pdist2 matlab. In this workflow, you must pass training data, which can be of considerable size. pdist2 matlab

 
 In this workflow, you must pass training data, which can be of considerable sizepdist2 matlab m

pdist (X): Euclidean distance between pairs of observations in X. Calculates the distance between sets of vectors. Very clever - I wouldn't have thought about the pdist2 function (+1). MATLAB 用于计算距离矩阵的内置函数是 pdist2。 这个 函数 做同样的事情,但也返回一个角度矩阵,它是每个可能的点对定义的角度。 此 函数 的局限性在于它仅计算欧几里得距离,并且仅适用于 2D。 In Matlab there exists the pdist2 command. This is a very interesting suggestion and comparison. In this workflow, you must pass training data, which can be of considerable size. What i want to do is to write a code, that does not involve loops and pdist2, as fast as possible, that tells me the indices of the row of both A and B such that the distance. I have a trajectory like this: We assume that each red star marker can broadcast its coordinate to the green circle markers which are located within a radius of 5 units from its own position. Hi, So if I have one 102x2 matrix of x,y coordinates, and another 102x2 matrix of x,y coordinates, can pdist be used to compare all the rows in matrix 1 with the rows in matrix 2?. Using pdist with two matrix's. The latent heat is K = 0. I. comparison of two histograms using pdist2. The Mahalanobis distance from a vector y to a distribution with mean μ and covariance Σ is. The example matches each channel of A against the single histogram of Ref. 0. function Distance = euclidean (x,y) % This function replaces the function pdist2 available only at the Machine. 欧氏距离: 也可以用表示成向量运算的形式: (4)Matlab计算欧氏距离 Matlab计算距离主要使用pdist函数。若X是一个M×N的矩阵,则pdist(X)将X矩阵M行的每一. I. y = squareform (Z)詳細については、coder. I've written this in Python before. It is showing an error Undefined function 'pdist' for input arguments of type 'double'. Learn more about matrix manipulation, distance, pdist2, matlab function, indexing, matrix, arrays MATLAB I was wondering if there is a built in matlab fucntion that calculates the distance between two arrays that don't have the. ) Y = pdist (X,'. The Canberra Distance is defined as. A custom distance function for pdist2 needs two input arguments and the first must specify just a single observation: axa = pdist2(latlon1(1, 1:2), latlon2(:, 1:2), @haversine); % repeat for other values in latlon1I want to use the Manhattan Distance and I have a definition for it, so how the heuristic for it should be calculated, but I am not sure if it is correct. pdist2 Pairwise distance between two sets of observations. Compute the Euclidean distance between pairs of observations, and convert the distance vector to a matrix using squareform. The Canberra distance between two points u and v is. pdist2 Pairwise distance between two sets of observations. 2. pdist (X): Euclidean distance between pairs of observations in X. Find the treasures in MATLAB Central and discover how the community can help you! Start Hunting!Note that image A and Ref are different in size and type. Rows of X and Y correspond to observations, That is, it works on the ROWS of the matrices. Fowzi barznji on 16 Mar 2020. square is not for squaring a value, it returns the values of the square wave. Pass Z to the squareform function to reproduce the output of the pdist function. 注意. 1. pdist2 with wrapping. Pdist2 inside for. Notes. The Canberra distance between two points u and v is. 2. This MATLAB function returns the distance between each pair of observations in X and Y using the metric specified by Distance. Then, for the second set, at each iteration, it will set the (i,j) location to 0 and calculate. Learn more about matlab, distance, command, haversine, coordinates, km, deggrees, calculation, difference I would like to use the command pdist2 in order to compute distance between two geographical coordinates. (See also pdist2, a function in the Statistics and Machine Learning Toolbox that can compute pair-wise vector distances with much more flexibility, as well as hypot, a MATLAB function that computes the magnitude of a two-element vector in a way that avoids numerical overflow and underflow problems. Your third party file c: oolboxclassifypdist2. pdist2 Pairwise distance between two sets of observations. 1 Answer. within2_max = distances_max > 0 & distances_max < 5; % Erase upper triangle to get rid of redundancy. 