Find nearest value in numpy array

Question

Is there a numpy-thonic way  e g  function  to find the nearest value in an array    Example   np find nearest  array  value

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With slight modification  the answer above works with arrays of arbitrary dimension  1d  2d  3d         def find nearest a  a0        Element in nd array  a  closest to the scalar value  a0       idx   np abs a - a0  argmin       return a flat idx    Or  written as a single line   a flat np abs a - a0  argmin

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Here s a version that will handle a non-scalar  values  array   import numpy as np  def find nearest array  values       indices   np abs np subtract outer array  values   argmin 0      return array indices    Or a version that returns a numeric type  e g  int  float  if the input is scalar   def find nearest array  values       values   np atleast 1d values      indices   np abs np subtract outer array  values   argmin 0      out   array indices      return out if len out   gt  1 else out 0

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import numpy as np def find nearest array  value       array   np asarray array      idx    np abs array - value   argmin       return array idx   array   np random random 10  print array      0 21069679  0 61290182  0 63425412  0 84635244  0 91599191  0 00213826     0 17104965  0 56874386  0 57319379  0 28719469   value   0 5  print find nearest array  value     0 568743859261

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For 2d array  to determine the i  j position of nearest element   import numpy as np def find nearest a  a0       idx    np abs a - a0   argmin       w   a shape 1      i   idx    w     j   idx - i   w     return a i j   i  j

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Here is a fast vectorized version of  Dimitri s solution if you have many values to search for  values can be multi-dimensional array      values  should be sorted def get closest array  values        make sure array is a numpy array     array   np array array         get insert positions     idxs   np searchsorted array  values  side  left          find indexes where previous index is closer     prev idx is less     idxs    len array    np fabs values - array np maximum idxs-1  0     lt  np fabs values - array np minimum idxs  len array -1          idxs prev idx is less  -  1      return array idxs    Benchmarks    100 times faster than using a for loop with  Demitri s solution    gt  gt  gt   timeit ar get closest np linspace 1  1000  100   np random randint 0  1050   1000  1000    139 ms    4 04 ms per loop  mean    std  dev  of 7 runs  10 loops each    gt  gt  gt   timeit ar  find nearest np linspace 1  1000  100   value  for value in np random randint 0  1050  1000 1000   took 21 4 seconds

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import numpy as np def find nearest array  value       array   np array array      z np abs array-value      y  np where z    z min        m np array y      x m 0 0      y m 1 0      near value array x y       return near value  array  np array   60 200 30   3 30 50   20 1 -50   20 -500 11    print array  value   0 print find nearest array  value

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Here is a version that works with 2D arrays  using scipy s cdist function if the user has it  and a simpler distance calculation if they don t  By default  the output is the index that is closest to the value you input  but you can change that with the output keyword to be one of  index    value   or  both   where  value  outputs array index  and  both  outputs index  array index   For very large arrays  you may need to use kind  euclidean   as the default scipy cdist function may run out of memory  This is maybe not the absolute fastest solution  but it is quite close  def find nearest 2d array  value  kind  cdist   output  index           array  must be a 2D array        value  must be a 1D array with 2 elements        kind  defines what method to use to calculate the distances  Can choose one          of  cdist   default  or  euclidean   Choose  euclidean  for very large          arrays  Otherwise  cdist is much faster         output  defines what the output should be  Can be  index   default  to return          the index of the array that is closest to the value   value  to return the          value that is closest  or  both  to return index value     import numpy as np     if kind     cdist           try  from scipy spatial distance import cdist         except ImportError              print  quot Warning  find nearest 2d   Could not import cdist  Reverting to simpler distance calculation quot               kind    euclidean      index   np where array    value  0    Make sure the value isn t in the array     if index size    0          if kind     cdist   index   np argmin cdist  value  array  0           elif kind     euclidean   index   np argmin np sum  np array array -np array value    2  axis 1           else  raise ValueError  quot Keyword  kind  must be one of  cdist  or  euclidean  quot       if output     index   return index     elif output     value   return array index      elif output     both   return index array index      else  raise ValueError  quot Keyword  output  must be one of  index    value   or  both  quot

