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Best answer by Werner_E

HARVEY HENSLEY wrote:

I know that this has been answered,

Yes, Valery again has found the Correct Answer himself 😉

Harvey, as already written I guess that the unit is responsible for the numeric algorithm taking larger steps and this may lead to inaccurate results. In our case it also seems to be responsible for the algorithm to try negative values for t2. But the unit is not responsible for Maximize to fail.

The real reason for Minimize to fail in this example is because Valery's function is returning a string for negative temperatures, Slightly change the function rho2 in your example above: just add "+0" at the end. This will not change any valid result but now for negative temperatures this function fails because it can't add a string and a number. Using this function makes Maximize() work - regardless of the unit °C.

I already showed this here http://communities.ptc.com/message/261839#261839 andI then delved a bit deeper into the subject here http://communities.ptc.com/message/261840#261840 and a new question grew up (why does "IsString()" not do the job?).

But the thread got quite confusing already and navigating in this forum isn't as easy and clearly as we were sed from the old collab.

Anyway, as a conclusion I would say that even if we can get it to work by omitting the string error message its the best idea to get rid of the unit nonetheless as you had shown in your first reply.

6 replies

H
HarveyHensley12-Amethyst
12-Amethyst
November 2, 2014

Two changes are needed in the MC15 file. First, the Maximize function needs to be part of a Solve block. Second, it can't use units with the independent variable.Maximize.png

V
24-Ruby IV
ValeryOchkov24-Ruby IVAuthor
24-Ruby IV
November 2, 2014

HARVEY HENSLEY wrote:

Two changes are needed in the MC15 file. First, the Maximize function needs to be part of a Solve block.

Thanks and sorry

The Maximize function needs to be part of a Solve block only in Prime 1 & 2.

See the top of my Mathcad 15 file.

And in Prime - no problem - see please second picture above

V
24-Ruby IV
ValeryOchkov24-Ruby IVAuthor
24-Ruby IV
November 2, 2014

I think it is one units bug in Mathcad 15. In Prime - all is OK here with units!

W
Werner_E25-Diamond I
25-Diamond I
November 2, 2014

Huuuh!! Whats that?? A late Halloween trick? Sure something for your Mathcad Madhouse collection, Valery.

Just adding +0 to your function rho makes the Maximize() function work correctly.

Not sure but it may have something to do with the fact, that for invalid (neagtive) temperatures we get now an invalid result rather than the string which your function would return.

1.png

V
24-Ruby IV
ValeryOchkov24-Ruby IVAuthor
24-Ruby IV
November 2, 2014

Werner Exinger wrote:

Huuuh!! Whats that?? A late Halloween trick? Sure something for your Mathcad Madhouse collection, Valery.

Yes. I think the problem is in my function wspD1PT (Region1 of the IAPWS-IF97 - water). Sometimes it returns string.

No problem with the wspDPT function (all regions):

Ro-Max.png

W
Werner_E25-Diamond I
25-Diamond I
November 2, 2014

Valery Ochkov wrote:

Werner Exinger wrote:

Huuuh!! Whats that?? A late Halloween trick? Sure something for your Mathcad Madhouse collection, Valery.

Yes. I think the problem is in my function wspD1PT (Region1 of the IAPWS-IF97 - water). Sometimes it returns string.

You may consider throwing an error using the error() function instead of returning an error string as calculation result.

See the last regions in the attached file here: http://communities.ptc.com/message/261842#261842

No problem with the wspDPT function (all regions):

Yes, but you still may run into precision problems as of the units. See my other post on this subject in this thread.

W
Werner_E25-Diamond I
25-Diamond I
November 2, 2014

OK, now it seems to be clear that the real problem is the string which the function returns in case of a negative temperature. When using units in numerical algorithm Mathcad usually uses different step sizes, different precision (we had this a few times in the past) and that may be the reason we are not running into this problem with Harvey's workaround whith a unitless independent variable.

When I replace Valery's error string by anything else - here a NaN but it could be 0 or even 1/0!! - Maximize works OK.

1.png

But ...... can anybody explain why maximize() still fails when I use IsString() instead of testing for the exact error string???

2.png

V
24-Ruby IV
ValeryOchkov24-Ruby IVAuthor
24-Ruby IV
November 3, 2014

Werner Exinger wrote:

in case of a negative temperature.

Sorry.

There is no negative temperature - in World and in Mathcad.

There are Kelvin (Rankine) and Celsius (Farenheit) scales.

