I hope the following simpler example will clarify. Notes explain what the
ratio is.
data1 =: _1 0j_1 1 0j1 _1 ,: _2 _1 0 1 2
NB. a square and a straight line
data2 =: 0 { data1 NB. a square
plot data1 NB. plot shows square as parallelogram
ratio data1 NB. this ratio is (1 - _1) % 2 - _2, see plot
0.5
'aspect 0.5' plot data1 NB. plot shows square as square
plot data2 NB. plot shows square as a parallelogram
ratio data2 NB. this ratio is (1 - _1) % 1 - _1, see plot
1
'aspect 1' plot data2 NB. plot show square as square
IFIPAD
1
VERSION
1.3 5
--Kip Murray
Sent from my iPad
> On Sep 21, 2013, at 8:26 AM, Raul Miller <[email protected]> wrote:
>
> Do you mean something like an average of the sum along the last dimension?
>
> If so, how important is it that any excess precision gets discarded?
>
> Thanks,
>
> --
> Raul
>
>> On Sat, Sep 21, 2013 at 8:38 AM, km <[email protected]> wrote:
>> Challenge: devise a verb ratio so that if
>>
>> data1 =: ((,-)2j1) ,: _1^(%~i:)60
>> data2 =: _1^(%~i:)60
>>
>> then
>>
>> ratio data1
>> 0.5
>> ratio data2
>> 1
>>
>> i.e., if data is complex plot data and r is the result of ratio data
>> then circles in
>>
>> 'aspect r' plot data
>>
>> appear circular.
>>
>> --Kip Murray
>>
>> Sent from my iPad
>>
>>> On Sep 21, 2013, at 4:08 AM, km <[email protected]> wrote:
>>>
>>> Try
>>>
>>> 'aspect 0.5' plot ((,-)2j1) ,: _1^(%~i:)60
>>>
>>> and
>>>
>>> 'aspect 1' plot _1^(%~i:)60
>>>
>>> --Kip Murray
>>>
>>> Sent from my iPad
>>>
>>>> On Sep 21, 2013, at 3:15 AM, Bo Jacoby <[email protected]> wrote:
>>>>
>>>> 'aspect 1' plot ((,-)2j1) ,: _1^(%~i:)60 NB. This makes the frame of the
>>>> plot square, but it has different units on the two axes, so the circle is
>>>> deformed. How do I make the circle circular?
>>>> plot ((,-)2j1),:_1^(%~i:)60 NB. This is different, but not correct
>>>> either.
>>>>
>>>>
>>>>> ________________________________
>>>>> Fra: Linda Alvord <[email protected]>
>>>>> Til: [email protected]
>>>>> Sendt: 3:39 lørdag den 21. september 2013
>>>>> Emne: Re: [Jprogramming] Plotting complex lists
>>>>>
>>>>>
>>>>> Square isn't so square either. Linda (Yet again, life is a series of
>>>>> approximations.)
>>>>>
>>>>> -----Original Message-----
>>>>> From: [email protected]
>>>>> [mailto:[email protected]] On Behalf Of Bo Jacoby
>>>>> Sent: Wednesday, September 18, 2013 9:52 PM
>>>>> To: [email protected]
>>>>> Subject: Re: [Jprogramming] Plotting complex lists
>>>>>
>>>>> Thanks Linda! The 'aspect 1' makes the plot square. Do you know how to
>>>>> make
>>>>> circles circular?
>>>>>
>>>>>
>>>>>> ________________________________
>>>>>> Fra: Linda Alvord <[email protected]>
>>>>>> Til: [email protected]
>>>>>> Sendt: 2:48 torsdag den 19. september 2013
>>>>>> Emne: Re: [Jprogramming] Plotting complex lists
>>>>>>
>>>>>>
>>>>>> Try replacing the last line with:
>>>>>>
>>>>>> 'aspect 1' plot circle,ellipse,:hyperbola
>>>>>>
>>>>>> Linda
>>>>>>
>>>>>> -----Original Message-----
>>>>>> From: [email protected]
>>>>>> [mailto:[email protected]] On Behalf Of Bo
>>>>>> Jacoby
>>>>>> Sent: Tuesday, September 17, 2013 12:00 PM
>>>>>> To: [email protected]
>>>>>> Subject: Re: [Jprogramming] Plotting complex lists
>>>>>>
>>>>>> One benefit of using complex numbers is that you may forget about
>>>>>> trigonometry.
>>>>>>
>>>>>> load'plot'
>>>>>> circle=._1^n=.(%~i:)60
>>>>>> ellipse=.(circle*-.a)+(+circle)*a=.0.8
>>>>>> hyperbola=.-:((+%)j.(-%))^n
>>>>>> plot circle,ellipse,:hyperbola
>>>>>>
>>>>>>
>>>>>>
>>>>>>
>>>>>>
>>>>>>
>>>>>>> ________________________________
>>>>>>> Fra: km <[email protected]>
>>>>>>> Til: "[email protected]" <[email protected]>
>>>>>>> Sendt: 0:40 tirsdag den 17. september 2013
>>>>>>> Emne: Re: [Jprogramming] Plotting complex lists
>>>>>>>
>>>>>>>
>>>>>>> Summary of results. The strategy of hyperbola below (plotting a
>>>>>>> complex
>>>>>> table) is not well known. Henry Rich found it and reported it.
>>>>>>>
>>>>>>> Bo Jacoby gave the best way to change the sign of the real part of a
>>>>>> complex number.
>>>>>>> Simply do [: + - .