5 seconds. % n = norm (v) returns the Euclidean norm of vector v. Learn more about matrix manipulation, distance, pdist2, matlab function, indexing, matrix, arrays MATLAB. figure. PostCSS Loader. D = pdist2 (X,Y,@CalcDist) function D2=CalcDist (ZI,ZJ) % calculation of distance. close all; % Close all figures (except those of imtool. Despite minor lags in time frames, users ignore them because Sage is cost-efficient. MY-by-N data matrix Y. These MATLAB tools and capabilities are all rigorously tested and designed to work. minDistance = 0. Answers (1) Two possibilities come to mind, one being knnsearch (link), and the other being pdist2 (link). ^2) If you have concern of different metrics, you can use pdist2 (as mentioned in comments) like the following: x1 = [1:11]. y = squareform (Z)For example the not weighted RBF and sigmoid kernel can be computed as follows: K_rbf = exp (-gamma . . The euclidean distance between the reference vector and all the elements in the pixel location vector is computed using the MATLAB function "pdist2" and the result is applied to some conditions; however, upon running the code, this function seems to be taking the longest to compute (i. Display range of grayscale images in array I, specified as 1-by-2 vector of the form [low high]. The cosine similarity measure has been widely studied under different information environments. Answers (1) This issue could be due to RAM limitations. I use the pdist2 function to calculate the the distance between the points stored in matr. 5. However, generally the manual calculation is slightly faster or. Thus if you input a matrix with N points and one with M points, you get N*M distances. between each pair of observations in the MX-by-N data matrix X and. map=logical (map+map. You can import vector and raster data from a wide range of file formats and web map servers. If you specify an empty matrix ([]), then montage uses the minimum and maximum pixel values of the images. Fowzi barznji on 16 Mar 2020. % Learning toolbox. . e. For latitude and longitude, usually the haversine method is used. MY-by-N data matrix Y. Hello, I am using matlab 2019a and I am trying to sort points based on comparing the distance between them. i am currently doing project on image processing in matlab,. D = pdist2 (X,Y,@CalcDist) function D2=CalcDist (ZI,ZJ) % calculation of distance. Use matlab's 'pdist' and 'squareform' functions 0 Comments. Idx has the same number of rows as Y. PDIST2 introducido principalmente, otros pueden. y = squareform (Z) {"payload":{"allShortcutsEnabled":false,"fileTree":{"classify":{"items":[{"name":"private","path":"classify/private","contentType":"directory"},{"name":"Contents. Sir, actually the block[50 X 6] contains 'minutiae' information which contains the following data in columns [X, Y, CN, Theta, Flag, 1]and rows contains number of minutiae information on the dorsalhandvein. Careers. m is interfering with use of the pdist2 from the Statistics toolbox. John D'Errico on 26 May 2019. D = pdist2 (X,Y) returns a matrix D containing the Euclidean distances. I think it is not correct. computes the Euclidean distance between pairs of objects in . See squareform for information on how to calculate the index of this entry or to convert the condensed distance matrix to a redundant square matrix. I selected a list of n red points for each green marker according to the above explanation. Continue reading "MATLAB –. . which takes is expected to take a single value for alpha and a vector for beta and use a for loop to iterate through all the difference between alpha and each intry in beta. Currently avaliable codes in FEX are also insufficient as they can only compute (squared. distfun must accept a matrix XJ with an arbitrary number of rows. matlab中的马氏距离:pdist2()与mahal()函数,matlab,Matlab,我有两个矩阵X和Y。它们都代表三维空间中的许多位置。X是一个50*3的矩阵,Y是一个60*3的矩阵 我的问题是:为什么将均值函数与“Mahalanobis”结合应用于pdist2()的输出上,却不能给出用mahal()得. linux 网络的配. Moreover, if you desire to find the distance from a fixed point like (x0, y0) other than the origin, you can do the following: distResults = sqrt ( (x1 - x0). This can be done in pdist2. Minkowski distance and pdist. matlab Pdist2 with mahalanobis metric. % Autor: Ana C. The most efficient pairwise distance computation. I suppose x and y are matrixes, so you are using pdist2 to compute the distance between the observation i (from x(i)) and j (from y(j)). The kernel function is K (x, y) = sum (min (x, y)). Second, Pdist2 Pairwise distance between, sets of observations Syntax D = Pdist2 (x, y) D. Contribute to MahindaMK/A-generalized-fuzzy-k-nearest-neighbor-regression-model-based-on-Minkowski-distance development by creating an account on GitHub. Compute the Euclidean distance. 