AND | Short-Circuit that the result of the relational operation is a logical matrix of For example, if A is a matrix, val is the maximum value and idx is its index. Thank you for your feedback. To complete the work of @VFDan, I benchmarked the 3 methods: the accepted one (custom loop), reduce, and find(max(arr)) on an array of 10000 floats. This is probably the best way, since its reliable and works on old browsers: It performs twice as many comparisons as necessary and will throw a RangeError on large arrays, though. The first step is finding the minimum value of the complete matrix with: The double min is needed to first find min of all columns, then find min of all those min values. More of a visual learner, check out my YouTube tutorial here. If A is a matrix, then max (A) is a row vector containing the maximum value of each column of A. -9. ; Check if the current element is greater than the accumulator. previous syntaxes. The sub2ind and ind2sub functions help to convert between original array indices and their linear version. A and returns an For higher-dimensional arrays, expand the syntax to match the array dimensions. Create a vector and compute its largest element. Knowing how to find where the max (or, really, min) values exist in a list is an important skill. Accelerate code by running on a graphics processing unit (GPU) using Parallel Computing Toolbox. To learn more about numpy, check out the official documentation here. Index array, returned as a vector, matrix, or multidimensional array. https://www.mathworks.com/help/matlab/ref/find.html Theme Copy maximum = max (max (A)); [x,y]=find (A==maximum) 4 Comments Sergio Novi Junior on 5 Jun 2020 Oscar, it will depend on your application. of their indices in I matches the order in which they % Function: Calculate the minimum value and its indices in a multidimensional array. If A is a multidimensional array, then max (A) operates along the first dimension of A whose size does not equal 1, treating the elements as vectors. Here, you'll learn all about Python, including how best to use it for data science. more information, see Tall Arrays. see Tall Arrays. If either A or B is single, https://www.mathworks.com/matlabcentral/answers/100813-how-do-i-find-the-indices-of-the-maximum-or-minimum-value-of-my-matrix, https://www.mathworks.com/matlabcentral/answers/100813-how-do-i-find-the-indices-of-the-maximum-or-minimum-value-of-my-matrix#answer_110162, https://www.mathworks.com/matlabcentral/answers/100813-how-do-i-find-the-indices-of-the-maximum-or-minimum-value-of-my-matrix#comment_415617, https://www.mathworks.com/matlabcentral/answers/100813-how-do-i-find-the-indices-of-the-maximum-or-minimum-value-of-my-matrix#comment_416949, https://www.mathworks.com/matlabcentral/answers/100813-how-do-i-find-the-indices-of-the-maximum-or-minimum-value-of-my-matrix#comment_816998, https://www.mathworks.com/matlabcentral/answers/100813-how-do-i-find-the-indices-of-the-maximum-or-minimum-value-of-my-matrix#comment_885080, https://www.mathworks.com/matlabcentral/answers/100813-how-do-i-find-the-indices-of-the-maximum-or-minimum-value-of-my-matrix#answer_175955, https://www.mathworks.com/matlabcentral/answers/100813-how-do-i-find-the-indices-of-the-maximum-or-minimum-value-of-my-matrix#comment_353727, https://www.mathworks.com/matlabcentral/answers/100813-how-do-i-find-the-indices-of-the-maximum-or-minimum-value-of-my-matrix#comment_960703, https://www.mathworks.com/matlabcentral/answers/100813-how-do-i-find-the-indices-of-the-maximum-or-minimum-value-of-my-matrix#comment_1426229, https://www.mathworks.com/matlabcentral/answers/100813-how-do-i-find-the-indices-of-the-maximum-or-minimum-value-of-my-matrix#answer_230702, https://www.mathworks.com/matlabcentral/answers/100813-how-do-i-find-the-indices-of-the-maximum-or-minimum-value-of-my-matrix#comment_1894690, https://www.mathworks.com/matlabcentral/answers/100813-how-do-i-find-the-indices-of-the-maximum-or-minimum-value-of-my-matrix#answer_394295, https://www.mathworks.com/matlabcentral/answers/100813-how-do-i-find-the-indices-of-the-maximum-or-minimum-value-of-my-matrix#answer_395336, https://www.mathworks.com/matlabcentral/answers/100813-how-do-i-find-the-indices-of-the-maximum-or-minimum-value-of-my-matrix#comment_1053366, https://www.mathworks.com/matlabcentral/answers/100813-how-do-i-find-the-indices-of-the-maximum-or-minimum-value-of-my-matrix#comment_2322445, https://www.mathworks.com/matlabcentral/answers/100813-how-do-i-find-the-indices-of-the-maximum-or-minimum-value-of-my-matrix#comment_2322550, https://www.mathworks.com/matlabcentral/answers/100813-how-do-i-find-the-indices-of-the-maximum-or-minimum-value-of-my-matrix#answer_282157, https://www.mathworks.com/matlabcentral/answers/100813-how-do-i-find-the-indices-of-the-maximum-or-minimum-value-of-my-matrix#comment_554931, https://www.mathworks.com/matlabcentral/answers/100813-how-do-i-find-the-indices-of-the-maximum-or-minimum-value-of-my-matrix#comment_725503, https://www.mathworks.com/matlabcentral/answers/100813-how-do-i-find-the-indices-of-the-maximum-or-minimum-value-of-my-matrix#comment_999022, https://www.mathworks.com/matlabcentral/answers/100813-how-do-i-find-the-indices-of-the-maximum-or-minimum-value-of-my-matrix#comment_999238, https://www.mathworks.com/matlabcentral/answers/100813-how-do-i-find-the-indices-of-the-maximum-or-minimum-value-of-my-matrix#answer_319610, https://www.mathworks.com/matlabcentral/answers/100813-how-do-i-find-the-indices-of-the-maximum-or-minimum-value-of-my-matrix#comment_568269, https://www.mathworks.com/matlabcentral/answers/100813-how-do-i-find-the-indices-of-the-maximum-or-minimum-value-of-my-matrix#comment_1065058, https://www.mathworks.com/matlabcentral/answers/100813-how-do-i-find-the-indices-of-the-maximum-or-minimum-value-of-my-matrix#answer_334271, https://www.mathworks.com/matlabcentral/answers/100813-how-do-i-find-the-indices-of-the-maximum-or-minimum-value-of-my-matrix#comment_651015, https://www.mathworks.com/matlabcentral/answers/100813-how-do-i-find-the-indices-of-the-maximum-or-minimum-value-of-my-matrix#answer_433045, https://www.mathworks.com/matlabcentral/answers/100813-how-do-i-find-the-indices-of-the-maximum-or-minimum-value-of-my-matrix#answer_429776, https://www.mathworks.com/matlabcentral/answers/100813-how-do-i-find-the-indices-of-the-maximum-or-minimum-value-of-my-matrix#answer_635314, https://www.mathworks.com/matlabcentral/answers/100813-how-do-i-find-the-indices-of-the-maximum-or-minimum-value-of-my-matrix#answer_1127347, https://www.mathworks.com/matlabcentral/answers/100813-how-do-i-find-the-indices-of-the-maximum-or-minimum-value-of-my-matrix#answer_1176375. To find the indices of all the locations where the maximum value (of the whole matrix) appears, you can use the "find" function. an empty array with the same size as A. Replace Values That Meet a Condition Sometimes it is useful to simultaneously change the values of several existing array elements. more information, see Tall Arrays. Sometimes it is useful to simultaneously change the values of several existing array elements. maxk(A,k,2) computes the Thus, linear indexing numbers the elements [row,col] You can use the logical and, or, and not operators to apply any number of conditions to an array; the number of conditions is not limited to one or two. Consider a 2-by-3-by-3 input array, A. https://www.mathworks.com/help/matlab/ref/find.html Theme Copy maximum = max (max (A)); [x,y]=find (A==maximum) 4 Comments Sergio Novi Junior on 5 Jun 2020 Oscar, it will depend on your application. You can unsubscribe anytime. A is real or complex. How to draw a truncated hexagonal tiling? To find a specific integer value, use the == operator. M = max (A) returns the maximum elements of an array. I favor the functional answers above for their neat factor but not their readability; but if I were more familiar with javascript then I might like them for that, too. Reload the page to see its updated state. A and returns a M = max(A) How can I choose just one of them? % First of all, identify the Matlab convention for numbering the elements of a multi-dimensional array. Find Array Elements That Meet a Condition. A by real(A) when returned as a scalar, vector, matrix, or multidimensional array. This function fully supports distributed arrays. then use angle(A) in the interval (-,] to break I edited the answer in another way. Based on your location, we recommend that you select: . Theme Copy max_num = 40 X = 4 Y = 5 While MATLAB displays arrays according to their defined sizes and shapes, they are actually stored in memory as a single column of elements. Create a vector and compute its maximum, excluding NaN values. , return [a.pop(a.index(max(a))) for _ in range(n)], Your email address will not be published. more information, see Run MATLAB Functions in Thread-Based Environment. not equal 1. You learned how to do this using the index() function, as well as with a for loop. Choose a web site to get translated content where available and see local events and offers. Together, row and col specify The first argument is the accumulated result of the reduction so far. M = max (A) returns the maximum elements of an array. Web browsers do not support MATLAB commands. For more information on the 'min' and 'max' functions, see the documentation pages listed below: https://www.mathworks.com/help/matlab/ref/max.html, https://in.mathworks.com/help/matlab/ref/min.html. are related to the linear indices in k by k A by abs(A) when vector. Creating a stair plot for sinewave function. This function fully supports tall arrays. MATLAB treats 15 14 12 2 10, 17 24 1 8 15 Privacy Policy. the index into the operating dimension. 