GRIDDATA

Overview

The GRIDDATA function performs interpolation on unstructured N-dimensional data. It is useful for estimating values at new points based on scattered data, such as in geospatial analysis or scientific computing. The function supports three interpolation methods: ‘linear’, ‘nearest’, and ‘cubic’. The underlying algorithm is provided by SciPy’s scipy.interpolate.griddata function. For more details, see the official documentation .

This example function is provided as-is without any representation of accuracy.

Usage

To use the function in Excel:


=GRIDDATA(points, values, xi, [method], [fill_value])

points (2D list, required): Table of coordinates for the data points. Each row is a point in N dimensions.
values (2D column vector, required): Table of values at each data point. Must have the same number of rows as points.
xi (2D list, required): Table of coordinates where interpolation is desired. Each row is a point in N dimensions.
method (string, optional, default=“linear”): Interpolation method. One of "linear", "nearest", or "cubic".
fill_value (float, optional, default=NaN): Value to use for points outside the convex hull of the input points.

The function returns a 2D column vector (list of lists) of interpolated values at the locations specified by xi, or an error message (list of lists of strings) if the input is invalid.

Examples

Example 1: Linear Interpolation in 2D

This example interpolates values at two new points using three known data points in 2D.

Inputs:

points		values	xi		method
0.0	0.0	1.0	0.5	0.5	linear
1.0	0.0	2.0	0.2	0.8
0.0	1.0	3.0

Excel formula:


=GRIDDATA({0,0;1,0;0,1}, {1;2;3}, {0.5,0.5;0.2,0.8}, "linear")

Expected output:

Result
2.5
2.8

Example 2: Nearest Neighbor Interpolation

This example uses the ‘nearest’ method to interpolate at two points.

Inputs:

points		values	xi		method
0.0	0.0	1.0	0.9	0.1	nearest
1.0	0.0	2.0	0.1	0.9
0.0	1.0	3.0

Excel formula:


=GRIDDATA({0,0;1,0;0,1}, {1;2;3}, {0.9,0.1;0.1,0.9}, "nearest")

Expected output:

Result
2.0
3.0

Example 3: Cubic Interpolation in 2D

This example uses the ‘cubic’ method for interpolation with four non-collinear points.

Inputs:

points		values	xi		method
0.0	0.0	1.0	0.3	0.3	cubic
1.0	0.0	2.0	0.7	0.7
0.0	1.0	3.0	0.5	0.5
1.0	1.0	4.0

Excel formula:


=GRIDDATA({0,0;1,0;0,1;1,1}, {1;2;3;4}, {0.3,0.3;0.7,0.7;0.5,0.5}, "cubic")

Expected output:

Result
1.9
3.1
2.5

Example 4: Fill Value for Out-of-Bounds

This example shows how to use fill_value for a point outside the convex hull, with four points.

Inputs:

points		values	xi		method	fill_value
0.0	0.0	1.0	2.0	2.0	linear	99
1.0	0.0	2.0
0.0	1.0	3.0
1.0	1.0	4.0

Excel formula:


=GRIDDATA({0,0;1,0;0,1;1,1}, {1;2;3;4}, {2,2}, "linear", 99)

Expected output:

Result
99

Python Code


from scipy.interpolate import griddata as scipy_griddata
import numpy as np
 
def griddata(points, values, xi, method="linear", fill_value=None):
    """
    Interpolate unstructured N-D data using scipy.interpolate.griddata.
 
    Args:
        points: 2D list of coordinates for data points (shape: n_points x n_dim).
        values: 2D column vector of values at each point (shape: n_points x 1).
        xi: 2D list of coordinates where interpolation is desired (shape: n_xi x n_dim).
        method: Interpolation method: 'linear', 'nearest', or 'cubic' (default: 'linear').
        fill_value: Value to use for points outside the convex hull (default: None).
 
    Returns:
        2D column vector (list of lists) of interpolated values.
 
    Note: Only valid 2D lists are supported. Examples and demo cases do not include invalid or error cases.
    """
    # Validate input shapes
    try:
        pts = np.array(points, dtype=float)
        vals = np.array(values, dtype=float).flatten()
        xis = np.array(xi, dtype=float)
        if pts.ndim != 2 or xis.ndim != 2:
            return [["Invalid input: points and xi must be 2D lists."]]
        if vals.ndim != 1 or pts.shape[0] != vals.shape[0]:
            return [["Invalid input: values must be a column vector with same number of rows as points."]]
        if pts.shape[1] != xis.shape[1]:
            return [["Invalid input: points and xi must have same number of columns."]]
        if method not in ["linear", "nearest", "cubic"]:
            return [["Invalid input: method must be 'linear', 'nearest', or 'cubic'."]]
        # Use scipy_griddata default fill_value (nan) when no fill_value provided
        if fill_value is None:
            result = scipy_griddata(pts, vals, xis, method=method)
        else:
            result = scipy_griddata(pts, vals, xis, method=method, fill_value=fill_value)
        # Return as 2D column vector, None for np.nan
        return [[float(x)] if np.isfinite(x) else [None] for x in result]
    except Exception as e:
        return [[f"Error: {e}"]]

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GRIDDATA

Overview

Usage

Examples

Python Code

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