How can I apply a function to every row column of a matrix in MATLAB

Question

You can apply a function to every item in a vector by saying  for example  v   1  or you can use the function arrayfun  How can I do it for every row column of a matrix without using a for loop

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Building on Alex s answer  here is a more generic function   applyToGivenRow     func  matrix    row  func matrix row       newApplyToRows     func  matrix  arrayfun applyToGivenRow func  matrix   1 size matrix 1    UniformOutput   false    takeAll     x  reshape  x      size x 1  2   size x 1     genericApplyToRows     func  matrix  takeAll newApplyToRows func  matrix      Here is a comparison between the two functions    gt  gt    Example myMx    1 2 3  4 5 6  7 8 9   myFunc     x   mean x   std x   sum x   length x     gt  gt  genericApplyToRows myFunc  myMx   ans         2     1     6     3      5     1    15     3      8     1    24     3   gt  gt  applyToRows myFunc  myMx      Error using    gt  arrayfun Non-scalar in Uniform output  at index 1  output 1  Set  UniformOutput  to false   Error in    gt    func matrix arrayfun applyToGivenRow func matrix  1 size matrix 1

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You may want the more obscure Matlab function bsxfun  From the Matlab documentation  bsxfun  applies the element-by-element binary operation specified by the function handle fun to arrays A and B  with singleton expansion enabled     gnovice stated above that sum and other basic functions already operate on the first non-singleton dimension  i e   rows if there s more than one row  columns if there s only one row  or higher dimensions if the lower dimensions all have size  1   However  bsxfun works for any function  including  and especially  user-defined functions   For example  let s say you have a matrix A and a row vector B  E g   let s say   A    1 2 3       4 5 6       7 8 9  B    0 1 2    You want a function power by col which returns in a vector C all the elements in A to the power of the corresponding column of B   From the above example  C is a 3x3 matrix   C    1 0 2 1 3 2       4 0 5 1 6 2       7 0 8 1 9 2    i e    C    1 2 9       1 5 36       1 8 81    You could do this the brute force way using repmat   C   A  repmat B  size A  1   1    Or you could do this the classy way using bsxfun  which internally takes care of the repmat step   C   bsxfun   x y  x  y  A  B    So bsxfun saves you some steps  you don t need to explicitly calculate the dimensions of A   However  in some informal tests of mine  it turns out that repmat is roughly twice as fast if the function to be applied  like my power function  above  is simple  So you ll need to choose whether you want simplicity or speed

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The accepted answer seems to be to convert to cells first and then use cellfun to operate over all of the cells  I do not know the specific application  but in general I would think using bsxfun to operate over the matrix would be more efficient  Basically bsxfun applies an operation element-by-element across two arrays  So if you wanted to multiply each item in an n x 1 vector by each item in an m x 1 vector to get an n x m array  you could use   vec1     stuff         n x 1 vector vec2     stuff         m x 1 vector result   bsxfun  times   vec1    vec2     This will give you matrix called result wherein the  i  j  entry will be the ith element of vec1 multiplied by the jth element of vec2   You can use bsxfun for all sorts of built-in functions  and you can declare your own  The documentation has a list of many  built-in functions  but basically you can name any function that accepts two arrays  vector or matrix  as arguments and get it to work

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None of the above answers worked  out of the box  for me  however  the following function  obtained by copying the ideas of the other answers works   apply func 2 cols     f M  cell2mat cellfun f num2cell M 1    UniformOutput  0      It takes a function f and applies it to every column of the matrix M   So for example   f     v   0 1 1 0  v    0 0 1    apply func 2 cols f  0 0 1 1 0 1 0 1     ans       0 00000   1 00000   0 00000   1 00000    0 10000   0 10000   1 10000   1 10000

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For completeness interest I d like to add that matlab does have a function that allows you to operate on data per-row rather than per-element  It is called rowfun  http   www mathworks se help matlab ref rowfun html   but the only  problem  is that it operates on tables  http   www mathworks se help matlab ref table html  rather than matrices

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Many built-in operations like sum and prod are already able to operate across rows or columns  so you may be able to refactor the function you are applying to take advantage of this   If that s not a viable option  one way to do it is to collect the rows or columns into cells using mat2cell or num2cell  then use cellfun to operate on the resulting cell array   As an example  let s say you want to sum the columns of a matrix M  You can do this simply using sum   M   magic 10                A 10-by-10 matrix columnSums   sum M  1       A 1-by-10 vector of sums for each column   And here is how you would do this using the more complicated num2cell cellfun option   M   magic 10                       A 10-by-10 matrix C   num2cell M  1                  Collect the columns into cells columnSums   cellfun  sum  C       A 1-by-10 vector of sums for each cell

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Stumbled upon this question answer while seeking how to compute the row sums of a matrix   I would just like to add that Matlab s SUM function actually has support for summing for a given dimension  i e a standard matrix with two dimensions   So to calculate the column sums do   colsum   sum M    or sum M  1    and for the row sums  simply do  rowsum   sum M  2    My bet is that this is faster than both programming a for loop and converting to cells     All this can be found in the matlab help for SUM

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I can t comment on how efficient this is  but here s a solution   applyToGivenRow     func  matrix    row  func matrix row      applyToRows     func  matrix  arrayfun applyToGivenRow func  matrix   1 size matrix 1       Example myMx    1 2 3  4 5 6  7 8 9   myFunc    sum   applyToRows myFunc  myMx

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Adding to the evolving nature of the answer to this question  starting with r2016b  MATLAB will implicitly expand singleton dimensions  removing the need for bsxfun in many cases   From the r2016b release notes      Implicit Expansion  Apply element-wise operations and functions to arrays  with automatic expansion of dimensions of length 1      Implicit expansion is a generalization of scalar expansion  With   scalar expansion  a scalar expands to be the same size as another   array to facilitate element-wise operations  With implicit expansion    the element-wise operators and functions listed here can implicitly   expand their inputs to be the same size  as long as the arrays have   compatible sizes  Two arrays have compatible sizes if  for every   dimension  the dimension sizes of the inputs are either the same or   one of them is 1  See Compatible Array Sizes for Basic Operations and   Array vs  Matrix Operations for more information   Element-wise arithmetic operators        -                  Relational operators      lt    lt     gt    gt            Logical operators      amp      xor  Bit-wise functions     bitand  bitor  bitxor  Elementary math functions     max  min  mod  rem  hypot  atan2  atan2d       For example  you can calculate the mean of each column in a matrix A    and then subtract the vector of mean values from each column with A -   mean A        Previously  this functionality was available via the bsxfun function    It is now recommended that you replace most uses of bsxfun with direct   calls to the functions and operators that support implicit expansion    Compared to using bsxfun  implicit expansion offers faster speed    better memory usage  and improved readability of code

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if you know the length of your rows you can make something like this   a rand 9 3   b rand 9 3    arrayfun   x1 x2 y1 y2 z1 z2  line  x1 x2   y1 y2   z1 z2     a   1  b   1  a   2  b   2  a   3  b   3

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With recent versions of Matlab  you can use the Table data structure to your advantage  There s even a  rowfun  operation but I found it easier just to do this   a   magic 6   incrementRow   cell2mat cellfun   x  x 1 table2cell table a    UniformOutput  0     or here s an older one I had that doesn t require tables  for older Matlab versions   dataBinner   cell2mat arrayfun   x  Binner a x    2   1 size a 1   UniformOutput  0

[matlab] How can I apply a function to every row/column of a matrix in MATLAB?

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