23 5 7 14 16 You clicked a link that corresponds to this MATLAB command: Run the command by entering it in the MATLAB Command Window. A is real, and by Welcome to datagy.io! Pandas Quantile: Calculate Percentiles of a Dataframe, Python: Count Number of Occurrences in List (6 Ways). M = max (A, [], 'all'); For previous releases, use: Theme. M = max(A,[],vecdim,nanflag) This is the most useful for working with images. Just a note for the provided answers above, answer from LanilT was the fastest! In this case, MATLAB compares elements of A by A. https://jsben.ch/wkd4c. MATLAB "is" functions also return logical arrays that indicate which elements of the input meet a certain condition. while the sizes of all other dimensions remain the same, unless size(A,dim) is 0. If X is a row vector, then The default for direction is 'first', This example shows how to filter the elements of an array by applying conditions to the array. Calculate with arrays that have more rows than fit in memory. The semicolon suppresses that. Check out my tutorial here, which will teach you different ways of calculating the square root, both without Python functions and with the help of functions. Inputs A and B must either be the same 'includenan' Include the NaN values complex. Find the treasures in MATLAB Central and discover how the community can help you! How to insert an item into an array at a specific index (JavaScript), Sort array of objects by string property value. If you can use linear indices, instead I would recommend: This will tell us the maximum value in A is 9 and it is located in element 6 of A. B preserves the order of any equal elements in Find indices and values of nonzero elements. Here's a solution that finds indices for the 5 largest values (which could include repeated values) using sort: [~, sortIndex] = sort (A (:), 'descend'); % Sort the values in descending order maxIndex = sortIndex (1:5); % Get a linear index into A of the 5 largest values A minor modification revised from the "reduce" version of @traxium 's solution taking the empty array into consideration: A stable version of this function looks like this: To find the index of the greatest value in an array, copy the original array into the new array and then sort the original array in decreasing order to get the output [22, 21, 7, 0]; now find the value 22 index in the copyNumbers array using this code copyNumbers.indexOf(numbers[0]); const max = arr.reduce((m, n) => Math.max(m, n)), then the indexes of the max, var index = arr.findIndex(i => i === max). than k elements. "=" should be replaced with "==", i.e. the first n indices corresponding to the nonzero This function fully supports thread-based environments. vector when X is an empty array or has no While we could use a for loop for this approach, we will use a list comprehension that allows us to be much more concise in our approach. Lets continue with any matrix A. Other MathWorks country If A is a vector, then returns a matrix whose columns contain the k largest If Use logical indexing with a simple assignment statement to replace the values in an array that meet a condition. max(A,[],___,'linear') if A is a matrix, then max(A,[],2) is a You can do it calling max only once and without find(which would need to got through whole 2D matrix): M is maximum, and r and c is row and column in A where it is located. This object can be a Vector, a list, a matrix, a data frame, etc. returns the k largest elements of A. Then we have printed the maximum value along with its row and column index. Generate C and C++ code using MATLAB Coder. more information, see Run MATLAB Functions in Thread-Based Environment. To find a noninteger value, use a tolerance value based on your data. that case, the data type of the other array can be single, duration, Suspicious referee report, are "suggested citations" from a paper mill. k is greater than or equal to the number of elements 3.3. The content of the myMeasurements array is coming from the ADC (analogRead) and hence it is 10 bits (0-1023).Unless the map function is used, they cannot be declared as a byte.I refrained from doing this because the map function reduces the resolution and it is likely that the values stored in the myMeasurements array are close to each other, i.e. Compatible Array Sizes for Basic Operations, Variable-Sizing Restrictions for Code Generation of Toolbox Functions, Code Generation for Complex Data with Zero-Valued Imaginary Parts, Run MATLAB Functions in Thread-Based Environment, Run MATLAB Functions with Distributed Arrays. You can also reference multiple elements at a time by specifying their indices in a vector. One thing to note about this is that this method will return the first instance of the maximum value in that iterable object. For Otherwise, You can reference the A(2,2) element Input matrices or vectors must be of equal size. A. Browse other questions tagged, Where developers & technologists share private knowledge with coworkers, Reach developers & technologists worldwide, There are many tutorials out there to get you the basic Matlab functions familiar :). Smallest number in array and its position, JavaScript return index of minimum and maximum number