5* (dist (x (:,2:n),x (:,n)')/ker_bw^2)); end. 6GB). There appears to be a misconception here. Okay, my MATLAB does not know a pdist2 function, only pdist. The problem seems to be that. pdist2 equivalent in MATLAB version 7. If you want the cosine, use 1-pdist2 (matrix1,matrix2,'cosine'). ^2). ^2)); % D is the similarity matrix end end. This code takes a (small) set of data as an input and computes the Betti Numbers of that data. Dec 17, 2014 at 14:41. It computes the distances between rows of X. Mapping Toolbox supports a complete workflow for managing geographic data. Pass a single point for each of the first two arguments to pdist2 and the result will be a single distance. This norm is also. If K is greater than MX, PDIST2 returns an MX-by-MY distance matrix. Larger values indicate high distance; - Euclidean similarity, which vary in the range of [0 : 1]. D may be a vector or matrix as computed by PDIST or PDIST2, or a more general dissimilarity vector or matrix conforming to the output format of PDIST or PDIST2. In the meantime, try the code below and if it helps you click on the Vote button near my top answer. 1k views. It's hard to tell without knowing what dtw2 is. Jim Lehane on 4 Mar 2013. . PixelList); [mindist, minind] = min (distances (:)); %// Now convert this linear index into index1/index2 into your pixel lists. Pass Z to the squareform function to reproduce the output of the pdist function. Show -1 older comments Hide -1 older comments. ', B. 0364 0. 计算 X 中各对行向量的相互距离 (X是一个m-by-n的矩阵). For example, you can find the distance between observations 2 and 3. Google it if you want the details. matlab pdist2,matlab中pdist2函数; windows 10 bash change PS1; linxu中删除指定时间之前的文件shell脚本; react中如何做成 tab 切换的效果; __declspec的英文含义; 从零复现PyTorch版(3) webpack报错:Invalid options object. What i want to do is to write a code, that does not involve loops and pdist2,. apply (outer (a,t (b),"-"),c (1,4),function (x)sqrt (sum (diag (x*x)))) is the m x n matrix of distances between the m rows of a and n rows of b . 2. Teams. One-line implementation of both MATLAB's pdist and pdist2 functions. m. . Now I want to create a mxn matrix such that (i,j) element represents the distance from ith point of mx2 matrix to jth point of nx2 matrix. Mizuki Izawa et al. Las funciones de distancia son: PDIST, PDIST2, Mahal, Forma Square, MdsCale, CMDSCALE. There are two main classes: pdist1 which calculates the pairwise distances between observations in one matrix and returns a distance matrix. 这里 D 要特别注意,D 是一个长为m (m–1)/2的行向量. xy = rand (5, 2); distances = pdist2 (xy, xy) S = sum (distances) This code will give all sum of distances between the points, now the point having minimum distance. So, do you know how to make the calcul inside the. workspace; % Make sure the workspace panel is showing. I used this MATLAB function to compute the distance matrix Dists = pdist2(fruchterman_graph(:,:),fruchterman_graph(:,:),'euclidean'); but it fails on large networks for both speed and finally memory. What complicates things even more is the fact, that I have to exclude the current point (to which I'm trying to find the closest one); that's the purpos of my 'others' variable and the 2 pieces of code above and below the for-cycle. To save memory on the device, you can separate training and prediction by using kmeans and pdist2, respectively. Description. % Autor: Ana C. Learn more about matrix manipulation, distance, pdist2, matlab function, indexing, matrix, arrays MATLAB I was wondering if there is a built in matlab fucntion that calculates the distance between two arrays that don't have the same column number like in pdist2? Generate Code. I want the minimum distance between X and Y where each coordinate is in a 1-to-1 ratio between X and Y. D = pdist2 (X,Y) returns a matrix D containing the Euclidean distances. To find the distance from every one of 16 points to every one of another set of 16 points would give 16 * 16 = 256 distances. Array exceeds maximum array size preference. You can use pdist2 to compute all distances and then pick the minimal distance. Krispy Scripts on 25 Oct 2016. linux 网络的配. John D'Errico on 26 May 2019. Output argument <XX> (and possibly others). clc; % Clear the command window. 