Interpolation for 1-D, 2-D, 3-D, and N-D gridded data in ndgrid format

In a future release, `interpn`

will not accept
mixed combinations of row and column vectors for the sample and query
grids. For more information, and recommendations for updating your
code, see Functionality being removed or changed.

returns
interpolated values of a function of `Vq`

= interpn(`X1,X2,...,Xn`

,`V`

,`Xq1,Xq2,...,Xqn`

)*n* variables
at specific query points using linear interpolation. The results always
pass through the original sampling of the function. `X1,X2,...,Xn`

contain
the coordinates of the sample points. `V`

contains
the corresponding function values at each sample point. `Xq1,Xq2,...,Xqn`

contain
the coordinates of the query points.

assumes
a default grid of sample points. The default grid consists of the
points, 1,2,3,...n`Vq`

= interpn(`V`

,`Xq1,Xq2,...,Xqn`

)_{i} in each dimension. The
value of n_{i} is the length of the ith dimension
in `V`

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

specifies
an optional, trailing input argument that you can pass with any of
the previous syntaxes. The `Vq`

= interpn(___,`method`

)`method`

argument can
be any of the following strings that specify alternative interpolation
methods: `'linear'`

, `'nearest'`

, `'pchip'`

,`'cubic'`

,
or `'spline'`

. The default method is `'linear'`

.

also
specifies `Vq`

= interpn(___,`method`

,`extrapval`

)`extrapval`

, a scalar value that is assigned
to all queries that lie outside the domain of the sample points.

If you omit the `extrapval`

argument for queries
outside the domain of the sample points, then based on the `method`

argument `interpn`

returns
one of the following:

The extrapolated values for the

`'spline'`

method`NaN`

values for interpolation methods other than`'spline'`

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