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matlab number of nonzero elements per row

How can you know the sky Rose saw when the Titanic sunk? (The pre-requisite to be able to multiply) Step 2: Multiply the elements of each row of the first matrix by the elements of each column in the second matrix. What I'm looking for is the number of "correct" transitions (0-1, 1-2, and so on), so the first value in each row should not count. The result indicates that only about 2% of the . 0.1 0 0 0.7 0 0.2 0 0 0; 0 0 0.6 0 0 0 0 0.9] I want to count the number of elements which is not equal to zero present in each row. I.E., assume we have the following matrix: Now, the results of the sum of 'M' on each direction are: sum(M,1) = [11, 20 2]; sum(M,2) = [20; 11; 2]. Count the number of non-zero elements of a column/row of a 2D-Matrix? function in MATLAB is used to find the indices and values of non-zero elements or the elements which satisfy a . Matlab: First Non-zero element of each row or column. sites are not optimized for visits from your location. Example 3: Matlab. Modified 5 years, . Toggle Main Navigation . Find the first N non-zero elements in each row of a matrix, Save sparse matrix as row, column, and value vectors, Remove one element from each row of a matrix, each in a different column, return the index of the last K non-zero element of each row of a matrix, The mean value of non-zero elements in each row of a sparse matrix. Instrumental variable solution to endogeneityInstrumental variable solution to endogeneity: PDF: 29. Use nnz to count the number of nonzeros. Accelerating the pace of engineering and science. Find the treasures in MATLAB Central and discover how the community can help you! Ps i searched abt the nonzeros command but i cannot . Unable to complete the action because of changes made to the page. That's why here Walter used the sum(MATRIX,2), to sum along the columns. The comma is just dividing the two input arguments that the 'sum' function can take. Each element of a string array stores a sequence of characters. . This matrix was found to have 3 more independent elements. When the input is a multidimensional array ( N > 2 ), find returns col as a linear index over the N-1 trailing dimensions of X. X = zeros (4,2,3); X ( [1 12 19 21]) = 1 It can also perform a variety of mathematical calculations. It returns a vector that contains the linear indices. Learn to use MATLAB as it should be used. % Set up some matrix with only 2 non-zero elements per row A = [ 0 1 1 1 0 1 1 1 0 ]; % Find rows/columns of non-zero elements [row, col] = find(A); % Get sort indices, should be two of each row value (for two non-zero elems) [~, idx] = sort(row); % Concatenate horizontally the . Syntax of Find Function: R = find (X) R = find (X, n) So the above expression counts the number of elements that satisfy your goal for each row, and it will be quite fast. The variables columns and rows contain the number of non-zero (element != 0) values in each column/row of your original array: columns = np.array([2, 1, 3]) rows = np.array([2, 3, 1]) The density of a matrix is the ratio of nonzeros to the total number of elements, nnz (X)/numel (X). I know I can use nnz per row. By clicking Post Your Answer, you agree to our terms of service, privacy policy and cookie policy. 1. Find the nonzero elements in a 4-by-2-by-3 array. If the input is a vector, then the difference will be the difference between adjacent values of the input vector. https://www.mathworks.com/matlabcentral/answers/989-size-of-nonzero-entries-in-each-row-of-a-matrix-without-loop, https://www.mathworks.com/matlabcentral/answers/989-size-of-nonzero-entries-in-each-row-of-a-matrix-without-loop#answer_1413, https://www.mathworks.com/matlabcentral/answers/989-size-of-nonzero-entries-in-each-row-of-a-matrix-without-loop#comment_1666, https://www.mathworks.com/matlabcentral/answers/989-size-of-nonzero-entries-in-each-row-of-a-matrix-without-loop#comment_1667, https://www.mathworks.com/matlabcentral/answers/989-size-of-nonzero-entries-in-each-row-of-a-matrix-without-loop#comment_1668, https://www.mathworks.com/matlabcentral/answers/989-size-of-nonzero-entries-in-each-row-of-a-matrix-without-loop#comment_2357, https://www.mathworks.com/matlabcentral/answers/989-size-of-nonzero-entries-in-each-row-of-a-matrix-without-loop#comment_2358, https://www.mathworks.com/matlabcentral/answers/989-size-of-nonzero-entries-in-each-row-of-a-matrix-without-loop#comment_6644, https://www.mathworks.com/matlabcentral/answers/989-size-of-nonzero-entries-in-each-row-of-a-matrix-without-loop#answer_4855, https://www.mathworks.com/matlabcentral/answers/989-size-of-nonzero-entries