interval

"extrap"

the extrapolation is performed by the defined method. yp=interp1(x,y,xp,method,"extrap")

real value

you can choose a real value for extrapolation, in this way yp(i) takes this value for xp(i) not in [x1,xn] interval, for example 0 (but also nan or inf). yi=interp1(x,y,xp,method, 0)

by default

the extrapolation is performed by the defined method (for spline method), and by nan for linear and nearest methods. yp=interp1(x,y,xp,method)

### Examples

```x=linspace(0,3,20);
y=x^2;
xx=linspace(0,3,100);
yy1=interp1(x,y,xx,'linear');
yy2=interp1(x,y,xx,'spline');
yy3=interp1(x,y,xx,'nearest');
plot(xx,[yy1;yy2;yy3],x,y,'*')
xtitle('interpolation of square function')
legend(['linear','spline','nearest'],a=2)```