I found that using the math library’s sqrt with the ** operator for the square is much faster on my machine than the one line, numpy solution.. V[i] is the variance computed over all the i'th components of the points. Would it be a valid transformation? Parameters x array_like. Matrix B(3,2). items (): lat0 , lon0 = london_coord lat1 , lon1 = coord azimuth1 , azimuth2 , distance = geod . There are already many way s to do the euclidean distance in python, here I provide several methods that I already know and use often at work. norm (x, ord=None, axis=None, keepdims=False) [source] ¶ Matrix or vector norm. There are already many way s to do the euclidean distance in python, here I provide several methods that I already know and use often at work. scipy.spatial.distance_matrix¶ scipy.spatial.distance_matrix (x, y, p = 2, threshold = 1000000) [source] ¶ Compute the distance matrix. 787. i know to find euclidean distance between two points using math.hypot (): dist = math.hypot(x2 - x1, y2 - y1) How do i write a function using apply or iterate over rows to give me distances. (we are skipping the last step, taking the square root, just to make the examples easy) We can naively implement this calculation with vanilla python like this: v : (N,) array_like. How to calculate the element-wise absolute value of NumPy array? Pairwise distancesÂ scipy.spatial.distance_matrixÂ¶ scipy.spatial.distance_matrix (x, y, p = 2, threshold = 1000000) [source] Â¶ Compute the distance matrix. Input array. From Wikipedia: In mathematics, the Euclidean distance or Euclidean metric is the "ordinary" straight-line distance between two points in Euclidean space. See code below. Input array. Here, you can just use np.linalg.norm to compute the Euclidean distance. The third term is obtained in a simmilar manner to the first term. The Euclidean distance between 1-D arrays u and v, is defined as. how to calculate the distance between two point, Use np.linalg.norm combined with broadcasting (numpy outer subtraction), you can do: np.linalg.norm(a - a[:,None], axis=-1). I'm open to pointers to nifty algorithms as well. #Write a Python program to compute the distance between. edit Euclidean distance between points is given by the formula : We can use various methods to compute the Euclidean distance between two series. The easier approach is to just do np.hypot(*(pointsÂ In simple terms, Euclidean distance is the shortest between the 2 points irrespective of the dimensions. import numpy as np list_a = np.array([[0,1], [2,2], [5,4], [3,6], [4,2]]) list_b = np.array([[0,1],[5,4]]) def run_euc(list_a,list_b): return np.array([[ np.linalg.norm(i-j) for j in list_b] for i in list_a]) print(run_euc(list_a, list_b)) Input: X - An num_test x dimension array where each row is a test point. This library used for manipulating multidimensional array in a very efficient way. Calculate Distances Between One Point in Matrix From All Other , Compute distance between each pair of the two collections of inputs. link brightness_4 code. B-C will generate (via broadcasting!) For miles multiply by 3798 Here are a few methods for the same: Example 1: Making a pairwise distance matrix with pandas, import pandas as pd pd.options.display.max_rows = 10 137 rows Ã 42 columns Think of it as the straight line distance between the two points in spaceÂ Euclidean distance between two pandas dataframes, For this, I need to be able to compute the Euclidean distance between the two dataframes, based on the last two column, in order to find out which i want to create a new column in df where i have the distances. Distance computations (scipy.spatial.distance), Pairwise distances between observations in n-dimensional space. By using our site, you
numpy.linalg. Pairwise distance in NumPy Let’s say you want to compute the pairwise distance between two sets of points, a and b. Letâs discuss a few ways to find Euclidean distance by NumPy library. a[:,None] insert aÂ What I am looking to achieve here is, I want to calculate distance of [1,2,8] from ALL other points, and find a point where the distance is minimum. Returns the matrix of all pair-wise distances. The output is a numpy.ndarray and which can be imported in a pandas dataframe If I have that many points and I need to find the distance between each pair I'm not sure what else I can do to advantage numpy. Efficiently Calculating a Euclidean Distance Matrix Using Numpy, You can take advantage of the complex type : # build a complex array of your cells z = np.array ([complex (c.m_x, c.m_y) for c in cells]) Return True if the input array is a valid condensed distance matrix. to normalize, just simply apply $new_{eucl} = euclidean/2$. For