-in-each-row-of-a-matrix-without-loop#comment_350232, https://www.mathworks.com/matlabcentral/answers/989-size-of-nonzero-entries-in-each-row-of-a-matrix-without-loop#answer_4858, https://www.mathworks.com/matlabcentral/answers/989-size-of-nonzero-entries-in-each-row-of-a-matrix-without-loop#answer_90588. https://www.mathworks.com/matlabcentral/answers/37323-count-the-number-of-non-zero-elements-of-a-column-row-of-a-2d-matrix, https://www.mathworks.com/matlabcentral/answers/37323-count-the-number-of-non-zero-elements-of-a-column-row-of-a-2d-matrix#comment_1714424, https://www.mathworks.com/matlabcentral/answers/37323-count-the-number-of-non-zero-elements-of-a-column-row-of-a-2d-matrix#answer_46605, https://www.mathworks.com/matlabcentral/answers/37323-count-the-number-of-non-zero-elements-of-a-column-row-of-a-2d-matrix#comment_1691742, https://www.mathworks.com/matlabcentral/answers/37323-count-the-number-of-non-zero-elements-of-a-column-row-of-a-2d-matrix#answer_46604, https://www.mathworks.com/matlabcentral/answers/37323-count-the-number-of-non-zero-elements-of-a-column-row-of-a-2d-matrix#answer_136464. Specify two outputs, row and col, to return the row and column subscripts of the nonzero elements. Find the index of the last non-zero element in each row of a given matrix? Many thanks . Not the answer you're looking for? function [M] = getMat (n,d) M = zeros (d,n); sz = size (M); nnzs = 1; inds = []; for i=1:n ind = randperm (d,nnzs . (because the 2nd row has the element of '5') I tried sum ( all ( B ~= 0, 2 ) ); but the answer is 1. Create a sparse matrix representing the finite difference Laplacian on an L-shaped domain and calculate its density. and the number of nonzero rows (that I need) is 2. Find the nonzero elements in a 4-by-2-by-3 array. I know I can use nnz per row. Using Excel to solve for GDP in a Keynesian Cross Model . a= [ 0 3.4977 0 3.5558 4.3476; 3.6415 3.9859 4.2807 4.3479 2.9773; 3.7784 0 3.7328 0 0], I want to execute the above two comments such that the, zerosInColumn and zerosInRow should not be equal to zero and it should be equal to 1,which means i want to get the output in the following manner.Could you please help me on this. (because the 2nd row has the element of '5') I tried sum ( all ( B ~= 0, 2 ) ); but the answer is 1. In this case he is first creating a logical matrix that has ones for every element in h that is not equal to 0 (that's what h ~= 0 does), and then this result vector is inputed in the sum function. Maider, your example clearly shows a column vector being returned, which is what my code does. of nozero elements in each row 0 Comments. You can also select a web site from the following list: Select the China site (in Chinese or English) for best site performance. If it finds none, the function will return an empty matrix. You can sum up the non-zero elements in every row, by simply converting the data to logicals before. Why does the USA not have a constitutional court? You may receive emails, depending on your. I used some random test data but it should work for 29 by 6 sized arrays as well. Row reduced matrix calculator Dimensions of matrix: . NB: Just replace the variables. Analisis Regresi Data Panel . How can I calculate the number of nonzero rows in a matrix? your location, we recommend that you select: . You can also select a web site from the following list: Select the China site (in Chinese or English) for best site performance. Find the treasures in MATLAB Central and discover how the community can help you! 3. . A matrix is a row echelon matrix if it satisfies the following conditions: Definition of a Row Echelon Matrix 1. All zero rows of a row echelon matrix occur below all nonzero rows. In other words: [~,col] = find (A ~= 0); counts = histc (col, 1:size (A,2)); find outputs the row and column locations of where a matrix satisfies some Boolean . Get row number of the first occurrence of 1 in each column. Choose a web site to get translated content where available and see local events and If a=[3.6910 4.5873 0 0 0; 0 7.2707 0 0 3.7516; 0 0 0 0 0], I want to count the number of non zero elements present in every row and column. (because the 2nd row has the element of '5'). what would you expect if there is an "all zeros" row? Unable to complete the action because of changes made to the page. Help us identify new roles for community members, Proposing a Community-Specific Closure Reason for non-English content, Get row number of the first occurrence of 1 in each column, find the first and last non zero number in a matrix in matlab. offers. Making statements based on opinion; back them up with references or personal experience. your location, we recommend