MATLAB Function Reference |

Two-dimensional data interpolation (table lookup)

**Syntax**

ZI = interp2(X,Y,Z,XI,YI) ZI = interp2(Z,XI,YI) ZI = interp2(Z,ntimes) ZI = interp2(X,Y,Z,XI,YI,method) ZI = interp2(...,method, extrapval)

**Description**

```
ZI = interp2(X,Y,Z,XI,YI)
```

returns matrix `ZI`

containing elements corresponding to the elements of `XI`

and `YI`

and determined by interpolation within the two-dimensional function specified by matrices `X`

, `Y`

, and `Z`

. `X`

and `Y`

must be monotonic, and have the same format ("plaid") as if they were produced by `meshgrid`

. Matrices `X`

and `Y`

specify the points at which the data `Z`

is given. Out of range values are returned as `NaNs`

.

`XI`

and `YI`

can be matrices, in which case `interp2`

returns the values of `Z`

corresponding to the points `(XI(i,j),YI(i,j))`

. Alternatively, you can pass in the row and column vectors `xi`

and `yi`

, respectively. In this case, `interp2`

interprets these vectors as if you issued the command `meshgrid(xi,yi)`

.

```
ZI = interp2(Z,XI,YI)
```

assumes that `X = 1:n`

and` Y = 1:m`

, where `[m,n] = size(Z)`

.

```
ZI = interp2(Z,ntimes)
```

expands `Z`

by interleaving interpolates between every element, working recursively for `ntimes`

. `interp2(Z)`

is the same as `interp2(Z,1)`

.

`ZI = interp2(X,Y,Z,XI,YI,`

specifies an alternative interpolation method:`method`

)

`'nearest'` |
Nearest neighbor interpolation |

`'linear'` |
Bilinear interpolation (default) |

`'spline'` |
Cubic spline interpolation |

`'cubic'` |
Bicubuc interpolation |

All interpolation methods require that `X`

and `Y`

be monotonic, and have the same format ("plaid") as if they were produced by `meshgrid`

. If you provide two monotonic vectors, `interp2`

changes them to a plaid internally. Variable spacing is handled by mapping the given values in `X`

, `Y`

, `XI`

, and `YI`

to an equally spaced domain before interpolating. For faster interpolation when `X`

and `Y`

are equally spaced and monotonic, use the methods `'*linear'`

, `'*cubic'`

, `'*spline'`

, or `'*nearest'`

.

specifies a method and a scalar value for ```
ZI = interp2(...,method, extrapval)
```

`ZI`

outside of the domain created by `X`

and `Y`

. Thus, `ZI`

equals `extrapval`

for any value of `YI`

or `XI`

that is not spanned by `Y`

or `X`

respectively. A method must be specified to use `extrapval`

. The default method is `'linear'`

.

**Remarks**

The `interp2`

command interpolates between data points. It finds values of a two-dimensional function underlying the data at intermediate points.

Interpolation is the same operation as table lookup. Described in table lookup terms, the table is `tab`

`=`

`[NaN,Y;`

`X,Z]`

and `interp2`

looks up the elements of `XI`

in `X`

, `YI`

in `Y`

, and, based upon their location, returns values `ZI`

interpolated within the elements of `Z`

.

**Examples**

**Example 1.** Interpolate the `peaks`

function over a finer grid.

[X,Y] = meshgrid(-3:.25:3); Z = peaks(X,Y); [XI,YI] = meshgrid(-3:.125:3); ZI = interp2(X,Y,Z,XI,YI); mesh(X,Y,Z), hold, mesh(XI,YI,ZI+15) hold off axis([-3 3 -3 3 -5 20])

**Example 2.** Given this set of employee data,

years = 1950:10:1990; service = 10:10:30; wage = [150.697 199.592 187.625 179.323 195.072 250.287 203.212 179.092 322.767 226.505 153.706 426.730 249.633 120.281 598.243];

it is possible to interpolate to find the wage earned in 1975 by an employee with 15 years' service:

**See Also**

`griddata`

, `interp1`

, `interp3`

, `interpn`

, `meshgrid`

interp1 | interp3 |

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