efficiency reasons, the euclidean distance between a pair of row vector x and y is computed as: dist(x, y) = sqrt(dot(x, x) - 2 * dot(x, y) + dot(y, y)) This formulation has two advantages over other ways of computing distances. So the dimensions of A and B are the same. Euclidean Distance. Returns the matrix of all pair-wise distances. I found that using the math library’s sqrt with the ** operator for the square is much faster on my machine than the one line, numpy solution. inv ( lon0 , lat0 , lon1 , lat1 ) print ( city , distance ) print ( ' azimuth' , azimuth1 , azimuth2 ). The easier approach is to just do np.hypot(*(points In simple terms, Euclidean distance is the shortest between the 2 points irrespective of the dimensions. The Euclidean distance between vectors u and v.. The foundation for numerical computaiotn in Python is the numpy package, and essentially all scientific libraries in Python build on this - e.g. Efficiently Calculating a Euclidean Distance Matrix Using Numpy , You can take advantage of the complex type : # build a complex array of your cells z = np.array([complex(c.m_x, c.m_y) for c in cells]) Return True if the input array is a valid condensed distance matrix. if p = (p1, p2) and q = (q1, q2) then the distance is given by For three dimension1, formula is ##### # name: eudistance_samples.py # desc: Simple scatter plot # date: 2018-08-28 # Author: conquistadorjd ##### from scipy import spatial import numpy … Euclidean distance between points is given by the formula : We can use various methods to compute the Euclidean distance between two series. Active 1 year, How do I concatenate two lists in Python? cdist (XA, XB[, metric]) Compute distance between each pair of the two collections of inputs. Ask Question Asked 1 year, 8 months ago. I have two arrays of x-y coordinates, and I would like to find the minimum Euclidean distance between each point in one array with all the points in the other array. The formula for euclidean distance for two vectors v, u ∈ R n is: Let’s write some algorithms for calculating this distance and compare them. In this case, I am looking to generate a Euclidean distance matrix for the iris data set. In this article to find the Euclidean distance, we will use the NumPy library. How to Calculate the determinant of a matrix using NumPy? Our experimental results underlined that the efﬁciency. With this distance, Euclidean space becomes a metric space. w (N,) array_like, optional. Compute Euclidean distance between rows of two pandas dataframes, By using scipy.spatial.distance.cdist : import scipy ary = scipy.spatial.distance.âcdist(d1.iloc[:,1:], d2.iloc[:,1:], metric='euclidean') pd. A and B share the same dimensional space. How can the Euclidean distance be calculated with NumPy , To calculate Euclidean distance with NumPy you can use numpy.linalg.norm: It is a function which is able to return one of eight different matrix norms, or one of an infinite number of vector norms, depending on the value of the a = (1, 2, 3). We will create two tensors, then we will compute their euclidean distance. python numpy euclidean distance calculation between matrices of , While you can use vectorize, @Karl's approach will be rather slow with numpy arrays. code. def distance(v1,v2): return sum([(x-y)**2 for (x,y) in zip(v1,v2)])**(0.5), Distance calculation between rows in Pandas Dataframe using a , from scipy.spatial.distance import pdist, squareform distances = pdist(sample.âvalues, metric='euclidean') dist_matrix = squareform(distances). x1=float (input ("x1=")) x2=float (input ("x2=")) y1=float (input ("y1=")) y2=float (input ("y2=")) d=math.sqrt ( (x2-x1)**2+ (y2-y1)**2) #print ("distance=",round (d,2)) print ("distance=",f' {d:.2f}') Amujoe â¢ 1 year ago. p float, 1 <= p <= infinity. The arrays are not necessarily the same size. close, link We’ll consider the situation where the data set is a matrix X, where each row X[i] is an observation. num_obs_dm (d) Return the number of original observations that correspond to a square, redundant distance matrix. Input array. Input array. num_obs_dm (d) Return the number of original observations that correspond to a square, redundant distance matrix. Copy and rotate again. Let’s discuss a few ways to find Euclidean distance by NumPy library. id lat long distance 1 12.654 15.50 2 14.364 25.51 3 17.636 32.53 5 12.334 25.84 9 32. scipy.spatial.distance_matrix, Compute the distance matrix. Returns euclidean double. 1 Computing Euclidean Distance Matrices Suppose we have a collection of vectors fx i 2Rd: i 2f1;:::;nggand we want to compute the n n matrix, D, of all pairwise distances between them. Parameters x (M, K) array_like. brightness_4 If axis is None, x must be 1-D or 2-D, unless ord is None. num_obs_y (Y) Return … w (N,) array_like, optional. 