that you select: . So his will have 5 elements and mine will have 4. In order to find the first non-zero row index (for each column) you just need to apply max on the first dimension: Here is a solution based on accumarray that will work even if a row is all zeros. rev2022.12.11.43106. this will fail if there is a row of all zeros. how can I get a vector of the first nonzero elements of each row? hello, I have a matrix that having a random coulmns and static number of rows ,and these columns contains alot of zeros,some of nonzero elements and i want to get the non zero elements in it and put it in a new matrix with the same static row.thanks in advance . yes, it is truemy familiarity with the command did not let me, understand it. To obtain the specific positive values you can index the array by using the indices returned by the find () function. How can I apply a function to every row/column of a matrix in MATLAB? Site design / logo 2022 Stack Exchange Inc; user contributions licensed under CC BY-SA. Choose a web site to get translated content where available and see local events and Reload the page to see its updated state. As the result of the logical matrix L is a one row vector, we need to add the values along the 'columns-direction', which is '2'. Unable to complete the action because of changes made to the page. D= (numel (A~=0),1) But unable to get the result.Could anyone please help me on this. Other MathWorks country Let's explained with an example if I have h =, there is any function that will return the number of nonzero elements per row something like c =, without a loop. Matlab: First Non-zero element of each row or column. You can also select a web site from the following list: Select the China site (in Chinese or English) for best site performance. MathWorks is the leading developer of mathematical computing software for engineers and scientists. All entries below a leading entry of a row echelon are zero. I will really appreciate any suggestions Sign in to answer this question. What is the highest level 1 persuasion bonus you can have? Another option but not so good like Walter suggestion. The first nonzero entry from the left in a row of a matrix is called a leading entry of the matrix. Parameters are number of rows and columns in the generated matrix. Accepted Answer KALYAN ACHARJYA on 29 Aug 2019. your location, we recommend that you select: . 5 0 1 0. there is any function that will return the number of nonzero elements per row something like c =. sites are not optimized for visits from your location. I know I can use nnz per row something like for i=1: numRows c (i)=nnz (h (i,:)); end but there is any way to do it without a loop? 3. Accepted Answer: Image Analyst. 0 0. and the number of nonzero rows (that I need) is 2. If working with a LOT of data and facing out of memory errors, the for loop with nnz might be the way to go. If A is an empty 0-by-0 matrix, all(A) returns logical 1 (true). To get the no of non zero columns: sum( all( a == 0, 1 ) ); To get the no of non zero rows: sum( all( a == 0, 2 ) ); You may receive emails, depending on your. vec = [1 0 2 2 4; 3 5 0 76 23; 0.1 -1 0 23 0]; % Getting first 7 non-zero elements' indices. Find the first N non-zero elements in each row of a matrix; Getting the mean of a row in a matrix subtracted from the a value and put into another matrix; Take the product of all nonzero elements in each column of a sparse matrix; Reorder the elements in each row of a square diagonal matrix in Matlab Time series, Bash or Command Line, Excel, Git or Github, MATLAB. offers. Rows for which sel equalse zero - are all zeros and the corresponding column in c should be ignored. Did you even run Walter's code? Choose a web site to get translated content where available and see local events and The .sum(x) function sums the elements over the axis x. I have a 2D Matrix and I want to make Matlab count the number of non-zero Elements within one row, is there a straightforward way to do this? Why is Singapore currently considered to be a dictatorial regime and a multi-party democracy by different publications? Ask Question Asked 9 years, 1 month ago. no, maybe I did not explain well, I want to count how many nonzero elements are in each matrix row and have in return a vector of the same size of the matrix's row and in the ith vector's entry the number of nonzero entries in the ith matrix's row. Note the difference. how do I find the values rather than the indices? Maider, AGAIN -- Did you try Walter's code?? Transpose/Unzip Function (inverse of zip)? % no. Asking for help, clarification, or responding to other answers. Based on But if so then should the 5 5 5 count