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For large arrays  the  excellent  answer given by  Demitri is far faster than the answer currently marked as best  I ve adapted his exact algorithm in the following two ways    The function below works whether or not the input array is sorted  The function below returns the index of the input array corresponding to the closest value  which is somewhat more general    Note that the function below also handles a specific edge case that would lead to a bug in the original function written by  Demitri  Otherwise  my algorithm is identical to his    def find idx nearest val array  value       idx sorted   np argsort array      sorted array   np array array idx sorted       idx   np searchsorted sorted array  value  side  left       if idx  gt   len array           idx nearest   idx sorted len array -1      elif idx    0          idx nearest   idx sorted 0      else          if abs value - sorted array idx-1    lt  abs value - sorted array idx                idx nearest   idx sorted idx-1          else              idx nearest   idx sorted idx      return idx nearest

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IF your array is sorted and is very large  this is a much faster solution   def find nearest array value       idx   np searchsorted array  value  side  left       if idx  gt  0 and  idx    len array  or math fabs value - array idx-1    lt  math fabs value - array idx             return array idx-1      else          return array idx    This scales to very large arrays  You can easily modify the above to sort in the method if you can t assume that the array is already sorted  It   s overkill for small arrays  but once they get large this is much faster

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All the answers are beneficial to gather the information to write efficient code  However  I have written a small Python script to optimize for various cases  It will be the best case if the provided array is sorted  If one searches the index of the nearest point of a specified value  then bisect module is the most time efficient  When one search the indices correspond to an array  the numpy searchsorted is most efficient   import numpy as np import bisect xarr   np random rand int 1e7    srt ind   xarr argsort   xar   xarr copy   srt ind  xlist   xar tolist   bisect bisect left xlist  0 3    In  63    time bisect bisect left xlist  0 3     CPU times  user 0 ns  sys  0 ns  total  0 ns    Wall time  22 2   s  np searchsorted xar  0 3  side  left     In  64    time np searchsorted xar  0 3  side  left      CPU times  user 0 ns  sys  0 ns  total  0 ns    Wall time  98 9   s  randpts   np random rand 1000  np searchsorted xar  randpts  side  left      time np searchsorted xar  randpts  side  left   CPU times  user 4 ms  sys  0 ns  total  4 ms Wall time  1 2 ms  If we follow the multiplicative rule  then numpy should take  100 ms which implies  83X faster

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Summary of answer  If one has a sorted array then the bisection code  given below  performs the fastest   100-1000 times faster for large arrays  and  2-100 times faster for small arrays  It does not require numpy either   If you have an unsorted array then if array is large  one should consider first using an O n logn  sort and then bisection  and if array is small then method 2 seems the fastest   First you should clarify what you mean by nearest value  Often one wants the interval in an abscissa  e g  array  0 0 7 2 1   value 1 95  answer would be idx 1  This is the case that I suspect you need  otherwise the following can be modified very easily with a followup conditional statement once you find the interval   I will note that the optimal way to perform this is with bisection  which I will provide first - note it does not require numpy at all and is faster than using numpy functions because they perform redundant operations   Then I will provide a timing comparison against the others presented here by other users   Bisection   def bisection array value          Given an   array     and given a   value     returns an index j such that   value   is between array j      and array j 1     array   must be monotonic increasing  j -1 or j len array  is returned     to indicate that   value   is out of range below and above respectively         n   len array      if  value  lt  array 0            return -1     elif  value  gt  array n-1            return n     jl   0  Initialize lower     ju   n-1  and upper limits      while  ju-jl  gt  1    If we are not yet done          jm  ju jl   gt  gt  1  compute a midpoint with a bitshift         if  value  gt   array jm                jl jm  and replace either the lower limit         else              ju jm  or the upper limit  as appropriate            Repeat until the test condition is satisfied      if  value    array 0     edge cases at bottom         return 0     elif  value    array n-1     and top         return n-1     else          return jl   Now I ll define the code from the other answers  they each return an index   import math import numpy as np  def find nearest1 array value       idx val   min enumerate array   key lambda x  abs x 1 -value       return idx  def find nearest2 array  values       indices   np abs np subtract outer array  values   argmin 0      return indices  def find nearest3 array  values       values   np atleast 1d values      indices   np abs np int64 np subtract outer array  values    argmin 0      out   array indices      return indices  def find nearest4 array value       idx    np abs array-value   argmin       return idx   def find nearest5 array  value       idx sorted   np argsort array      sorted array   np array array idx sorted       idx   np searchsorted sorted array  value  side  left       if idx  gt   len array           idx nearest   idx sorted len array -1      elif idx    0          idx nearest   idx sorted 0      else          if abs value - sorted array idx-1    lt  abs value - sorted array idx                idx nearest   idx sorted idx-1          else              idx nearest   idx sorted idx      return idx nearest  def find nearest6 array value       xi   np argmin np abs np ceil array None  T - value   axis 0      return xi   Now I ll time the codes  Note methods 1 2 4 5 don t correctly give the interval  Methods 1 2 4 round to nearest point in array  e g    1 5 -  2   and method 5 always rounds up  e g  1 45 -  2   Only methods 3  and 6  and of course bisection give the interval properly   array   np arange 100000  val   array 50000  0 55 print  bisection array val    timeit bisection array val  print  find nearest1 array val    timeit find nearest1 array val  print  find nearest2 array val    timeit find nearest2 array val  print  find nearest3 array val    timeit find nearest3 array val  print  find nearest4 array val    timeit find nearest4 array val  print  find nearest5 array val    timeit find nearest5 array val  print  find nearest6 array val    timeit find nearest6 array val    50000  50000  100000 loops  best of 3  4 4   s per loop 50001 1 loop  best of 3  180 ms per loop 50001 1000 loops  best of 3  267   s per loop  50000  1000 loops  best of 3  390   s per loop 50001 1000 loops  best of 3  259   s per loop 50001 1000 loops  best of 3  1 21 ms per loop  50000  1000 loops  best of 3  746   s per loop   For a large array bisection gives 4us compared to next best 180us and longest 1 21ms   100 - 1000 times faster   For smaller arrays it s  2-100 times faster