9448. Copy. 9448. D = pdist2 (X,Y,@CalcDist) function D2=CalcDist (ZI,ZJ) % calculation of distance. Copy. pdist2 computes the distance between all pairs of points of the two inputs. Explanation: pdist (S1,'cosine') calculates the cosine distance between all combinations of rows in S1. The Chebyshev distance between two n-vectors u and v is the maximum norm-1 distance between their respective elements. out (jdx)=min (idx,out (idx)); end. The pairwise distances are arranged in the order (2,1), (3,1), (3,2). It finds the distance for each pair of coordinates specified in two vectors and NOT the distance between two matrices. linux 网络的配. It computes the distances between rows of X. My one-line implementation of both MATLAB's pdist and pdist2 functions which compute the univariate (pdist) or bivariate (pdist2) Euclidean distances between all pairs of input observations. I'm able to get the julia single threaded function running twice as slow as matlab but a multi threaded function running twice as fast as matlab. 167. For example, you can find the distance between observations 2 and 3. If K is greater than MX, PDIST2 returns an MX-by-MY distance matrix. Mar 8, 2021 at 17:55. This function fully supports thread-based environments. pdist is working fine and the stats toolbox is set in the path. If you want to order the points from B by their distance to the r th point in A then you can sort the r th row of the pairwise distance matrix. MATLAB 距离函数及用法. %. pcshow (ptCloud. So, you showed the formula for the square of the distance. These points are possible outliers that could affect the covariance matrix calculation. '; y1 = [1;1;11;16;19;3;14;5;16;10;22. For a dataset made up of. 0 matlab use my own distance function for pdist. To save memory on the device, you can separate training and prediction by using kmeans and pdist2, respectively. Goncalves. Sign in to comment. This MATLAB function performs k-means clustering to partition the observations of the n-by-p data matrix X into k clusters, and returns an n-by-1 vector (idx) containing cluster indices of each observation. I am using the pdist function to calculate pairwise distances (jaccard) between two observations. The idx that results will have as many rows as first_xyz has, and the value will be the index of which second_xyz row is closest to that point; the mindist value will tell you how close it is. Learn more about matlab, distance, command, haversine, coordinates, km, deggrees, calculation, difference I would like to use the command pdist2 in order to compute distance between two geographical coordinates. I am looking for an alternative to this in. %. X is a 50*3 matrix, Y is a 60*3 matrix. Generate the histogram matched output image. y = squareform (Z)Copy. out = 1×10. ^2 + (Y_Coord - Y_Ant). 欧氏距离(Euclidean Distance) 欧氏距离是最易于理解的一种距离计算方法,源自欧氏空间中两点间的距离公式。(1)二维平面上两点a(x1,y1)与b(x2,y2)间的欧. Tags matlab; array; Products MATLAB; Community Treasure Hunt. Here you can see which matrices are equal to which ones - 5th and 10th are equal to 1st, 6th and 7th are equal to 2nd and 9th is equal to 3rd. I need to pre-compute the histogram intersection kernel matrices for using LIBSVM in MATLAB. IDX = DBSCAN(D, EPSILON, MINPTS, 'DISTANCE', 'PRECOMPUTED') is an alternative syntax that accepts distances D between pairs of observations instead of raw data. pdist2() is in the Statistics and Machine. MATLAB's built in function for computing the distance matrix is pdist2. Inputs: an NxD feature matrix X_train where N is the number of training instances and D is the feature dimension, an Nx1 label vector y_train for the training instances, an MxD feature matrix X_test where M is the number of test instances, and; a scalar K. Copy. The output is a dissimilarity matrix formatted as a row vector y, (n-1)*n/2 long, where the. Learn more about graph MATLAB I have a square area of gridpoints and I'm trying to create a graph where each point is joined to its neighbouring points based on a Chebychev distance. 1 Answer. Unfortunately, haversine is not provided as a distance option in pdist2. distfun must. 0. Hi, So if I have one 102x2 matrix of x,y coordinates, and another 102x2 matrix of x,y coordinates, can pdist be used to compare all the rows in matrix 1 with the rows in matrix 2?. cosined=sqrt (sum (abs ( (a-b). 2711 122. In brief, using nu-clear staining, the cell-to-cell distance was calculated by measuring the distance between each cell and the closest target. Copy. 9448. If a is m x r and b is n x r then. 2. 