All calculation are equal but complex number are more equal...?

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mcc
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All calculation are equal but complex number are more equal...?

Post by mcc » Fri Nov 16, 2018 7:32 am

Hi,

I have a complex 2x2 matrix on the stack, position X.
It is filled with complex numbers != 0.
I enter "2" and press Y^X ... and get "Invalid Type"

Same setup...same matrix at position X of the stack.
I press X^2 and the result is returned in the matrix.

Why doesn't the first work but the second does ?
From the mathematical point of view they are the same.

Cheers!
mcc
DM 42 - SN: 00373, Firmware v.:3.11. / 3.11. as compiled by SwissMicros

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Walter
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Re: All calculation are equal but complex number are more equal...?

Post by Walter » Fri Nov 16, 2018 8:25 am

AFAIK (IIRC) matrix exponentiation isn't defined for the general case.
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ijabbott
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Re: All calculation are equal but complex number are more equal...?

Post by ijabbott » Fri Nov 16, 2018 8:40 am

The real HP-42S does the same thing.

mcc
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Re: All calculation are equal but complex number are more equal...?

Post by mcc » Fri Nov 16, 2018 9:14 am

Hi,
ijabbott wrote:
Fri Nov 16, 2018 8:40 am
The real HP-42S does the same thing.
...repeating (possible) bug/annoyance with a new implementation make not
better.... ;)

Here is the defintion of matrix exponential:
https://en.wikipedia.org/wiki/Matrix_exponential

Looks way more stuff as "doesn't work in general" but is far beyond
the stuff I would understood...

Is there a mathmatician here ? :)

Cheers!
mcc
DM 42 - SN: 00373, Firmware v.:3.11. / 3.11. as compiled by SwissMicros

grsbanks
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Re: All calculation are equal but complex number are more equal...?

Post by grsbanks » Fri Nov 16, 2018 9:28 am

mcc wrote:
Fri Nov 16, 2018 9:14 am
...repeating (possible) bug/annoyance with a new implementation make not
better.... ;)
True, but any HP-42S program that relies on this behaviour will be broken if this is "fixed".

That is why s good simulator will simulate the behaviour of the original exactly, warts & all. Even the bits that are not necessarily mathematically correct.
Not SwissMicros staff, just an enthusiast.

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Walter
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Re: All calculation are equal but complex number are more equal...?

Post by Walter » Fri Nov 16, 2018 9:19 pm

mcc wrote:
Fri Nov 16, 2018 7:32 am
I have a complex 2x2 matrix on the stack, position X.
It is filled with complex numbers != 0.
I enter "2" and press Y^X ... and get "Invalid Type"

Same setup...same matrix at position X of the stack.
I press X^2 and the result is returned in the matrix.

Why doesn't the first work but the second does ?
From the mathematical point of view they are the same.
No, they are not. X^2 is clearly defined as multiplying the matrix by itself. Y^X, on the other hand, opens Pandora's box by allowing also noninteger exponents - for such cases, however, matrix exponentiation is not defined as is written in Wikipedia as well. So, since the calculator can't impede you from entering or using noninteger X in Y^X operating on a matrix Y, it doesn't allow Y^X operating on matrices at all. This is a wise decision IMHO.
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whuyse
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Re: All calculation are equal but complex number are more equal...?

Post by whuyse » Sat Nov 17, 2018 9:24 am

X^2 will square all the matrix elements, it will not square the matrix.
Only (all?) single-argument functions will work on all elements of the matrix.
Eg. MOD doesn't work, but SIN, IP, SIGN, XTOA etc. work.

Cheers, Werner
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ijabbott
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Re: All calculation are equal but complex number are more equal...?

Post by ijabbott » Sat Nov 17, 2018 10:04 am

whuyse wrote:
Sat Nov 17, 2018 9:24 am
X^2 will square all the matrix elements, it will not square the matrix.
Only (all?) single-argument functions will work on all elements of the matrix.
Eg. MOD doesn't work, but SIN, IP, SIGN, XTOA etc. work.

Cheers, Werner
Also, the +, -, *, / operations between a number and a matrix apply the operation to each element of the matrix, so they could have done the same thing for y^x, at least when Y is a matrix and X is a number.

It shouldn't be too hard to write a program to raise a square matrix to an integer power (assuming the matrix is invertible in the case of negative powers), but to optimize the number of matrix multiplications required, the absolute value of the exponent should be decomposed into a sum of powers of 2. In fact, Gerald H has already written such a program and posted it on the HP-Museum forum: http://www.hpmuseum.org/forum/thread-3096.html

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Walter
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Re: All calculation are equal but complex number are more equal...?

Post by Walter » Sat Nov 17, 2018 12:32 pm

whuyse wrote:
Sat Nov 17, 2018 9:24 am
X^2 will square all the matrix elements, it will not square the matrix.
Rats! :shock: I tend to forget that. :? I was reacting on the "matrix exponential" quoted by mcc.
whuyse wrote:
Sat Nov 17, 2018 9:24 am
Only (all?) single-argument functions will work on all elements of the matrix.
Eg. MOD doesn't work, but SIN, IP, SIGN, XTOA etc. work.
Not all. 1/x inverts the matrix. Consistency, you're called HP. ;)
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Thomas Okken
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Re: All calculation are equal but complex number are more equal...?

Post by Thomas Okken » Sat Nov 17, 2018 1:39 pm

Walter wrote:
Sat Nov 17, 2018 12:32 pm
whuyse wrote:
Sat Nov 17, 2018 9:24 am
Only (all?) single-argument functions will work on all elements of the matrix.
Eg. MOD doesn't work, but SIN, IP, SIGN, XTOA etc. work.
Not all. 1/x inverts the matrix. Consistency, you're called HP. ;)
No, it doesn't. INVRT inverts a matrix, 1/x inverts its elements.
Last edited by Thomas Okken on Sat Nov 17, 2018 1:55 pm, edited 1 time in total.

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