1D interpolation in nearest, linear or spline mode
Syntax
yp = interp1(y, xp)yp = interp1(x, y, xp)yp = interp1(.., xp, method)yp = interp1(.., xp, method, extrapolation)
Arguments
 x
 vector of at least 2 real numbers: Abscissas of known interpolation nodes, without duplicates. By default,
 if
y
is a vector:x=1:length(y)
.  if
y
is a matrix or an hypermatrix:x=1:size(y,1)
.
 if
 y
 vector, matrix or hypermatrix of real or complex numbers: values at known interpolation nodes, at the corresponding
x
abscissas. if
y
is a vector,x
andy
must have the same length.  if
y
is a matrix or an hypermatrix, we must havelength(x)==size(y,1)
. Each column ofy
is then interpolated versus the samex
abscissas, for the givenxp
.
 if
 xp
 scalar, vector, matrix or hypermatrix or decimal numbers: abscissas of points whose values
yp
must be computed according to data of interpolation nodes.  yp
 vector, matrix, or hypermatrix of numbers: interpolated
y
values at the givenxp
. if
y
is a vector:yp
has the size ofxp
.  if
y
is a matrix or an hypermatrix: if
xp
is a scalar or a vector:size(yp)
is[length(xp) size(y)(2:$)]
 if
xp
is a matrix or an hypermatrix:size(yp)
is[size(xp) size(y)(2:$)]
 if
 if
 method
 string defining the interpolation method. Possible values and processing are:
"linear": linear interpolation between consecutive nodes, used by default. "spline": interpolation by cubic splines "nearest": for each value xp(j), yp(j) takes the value or y(i) corresponding to x(i) the nearest neighbor of xp(j)
 extrapolation
 string or number defining the yp(j) components for xp(j) values outside the [x(1)=min(x),x($)=max(x)] interval. We suppose herebelow that
x
andy
have already been sorted accordingly."extrap": interp1(x,y,xp, method, "extrap")
is equivalent tointerp1(x,y,xp, method, method)
."linear": Can be used with the "spline"
(and obviously"linear"
) interpolation methods."periodic": This extrapolation type can be used with the "linear"
or"spline"
interpolation methods. Then: ify
is a vector,y(1)==y($)
is required ; otherwisey(1,:)==y($,:)
is required."edgevalue": Then yp(i)=y(1)
for everyxp(i)<x(1)
, andyp(i)=y($)
for everyxp(i)>x($)
.padding: padding
is a decimal or complex number used to setyp(i)=padding
for everyxp(i) ∉ [min(x),max(x)]
. Example:yi=interp1(x,y,xp,method, 0)
.(none): By default, the extrapolation is performed by splines when splines are used for the interpolation, and by padding with %nan when the interpolation is linear or by "nearest" node.
Description
Given (x,y,xp)
, this function computes the yp components corresponding to xp by the interpolation between known data provided by (x,y) nodes.
x
is priorly sorted in ascending order, and y
values or per column are then sorted accordingly.
Interpolation of complex values: When y
is complex, its real and imaginary parts are interpolated separately, and then added to build the complex yp
.
interp1(x,y,xp,"nearest"): For any xp at the middle of an [x(i),x(i+1)]
interval, the upper bound x(i+1)
is considered as the nearest x
value, and yp=y(i+1)
is assigned.
linear interpolations
They are performed through the linear_interpn(..)
function, with the corresponding "edgevalue"→"C0"
, "linear"→"natural"
, "periodic"→"periodic"
extrapolation option.
spline interpolations
interp1(..,xp,"spline") or interp1(..,xp,"spline","spline") or interp1(..,xp,"spline","extrap") use not_a_knot
edges conditions. Extrapolation is performed by using both spline polynomials computed at the (x,y)
edges.
interp1(..,xp,"spline","edgevalue") uses not_a_knot
edges conditions and then calls interp(..,"C0")
to perform the actual interpolation and extrapolation.
interp1(..,xp,"spline","periodic") calls both splin(..)
and then interp(..)
with their "periodic"
option.
interp1(..,xp,"spline","linear") calls splin(..,"natural")
for linear edges conditions, and then feeds interp(..,"linear")
.
Examples
x = linspace(0, 10, 11)';y = sin(x);xx = linspace(0,10,1000)';yy2 = interp1(x, y, xx, 'linear');yy1 = interp1(x, y, xx, 'nearest');yy3 = interp1(x, y, xx, 'spline');clfh = plot(xx, [yy1 yy2 yy3], x, y, '.')h(1).mark_size = 8;title "Interpolation of a poorly sampled sin() function" fontsize 3legend(['nearest','linear','spline','nodes'], "in_lower_left");
See also
 interp — cubic spline evaluation function
 splin — cubic spline interpolation
 linear_interpn — n dimensional linear interpolation
History
Version  Description 
6.1.1 

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