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originman6
3 Posts |
 Posted - 09/06/2011 : 7:42:30 PM
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Hello,
First, sorry for my English is not correct.
Kindly let me know:
1) How to write in data values in A(x) or B(y), the numbers like in Fig. 1
2) If it is possible ( and how?), considering an initial set of experimental determinations, to make graphs just like this (Fig. 2)(incluse chords – in this case all equal , but even if not all equal - and curve) on the Graphical Differentiation , represented by the red smooth curve and obtained by the chord - area method:” To find the slope, we draw a curve through the chords in such a manner that the sum of the areas of the triangles for which the chords form the upper sides, is equal to the sum of the areas of the triangles for which the chords form the lower sides.”
Thanks in advance
P.S. Also in this topic I had difficulty to write and to paste the numbers written in exponential form with Word: I was forced to use the image |
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Hideo Fujii
USA
1582 Posts |
Posted - 09/07/2011 : 11:32:38 AM
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Hi originman6,
I cannot understand what you want well, but let me say as below...
1) You can calculate exponential (like 2^3 or 2^-2) in a cell, in a cell block, or in a whole column using Set Column Values tool. See the following section in Origin help:
UserGuide> "Workbooks Worksheets & Worksheet Columns">
"Simple Manipulation of Worksheet Datasets"> Quick Start[/code]
and the following sections. To perform this, highlight a cell (or a cell black in a column, or a column header), right-click it, and choose "Set Column Values" flyout.
2) I'm not sure whether you want to draw a "fit" exponential curve over a column chart, or to draw a exponential distribution overlay on a histogram... If in the first case, you can use the "Quick Fit" tool ("Gadget: Quick Fit" menu) for a column plot as in the screenshot below.
If in the second case, first make a histogram for the source data ("Plot: Statistics: Histogram" menu), double-click the plot to show Plot Details dialog, choose "Data" tab, and choose "Exponential" for the Distribution Curve.
If the main issue is your "the chord - area method", I have no idea how to do it.
Hope this helps you to start working in Origin.
--Hideo Fujii
OriginLab |
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originman6
3 Posts |
Posted - 09/07/2011 : 6:00:04 PM
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Hi Hideo Fujii ,
thank you very much for your reply and now I'll explain you my problem.
Measuring concentration as a function of time, I get this set data:
t (min) = 0, 50, 100,150, 200, 250, 300
C (mol/dm3) = 50 x10-3, 38x10-3, 30.6x10-3, 25.6x10-3, 22.2x10-3, 19.5x10-3, 17.4x10-3
To obtain the derivative dC/dt, we must differentiate concentration versus time data either numerically and graphically by three methods: graphical differentiation, numerical differentiation formulas, differentiation of a polynomial fit to the data. I want to compare the results by three methods.
In particular, I am interested in the differentiation graphical and therefore in short:
a) for each interval, to calculate delta t and delta C
b) to plot these values (delta C/delta t) as a histogram versus ti
c) next to draw in the smooth curve that best approximates the area under the histogram
d) to read estimates of the dC/dt from this curve at the data points t1, t2,…
At point c) I should draw (manually by the pencil) the smooth curve “by sight” for equal area (does anyone know an “alternative algorithm or method (for instance, to count the small squares of the graph/squared paper?...) “ instead “by sight”?) . I want the red smooth curve by sight is drawn just by Origin. Once made the graph, I can read the values dC/dt directly with the mouse zooming the concerned intersection of the curve in the graph?
Practically, I want, for my data, the graph by chord-area method (triangles A = triangles B, as mentioned in the previous topic) like in generic Fig.3 :
In Origin, the rectangles of the histogram are separated with small space, how to get contiguous rectangles as in Figure 3?
N.B : How do you write dm^3 in Origin? That is, the number 3 in exponential form in the word (dm) in cell "Units"?
How do you write the symbol "delta" (or the special symbol, letter top/down...) in this topic?
Thanks in advance
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Edited by - originman6 on 09/08/2011 05:51:28 AM |
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easwar
USA
1964 Posts |
Posted - 09/08/2011 : 1:14:48 PM
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Hi,
Searching for equal-area graphical differentiation, I found this link that gives an exact example similar to what you posted:
http://www.engin.umich.edu/~cre/appendix/html/CDROM-Appendix-A.pdf
I took the data from the above PDF and was able to reproduce their numbers in Origin.
Here is what I did:
1> put the x and y data in columns 1 and 2
2> add two more columns
3> Set the formula for column 3 to be:
col(1)[i-1]+(col(1)[i]-col(1)[i-1])/2
4> Set the formula for column 4 to be:
(col(2)[i]-col(2)[i-1])/(col(1)[i]-col(1)[i-1])
This basically computes the mid point of your intervals and the difference data
5> Set the third column as type X, and make a Column plot of the 4th column (NOT Histogram. I think you mean column plot, histogram does not make sense here). You can go to Plot Details and then set the gap between bars to zero and turn off fill color etc.
6> Go to Nonlinear fitter tool and define a new function:
y=A*exp(-x)
I think there is a typo in the PDF, the function they mention cannot fit the data
7> Fit the data in the graph with this new function, either letting the parameter A to vary (I then get A=1001.007), or set A=1000 in which case you are not really fitting, but creating an output curve, which is fine
8> In the fitter use the "Find Y from X" feature which will add a sheet for finding new Y values for given X values. Then you can put in your X values and get desired Y values. I was then able to get the Y values that are quoted in that PDF.
