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How to search a Matrix for a number bounded by another number?

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Re: How to search a Matrix for a number bounded by another number?

Forgive me, I made a mistake in applying your work and assumed the error was due to the first column of data not being integers.

Re: How to search a Matrix for a number bounded by another number?

Daniel Sochor wrote:

Forgive me, I made a mistake in applying your work and assumed the error was due to the first column of data not being integers.

I guess the error was because you had set ORIGIN to 1 and my routines assume the default ORIGIN=0.

Re: How to search a Matrix for a number bounded by another number?

In your third tricky example, what is the 0 doing in the match function? Is it looking for a match of 0 in the trimmed columns of Zx?

Re: How to search a Matrix for a number bounded by another number?

Daniel Sochor wrote:

In your third tricky example, what is the 0 doing in the match function? Is it looking for a match of 0 in the trimmed columns of Zx?

No, match() looks for zeros but not in the trimmed matrix Zx. As usual in math expressions are evaluated from inside to out, so match() does not know anything about trim(), which is applied later.

The vectorized boolean expression, the comparisons combined with AND, returns a vector consisting of 0's and 1's. 0 means FALSE and 1 means TRUE (actually any number unequal to zero is considered TRUE in Mathcad). Vectorization is necessary as we cannot compare a vector with a scalar and so we would get an error.

1.png

We are interested in those values of matrix Zx, column 2, where we get a 1 in the above vector. But as Mathcad does not offer a counterpart to trim (lets say keep()) we look for the zeros.We use match() to get the indices/the positions of all zeros - the index numbers of the rows we don't want to keep. So if you changed ORIGIN from 0 to 1, the zero in match() is a zero you should not change ;-)

2.png

Now we can use this vector of indices as the second argument for trim() to delete all rows in the matrix Zx which do not fulfill your constraints. The result is a multiple column matrix and we select the second column of that matrix to finish and get the values you are interested in.

3.png

Upon further thinking about this method I guess that

4.png

is a bit more efficient and better looking as we select the second column of Zx first and then trim only that column. Maybe just a matter of personal taste.

Re: How to search a Matrix for a number bounded by another number?

Thank you for this great explanation Werner, I now understand it and am employing it throughout this calculation.

A question about Ceil() that may not be related but maybe I can ask it here;

In the attached MathCAD, the Ceil() function sets 0.375in to variable taRec. However, MathCAD appears to be treating taRec as being above 0.375in. You can see this by moving the taRec=0.375in down slightly (so it's definition supersedes the definition that has the Ceil() function) and the results of your trim & match function change to include angles with a thickness of 3/8in and 7/16in (the seventh column of the matrix is the angle thickness) instead of just 7/16in. Is there something that must be changed in the Ceil() function so the return value stays at 0.375in?

Re: How to search a Matrix for a number bounded by another number?

A question about Ceil() that may not be related but maybe I can ask it here;

In the attached MathCAD, the Ceil() function sets 0.375in to variable taRec. However, MathCAD appears to be treating taRec as being above 0.375in.

...which indeed it is (very slightly) because of roundoff errors - presumeably because of unit conversions (m <--> in)

1.png

In programming there is a rule that you never should ask that a given float value is exactly equal to another but that you rather should ask if the two value are sufficent near (the absolute value of their difference is smaller than a given small value epsilon like 10^-15).

You can apply a similar workaround in your case

2.png

As your values are in steps of 1/16" this should not have any bad side effects, i guess.

There is also another workaround available here, but I am not sure if it will work always in other cases, too:

3.png

Re: How to search a Matrix for a number bounded by another number?

Thank you again Werner. I have previously been unaware of the concept of a float values. I'll have to look else where in my worksheet for areas where I ask if values are equal to each other and add this 10^+/-15 factor.

Re: How to search a Matrix for a number bounded by another number?

Daniel Sochor wrote:

Thank you again Werner. I have previously been unaware of the concept of a float values. I'll have to look else where in my worksheet for areas where I ask if values are equal to each other and add this 10^+/-15 factor.

As an alternative you may try to uncheck "Use exact equality for comparisons and truncation" on the "Calculation" tab of the Worksheet Options.