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Gridded data interpolation

Use `griddedInterpolant`

to perform
interpolation on a 1-D, 2-D, 3-D, or N-D gridded data set. `griddedInterpolant`

returns
the interpolant `F`

for
the given dataset. You can evaluate `F`

at a set
of query points, such as `(xq,yq)`

in 2-D, to produce
interpolated values `vq = F(xq,yq)`

.

Use `scatteredInterpolant`

to
perform interpolation with scattered data.

`F = griddedInterpolant`

`F = griddedInterpolant(x,v)`

`F = griddedInterpolant(X1,X2,...,Xn,V)`

`F = griddedInterpolant(V)`

`F = griddedInterpolant({xg1,xg2,...,xgn},V)`

`F = griddedInterpolant(___,Method)`

`F = griddedInterpolant(___,Method,ExtrapolationMethod)`

creates
an empty gridded data interpolant object.`F`

= griddedInterpolant

creates
a 2-D, 3-D, or N-D interpolant using a full grid of sample points passed as a set
of `F`

= griddedInterpolant(`X1`

,`X2`

,...,`Xn`

,`V`

)`n`

-dimensional arrays `X1,X2,...,Xn`

.
The `V`

array contains the sample values associated
with the point locations in `X1,X2,...,Xn`

. Each
of the arrays `X1,X2,...,Xn`

must be the same size
as `V`

.

uses
the default grid to create the interpolant. When you use this syntax, `F`

= griddedInterpolant(`V`

)`griddedInterpolant`

defines
the grid as a set of points whose spacing is `1`

and
range is [`1`

, `size(V,i)`

] in the `i`

th
dimension. Use this syntax when you want to conserve memory and are
not concerned about the absolute distances between points.

specifies `F`

= griddedInterpolant(`{xg1,xg2,...,xgn}`

,`V`

)`n`

grid vectors to describe
an `n`

-dimensional grid of sample points. Use this
syntax when you want to use a specific grid and also conserve memory.

specifies
an interpolation method: `F`

= griddedInterpolant(___,`Method`

)`'linear'`

, `'nearest'`

, `'next'`

, `'previous'`

, `'pchip'`

, `'cubic'`

,
or `'spline'`

. You can specify `Method`

as
the last input argument in any of the first four syntaxes.

specifies
both the interpolation and extrapolation methods. `F`

= griddedInterpolant(___,`Method`

,`ExtrapolationMethod`

)`griddedInterpolant`

uses `ExtrapolationMethod`

to
estimate the value when your query points fall outside the domain
of your sample points. Specify `Method`

and `ExtrapolationMethod`

together
as the last two input arguments in any of the first four syntaxes.

Use `griddedInterpolant`

to create the interpolant, `F`

.
Then you can evaluate `F`

at specific points using
any of the following syntaxes:

`Vq = F(Xq)`

specifies the query points in the matrix`Xq`

. Each row of`Xq`

contains the coordinates of a query point.`Vq = F(xq1,xq2,...,xqn)`

specifies the query points`xq1,xq2,...,xqn`

as column vectors of length`m`

representing`m`

points scattered in`n`

-dimensional space.`Vq = F(Xq1,Xq2,...,Xqn)`

specifies the query points using the`n`

-dimensional arrays`Xq1,Xq2,...,Xqn`

, which define a full grid of points.`Vq = F({xgq1,xgq2,...,xgqn})`

specifies the query points as grid vectors. Use this syntax to conserve memory when you want to query a large grid of points.

It is quicker to evaluate a

`griddedInterpolant`

object`F`

at many different sets of query points than it is to compute the interpolations separately using`interp1`

,`interp2`

,`interp3`

, or`interpn`

. For example:% Fast to create interpolant F and evaluate multiple times F = griddedInterpolant(X1,X2,V) v1 = F(Xq1) v2 = F(Xq2) % Slower to compute interpolations separately using interp2 v1 = interp2(X1,X2,V,Xq1) v2 = interp2(X1,X2,V,Xq2)

`fillmissing`

| `filloutliers`

| `interp1`

| `interp2`

| `interp3`

| `interpn`

| `meshgrid`

| `ndgrid`

| `scatteredInterpolant`

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