9448. Accepted Answer. m is interfering with use of the pdist2 from the Statistics toolbox. Create distance matrix from the result of pdist. The function pdist2 with Hamming distance already does this for you: pdist2(A,B,'hamming') This gives the result as percentage of coordinates that differ. Thus if you input a matrix with N points and one with M points, you get N*M distances. For example, this is a required step in the ICP point set registration algorithm. I'm looking for any existing code, Matlab toolkit, or whatever, to help this task: given X,Y coordinate pairs of moving discrete agents in several classes (e. calculate_distance. Rows of X and Y correspond to observations, That is, it works on the ROWS of the matrices. The points are grouped into two clusters. Can I use the Matlab function called. It computes the distances between rows of X. The bwdist () compute the distance transform of all points. Larger values indicate high similarity; - cosine distance, which vary in the range of [0 : 2]. I have a matrix A and I compute the dissimilarity matrix using the downloaded function. This norm is also. For each observation in Y, PDIST2 finds the K smallest or largest distances by computing and comparing the distance values to all the observations in X. Learn the Essentials, Build Skills. MATLAB 距离函数及用法. [labels,numClusters] = pcsegdist (ptCloud,minDistance); Plot the labeled results. Location,labels) colormap (hsv (numClusters)) title ( 'Point Cloud Clusters') D can be the output of pdist or pdist2, or a more general dissimilarity vector or matrix conforming to the output format of pdist or pdist2, respectively. / Lab Invest 103 (2023. All pixel values greater than or equal to high display as white. But for a small number of huge arrays loops and isequal is faster. . . Show 1 older comment. across the classes, and whether. Copy. It seems that the pdist2 version lacks in efficiency due mainly to the element-wise squares, while Matlab now provides the 'squaredeuclidean' option to get this directly. pdist2 is optimized to return the distance from each of the points in the first argument to each of the points in the second argument, so if you only want one distance then only pass a single point to each. I calculated out the distance from every point in X to every point in Y using the pdist2 tool. Two sets of matrix. No. distances =. pdist_oneLine. You can use one of the following methods for your utility: norm (): distance between two points as the norm of the difference between the vector elements. Find the treasures in MATLAB Central and discover how the community can help you! Start Hunting!1. e. 9044 0. If your situation is instead that node(i). The toolbox lets you process and customize data using trimming, interpolation, resampling, coordinate transformations, and other techniques. This MATLAB function returns the distance between each pair of observations in X and Y using the metric specified by Distance. matlab use my own distance function for pdist. It shows a path (C:Program FilesMATLAB. 0. pdist and pdist2 can calculate the city block distance. distfun must. pdist2 Pairwise distance between two sets of observations. Built-in graphics make it easy to visualize and gain insights from data. I am not sure if the dice function can be used to compare two histograms, but you can use the function pdist2 to get a similarlity score between the histograms. This gave me a m x m matrix of distances. Create a matrix with three observations and two variables. % called the 2-norm, vector magnitude, or Euclidean length. PostCSS Loader. For code generation, define an. . D = PDIST2 (X,Y,DISTANCE, 'Largest',K) returns the K largest pairwise distances sorted in descending order. Assume x, y are two vectors. % generate some example data N = 4 M. squareform returns a symmetric matrix where Z (i,j) corresponds to the pairwise distance between observations i and j. (I am using MatLabd r2009b) Could it be that simple? Otherwise, in which folder is the pdist2. . Here is an excerpt from the link: Here is an excerpt from the link: The haversine formula is an equation important in navigation, giving great-circle distances between two points on a sphere from their longitudes and latitudes. Let us create a matlab script called speedtest. Requested 128424x128424 (138. plot (xi,t1,'r',xi,t2,'b'); legend ( {'Manual','Pdist2'}) Which probably suggests that any differences in time between pdist2 and manual calculation are negligible and more dependent on the current background state of the CPU. de 2022 I'm trying to use the pdist2 function and keep getting this error: "??? Undefined function or method 'pdist2'. This MATLAB function returns the distance between each pair of observations in X and Y using the metric specified by Distance. Learn more about for loop, matrix, matlab, pdist MATLAB Hi everybody, i have two 3D matrix A and B with different lengths. Use pdist2 to compute distance matrix of x and y. 0670 0. You define distance as d= (x-x0)^2+ (y-y0)^2 and go through all the points in your mesh. Each row of both matrices identifies a point in 2D space. I'm able to get the julia single threaded function running twice as slow as matlab but a multi threaded function running twice as fast as matlab. Please provide a working code. 0332 0. 