Re: Maxima & Minima

• To: mathgroup at smc.vnet.net
• Subject: [mg53731] Re: [mg53703] Maxima & Minima
• From: yehuda ben-shimol <benshimo at bgu.ac.il>
• Date: Tue, 25 Jan 2005 05:03:38 -0500 (EST)
• References: <200501240837.DAA28176@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```I assume that your data is discrete and you cannot use differentiation.
Also note that there is also local minima and maxima.
So,
The position of (local) maximal points are
maxpositions=Flatten[Position[Ordering[#, -1] & /@ Partition[Last /@
data, 3, 1], {2}]] + 1
that in your case are the positions
{4, 9, 17, 34, 68}
The values of data of these points are given by
data[[maxpositions]]
and these are

{{0.53, 1.3059}, {0.58, 1.31146}, {0.66, 1.32175}, {0.83, 1.81008}, {1.71, \
1.72145}}

Similarly for (local) minima points
minpositions=Flatten[Position[Ordering[#, 1] & /@ Partition[Last /@
data, 3, 1], {2}]] + 1
that in your case are the positions
{2, 5, 10, 18, 62}
The values of data of these points are given by
data[[minpositions]]
and these are
{{0.51, 1.30244}, {0.54, 1.30544}, {0.59, 1.31105}, {0.67, 1.32041}, {
1.11, 0.0324386}}
yehuda

nilaakash wrote:

>Dear Friends,
>                  Suppose I have some points. If you plot these points
>you will see there are few maxima and minima. I want to find only
>those maxima and minima points. Is there any process to findout only
>those max & min coordinates. (both x & y points).
>
>data={{0.5, 1.30301}, {0.51, 1.30244}, {0.52, 1.30533}, {0.53,
>1.3059}, {0.54,
>    1.30544}, {0.55, 1.30816}, {0.56, 1.30942}, {0.57, 1.30952},
>{0.58,
>    1.31146}, {0.59, 1.31105}, {0.6, 1.31357}, {0.61, 1.31614}, {0.62,
>    1.31636}, {0.63, 1.31782}, {0.64, 1.31977}, {0.65, 1.31993},
>{0.66,
>    1.32175}, {0.67, 1.32041}, {0.68, 1.32705}, {0.69, 1.33001}, {0.7,
>    1.33689}, {0.71, 1.34665}, {0.72, 1.35868}, {0.73, 1.37899},
>{0.74,
>    1.40351}, {0.75, 1.44677}, {0.76, 1.49938}, {0.77, 1.56417},
>{0.78,
>    1.6265}, {0.79, 1.68231}, {0.8, 1.73439}, {0.81, 1.77567}, {0.82,
>    1.79751}, {0.83, 1.81008}, {0.84, 1.80272}, {0.85, 1.78359},
>{0.86,
>    1.74827}, {0.87, 1.69779}, {0.88, 1.63964}, {0.89, 1.57302}, {0.9,
>    1.49157}, {0.91, 1.40873}, {0.92, 1.32168}, {0.93, 1.22632},
>{0.94,
>    1.12993}, {0.95, 1.03509}, {0.96, 0.940307}, {0.97, 0.843889},
>{0.98,
>    0.750626}, {0.99, 0.658783}, {1., 0.571786}, {1.01, 0.490484},
>{1.02,
>    0.414139}, {1.03, 0.342955}, {1.04, 0.27755}, {1.05, 0.219544},
>{1.06,
>    0.169213}, {1.07, 0.126781}, {1.08, 0.091582}, {1.09, 0.0642237},
>{1.1,
>    0.0444826}, {1.11, 0.0324386}, {1.21, 0.17094}, {1.31, 0.721742},
>{1.41,
>    1.17931}, {1.51, 1.49921}, {1.61, 1.67064}, {1.71, 1.72145},
>{1.81,
>    1.69853}, {1.91, 1.6343}, {2.01, 1.54399}, {2.11, 1.45614}, {2.21,
>    1.36254}, {2.31, 1.27609}, {2.41, 1.19319}, {2.51, 1.12123},
>{2.61,
>    1.04736}, {2.71, 0.98465}, {2.81, 0.925526}, {2.91, 0.871404},
>{3.01,
>    0.821615}, {3.11, 0.77698}, {3.21, 0.732385}, {3.31, 0.693622},
>{3.41,
>    0.655827}, {3.51, 0.623108}, {3.61, 0.591913}, {3.71, 0.562528},
>{3.81,
>    0.534357}, {3.91, 0.50876}, {4.01, 0.484918}, {4.11, 0.463476},
>{4.21,
>    0.441866}, {4.31, 0.422324}, {4.41, 0.4049}, {4.51, 0.387806},
>{4.61,
>    0.371429}, {4.71, 0.356785}, {4.81, 0.3418}, {4.91, 0.328734}}
>
> Thanks
>
> nilaakash
>
>
>

```

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