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 > > >

**References**:**Maxima & Minima***From:*nilaakash@gmail.com (nilaakash)