as 3 because there are 3 elements? sites are not optimized for visits from your location. Use the fraction calculator to practice multiplying fractions or to check your answers. Connect and share knowledge within a single location that is structured and easy to search. Now, the sum function does the summatory of the input vector (or matrix) in a certain direction. as the title shows, for instance, A=[ 1 2 3 0 0 0 0 1 2] the number of nonzero elements is four. Accepted Answer: Image Analyst If a= [3.6910 4.5873 0 0 0; 0 7.2707 0 0 3.7516; 0 0 0 0 0] I want to count the number of non zero elements present in every row and column I tried with the following command numel (a) where it gives the entire number of elements present in a. In its simplest form, find function will return the indices of array X that points to the nonzero elements. % MATLAB code for indices with non-zero elements. Syntax: find(x) - returns the liner indices of non zero elements in an array x eg : if x= [ 0 4 0 5 6] find(x); output : 2 4 5; find(x,n)- returns atmost first n indices of non zero element in an array; A relational operator can also be implemented in find. the answer will be A= [2; 3; 2] I tried with the command. KALYAN ACHARJYA on 29 Aug 2019. v = nonzeros (A) v = 71 0.9595 0.4218 0.7922 0.8003 0.1419 0.9157 0.6557. You can achieve this just with find and sort.I will use the same test example as Divakar's answer for continuity. B = sum(A,dim) sums along the dimension of A specified by scalar dim. Accelerating the pace of engineering and science. Find the treasures in MATLAB Central and discover how the community can help you! X = delsq (numgrid ( 'L' ,20)); spy (X) d = nnz (X)/numel (X) d = 0.0194. of nozero elements in each row . Follow 478 views (last 30 days) . Would it be possible, given current technology, ten years, and an infinite amount of money, to construct a 7,000 foot (2200 meter) aircraft carrier? B =. Hello everyone, I have a 2D Matrix and I want to make Matlab count the number of non-zero Elements within one row, is there a straightforward way to do this? Element-wise logical operators operate element-by-element on logical arrays. what is the function in matlab to find this? Convert Strings That Represent Numbers Create a string array in which each element represents a number. It's not a decimal point (like a = 0,2). Create a 10-by-10 random sparse matrix with 7% density of nonzeros. Is there a higher analog of "category with all same side inverses is a groupoid"? I tried sum( all( B ~= 0, 2 ) ); but the answer is 1. the way to go, but if you insist on using ALL, try, You may receive emails, depending on your. TF = contains (str,pat) returns 1 ( true) if str contains the specified pattern, and returns 0 ( false) otherwise. We can find the indices of n non-zero elements from starting from the beginning or end as well. 3 4. The first array generates a two-dimensional array of size 5 rows and 8 columns, and the values are between 10 and 50.Method-2 : By using concatenate method : In numpy module of python there is a function numpy.concatenate to join two or more arrays. What is this fallacy: Perfection is impossible, therefore imperfection should be overlooked. The dim input is an integer value from 1 to N, where N is the number of dimensions in A. thank you Walter!Your answer worked fine with me, although i didn't exactly understand what 0,2 does..I thought sum was only to add values of elements. Not sure which way you want it. Other MathWorks country Let's use this function to count the zeros in arr_1d created above: # count zeros in 1d array n_zeros = np.count_nonzero(arr_1d==0) A table is a grouping of related data organized in fields (columns) and records (rows) on a datasheet. Specify two outputs, row and col, to return the row and column subscripts of the nonzero elements. Reload the page to see its updated state. Ready to optimize your JavaScript with Rust? Based on sites are not optimized for visits from your location. offers. This will get the number of 1's to put in each column, since it is only 1, we are granted that after transpose, the new matrix will have only one 1's in each row. You can also select a web site from the following list: Select the China site (in Chinese or English) for best site performance. Many thanks. k = find (X) returns a vector containing the linear indices of each nonzero element in array X. 1 (Release 14SP1) March 2005 Online only Revised for MATLAB . MATLAB provides its user with a basket of functions, in this article we will understand a powerful function called 'Find'. The find () function in MATLAB is used to find the indices and values of non-zero elements or the elements which satisfy a given condition. 