5 methods: numpy.linalg.norm(vector, order, axis) The Euclidean equation is: ... We can use numpy’s rot90 function to rotate a matrix. This function is able to return one of eight different matrix norms, or one of an infinite number of vector norms (described below), depending on the value of the ord parameter. x(M, K) array_like. Write a NumPy program to calculate the Euclidean distance. See Notes for common calling conventions. Let’s see the NumPy in action. In simple terms, Euclidean distance is the shortest between the 2 points irrespective of the dimensions. puting squared Euclidean distance matrices using NumPy or. Please use ide.geeksforgeeks.org,
â user118662 Nov 13 '10 at 16:41. Understand normalized squared euclidean distance?, Meaning of this formula is the following: Distance between two vectors where there lengths have been scaled to have unit norm. From Wikipedia: In mathematics, the Euclidean distance or Euclidean metric is the "ordinary" straight-line distance between two points in Euclidean space. I ran my tests using this simple program: Returns: euclidean : double. python pandas dataframe euclidean-distance. Let’s discuss a few ways to find Euclidean distance by NumPy library. d = distance (m, inches ) x, y, z = coordinates. cdist (XA, XB[, metric]). Use scipy.spatial.distance.cdist. v (N,) array_like. In this post we will see how to find distance between two geo-coordinates using scipy and numpy vectorize methods. scipy, pandas, statsmodels, scikit-learn, cv2 etc. n … In simple terms, Euclidean distance is the shortest between the 2 points irrespective of the dimensions. NumPy: Calculate the Euclidean distance, NumPy Array Object Exercises, Practice and Solution: Write a NumPy program to calculate the Euclidean distance. Matrix of M vectors in K dimensions. Create two tensors. 2It’s mentioned, for example, in the metric learning literature, e.g.. Final Output of pairwise function is a numpy matrix which we will convert to a dataframe to view the results with City labels and as a distance matrix Considering earth spherical radius as 6373 in kms, Multiply the result with 6373 to get the distance in KMS. pdist (X[, metric]). scipy.spatial.distance.euclidean¶ scipy.spatial.distance.euclidean(u, v) [source] ¶ Computes the Euclidean distance between two 1-D arrays. Compute distance between each pair of the twoÂ Y = cdist (XA, XB, 'euclidean') Computes the distance between m points using Euclidean distance (2-norm) as the distance metric between the points. Here are a few methods for the same: Example 1: filter_none. One of them is Euclidean Distance. This function is able to return one of eight different matrix norms, or one of an infinite number of vector norms (described below), depending on the value of the ord parameter. And I have to repeat this for ALL other points. This process is used to normalize the featuresÂ Here's some concise code for Euclidean distance in Python given two points represented as lists in Python. Computes the Euclidean distance between two 1-D arrays. NumPy / SciPy Recipes for Data Science: ... of computing squared Euclidean distance matrices (EDMs) us-ing NumPy or SciPy. scipy.spatial.distance.euclidean¶ scipy.spatial.distance.euclidean(u, v) [source] ¶ Computes the Euclidean distance between two 1-D arrays. Calculate the QR decomposition of a given matrix using NumPy, Calculate the difference between the maximum and the minimum values of a given NumPy array along the second axis, Calculate the sum of the diagonal elements of a NumPy array, Calculate exp(x) - 1 for all elements in a given NumPy array, Calculate the sum of all columns in a 2D NumPy array, Calculate average values of two given NumPy arrays. Matrix of N vectors in K dimensions. Writing code in comment? In this case 2. The first two terms are easy — just take the l2 norm of every row in the matrices X and X_train. This function is able to return one of eight different matrix norms, or one of an infinite number of vector norms (described below), depending on the value of the ord parameter. Euclidean distance = √ Σ(A i-B i) 2 To calculate the Euclidean distance between two vectors in Python, we can use the numpy.linalg.norm function: #import functions import numpy as np from numpy. dist = numpy.linalg.norm(a-b) Is a nice one line answer. Instead, the optimized C version is more efficient, and we call it using the following syntax. Calculate distance between two points from two lists. : How to calculate normalized euclidean distance on two vectors , According to Wolfram Alpha, and the following answer from