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How to code FOR within Interval correctly?

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]
POSTED BY: Julia Ilkiv
2 Replies

Firstly the (2 STEP) misses a comma

comma missed

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. 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, Floor, and Ceiling to make reals into integers.

POSTED BY: Udo Krause

Thank You!

POSTED BY: Julia Ilkiv
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