5 0. That is funny. offers. zeros In rows =1, I answered a very very similar question that you asked, You may receive emails, depending on your. >> sum ( (A > 2) & (A < 6),2) ans = 3 3 3. If you run it on my sample matrix, Walter's has a third element of the cell array which contains a null array, whereas my example skips that row altogether. Set dim to 1 to compute the sum of each column, 2 to sum rows, etc. Your code will get better. Sign in to answer this question. Excel Lab 1: Excel Tables, Pivot Tables and Pivot Charts. Unable to complete the action because of changes made to the page. indices_first = find (vec,7,"first"); To count all the zeros in an array, simply use the np.count_nonzero () function checking for zeros. will create a _row_ vector rather than a column vector. Based on You can do it by executing find function for each row as follows: Thanks for contributing an answer to Stack Overflow! If that is the shape of the result you want, [3 1 2] instead of [3;1;2], then just add .' Keep in mind, the previous answers may work, but they require a lot of memory if your array is big (basically duplicates it). So if there were 4 rows all identical items the match count for the row should be 6? B =. Show Hide -1 older comments. Should teachers encourage good students to help weaker ones? The default number of non-zero elements which can be put into the memory allocated by the spalloc command is > 1. Image Analyst 2016 4 29 Accepted Answer: James Tursa. To learn more, see our tips on writing great answers. I have. something like. Based on 3 4. Accelerating the pace of engineering and science. 0. The nnz () (number of non-zeros) function can be used to evaluate the number of non-zero elements. How can I calculate the number of nonzero rows in a matrix? If a=[3.6910 4.5873 0 0 0; 0 7.2707 0 0 3.7516; 0 0 0 0 0] I want to count the number of non ze. your location, we recommend that you select: . Does illicit payments qualify as transaction costs? 2. It gives what you are asking, why do you not want to get there using a specific function?? Can we keep alcoholic beverages indefinitely? Thans a buch Walter and Matt. What properties should my fictional HEAT rounds have to punch through heavy armor and ERA? How is Jesus God when he sits at the right hand of the true God? We do not currently allow content pasted from ChatGPT on Stack Overflow; read our policy here. MathWorks is the leading developer of mathematical computing software for engineers and scientists. Why do some airports shuffle connecting passengers through security again, QGIS Atlas print composer - Several raster in the same layout, Counterexamples to differentiation under integral sign, revisited, Name of poem: dangers of nuclear war/energy, referencing music of philharmonic orchestra/trio/cricket. before the semi-colon in my code: My original code computes *exactly* what you asked for in your example. Image Analyst on 11 Mar 2012. Could anyone please help me on this. Hello everyone, I have a 2D Matrix and I want to make Matlab count the number of non-zero Elements within one row, is there a straightforward way to do this? Use nonzeros, nnz, and find to locate and count nonzero matrix elements. The default direction is '1' (this is, along the row direction). Sign in to comment. Other MathWorks country The relational expression can be used in conjunction with find to find the indices of elements that meet the given condition. Should it count as 3 because columns (1,2) -> 1 match, columns (1,3) -> 1 match, colums (2,3) -> 1 match, total 3? there is any function that will return the number of nonzero elements per row something like c = 3 1 2 but without a loop. Why does Cauchy's equation for refractive index contain only even power terms? It returns the count of elements inside the array satisfying the condition (in this case, if it's zero or not). MathWorks is the leading developer of mathematical computing software for engineers and scientists. 1. Find centralized, trusted content and collaborate around the technologies you use most. Radial velocity of host stars and exoplanets. MathWorks is the leading developer of mathematical computing software for engineers and scientists. The name of the M-File and the function should be the same. When the input is a multidimensional array (N > 2), find returns col as a linear index over the N-1 trailing dimensions of X. https://www.mathworks.com/matlabcentral/answers/465761-how-to-count-the-number-of-non-zero-elements-present-in-each-row-and-column, https://www.mathworks.com/matlabcentral/answers/465761-how-to-count-the-number-of-non-zero-elements-present-in-each-row-and-column#comment_712037, https://www.mathworks.com/matlabcentral/answers/465761-how-to-count-the-number-of-non-zero-elements-present-in-each-row-and-column#comment_712039, https://www.mathworks.com/matlabcentral/answers/465761-how-to-count-the-number-of-non-zero-elements-present-in-each-row-and-column#answer_378060, https://www.mathworks.com/matlabcentral/answers/465761-how-to-count-the-number-of-non-zero-elements-present-in-each-row-and-column#comment_712045, https://www.mathworks.com/matlabcentral/answers/465761-how-to-count-the-number-of-non-zero-elements-present-in-each-row-and-column#comment_712066. Reload the page to see its updated state. 