W
Werner_E25-Diamond I
25-Diamond I
November 3, 2014

Valery Ochkov wrote:

Werner Exinger wrote:

in case of a negative temperature.

Sorry.

There is no negative temperature - in World and in Mathcad.

There are Kelvin (Rankine) and Celsius (Farenheit) scales.

We were not talking about absolute temperatures!

http://en.wikipedia.org/wiki/Negative_temperature

But ...

http://www.youtube.com/watch?v=yTeBUpR17Rw (Its nice to see someone explain things that enthusiastic!)

http://www.quantum-munich.de/research/negative-absolute-temperature/

Sorry or not, I still think you should use the error() function instead of returning a string.

W
Werner_E25-Diamond I
25-Diamond I
November 2, 2014

Here is some additional baublery with Maximize and units.

Even if we may not call it a bug it sure can be called a very bad implementation. At least the reference (OK, there is no reference since M12) and the help should point out that the function should be used unitless.

1.png

H
HarveyHensley12-Amethyst
12-Amethyst
November 3, 2014

I know that this has been answered, but I think this might be useful. I think the problem in MC15 is that the deg C unit is not truly a unit...it is a function. Note that my earlier suggestions changed the function so that the variable was unitless, and the deg C function was applied in the density argument. Also note that the only example involving deg C that Werner gave that got the right answer when the independent variable had deg C as a " unit" was the one that had deg C eliminated by cancelation of numerator and denominator.

Further, look at the following comparison:

maximize_deg_c_issue.png

Note that the lack of conctraints is not the issue as I had earlier suggested.. It appears that the difference is the independent arguement. Werner has shown that the independent variable can have units, but in this case deg C is not a unit. Apparently this got changed for Prime.

W
Werner_E25-Diamond IAnswer
25-Diamond I
November 3, 2014

HARVEY HENSLEY wrote:

I know that this has been answered,

Yes, Valery again has found the Correct Answer himself 😉

Harvey, as already written I guess that the unit is responsible for the numeric algorithm taking larger steps and this may lead to inaccurate results. In our case it also seems to be responsible for the algorithm to try negative values for t2. But the unit is not responsible for Maximize to fail.

The real reason for Minimize to fail in this example is because Valery's function is returning a string for negative temperatures, Slightly change the function rho2 in your example above: just add "+0" at the end. This will not change any valid result but now for negative temperatures this function fails because it can't add a string and a number. Using this function makes Maximize() work - regardless of the unit °C.

I already showed this here http://communities.ptc.com/message/261839#261839 andI then delved a bit deeper into the subject here http://communities.ptc.com/message/261840#261840 and a new question grew up (why does "IsString()" not do the job?).

But the thread got quite confusing already and navigating in this forum isn't as easy and clearly as we were sed from the old collab.

Anyway, as a conclusion I would say that even if we can get it to work by omitting the string error message its the best idea to get rid of the unit nonetheless as you had shown in your first reply.

H
HarveyHensley12-Amethyst
12-Amethyst
November 3, 2014

Werner Exinger wrote:

Harvey, as already written I guess that the unit is responsible for the numeric algorithm taking larger steps and this may lead to inaccurate results. In our case it also seems to be responsible for the algorithm to try negative values for t2.

I finally got caught up with all of your investigations and results. It looks like you have the answer regarding the temperatures below the triple point of water. I guess you meant in the quote above that the unit affects the step size because it affects the magnitude of the variable. In my function definition, the independent variable has a magnitude of one. In Valery's definition, the magnitude is 100 (~275 K). If the first step by Maximize is a constant percent of the initial guess, then the step sizes will be quite different for the two functions. Thus, the first step for Valery's function may go below the triple point. The comment you supplied elsewhere explored these differences with examples in lengths.

Now the question is "why does Prime get the answer"? I don't think it has anything to do with units. It must be a change in the optimization algorithm. Maximize and minimize algorithms have been changed to KNITRO methods. Probably a smaller initial step size is being used. Or, maybe the new algorithms handle the non number results in a manner like your demos.

V
24-Ruby IV
ValeryOchkov24-Ruby IVAuthor
24-Ruby IV
November 7, 2014

Valery Ochkov wrote:

I have an error by using Minimize & Maximize in Mathcad 15.

MinMaxError.png

It is more better not download any Mathcad-function on your computer but do a link on clowd Mathcad-function.

Wen I see an error in my cloud Mathcad-function (in wspD1PT for ezample) I correct it and now problem over the World

Compare pls old (above) and new (below) Mathcad worksheet with a reference on the cloud function:

wspDPT-new.png

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