You do not mention what version of Origin you have, so if you don't have latest, download the demo and try the above procedure. Contact tech support if you have further questions - use the Send File to Tech Support link on top of page - you could then send your data as well.
Easwar
OriginLab
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originman6
3 Posts |
Posted - 09/19/2011 : 07:53:39 AM
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Easwar, Thank you and forgive me if I reply late.
I already knew the link pdf which you have posted and it is right, but the example uses a known function (f (x) = 1000 (1 - exp (-x)). How do I find or choose the proper similar function in this my case and other cases in the future? or, more precisely, with Origin, how do I use only data set without knowing/using the function?
Also, with OriginPro 8.5.1, I followed your steps:
a) I got the same values as in your Fig 1 "Book 1", but does not appear to me the 2 green little padlock next to C(X2) and D(Y2) (why? How does ?)
b) in your Fig2 "Book3", using (Tools, Fitting Function Organizer, User defined ... ..) the your function “by utent” (y = A * exp (-x) and/with A = 1000; by the way, how do you "letting the parameter A to vary (I then get A=1001.007)"), my results differ slightly from yours, and more precisely:
to X value: 0 corresponds Y value: "undefined value" with symbol: a series of hash; but, when I clicked twice on this symbol, give me Y value = 1001.00656 (your value: 1000)
to X value: 0.2 corresponds Y value : 819.55486 (instead of your value: 818.73075)
X value: 0.4 , Y value: 670.99477 (your value: 670.32005)
X value: 0.6 , Y value: 549.36405 (your: 548.81164)
X value: 0.8 , Y value: 449.78124 (your: 449.32896)
X value: 1 , Y value: 368.24974 (your: 367.87944)
Why? Where I went wrong?
c) in your Fig3 "Graph1", your red smooth line begins above the first step and ends (under) in the last step of touching the vertical line (ordinate) at mid X value = 1; my red line, however, begins with the "half” under the first step and ends at the" half "over the last step: that is, the part initial and final of your graph are absent. How can I get your same graph?
d) How did you post / paste the pictures Origin (Book1, Book3 and Graph1) of your previosus topic ?
e)Once made the graph, you can read with Origin (how?) the values dC/dt directly with the mouse on red smooth line, zooming the concerned intersection of the curve in the graph?
Also,I'm sorry if I ask again:
f) How do you write dm^3 in Origin? That is, the number 3 in exponential form in the word (dm) in cell "Units"?
g) How do you write the symbol "delta" (or the special symbol, letter top/down...) in this topic and in the Origin?
Thanks in advance
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Edited by - originman6 on 09/20/2011 07:47:53 AM |
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easwar
USA
1964 Posts |
Posted - 09/21/2011 : 12:31:04 PM
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Hi,
See answers below:
Also I suggest you look at help file for more info, and then contact tech support directly for specific issues.
Easwar
OriginLab
quote:
How do I find or choose the proper similar function in this my case and other cases in the future? or, more precisely, with Origin, how do I use only data set without knowing/using the function?
I think you need to know what function is appropriate for your data. You can try multiple functions and see what fits best, that is one way. If you just want to overlay a curve and NOT fit, you could use set column values to generate another dataset using any function and then plot that on the same graph.
quote:
a) I got the same values as in your Fig 1 "Book 1", but does not appear to me the 2 green little padlock next to C(X2) and D(Y2) (why? How does ?)
In set values dialog did you select the recalculate drop-down to be auto or manual? See details on recalculation in help file
quote:
b) in your Fig2 "Book3", using (Tools, Fitting Function Organizer, User defined ... ..) the your function “by utent” (y = A * exp (-x) and/with A = 1000; by the way, how do you "letting the parameter A to vary (I then get A=1001.007)"), my results differ slightly from yours, and more precisely:
to X value: 0 corresponds Y value: "undefined value" with symbol: a series of hash; but, when I clicked twice on this symbol, give me Y value = 1001.00656 (your value: 1000)
to X value: 0.2 corresponds Y value : 819.55486 (instead of your value: 818.73075)
X value: 0.4 , Y value: 670.99477 (your value: 670.32005)
X value: 0.6 , Y value: 549.36405 (your: 548.81164)
X value: 0.8 , Y value: 449.78124 (your: 449.32896)
X value: 1 , Y value: 368.24974 (your: 367.87944)
Why? Where I went wrong?
I used the findx/y functionality, you can change the x values in that table.
quote:
c) in your Fig3 "Graph1", your red smooth line begins above the first step and ends (under) in the last step of touching the vertical line (ordinate) at mid X value = 1; my red line, however, begins with the "half” under the first step and ends at the" half "over the last step: that is, the part initial and final of your graph are absent. How can I get your same graph?
The fit curve can be extended to the axis range - there is control for that in the NLFit dialog.
quote:
d) How did you post / paste the pictures Origin (Book1, Book3 and Graph1) of your previosus topic ?
Just a screen shot saved as picture...
quote:
e)Once made the graph, you can read with Origin (how?) the values dC/dt directly with the mouse on red smooth line, zooming the concerned intersection of the curve in the graph?
You can use screen reader or data reader.
quote:
Also,I'm sorry if I ask again:
f) How do you write dm^3 in Origin? That is, the number 3 in exponential form in the word (dm) in cell "Units"?
g) How do you write the symbol "delta" (or the special symbol, letter top/down...) in this topic and in the Origin?
See help file, there is support for super-subscript for text labels
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Particular use of OriginPro 8