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Aide de Scilab >> Interpolation > interp1

interp1

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).

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 and y must have the same length.
  • if y is a matrix or an hypermatrix, we must have length(x)==size(y,1). Each column of y is then interpolated versus the same x abscissas, for the given xp.

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 given xp.
  • if y is a vector: yp has the size of xp.

  • if y is a matrix or an hypermatrix:
    • if xp is a scalar or a vector: size(yp) is [length(xp) size(y)(2:$)]
    • if xp is a matrix or an hypermatrix: size(yp) is [size(xp) size(y)(2:$)]

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 here-below that x and y have already been sorted accordingly.

"extrap": interp1(x,y,xp, method, "extrap") is equivalent to interp1(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: if y is a vector, y(1)==y($) is required ; otherwise y(1,:)==y($,:) is required.
"edgevalue": Then yp(i)=y(1) for every xp(i)<x(1), and yp(i)=y($) for every xp(i)>x($).
padding: padding is a decimal or complex number used to set yp(i)=padding for every xp(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');
clf
h = plot(xx, [yy1 yy2 yy3], x, y, '.')
h(1).mark_size = 8;
title "Interpolation of a poorly sampled sin() function" fontsize 3
legend(['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

VersionDescription
6.1.1
  • For complex y values, imag(y) is no longer ignored: real(y) and imag(y) parts are separately interpolated.
  • "periodic" extrapolation added for the linear and spline interpolations.
  • "edgevalue" extrapolation added for all nearest, linear and spline interpolations.
  • "linear" extrapolation added for the spline interpolation.
  • When xp is an hypermatrix and size(xp,1)==1, size(yp) is now always [size(xp) size(y)(2,$) instead of [size(xp,2:$), size(y)(2,$).
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Last updated:
Mon Jan 03 14:33:06 CET 2022