NEAREST_ND_INTERP
This function interpolates scattered multidimensional data by assigning each query point the value of the nearest known sample point. It is suitable when a piecewise constant approximation is acceptable.
For each query point \mathbf{x}, the output is \hat{v}(\mathbf{x}) = v_{i^*} where i^* = \arg\min_i \|\mathbf{x} - \mathbf{x}_i\|.
Excel Usage
=NEAREST_ND_INTERP(points, values, xi)points(list[list], required): Data point coordinates (n_points, n_dims)values(list[list], required): Data values (n_points, 1)xi(list[list], required): Query points (n_new_points, n_dims)
Returns (list[list]): A 2D list of interpolated values, or an error message (str) if invalid.
Example 1: Nearest-neighbor on 2D unit square
Inputs:
| points | values | xi | ||
|---|---|---|---|---|
| 0 | 0 | 0 | 0.1 | 0.1 |
| 1 | 0 | 1 | ||
| 0 | 1 | 1 | ||
| 1 | 1 | 2 |
Excel formula:
=NEAREST_ND_INTERP({0,0;1,0;0,1;1,1}, {0;1;1;2}, {0.1,0.1})Expected output:
0
Example 2: Multiple query points in 2D
Inputs:
| points | values | xi | ||
|---|---|---|---|---|
| 0 | 0 | 0 | 0.1 | 0.1 |
| 1 | 0 | 1 | 0.9 | 0.9 |
| 0 | 1 | 1 | ||
| 1 | 1 | 2 |
Excel formula:
=NEAREST_ND_INTERP({0,0;1,0;0,1;1,1}, {0;1;1;2}, {0.1,0.1;0.9,0.9})Expected output:
| Result |
|---|
| 0 |
| 2 |
Example 3: Nearest-neighbor in 3D tetrahedron
Inputs:
| points | values | xi | ||||
|---|---|---|---|---|---|---|
| 0 | 0 | 0 | 10 | 0.2 | 0.1 | 0.1 |
| 1 | 0 | 0 | 20 | |||
| 0 | 1 | 0 | 30 | |||
| 0 | 0 | 1 | 40 |
Excel formula:
=NEAREST_ND_INTERP({0,0,0;1,0,0;0,1,0;0,0,1}, {10;20;30;40}, {0.2,0.1,0.1})Expected output:
10
Example 4: Multiple queries on 2D grid pattern
Inputs:
| points | values | xi | ||
|---|---|---|---|---|
| 0 | 0 | 5 | 0.4 | 0.4 |
| 2 | 0 | 10 | 1.6 | 0.4 |
| 0 | 2 | 15 | 1.6 | 1.6 |
| 2 | 2 | 20 |
Excel formula:
=NEAREST_ND_INTERP({0,0;2,0;0,2;2,2}, {5;10;15;20}, {0.4,0.4;1.6,0.4;1.6,1.6})Expected output:
| Result |
|---|
| 5 |
| 10 |
| 20 |
Python Code
import numpy as np
from scipy.interpolate import NearestNDInterpolator as scipy_NearestNDInterpolator
def nearest_nd_interp(points, values, xi):
"""
Nearest neighbor interpolation in N > 1 dimensions.
See: https://docs.scipy.org/doc/scipy/reference/generated/scipy.interpolate.NearestNDInterpolator.html
This example function is provided as-is without any representation of accuracy.
Args:
points (list[list]): Data point coordinates (n_points, n_dims)
values (list[list]): Data values (n_points, 1)
xi (list[list]): Query points (n_new_points, n_dims)
Returns:
list[list]: A 2D list of interpolated values, or an error message (str) if invalid.
"""
try:
def to2d(x):
return [[x]] if not isinstance(x, list) else x
# Normalize inputs to 2D lists
points = to2d(points)
values = to2d(values)
xi = to2d(xi)
# Validate inputs are lists
if not isinstance(points, list) or not isinstance(values, list) or not isinstance(xi, list):
return "Error: Invalid input: points, values, and xi must be 2D lists."
# Validate all elements are lists
if not all(isinstance(row, list) for row in points):
return "Error: Invalid input: points must be a 2D list."
if not all(isinstance(row, list) for row in values):
return "Error: Invalid input: values must be a 2D list."
if not all(isinstance(row, list) for row in xi):
return "Error: Invalid input: xi must be a 2D list."
# Validate non-empty
if len(points) == 0 or len(values) == 0 or len(xi) == 0:
return "Error: Invalid input: points, values, and xi must be non-empty."
# Validate consistent dimensions
if len(points) != len(values):
return "Error: Invalid input: points and values must have the same number of rows."
# Validate all rows have same length
n_dims = len(points[0])
if n_dims == 0:
return "Error: Invalid input: points must have at least one column."
if not all(len(row) == n_dims for row in points):
return "Error: Invalid input: all rows in points must have the same length."
n_dims_xi = len(xi[0])
if n_dims_xi == 0:
return "Error: Invalid input: xi must have at least one column."
if not all(len(row) == n_dims_xi for row in xi):
return "Error: Invalid input: all rows in xi must have the same length."
if n_dims != n_dims_xi:
return "Error: Invalid input: points and xi must have the same number of columns."
# Validate values is single column
if not all(len(row) == 1 for row in values):
return "Error: Invalid input: values must have exactly one column."
# Convert to numpy arrays and validate numeric values
try:
points_arr = np.array(points, dtype=float)
values_arr = np.array(values, dtype=float).flatten()
xi_arr = np.array(xi, dtype=float)
except (ValueError, TypeError):
return "Error: Invalid input: all elements must be numeric."
# Check for NaN or inf values
if np.any(np.isnan(points_arr)) or np.any(np.isinf(points_arr)):
return "Error: Invalid input: points contains non-finite values."
if np.any(np.isnan(values_arr)) or np.any(np.isinf(values_arr)):
return "Error: Invalid input: values contains non-finite values."
if np.any(np.isnan(xi_arr)) or np.any(np.isinf(xi_arr)):
return "Error: Invalid input: xi contains non-finite values."
# Perform interpolation
try:
interp = scipy_NearestNDInterpolator(points_arr, values_arr)
result = interp(xi_arr)
except Exception as exc:
return f"Error: scipy.interpolate.NearestNDInterpolator error: {exc}"
# Validate result
if not isinstance(result, np.ndarray):
return "Error: scipy.interpolate.NearestNDInterpolator error: unexpected result type."
# Check for NaN or inf in result
if np.any(np.isnan(result)) or np.any(np.isinf(result)):
return "Error: scipy.interpolate.NearestNDInterpolator error: result contains non-finite values."
# Convert to 2D list
result_2d = [[float(val)] for val in result]
return result_2d
except Exception as e:
return f"Error: {str(e)}"Online Calculator
Data point coordinates (n_points, n_dims)
Data values (n_points, 1)
Query points (n_new_points, n_dims)