in array. What are some tools or methods I can purchase to trace a water leak? elements along the first dimension whose size does not equal 1. To get this, assign the result of the call to max to a two element vector instead of just a single variable. If A is an Using true and false logical indicators is another useful way to index into arrays, particularly when working with conditional statements. The difference is that A(B) uses logical indexing, whereas A(I) uses linear indexing. then C is single. If you create a copy of the array and sort it descending, the first element of the copy will be the largest. For example, consider a 3-by-3 matrix. How do I return the response from an asynchronous call? OR | ismember. Next, find the elements in A that are less than 9 and even numbered. If A is a multidimensional array, then max (A) operates along the first dimension of A whose size does not equal 1, treating the elements as vectors. Like this one best. You have a modified version of this example. This function fully supports GPU arrays. Elements Equal to Specific Values. Index, returned as a scalar, vector, matrix, or multidimensional array. To find the indices of all the locations where the maximum value (of the whole matrix) appears, you can use the "find" function. complex. Do you want to open this example with your edits? The Python enumerate() function is an incredible function that lets us iterate over an iterable item, such as a list, and access both the index and the item. k is an empty matrix Other MathWorks country sites are not optimized for visits from your location. While the following array is displayed as a 3-by-3 matrix, MATLAB stores it as a single column made up of the columns of A appended one after the other. This function fully supports tall arrays. This function fully supports distributed arrays. Accelerating the pace of engineering and science. Other MathWorks country sites are not optimized for visits from your location. For example, say you want to know if the elements of a matrix A are less than the corresponding elements of another matrix B. If A is a multidimensional array, then elements of each column of A. Use the find function to get the index of the element equal to 8 that satisfies the conditions. elements are the maximums computed over each page of To apply a single condition, start by creating a 5-by-5 matrix that contains random integers between 1 and 15. While linear indexing can be less intuitive visually, it can be powerful for performing certain computations that are not dependent on the size or shape of the array. You clicked a link that corresponds to this MATLAB command: Run the command by entering it in the MATLAB Command Window. then max(A,[],[1 2]) computes the maximum over all elements Choose a web site to get translated content where available and see local events and offers. Use the logical not operator on X to locate the zeros. max(A) returns an empty array with the same To directly find the elements in X that satisfy the condition X<5, use X (X<5) . Vector of dimensions, specified as a vector of positive integers. You can return the nonzero values in X using X(k). NaN values in A while [C,I] = max(.) If Y is a multidimensional array, then find returns a column vector of the linear indices of the result. Is email scraping still a thing for spammers. . MathWorks is the leading developer of mathematical computing software for engineers and scientists. then use imag(A) to break ties. source: https://www.mathworks.com/help/matlab/ref/max.html. M = max (A (:)); 4 Comments. information, see Run MATLAB Functions with Distributed Arrays (Parallel Computing Toolbox). B = maxk(A,k,dim) Finally, find the elements in A that are less than 9 and even numbered and not equal to 2. 3.3. For example, access the elements in the first through third row and the second through fourth column of A. The size 10 12 19 21 3 Do German ministers decide themselves how to vote in EU decisions or do they have to follow a government line? You have a modified version of this example. the linear indices to the elements in X that are This preserves the relation X(row(i),col(i)) == v(i). Can an overly clever Wizard work around the AL restrictions on True Polymorph? For M = max(A,[],'all') in the operating dimension, then maxk sorts the input find (A<9 & ~mod (A,2) & A~=2) ans = 14 The result indicates that A (14) = 8. For example, return the entire third column of A. For example, find(x,1) returns If A is a multidimensional array, then Because of this, this section will teach you how to use a Python for loop to find the indices of the highest value in a Python list. @traxium While your explanation is great, the example could be clearer for those less into functional programming if we used more descriptive variables. 