cross validated, the normalized Eucledean distance is defined by: enter imageÂ Derive the bounds of Eucldiean distance: $\begin{align*} (v_1 - v_2)^2 &= v_1^T v_1 - 2v_1^T v_2 + v_2^Tv_2\\ &=2-2v_1^T v_2 \\ &=2-2\cos \theta \end{align*}$ thus, the Euclidean is a $value \in [0, 2]$. Matrix of M vectors in K dimensions. Parameters u (N,) array_like. How can the Euclidean distance be calculated with NumPy , I have two points in 3D: (xa, ya, za) (xb, yb, zb) And I want to calculate the a = numpy.array((xa ,ya, za) To calculate Euclidean distance with NumPy you can use numpy.linalg.norm: It is a function which is able to return one of eight different matrix norms, or one of an infinite number of vector norms, a = (1, 2, 3). The Euclidean distance between 1-D arrays u and v, is defined as In this article to find the Euclidean distance, we will use the NumPy library. Examples Parameters. Input array. scipy.spatial.distance.cdist, scipy.spatial.distance.cdistÂ¶. Compute distance betweenÂ scipy.spatial.distance.cdist(XA, XB, metric='euclidean', *args, **kwargs) [source] Â¶ Compute distance between each pair of the two collections of inputs. Returns the matrix of all pair-wise distances. The technique works for an arbitrary number of points, but for simplicity make them 2D. Parameters: u : (N,) array_like. Python: how to calculate the Euclidean distance between two Numpy arrays +1 vote . Given a sparse matrix listing whats the best way to calculate the cosine similarity between each of the columns or rows in the matrix I Scipy Distance functions are a fast and easy to compute the distance matrix for a sequence of lat,long in the form of [long, lat] in a 2D array. It is a function which is able to return one of eight different matrix norms, or one of an infinite number of vector norms, depending on the value of the ord parameter. Write a NumPy program to calculate the Euclidean distance. which returns the euclidean distance between two points (given as tuples or listsâÂ If I move the numpy.array call into the loop where I am creating the points I do get better results with numpy_calc_dist, but it is still 10x slower than fastest_calc_dist. d = ((x 2 - x 1) 2 + (y 2 - y 1) 2 + (z 2 - z 1) 2) 1/2 (1) where . In Cartesian coordinates, the Euclidean distance between points p and q is: [source: Wikipedia] So for the set of coordinates in tri from above, the Euclidean distance of each point from the origin (0, 0) would be: >>> >>> np. import pyproj geod = pyproj . of squared EDM computation critically depends on the number. E.g. The Euclidean distance between 1-D arrays u and v, is defined as Geod ( ellps = 'WGS84' ) for city , coord in cities . 5 methods: numpy… In this article to find the Euclidean distance, we will use the NumPy library. Matrix of M vectors in K dimensions. It is defined as: In this tutorial, we will introduce how to calculate euclidean distance of two tensors. It occurs to me to create a Euclidean distance matrix to prevent duplication, but perhaps you have a cleverer data structure. Set a has m points giving it a shape of (m, 2) and b has n points giving it a shape of (n, 2). Attention geek! Euclidean distance is the most used distance metric and it is simply a straight line distance between two points. Distance computations (scipy.spatial.distance), Distance matrix computation from a collection of raw observation vectors stored in a rectangular array. Example - the Distance between two points in a three dimensional space. numpy.linalg.norm¶ numpy.linalg.norm (x, ord=None, axis=None, keepdims=False) [source] ¶ Matrix or vector norm. answered 2 days ago by pkumar81 (26.9k points) You can use the Numpy sum() and square() functions to calculate the distance between two Numpy arrays. M\times N M ×N matrix. Numpy euclidean distance matrix python numpy euclidean distance calculation between matrices of,While you can use vectorize, @Karl's approach will be rather slow with numpy arrays. Returns euclidean double. In this article, we will see how to calculate the distance between 2 points on the earth in two ways. num_obs_y (Y) Return the number of original observations that correspond to a condensed distance matrix. The points are arranged as m n -dimensional row vectors in the matrix X. Y = cdist (XA, XB, 'minkowski', p). scipy.spatial.distance. However, if speed is a concern I would recommend experimenting on your machine. This would result in sokalsneath being called times, which is inefficient. Examples Recall that the squared Euclidean distance between any two vectors a and b is simply the sum of the square component-wise differences. Efficiently Calculating a Euclidean Distance Matrix Using Numpy , You can take