>>>>>>>
>>>>>>>
>>>>>>>
>>>>>>> NB. Complex Analytic Geometry
>>>>>>>
>>>>>>>
>>>>>>> NB. How to calculate complex number lists and tables for NB. plotting
>>>>>>> lines, circles, ellipses, and hyperbolas. How to NB. modify these
>>>>>>> tables to achieve translations, rotations, NB. and reflections. Begin
>>>>>>> with preliminaries:
>>>>>>>
>>>>>>>
>>>>>>> steps =: {.@] + -~/@] * [ %~ [: i. >:@[
>>>>>>>
>>>>>>> NB. n steps a,b produces n+1 equally spaced values from a to b
>>>>>>>
>>>>>>> to =: 512 steps , NB. Usage a to b for 512 steps from a to b
>>>>>>>
>>>>>>> sin =: 1&o.
>>>>>>>
>>>>>>> cos =: 2&o.
>>>>>>>
>>>>>>> sinh =: 5&o.
>>>>>>>
>>>>>>> cosh =: 6&o.
>>>>>>>
>>>>>>> arcsinh =: _5&o.
>>>>>>>
>>>>>>>
>>>>>>> NB. Now, results
>>>>>>>
>>>>>>>
>>>>>>> line =: 2 : 'm + (n-m)*]'
>>>>>>>
>>>>>>> NB. A line B [ t is point "t of the way from A to B". Command NB.
>>>>>>> NB. plot 0 line 1j1 [ _1 to 2
>>>>>>> NB.
>>>>>>> NB. shows the line segment from _1j_1 to 2j2
>>>>>>>
>>>>>>> NB. You are plotting a list of 513 complex numbers.
>>>>>>>
>>>>>>>
>>>>>>> parabola =: 1 : '] j. (1 % 4 * m) * *:'
>>>>>>>
>>>>>>> NB. p parabola x produces point x j. y on parabola NB. (*: x) = 4*p*y
>>>>>>> . Command NB.
>>>>>>> NB. plot 1r4 parabola _2 to 2
>>>>>>> NB.
>>>>>>> NB. plots parabola y = *: x for x from _2 to 2
>>>>>>>
>>>>>>> NB. You are plotting a list of 513 complex numbers.
>>>>>>>
>>>>>>>
>>>>>>> ellipse =: 2 : '((m * cos) j. n * sin) 0 to 2p1'
>>>>>>>
>>>>>>> NB. Suggested by Henry Rich
>>>>>>>
>>>>>>> NB. Command
>>>>>>> NB.
>>>>>>> NB. plot a ellipse b
>>>>>>> NB.
>>>>>>> NB. plots the ellipse 1 = (*: x % a) + *: y % b .
>>>>>>>
>>>>>>> NB. If a = b you get the circle (*: x) + (*: y) = *: a
>>>>>>>
>>>>>>>
>>>>>>> hyperbola =: 2 : '[: (,: +) (n * sinh) j. m * cosh'
>>>>>>>
>>>>>>> NB. Suggested by Henry Rich
>>>>>>>
>>>>>>> toh =: [: to/ [: arcsinh %~
>>>>>>>
>>>>>>> NB. b toh c,d is (arcsinh c%b) to (arcsinh d%b)
>>>>>>>
>>>>>>> NB. Command
>>>>>>> NB.
>>>>>>> NB. plot a hyperbola b [ b toh c,d
>>>>>>> NB.
>>>>>>> NB. plots y^2/a^2 - x^2/b^2 = 1 for x from c to d.
>>>>>>>
>>>>>>> NB. Remember the pattern b [ b toh c,d
>>>>>>>
>>>>>>> NB. You are plotting rows of a 2 by 513 table to get the two NB.
>>>>>>> branches of the hyperbola.
>>>>>>>
>>>>>>>
>>>>>>> NB. Rotations, translations, and reflections
>>>>>>>
>>>>>>> NB. Multiply a complex number list or table by (^&j. theta) NB. to
>>>>>>> rotate all of its points by theta radians. The center NB. of rotation
>>>>>>> is the origin 0 = 0j0 .
>>>>>>>
>>>>>>> NB. Add 5j3 to a complex list or table to move all of its points NB.
>>>>>>> the distance and direction of 5j3 from 0j0.
>>>>>>>
>>>>>>> NB. Use (+ list) or (+ table) (monadic + is conjugate) to NB. reflect
>>>>>>> all the points of the list or table across the NB. line through 0j0
>>>>>>> and
>>>>>>> 1j0 -- the x-axis. Afterwards NB. multiply by (^&j. theta) to achieve
>>>>>>> a reflection across NB. the line through 0j0 and (^&j. theta).
>>>>>>>
>>>>>>> NB. Multiply a positive number p times a list or table to NB. achieve
>>>>>>> an expansion from 0 or compression toward 0 NB. according as p > 1
>>>>>>> or p < 1 .
>>>>>>>
>>>>>>> NB. If you want to combine several operations do the NB. reflection
>>>>>>> first and the translation last.
>>>>>>>
>>>>>>> NB. Example
>>>>>>> NB.
>>>>>>> NB. plot (^&j. theta) * p parabola _2 to 3 NB.
>>>>>>> NB. plots a parabola rotated by theta radians, with 0j0 NB. the center
>>>>>>> of rotation. If theta is _1r2p1 (that is NB. - pi%2 radians) you have
>>>>>>> converted a (*: x) = 4 * p * y NB. parabola into a (*: y) = 4 * p *
>>>>>>> x parabola.
>>>>>>>
>>>>>>>
>>>>>>> --Kip Murray
>>>>>>>
>>>>>>> Sent from my iPad
>>>>>>>
>>>>>>> ----------------------------------------------------------------------
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>>>>>> ----------------------------------------------------------------------
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>>>>>
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>>>> ----------------------------------------------------------------------
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>> ----------------------------------------------------------------------
>> For information about J forums see http://www.jsoftware.com/forums.htm
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