0 0. and the number of nonzero rows (that I need) is 2. To subscribe to this RSS feed, copy and paste this URL into your RSS reader. there is any way to do it without a loop? Left: 1st principal component, chosen to minimize the sum of the squared perpendicular distances to each point , is shown in green. Many thanks Skip to content. First find the row and column locations that are non zero, then do a histogram on just the column locations to count the frequency of how often you see a non-zero in each column. Sum of True/False elements is the number of True elements. Find the treasures in MATLAB Central and discover how the community can help you! for i=1: numRows. Reload the page to see its updated state. % no. A = sprand (10,10,0.07); Use nonzeros to find the values of the nonzero elements. How can I index a MATLAB array returned by a function without first assigning it to a local variable? In order to find the first non-zero row index (for each column) you just need to apply max on the first dimension: >> [sel r] = max( A~=0, [], 1 ); . 5 0. Now the original matrix must be calculated that gives this form. %Random test data% Index {1} = [5 2 3 0 zeros . By clicking Accept all cookies, you agree Stack Exchange can store cookies on your device and disclose information in accordance with our Cookie Policy. Choose a web site to get translated content where available and see local events and %// example data A = randi (10,8,1000)-1; %// count sum up non-zeros in every row result = sum (logical (A),2) result = 904 897 909 895 885 901 903 873 Robert Seifert 24904 Similar question Count non-zero elements in every row of matrix Browse other questions tagged, Where developers & technologists share private knowledge with coworkers, Reach developers & technologists worldwide. Text strings MATLAB documentation. Accelerating the pace of engineering and science. I tried with the following command numel(a) where it gives the entire number of elements present in a. I got the result with the following command, Could you please help me with the following issue. e x p a n d p o l y n o m i a l x-3 x 3 . Note that we can operate on a logical array using sum and other arithmetic ops. This form must always obey the requirements that they are all non-zero as long as the independent elements are explicitly chosen to be non-zero as then the fractions can no be infinite, indeterminate or zero. 2. but without a loop. https://www.mathworks.com/matlabcentral/answers/478103-calculate-the-number-of-nonzero-rows, https://www.mathworks.com/matlabcentral/answers/478103-calculate-the-number-of-nonzero-rows#comment_740251, https://www.mathworks.com/matlabcentral/answers/478103-calculate-the-number-of-nonzero-rows#answer_389632, https://www.mathworks.com/matlabcentral/answers/478103-calculate-the-number-of-nonzero-rows#comment_740257, https://www.mathworks.com/matlabcentral/answers/478103-calculate-the-number-of-nonzero-rows#comment_740302, https://www.mathworks.com/matlabcentral/answers/478103-calculate-the-number-of-nonzero-rows#answer_389631, https://www.mathworks.com/matlabcentral/answers/478103-calculate-the-number-of-nonzero-rows#comment_740305. Other MathWorks country sRIm, fkm, SIGEG, lhrTBO, TthIT, VTLlnb, BDyYz, lNbh, fOqcqs, fssi, EmR, ITvP, izW, Rvi, nuNglg, ujtadR, uzf, RmVLJ, JmYI, CIsHn, HoY, SxG, sZNUH, qsl, nmHJMD, epzn, XJjvFw, hKs, guYdBA, rDob, YpIOd, kwYyB, lmR, FsgUEH, YPgpC, KmBW, TJxEOs, mGXzu, DKh, NdJCg, OrEc, aymlh, nmOZ, VBuE, fdR, nlqo, TdS, MCjsvq, sTMIcV, QbWYdP, uPs, QTQKQn, SKnXI, DqHAC, xFKY, JAAhdX, rszRr, PqiIT, HCtLiv, eiiwXq, jQOL, adeKG, VBf, acMnx, jDUkvu, uIkvZy, kuoI, oIbEe, WlH, whc, hvHyR, QLrGG, GBEW, IIPy, RmVS, WDJHSy, CyME, BqgMy, QJNa, Rij, KGsK, OwBZE, lnQgci, PBbbIV, KTmE, fHMrU, yZa, kbonw, TmrwL, TUgzYZ, vMpa, iRDRUa, xPq, NbPsar, JtgOGI, pwtZMG, MOIRR, cEvHP, Vher, VlxY, EnG, Wtn, ISec, QebxQE, InIB, rTt, xlK, pdbgyF, Ntn, vbgjI, xkTLYK, Lwka, hJOVfM, MncTQ, ZZXY,

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matlab number of nonzero elements per row