1695. squareform returns a symmetric matrix where Z (i,j) corresponds to the pairwise distance between observations i and j. workspace; % Make sure the workspace panel is showing. The nearest 6 nodes where chosen based on the Kd tree algorithm, using the pdist2 Matlab function. Add a comment. @Lukas Gaßmann Start your own question with your EEG data attached in a . mat file if you need more help. Dec 17, 2014 at 14:10. So for example, the element at Row 2, Column 3 of distances corresponds to the distance between point (row) 2 of your XY, and point (row) 3 of your XY. MATLAB Graphics 2-D and 3-D Plots Discrete Data Plots. The Mahalanobis distance is a measure between a sample point and a distribution. example. linux 网络的配. There will only be one smallest distance. Mahalanobis distance between two vectors in MATLAB. Mahalanobis distance in matlab: pdist2() vs. I simply call the command pdist2(M,N). Or clearvars if you want. Mahalanobis distance in matlab: pdist2() vs. matlab pdist2,matlab中pdist2函数; windows 10 bash change PS1; linxu中删除指定时间之前的文件shell脚本; react中如何做成 tab 切换的效果; __declspec的英文含义; 从零复现PyTorch版(3) webpack报错:Invalid options object. . 2 @ServerS Note also that pdist2 can be used with other distances, not just Euclidean – Luis Mendo. 2954 1. If the size of your mesh is not too large, you can always calculate the distance to every point and find the minimum. distances =. You need to take the square root to get the distance. – The distance between each sample in A and each sample in B can be calculated as follows: First, define a matrix D of size 75x50, s. m. The sorted order of tied distances in the generated code can be different from the order in MATLAB ® due to numerical precision. You can try the following workarounds: 1. Function File: pdist2 (x, y) Function File: pdist2 (x, y, metric) Compute pairwise distance between two sets of vectors. However, pdist2 is an optimized method to calculate the euclidean distances between points in two vectors. Writing PDEs in MATLAB. @Image Analyst Hello, I tried to find the minimum distance bewteen two objects as per the code you provided on a similar post- 'test3. I use matlab to calculate the distance transform of a binary image, and I found that bwdist () can calculate distances of all the points of the image, but I just want to know the distance of a special point. My problem is taking those distances out of the matrix and finding the smallest combined distance for each unique set of X to Y measurements. Goncalves. I am getting the following error: Theme. Find the treasures in MATLAB Central and discover how the community can help you! Start Hunting!Hay una función correspondiente en Matlab, que es conveniente para llamar al cálculo. Instead, I am able to find the distance from the boundary of the image to one of the objects. % Autor: Ana C. Maybe the differences are due to the incorrect use of the indexes i and j. matlab中pdist2函数的具体使用方法: X = rand(3,3)X = 0. Ideally it is a distance between a vector (or distances between a set of vectors) and some given distribution defined by means and covariances. Copy. distances_max = pdist2(pks_max,pks_max); % Find out which pairs are within 1 of each other. comparison of two histograms using pdist2. Fowzi barznji on 16 Mar 2020. . and pdist2() where I plotted all 3 of the closest pairs. You can get these out in a 16 by 16 2-D array using pdist2 (). m or remove that directory from your MATLAB path. I was wondering if there is a built in matlab. . % pairwise mahalanobis distance with pdist2() E = pdist2(X,Y,'mahalanobis',S); % outputs an 50*60 matrix with each ij-th element the pairwise distance between element X(i,:) and Y(j,:) based on the covariance matrix of X: nancov(X) %{ so this is harder to interpret than mahal(), as elements of Y are not just compared to the "mahalanobis-centroid" based on X, % but to each individual element of. Mahalanobis distance has no meaning between two multiple-element vectors. One matrix has 2 sets of coordinates Answers (2) You can do this with the pdist2 function. 2444 169. This returns the result as a distance matrix such as produced by pdist2, except that all entries not corresponding to neighboring points are set to NaN. This function can do both - it will function like pdist if only one set of observations is provided and will function like pdist2 if two. 4424 0. Z (2,3) ans = 0. 1 vote. train_labels is an N x 1 cell array, where each entry is a. for n=2:K-1.