topic Re: cspline with oscilating data in PTC Mathcad
https://community.ptc.com/t5/PTC-Mathcad/cspline-with-oscilating-data/m-p/257905#M100874
<HTML><HEAD></HEAD><BODY><BLOCKQUOTE><TABLE border="1"><TBODY><TR><TD><P>I checked it by choosing a value of moment ( say 375) and there are three possible curvature values that could produce this moment value.will be correct. </P></TD></TR></TBODY></TABLE></BLOCKQUOTE><P>I see, so your inverse is, mathematically spoken, not a function but just a general relation which is, as you pointed ot, not unique. Functional operators like integrals are defined for functions only - the outcome has to be unique for every abscissa value, which is not true for the inverse of M(Phi). So there is not much you could do analytically with Phi(M).</P><P>What should Phi(375) yield? A vector with three values?</P><P>How would you define integration over Phi(M)?</P><P>What should be the outcome of the definite integral int(Phi(M),M,350,400)?</P><P>This wouldn't all make much sense.</P><P></P><P>The only thing you can do is to turn your inverse into a function by restricting the Phi-range like your pocket calculator does if you ask for the inverse of sinus. arcsin(0.5) yields pi/6, but of course arcsin/0.5) has an infinite number of values (pi/6 + k*2*pi and 5*pi/6 + k*2*pi, with k=integer). But your calculator (and also Mathcad) restricts the angle to the range -pi/2 to pi/2 which makes the inverse a function with unique function values and that way analytical operation like integrals are valid.</P><P></P><P>You can do the same with your Phi(M). Restrict phi to the range 0 to 0.005 (approx.) and you have a function you are able to integrate. From your graph I see you can create three different functions Phi(M). You are able to integrate each of them frim 350 to 400. But what will you do with the three results?</P><P>I am not sure if this would be of help to you. And to automatically determine the number of possible inverse functions and determinig the exact phi-ranges could be a bit cumbersome.</P><P>So whatever you have to calculate by the integral of Phi(M), either it is sufficient to use the Phi-range up to the first maximum only or there may be another way to obtain it?</P><P></P><P></P><P><IMG __jive_id="66854" alt="05.02.png" class="jive-image" src="https://community.ptc.com/legacyfs/online/66854_05.02.png" /></P></BODY></HTML>Wed, 05 Feb 2014 02:22:23 GMTWerner_E2014-02-05T02:22:23Zcspline with oscilating data
https://community.ptc.com/t5/PTC-Mathcad/cspline-with-oscilating-data/m-p/257901#M100870
I have a curve I'm trying to fit with cspline and interp (see the attached calculation). Unfortunately, my y axis data oscilates so I had to write my function in terms of the x axis and use csort to make everything work. I was able to get a function M(phi) which works, but whatThu, 03 May 2018 16:31:10 GMThttps://community.ptc.com/t5/PTC-Mathcad/cspline-with-oscilating-data/m-p/257901#M100870ptc-12999622018-05-03T16:31:10ZRe: cspline with oscilating data
https://community.ptc.com/t5/PTC-Mathcad/cspline-with-oscilating-data/m-p/257902#M100871
<HTML><HEAD></HEAD><BODY><BLOCKQUOTE><TABLE border="1"><TBODY><TR><TD><P>I was able to get a function M(phi) which works, but what I really need is phi(M) of an integral I need to perform on phi. </P></TD></TR></TBODY></TABLE></BLOCKQUOTE><P>Its the othe way round, isn't it? In your sheet you have phi(M) and are asking for M(phi)</P><P></P><P>I can't test it without the Excel data but the attached file should help finding the inverse function(s).</P><P>I haven't looked at your various calculations before or where the data vectors come from - I just worked from the definition of your function phi_curve depending on the two vectors M_sort1 and Phi_sort1 and simply switched those vectors. Hope thats what you need.</P><P>Also showed how to get the inverse of any function using a solve block.</P></BODY></HTML>Wed, 05 Feb 2014 00:03:10 GMThttps://community.ptc.com/t5/PTC-Mathcad/cspline-with-oscilating-data/m-p/257902#M100871Werner_E2014-02-05T00:03:10ZRe: cspline with oscilating data
https://community.ptc.com/t5/PTC-Mathcad/cspline-with-oscilating-data/m-p/257903#M100872
