# How to code FOR within Interval correctly?

**URL:** <https://community.wolfram.com/t/how-to-code-for-within-interval-correctly/5276>\
**Category:** Questions\
**Tags:** wolfram-engine\
**Created:** [March 29, 2015, 8:14pm UTC](https://community.wolfram.com/t/how-to-code-for-within-interval-correctly/5276 "2015-03-29T20:14:05Z")\
**Posts on this page:** 3\
**Page:** 1

<div class="post-metadata">

**Author:** ![juliailkiv](https://yyz1.discourse-cdn.com/wolfram/user_avatar/community.wolfram.com/juliailkiv/32/18030_2.png) [@juliailkiv](https://community.wolfram.com/u/juliailkiv)\
**Post date:** [March 29, 2015, 8:14pm UTC](https://community.wolfram.com/t/how-to-code-for-within-interval-correctly/5276/1 "2015-03-29T20:14:05Z")

</div>

Help me please to write `For` correctly..  
I’ve the 1-st step of algorithm and finally it outputs two intervals : `1)Interval[{1.25677,3.25203},{5.511,5.58272}]`  
My problem is in the 2-nd step, because I’ve to do some conditions within previous first interval `{1.25677,3.25203}` and output a new interval.  
So `For` has to work from beginning of this interval to the end.

```
X = {-2, 6}
spkw = {105.056, 89.2249, 17.7361, 7.25929, 7.25929, 7.25929, 7.25929,
   1.09386, 
  1.09386, -7.35382, -12.5073, -11.929, -11.929, -15.429, -8.63312,
-6.34314, -14.3807, -16.7907, -18.933, -12.3896, -3.021, -22.0262,
-25.7865, -18.8033, -9.07591, -9.18036, -8.49959, -9.24378, -7.32337,
-0.271835, -0.270096, 0.123206, 0.156523, 0.465142, 4.12922, 4.23318, 
  8.03654, 8.20981, 12.1518, 12.3944}
spkn = {73.5426, 66.8007, 24.6942, 16.4029, 0.726929, 
  0.314512, -1.23002, -1.23002, -3.90668, -10.8276, -14.2065,
-13.0895, -18.656, -20.1709, -8.79676, -8.79676, -11.2319, -13.9771, 
-15.1407, -2.50312, -4.72374, -32.4496, -34.2958, -21.0455, -2.45882, 
-2.45882, -2.45882, -2.45882, -2.45882, -2.45882, -2.45882, -1.70357, 
-1.70357, -1.11799, 6.1251, 6.36752, 6.36752, 6.60995, 14.0955, 
  14.5803}
spmw = {243.475, 213.305, 83.8004, 67.1081, 67.1081, 67.1081, 67.1081,
   59.4226, 59.4226, 49.9772, 45.1635, 45.6272, 45.6272, 43.4397, 
  46.8376, 47.4101, 46.6214, 47.3535, 48.75, 42.5447, 33.1761, 
  61.6839, 68.2644, 53.4787, 29.1603, 29.4279, 27.6409, 30.1061, 
  22.9045, -5.30161, -5.30859, -6.88938, -7.0313, -8.37913, -24.8675, 
-25.3613, -44.3781, -45.2877, -66.9686, -68.3634}
spmn = {180.448, 167.6, 91.3225, 78.1123, 56.5579, 55.9978, 53.9271, 
  53.9271, 50.6364, 42.898, 39.742, 40.6374, 36.4626, 35.5158, 
  41.2028, 41.2028, 40.9639, 41.7978, 42.5563, 30.5716, 32.7923, 
  74.3811, 77.6119, 49.5569, 3.09017, 3.09017, 3.09017, 3.09017, 
  3.09017, 3.09017, 3.09017, 0.0546329, 
  0.0546329, -2.5028, -35.0967, -36.2482, -36.2482, -37.5209, 
-78.6912, -81.4791}
spfw = {33.3632, 43.263, 51.6709, 55.5421, 57.1266, 57.2511, 57.3756, 
  58.059, 58.0778, 58.1995, 56.846, 55.1903, 54.5739, 53.0828, 
  51.1542, 48.9959, 48.0325, 42.2533, 36.408, 30.7952, 30.1551, 
  28.6446, 23.138, 19.4168, 6.47053, 5.90328, 
  5.32951, -0.513959, -0.750527, -6.38895, -6.39157, -6.39418, 
-6.36456, -6.09357, -6.28599, -5.25369, -4.19539, -2.18625, -0.133803,
   2.90414, 6.171}
spfn = {33.3632, 40.2933, 46.5882, 51.9781, 55.5583, 55.5708, 55.5762,
   55.4604, 55.4393, 55.0045, 530116, 51.1309, 50.4546, 48.1226, 
  45.6012, 43.402, 42.066, 37.5522, 32.6864, 28.1979, 28.0685, 
  25.7067, 17.5943, 
  13.5547, -2.97428, -3.21054, -3.36422, -5.05466, -5.1301, -6.4392, 
-6.76879, -6.48231, -7.20196, -7.00719, -7.53373, -6.00246, -4.41058, 
-2.8187, -1.16621, 2.35765, 6.04694}
(*1 STEP*)
myintervals1 = Reap[For[i = 1, i < Length@spfn, i++,
    If[! (((0 < spfn[[i]]) && (0 < spfn[[i + 1]])) || ((spfw[[i]] < 
            0) && (spfw[[i + 1]] < 0))),
     Sow[Interval[{-spmn[[i]]/spkn[[i]], -spmw[[i]]/spkw[[i]]}]]]]] [[
  2, 1]]
Print["1)", myint1 = Join @@ myintervals1]
myint11 = myint1[[1]];
myint12 = myint1[[2]];
Print["width of interval ", myint11, " : ", 
 widthmyint11 = Max[myint1[[1]]] - Min[myint1[[1]]]]
Print["width of interval ", myint12 , " : ", 
 widthmyint12 = Max[myint1[[2]]] - Min[myint1[[2]]]]

(*2 STEP*)
myintervals2 = 
 Reap[For[j = Min[myint1[[1]]], j <= Max[myint1[[1]]], j++
     If[spfn[[j]]*spfn[[j + 1]] < 0 && spfw[[j]]*spfw[[j + 1]] < 0,
      Sow[
       Interval[{Min[-spmn[[j]]/spkn[[j]], -spmw[[j]]/spkw[[j]]], 
         Max[-spmn[[j]]/spkn[[j]], -spmw[[j]]/spkw[[j]]]}]]
      ]
    ]
   ][[2, 1]]
Print["2)", myintervals2]

