| Re: how to get the index of the maximum element in each row for a 2D matrix efficiently [message #36279] |
Tue, 02 September 2003 10:12 |
JD Smith
Messages: 850
Registered: December 1999
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Senior Member |
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On Sat, 30 Aug 2003 13:33:46 -0700, Henry Roe wrote:
>> Starting with v5.6, MAX will do this for you with its own DIMENSION
>> keyword. Remember that in IDL dimensions start, perversely, with 1, as
>> opposed to everything else, which is 0 based. As of now we can thread
>> the following:
>>
>> TOTAL
>> PRODUCT
>> MIN
>> MAX
>> MEDIAN
>>
>> The only remaining operators I wish could be dimensionally threaded in
>> this way are AND, OR, and especially the new && and || short-circuiting
>> ops.
>>
>> JD
>
> Standard deviation or variance is also a useful function; e.g. if you
> have a stack of images and want the stdev in each pixel. (I wrote a
> bunch of call_external fortran routines to do all these before v5.6; I
> think stdev_in_1d is the only one that has not been made redundant.)
Luckily, the variance can be computed directly from its definition as
the mean square deviation, using only TOTAL, and a little REBIN magic,
e.g.:
IDL> a=randomu(sd,10,10,10)
IDL> var=total((a-rebin(total(a,3)/10.,10,10,10,/SAMPLE))^2,3)/(1 0.-1)
IDL> print,variance(a[0,0,*])
0.190512
IDL> print,var[0,0]
0.190512
To make this general for any array size and any summed dimension `d',
you need a way to expand an arbitrary array along an arbitrary
dimension (the selfsame one over which it was just collapsed). REBIN
and REFORM together can do this for you:
s1=(s2=size(a,/dimensions)) & s2[d-1]=1L
var=total((a-rebin(reform(total(a,d)/s1[d-1],s2),s1,/SAMPLE) )^2,d)/(s1[d-1]-1.)
The key ingredient above is the formidable looking:
rebin(reform(total(a,d)/s1[d-1],s2),s1,/SAMPLE)
All this is doing is taking the mean of an array over a given
dimension, and then inflating this result to match the original array
dimensions. Notice the use of vector inputs to REBIN and REFORM (s2 &
s1), which makes treating general arrays/dimensions trivial. This
same approach could be used for any such generic collapse/inflate
operation, e.g.:
s1=(s2=size(a,/dimensions)) & s2[d-1]=1L
median_inflated=rebin(reform(median(a,DIMENSION=d),s2),s1,/S AMPLE)
JD
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| Re: how to get the index of the maximum element in each row for a 2D matrix efficiently [message #36284 is a reply to message #36279] |
Sat, 30 August 2003 13:33  |
henrygroe
Messages: 30
Registered: August 2003
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Member |
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>
> Starting with v5.6, MAX will do this for you with its own DIMENSION
> keyword. Remember that in IDL dimensions start, perversely, with 1,
> as opposed to everything else, which is 0 based. As of now we can
> thread the following:
>
> TOTAL
> PRODUCT
> MIN
> MAX
> MEDIAN
>
> The only remaining operators I wish could be dimensionally threaded in
> this way are AND, OR, and especially the new && and ||
> short-circuiting ops.
>
> JD
Standard deviation or variance is also a useful function; e.g. if you
have a stack of images and want the stdev in each pixel. (I wrote a
bunch of call_external fortran routines to do all these before v5.6;
I think stdev_in_1d is the only one that has not been made redundant.)
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| Re: how to get the index of the maximum element in each row for a 2D matrix efficiently [message #36295 is a reply to message #36290] |
Fri, 29 August 2003 15:23 |
xje4e
Messages: 18
Registered: February 2002
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Junior Member |
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> Starting with v5.6, MAX will do this for you with its own DIMENSION
> keyword. Remember that in IDL dimensions start, perversely, with 1,
> as opposed to everything else, which is 0 based. As of now we can
> thread the following:
>
> TOTAL
> PRODUCT
> MIN
> MAX
> MEDIAN
>
> The only remaining operators I wish could be dimensionally threaded
in
> this way are AND, OR, and especially the new && and ||
> short-circuiting ops.
>
> JD
Oh, Yeah! Finally they did it, although it has been implemented in
matlab for a long time. And I found it in IDL 5.5 in ENVI3.5 too.
Cheers,
Jin
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| Re: how to get the index of the maximum element in each row for a 2D matrix efficiently [message #36300 is a reply to message #36295] |
Fri, 29 August 2003 12:05 |
JD Smith
Messages: 850
Registered: December 1999
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Senior Member |
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On Fri, 29 Aug 2003 10:34:52 -0700, Xiaoying Jin wrote:
> Hi, there,
>
> Suppose we have a 2D dimension matrix A(i,j), I want to get the index of
> the max element in each row.
>
> Basicly, we can do a for loop on each row, then use 'max' function to
> get the index for each row. But for a matrix having many rows, that will
> be pretty slow-->not efficient. Is there a function that can return what
> I want if I input a 2D matrix.
>
> In the previous version, 'total' function can only get the total values
> of the whole matrix. Now it can get the total values on each dimension
> by setting the keyword 'dimension'.
>
> So how is 'max' working?
Starting with v5.6, MAX will do this for you with its own DIMENSION
keyword. Remember that in IDL dimensions start, perversely, with 1,
as opposed to everything else, which is 0 based. As of now we can
thread the following:
TOTAL
PRODUCT
MIN
MAX
MEDIAN
The only remaining operators I wish could be dimensionally threaded in
this way are AND, OR, and especially the new && and ||
short-circuiting ops.
JD
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