12 17 14 14 8 In this final section, youll learn how to use numpy in order to find the indices of the items with the highest values in a given Python list. The result is a list of the elements in A that satisfy both conditions. second argument to reduce(). Find centralized, trusted content and collaborate around the technologies you use most. values for v. The row and column subscripts, row and col, k is also a row vector. Generate C and C++ code using MATLAB Coder. k-by-n matrix. max(A) returns the maximum of Learn how not only to compute the maximum or minimum value in an Array, but also how to obtain their exact location or index within the matrix M = max(A,[],nanflag) The red dashed curve indicates the critical refractive index values, at which f s /(r = 1). AND | Short-Circuit The 'find' command only returns the indices of all the non-zero elements of a matrix. Getting the index of the returned max or min item using max()/min() on a list. Choose a web site to get translated content where available and see local events and offers. Lets first see what the code looks like and then explore the why and how of it works: In the final section of this tutorial, youll learn how to use numpy to find the indices of the max item of a list. For example, to access a single element of a matrix, specify the row number followed by the column number of the element. Store the result in B. Partition large arrays across the combined memory of your cluster using Parallel Computing Toolbox. array. max(A) operates along the first dimension of This function fully supports thread-based environments. In list ( 6 Ways ) tutorial here the official documentation here technologies use... Containing the maximum value along with its row and column index list a! The 'find ' command only returns the maximum value of each column of a data science one of them elements. How to insert an item into an array a web site to get this, the. A multi-dimensional array you want to open this example with your edits the of. Accelerate code by running on a list, a data frame, etc entire. The combined memory of your cluster using Parallel Computing Toolbox ) two element instead!, answer from LanilT was the fastest at a specific integer value, use the logical not on. Be a vector of positive integers, etc nanflag ) this is a! Is real, and by Welcome to datagy.io the maximum elements of each column of a by https... Same 'includenan ' Include the NaN values equal to the linear indices k... Functions also return logical arrays that have more rows than fit in memory with images -, to! By A. https: //jsben.ch/wkd4c for loop want to open this example with your edits of the element code... Documentation here reference the a ( 2,2 ) element input matrices or vectors must be equal... The zeros the sub2ind and ind2sub Functions help to convert between original indices. Logical not operator on X to locate the zeros vecdim, nanflag ) this the. Max or min item using max (. related to the nonzero values in a are! Copy will be the largest satisfy both conditions entire third column of a max... Find the treasures in MATLAB Central and discover how the community can help!!: Run the command by entering it in the first n indices corresponding to the nonzero values in X X! Syntax to match the array and Sort it descending, the first dimension of this function fully Thread-Based! Important skill the nonzero this function fully supports Thread-Based environments non-zero elements of each column of.. Then find returns a m = max ( a, dim ) is a array... Input matrices or vectors must be of equal size this function fully supports Thread-Based environments a of. The same 'includenan ' Include the NaN values complex ( JavaScript ), Sort array of objects by string value. Help you Count number of the elements in the first n indices corresponding to the number the... Multiple elements at a time by specifying their indices in a while [,... At a time by specifying their indices in k by k a by real ( a to!, to access a single element of a multi-dimensional array store the.! Occurrences in list ( 6 Ways ) Calculate with arrays that indicate which of... This MATLAB command Window, vector, matrix, or multidimensional array k... From LanilT was the fastest you can reference the a ( B ) uses logical indexing, whereas a:... The number of the result Y is a list is an empty matrix other MathWorks sites... In this case, MATLAB compares elements of an array can I just. Of any equal elements in find indices and values of several existing array elements compute its,... Pandas Quantile: Calculate Percentiles of a by real ( a ) is a list an. And scientists find index of max value in array matlab item using max ( a, dim ) is 0: //jsben.ch/wkd4c a is,. Software for engineers and scientists indicate which elements of the result argument the... Of them remain the same, unless size ( a ) how can I choose just one of?. Related to the linear indices in k by k a by abs ( a ) vector. Maximum elements of a column subscripts, row and column index and their linear version greater. Indices and values of nonzero elements find returns a column vector of the elements in a,! To insert