```

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<div class="post-metadata">

**Author:** ![sukrause](https://yyz1.discourse-cdn.com/wolfram/user_avatar/community.wolfram.com/sukrause/32/41348_2.png) [@sukrause](https://community.wolfram.com/u/sukrause)\
**Post date:** [March 30, 2015, 1:23pm UTC](https://community.wolfram.com/t/how-to-code-for-within-interval-correctly/5276/2 "2015-03-30T13:23:24Z")

</div>

Firstly the (_2 STEP_) misses a comma

 ![comm469779_1.PNG](https://global.discourse-cdn.com/wolfram/original/3X/d/9/d952f1825d94a7285b5b49fc7b93dc621ff87d26.png)

but that’s not the only problem.If running the second step, have a close look to the iteration variable `j` which is used as index too

```
Out[10]= {Interval[{2.35475, 2.84411}], Interval[{1.25677, 3.21293}], 
 Interval[{1.25677, 3.20553}], Interval[{1.25677, 3.25203}], 
 Interval[{5.511, 5.58272}]}

During evaluation of In[10]:= 1)Interval[{1.25677,3.25203},{5.511,5.58272}]
During evaluation of In[10]:= width of interval {1.25677,3.25203} : 1.99526
During evaluation of In[10]:= width of interval {5.511,5.58272} : 0.0717154

    In[17]:= (*2 STEP*)myintervals2 = 
     Reap[For[j = Min[myint1[[1]]], j <= Max[myint1[[1]]], j++ , 
        If[spfn[[j]]*spfn[[j + 1]] < 0 && spfw[[j]]*spfw[[j + 1]] < 0, 
         Sow[Interval[{Min[-spmn[[j]]/spkn[[j]], -spmw[[j]]/spkw[[j]]], 
            Max[-spmn[[j]]/spkn[[j]], -spmw[[j]]/spkw[[j]]]}]]]]][[2, 1]]
    
    During evaluation of In[17]:= Part::pkspec1: The expression 1.2567695073246514` cannot be used as a part specification. >>
    During evaluation of In[17]:= Part::pkspec1: The expression 2.2567695073246514` cannot be used as a part specification. >>
    During evaluation of In[17]:= Part::pkspec1: The expression 1.2567695073246514` cannot be used as a part specification. >>
    During evaluation of In[17]:= General::stop: Further output of Part::pkspec1 will be suppressed during this calculation. >>
    During evaluation of In[17]:= Part::partw: Part 1 of {} does not exist. >>
    Out[17]= {Null, {}}[[2, 1]]
    
    Print["2)", myintervals2]
    
    In[18]:= Min[myint1[[1]]]
    Out[18]= 1.25677
    
    In[19]:= Max[myint1[[1]]]
    Out[19]= 3.25203

```

Do you see it? `j` runs from real `1.25677` to real `3.25203` and is used as index to expressions. But expressions in Mathematica do not have real indices, see [Part](http://reference.wolfram.com/language/ref/Part.html). Interestingly enough they do not state that `Part` takes only integers or lists of integers but they seem to understand that by using symbols like `i`, `j`, … usually meaning integers in mathematics and physics.

See [Round](http://reference.wolfram.com/language/ref/Round.html), [Floor](http://reference.wolfram.com/language/ref/Floor.html), and [Ceiling](http://reference.wolfram.com/language/ref/Ceiling.html) to make reals into integers.

---

<div class="post-metadata">

**Author:** ![juliailkiv](https://yyz1.discourse-cdn.com/wolfram/user_avatar/community.wolfram.com/juliailkiv/32/18030_2.png) [@juliailkiv](https://community.wolfram.com/u/juliailkiv)\
**Post date:** [March 30, 2015, 4:32pm UTC](https://community.wolfram.com/t/how-to-code-for-within-interval-correctly/5276/3 "2015-03-30T16:32:57Z")

</div>

Thank You!