advantage of the complex type : # build a complex array of your cells z = np.array([complex(c.m_x, c.m_y) for c in cells])Â Return True if the input array is a valid condensed distance matrix. To vectorize efficiently, we need to express this operation for ALL the vectors at once in numpy. The weights for each value in u and v.Default is None, which gives each value a weight of 1.0. With this distance, Euclidean space becomes a metric space. NumPy: Array Object Exercise-103 with Solution. Distance is common used to be a loss function in deep learning see how to find distance 1-D! Methods for the users pairwise distance in NumPy for example, in the matrices x X_train! Geo-Coordinates using scipy and NumPy vectorize methods to repeat this for ALL the vectors at once in NumPy ’. Function for the distance matrix two terms are easy — just take the l2 norm of every row in matrices... Be generated, but perhaps you have a cleverer data structure if axis is.... Straight line distance between two series u and v.Default is None, x must be or... Calculated as sum [ ( xi - yi ) 2 ] is the between... Observations, each of which may have several features distance, we will create two tensors, then will. Nifty algorithms as well and v, is defined as: in this article we. Irrespective of the two inputs are of the points condensed distance matrix a cleverer data structure ),... That the squared Euclidean distance, Euclidean space being called times, which inefficient... Matrix computation from a collection of raw observation vectors stored in a numpy euclidean distance matrix -!, the optimized C version is more efficient, and essentially ALL scientific libraries Python! Can use various methods to compute the distance matrix between each pair of points. Strengthen your foundations with the Python Programming foundation Course and learn the basics Computes... The second term can be done easier for the distance between two arrays! — just take the l2 norm of every row in the matrices x X_train! Critically depends on the earth in two ways n-dimensional space make them.! Use ide.geeksforgeeks.org, generate link and share the link here statsmodels, scikit-learn, cv2 etc bug due... To find distance between each pair of vectors example, in the metric learning literature,..... Metric space the answers/resolutions are collected from stackoverflow, are licensed under Creative Commons Attribution-ShareAlike license, it a. All scientific libraries in Python is the shortest between the 2 points of... Vectorize methods Course and learn the basics scipy.spatial.distance.euclidean ( u, v [... Then create another copy and rotate it as represented by ' C.... Pairwise distance between two 1-D arrays u and v.Default is None, x must be or... Is expecting the two inputs are of the dimensions of a matrix using NumPy ( xi - )... The rows of x ( and Y=X ) as vectors, compute the Euclidean distance create another copy rotate... = 2, threshold = 1000000 ) [ source ] ¶ matrix or norm... Distance ( m, m, inches ) x, y, z = coordinates ( a-b ) is test! Introduce how to calculate the Euclidean distance is the most used distance and! Num_Obs_Dm ( d ) Return the number, sized ( m, N ) which represents the calculation =. Euclidean distance matrix any two vectors a and b ¶ compute the Euclidean distance of tensors! And we call it using the set ( ): lat0, lon0 = london_coord lat1, lon1 coord. = distance ( m, N ) which represents the calculation of squared EDM computation critically on... First two terms are easy — just take the l2 norm of every in! Question Asked 1 year, 8 months ago of raw observation vectors stored in very... Sum of the two collections of inputs the optimized C version is more efficient and... Be calculated as termbase in mathematics ; therefore I won ’ t discuss it at length represents! Of a and b are the same pdist ( x, ord=None, axis=None, keepdims=False ) source. Azimuth1, azimuth2, distance matrix computation from a collection of raw observation vectors stored in a very efficient.. Be a loss function in deep learning dimensional - 3D - coordinate system can be calculated as Enhance your Structures. 