<HTML><HEAD></HEAD><BODY><P>Thanks,</P><P></P><P>Unfortunately, that didn't quite work, at least I don't think it did. When you sort by the moment (Y axis in the picture below) the order doesn't make sense anymore when you turn it into a continuous function. I checked it by choosing a value of moment ( say 375) and there are three possible curvature values that could produce this moment value. The cspline function when sorting by moment produces a curvature value of ~.026 which is correct in one instance, but I don't think my integration will be correct. <IMG __jive_id="66850" class="jive-image-thumbnail jive-image" onclick="" alt="Moment-curvature-p157.jpg" src="https://community.ptc.com/legacyfs/online/66850_Moment-curvature-p157.jpg" width="450" /></P></BODY></HTML>Wed, 05 Feb 2014 01:09:35 GMThttps://community.ptc.com/t5/PTC-Mathcad/cspline-with-oscilating-data/m-p/257903#M100872ptc-12999622014-02-05T01:09:35ZRe: cspline with oscilating data
https://community.ptc.com/t5/PTC-Mathcad/cspline-with-oscilating-data/m-p/257904#M100873
<HTML><HEAD></HEAD><BODY><P>Also, I forgot to say, but below the first portion of the calculation (original attachment) where I define the functions is an intermediate results section. I placed values from the Excel file in here so that you can see the numerical results for a particular line of Excel data. </P><P></P><P>That's where the above moment-curvature curve comes from. </P></BODY></HTML>Wed, 05 Feb 2014 01:15:26 GMThttps://community.ptc.com/t5/PTC-Mathcad/cspline-with-oscilating-data/m-p/257904#M100873ptc-12999622014-02-05T01:15:26ZRe: cspline with oscilating data
https://community.ptc.com/t5/PTC-Mathcad/cspline-with-oscilating-data/m-p/257905#M100874
<HTML><HEAD></HEAD><BODY><BLOCKQUOTE><TABLE border="1"><TBODY><TR><TD><P>I checked it by choosing a value of moment ( say 375) and there are three possible curvature values that could produce this moment value.will be correct. </P></TD></TR></TBODY></TABLE></BLOCKQUOTE><P>I see, so your inverse is, mathematically spoken, not a function but just a general relation which is, as you pointed ot, not unique. Functional operators like integrals are defined for functions only - the outcome has to be unique for every abscissa value, which is not true for the inverse of M(Phi). So there is not much you could do analytically with Phi(M).</P><P>What should Phi(375) yield? A vector with three values?</P><P>How would you define integration over Phi(M)?</P><P>What should be the outcome of the definite integral int(Phi(M),M,350,400)?</P><P>This wouldn't all make much sense.</P><P></P><P>The only thing you can do is to turn your inverse into a function by restricting the Phi-range like your pocket calculator does if you ask for the inverse of sinus. arcsin(0.5) yields pi/6, but of course arcsin/0.5) has an infinite number of values (pi/6 + k*2*pi and 5*pi/6 + k*2*pi, with k=integer). But your calculator (and also Mathcad) restricts the angle to the range -pi/2 to pi/2 which makes the inverse a function with unique function values and that way analytical operation like integrals are valid.</P><P></P><P>You can do the same with your Phi(M). Restrict phi to the range 0 to 0.005 (approx.) and you have a function you are able to integrate. From your graph I see you can create three different functions Phi(M). You are able to integrate each of them frim 350 to 400. But what will you do with the three results?</P><P>I am not sure if this would be of help to you. And to automatically determine the number of possible inverse functions and determinig the exact phi-ranges could be a bit cumbersome.</P><P>So whatever you have to calculate by the integral of Phi(M), either it is sufficient to use the Phi-range up to the first maximum only or there may be another way to obtain it?</P><P></P><P></P><P><IMG __jive_id="66854" alt="05.02.png" class="jive-image" src="https://community.ptc.com/legacyfs/online/66854_05.02.png" /></P></BODY></HTML>Wed, 05 Feb 2014 02:22:23 GMThttps://community.ptc.com/t5/PTC-Mathcad/cspline-with-oscilating-data/m-p/257905#M100874Werner_E2014-02-05T02:22:23ZRe: cspline with oscilating data
https://community.ptc.com/t5/PTC-Mathcad/cspline-with-oscilating-data/m-p/257906#M100875
<HTML><HEAD></HEAD><BODY><P>Thanks Werner. That was very clear and helpful. </P><P></P><P>I think my solution, like you said much more eloquently, is to break the data up into specific groups for which a proper function can be defined and then doing a piecewise integration based on those ranges and limits. </P></BODY></HTML>Wed, 05 Feb 2014 17:49:36 GMThttps://community.ptc.com/t5/PTC-Mathcad/cspline-with-oscilating-data/m-p/257906#M100875ptc-12999622014-02-05T17:49:36Z