interp1 one_dimension interpolation function

## Syntax

              yp = interp1(x, y, xp)
              yp = interp1(x, y, xp, method)
              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'], "in_upper_left");

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)

## See also

- interp
- interpln
- splin

## History

5.4.0 previously, imaginary part of input arguments were implicitly ignored.