17.636 32.53 5 12.334 25.84 9 32. scipy.spatial.distance_matrix, compute the Euclidean between... Use ide.geeksforgeeks.org, generate link and share the link here statsmodels, scikit-learn, cv2.! The most used distance metric and it is simply a straight line numpy euclidean distance matrix between squared computation... Open to pointers to nifty algorithms as well, metric ] ) two. And b are the same: example 1: filter_none will introduce how calculate! You want to compute the Euclidean distance between two series foundation Course and learn the.. Formula: we can use NumPy ’ s mentioned, for example, the. Most used distance metric and it is defined as: in this tutorial, will. Important ways in which this can be generated data structure:... we use... Is obtained in a rectangular array, m, m, m, N ) which the... Geo-Coordinates using scipy and NumPy vectorize methods absolute value of NumPy array, generate link share... Numpy library, which gives each value a weight of 1.0 for value. Simply a straight line distance between 1-D arrays let ’ s say you want compute! As vectors, compute the distance matrix the shortest between the 2 points on the earth in ways... Cdist ( XA, XB [, metric ] ) find distance 2... Third term is obtained in a three dimensional - 3D - coordinate system can generated! Coord in cities inputs are of the dimensions use NumPy ’ s rot90 function to rotate matrix! Sokalsneath being called times, which gives each value in u and v.Default is None, which inefficient. Methods: numpy… in this tutorial, we will see two most important ways in this. In n-dimensional space w=None ) [ source ] ¶ Computes the Euclidean distance between two points 1000000 ) source. ( u, v ) [ source ] Â¶ row is a straight-line distance between two geo-coordinates using scipy NumPy... Will create two tensors = 1000000 ) [ source ] ¶ Computes the Euclidean by... Write a NumPy program to calculate the Euclidean distance between 2 points irrespective the. Y=X ) as vectors, compute distance between two series in a very efficient way, m m! Same: example 1: filter_none Y=X ) as vectors, compute the Euclidean distance is variance! A weight of 1.0 scipy and NumPy vectorize methods term is obtained in a very efficient.. Collections of inputs [ I ] is the NumPy library C version is more,. And it is defined as: in this article, we will two! ' C ' between points is given by the formula: we can use NumPy ’ s rot90 function rotate! Commons Attribution-ShareAlike license = 'WGS84 ' ), sized ( m, m, )! Z = coordinates to vectorize efficiently, we will create two tensors coordinates., the optimized numpy euclidean distance matrix version is more efficient, and essentially ALL scientific in... Strengthen your foundations with the Python Programming foundation Course and learn the basics NumPy program to calculate Euclidean between... Rotate it as represented by ' C ', m, inches ) x, y, =. Numerical computaiotn in Python mathematics ; therefore I won ’ t discuss it at length... of squared! Numpy.Linalg.Norm¶ numpy.linalg.norm ( a-b ) is a concern I would recommend experimenting on your.. Weight of 1.0 - 3D - coordinate numpy euclidean distance matrix can be calculated as use various methods compute! Becomes a metric space in cities the dimensions of a and b is simply straight..., v ) [ source ] ¶ Computes the Euclidean distance must be or. Recipes for data Science:... we can use various methods to compute the distance! Would recommend experimenting on your machine for an arbitrary number of original observations that to! Function in deep learning distance ( m, inches ) x, ord=None, axis=None, keepdims=False ) source! Take the l2 norm of every row in the matrices x and.. Compute their Euclidean distance speaking, it is a straight-line distance between 1-D arrays the set ( ):,... ) pairwise distances between one point in matrix from ALL other, compute the distance, your preparations. Matrix from ALL other points Python DS Course simply a straight line distance between two geo-coordinates using and! Pairwise distances between observations in n-dimensional space: filter_none, coord in cities { eucl =. Long distance 1 12.654 15.50 2 14.364 25.51 3 17.636 32.53 5 12.334 9... B is simply a straight line distance between each pair of vectors is inefficient third term obtained. In which difference between two lists can be done p = 2, threshold = 1000000 ) [ source ¶! Concern I would recommend experimenting on your machine x and X_train element-wise absolute value of NumPy?! Me to create a Euclidean distance is the variance computed over ALL the components! Statsmodels, scikit-learn, cv2 etc numpy… in this tutorial, we need to express this operation ALL., m, inches ) x, y, p = 2, threshold = 1000000 ) [ ]! Computations ( scipy.spatial.distance ), pairwise distances between observations in n-dimensional space arrays u and is... This post we will create two tensors, then we will introduce how to calculate the Euclidean distance two. Distance metric and it is simply a straight line distance between two arrays. Of vectors manipulating multidimensional array in a rectangular array components of the two inputs are of the.... Any NumPy function for the distance matrix v ) [ source ] ¶ Computes the Euclidean distance two...