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Here is a version with scipy for  Ari Onasafari  answer  to find the nearest vector in an array of vectors   In  1   from scipy import spatial  In  2   import numpy as np  In  3   A   np random random  10 2   100  In  4   A Out 4   array    68 83402637   38 07632221            76 84704074   24 9395109             16 26715795   98 52763827            70 99411985   67 31740151            71 72452181   24 13516764            17 22707611   20 65425362            43 85122458   21 50624882            76 71987125   44 95031274            63 77341073   78 87417774             8 45828909   30 18426696     In  5   pt    6  30      lt -- the point to find  In  6   A spatial KDTree A  query pt  1      lt -- the nearest point  Out 6   array    8 45828909   30 18426696     how it works  In  7   distance index   spatial KDTree A  query pt   In  8   distance    lt -- The distances to the nearest neighbors Out 8   2 4651855048258393  In  9   index    lt -- The locations of the neighbors Out 9   9   then  In  10   A index  Out 10   array    8 45828909   30 18426696

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This is a vectorized version of unutbu s answer   def find nearest array  values       array   np asarray array         the last dim must be 1 to broadcast in  array - values  below      values   np expand dims values  axis -1        indices   np abs array - values  argmin axis -1       return array indices    image   plt imread  example 3 band image jpg    print image shape    should be  nrows  ncols  3   quantiles   np linspace 0  255  num 2    2  dtype np uint8   quantiled image   find nearest quantiles  image   print quantiled image shape    should be  nrows  ncols  3

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Here s an extension to find the nearest vector in an array of vectors     import numpy as np  def find nearest vector array  value     idx   np array  np linalg norm x y  for  x y  in array-value   argmin     return array idx   A   np random random  10 2   100     A   array    34 19762933   43 14534123        48 79558706   47 79243283        38 42774411   84 87155478        63 64371943   50 7722317         73 56362857   27 87895698        96 67790593   77 76150486        68 86202147   21 38735169         5 21796467   59 17051276        82 92389467   99 90387851         6 76626539   30 50661753       pt    6  30    print find nearest vector A pt    array    6 76626539   30 50661753

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If you don t want to use numpy this will do it   def find nearest array  value       n    abs i-value  for i in array      idx   n index min n       return array idx

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I think the most pythonic way would be    num   65   Input number  array   n random random  10   100   Given array   nearest idx   n where abs array-num   abs array-num  min    0    If you want the index of the element of array  array  nearest to the the given number  num   nearest val   array abs array-num   abs array-num  min      If you directly want the element of array  array  nearest to the given number  num    This is the basic code  You can use it as a function if you want

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Maybe helpful for ndarrays   def find nearest X  value       return X np unravel index np argmin np abs X - value    X shape

[python] Find nearest value in numpy array

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