an item into an array purchase to trace a water leak indexing whereas. The same 'includenan ' Include the NaN values complex k a by abs (,! An item into an array at a time by specifying their indices in a list is an skill... Using the index of minimum and maximum number in array and its position, JavaScript index. Choose a web site to get the index of minimum and maximum number in array Count! Discover how the community can help you in MATLAB Central and discover how the community can you... About Python, including how best to use it for data science for numbering the elements in the command... X to locate the zeros (: ) ) ; 4 Comments empty! '', i.e GPU ) using Parallel Computing Toolbox ) elements of a a... Real, and by Welcome to datagy.io k is greater than or equal to 8 that satisfies the conditions the... Value based on your data code by running on a graphics processing unit ( GPU ) using Computing! Be the same 'includenan ' Include the NaN values in X find index of max value in array matlab (., Python: Count number of the copy will be the same size a! A. https: //jsben.ch/wkd4c first of all, identify the MATLAB command: Run the command by entering in... A graphics processing unit ( GPU ) using Parallel Computing Toolbox ) an array. X to locate the zeros use most the indices of all the non-zero elements a., ] to break I edited the answer in another way ( k ) higher-dimensional arrays expand. Best to use it for data science elements in a while [ C, I ] = (! To insert an item into an array at a time by specifying their in. Arrays that indicate which elements of a Dataframe, Python: Count number of find index of max value in array matlab list... Input matrices or vectors must be of equal size learn more about numpy check! And col specify the first dimension whose size does not equal 1 indices corresponding to the number of 3.3... Y is a multidimensional array ; check if the current element is greater than or to! Logical indexing, whereas a ( B ) uses linear indexing you learned how insert! Column subscripts, row and the second through fourth column of a do you to... Learner, check out my YouTube tutorial here, assign the result in Partition. And the second through fourth column of a nonzero this function fully Thread-Based. Fourth column of a Dataframe, Python: Count number of Occurrences list... You learned find index of max value in array matlab to insert an item into an array at a specific (. Computing Toolbox ), etc you use most and discover how the community help!, as well as with a for loop vector of the copy will be the.. ) operates along the first instance of the copy will be the same 'includenan Include! Each column of a by A. https: //jsben.ch/wkd4c find centralized, trusted content and around. K a by abs ( a ) in the MATLAB convention for numbering the elements in a [... 17 24 1 8 15 Privacy Policy, as well as with a for loop simultaneously. List is an important skill can reference the a ( I ) uses linear indexing:! Number of the elements in find indices and values of nonzero elements by running on graphics., ] to break I edited the answer in another way method will the! The elements of an array at a time by specifying their indices in a list of linear... Convert between original array indices and values of several existing array elements 15 14 12 10. Sort it descending, the first through third row and column index Toolbox ) is Functions... ) is a multidimensional array, returned as a vector, matrix specify., vecdim, nanflag ) this is the leading developer of mathematical Computing software for engineers and scientists and... Than fit in memory you select: your location must be of equal size, I ] = (... Toolbox ) replace values that Meet a certain Condition that this method will the. List ( 6 Ways ) MATLAB convention for numbering the elements in a that satisfy both.! ) in the MATLAB convention for numbering the elements in find indices and linear. Vector and compute its maximum, excluding NaN values complex -, ] to break ties returns a m max. 2 10, 17 24 1 8 15 Privacy Policy than or equal to the of... That satisfy both conditions Welcome to datagy.io first argument is the accumulated result of the result in B. large! Useful to simultaneously change the values of several existing array elements indexing, whereas a ( I ) uses indexing! I ] = max ( a ) when vector official documentation here where the max a! Check out the official documentation here that Meet a Condition Sometimes it is useful simultaneously! Case, MATLAB compares elements of the array dimensions Include the NaN values complex row and col the. This case, MATLAB compares elements of a matrix, or multidimensional array ind2sub Functions help to between! Inputs a and returns an for higher-dimensional arrays, expand the syntax match. Count number of elements 3.3 a time by specifying their indices in k by a. In the interval ( -, ] to break I edited the answer another.

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