Locating a Value in an Array

QUESTION: I have a specific value in a variable. I also have an vector of numbers. I would like to know which number in the vector is closest to this specific value. Is this possible in IDL?

ANSWER: Yes it is. Any you don't even have to write much code. IDL comes supplied with a function, named VALUE_LOCATE that will locate the index or bin into which the value will fall in the vector. You only have to check the two numbers in the vector on either side of the value to find the one that is closest to the value of interest. The only requirement is that the vector be monotonic.

Here is an example. Let's create a vector of random numbers, scaled from 0 to 100. We order the numbers monotonically by sorting them. Let our number be 35.49. The code looks like this:

   numbers = Randomu(-3L, 100) * 100
   vector = numbers[Sort(numbers)]
   number = 35.49
   Print, vector, Format='(5(F8.5, 2x))'

    1.34482   2.30946   3.78892   4.76031   5.30457
    6.03181   6.53659   7.77949   8.06289   9.60160
   10.37163  12.94588  14.23935  14.41299  15.02469
   15.02520  15.05062  15.24265  16.03849  16.79812
   17.62360  18.16930  20.05267  20.82457  20.86735
   21.80577  22.12472  24.61838  25.24579  26.00675
   26.92315  27.21987  27.58947  28.45428  28.65941
   29.94843  30.92342  31.06136  37.60961  39.33375
   40.37521  40.72172  43.31953  45.95522  46.11599
   48.19300  48.34519  49.28960  49.95216  50.21213
   51.35687  52.45319  52.61188  53.49831  53.85007
   53.98211  54.26877  55.82491  58.07864  58.91006
   58.92422  60.33495  60.47414  61.19120  63.82545
   65.41214  66.57166  69.29688  69.95847  71.33233
   71.97324  72.76243  73.09625  74.11166  74.14523
   76.69299  77.33408  78.73590  79.13095  79.84335
   80.40787  80.79518  81.81299  82.29399  82.47205
   83.12454  84.32928  87.45479  88.86303  89.49042
   89.79157  91.89655  94.76508  95.45557  95.70988
   95.99263  96.17569  97.31122  98.47027  99.83736

Next, we find the "bin" or "index" that our number will fall into.

   bin = Value_Locate(vector, number )
   Print, bin
      37
   Print, vector[bin], vector[bin+1]
      31.0614      37.6096

To find the closest value, we simple check the two vector values that bracket our chosen number. Make sure you check to see if your number actually lies within the values of the vector.

   CASE 1 OF
      bin EQ -1: closest = vector[0]
      bin EQ (N_Elements(vector)-1): closest = vector[N_Elements(vector)-1]
      ELSE: IF Abs(vector[bin] - number) GT Abs(vector[bin+1] - number) THEN $
               closest = vector[bin+1] ELSE closest = vector[bin]
   ENDCASE

In this case, the nearest value is vector[38] = 37.6096.

Stepehen Hallsworth points out to me that you can do this pretty much with a single line of IDL code, like this:

   near = Min(Abs(vector - number), index)

Note that in this formulation vector doesn't need to be ordered. The variable index gives the index of the value in vector nearest to number. The variable near gives the absolute difference of the vector value at index from the number. The closest value is give by vector[index].