| efficient matrix multiplication [message #3817] |
Fri, 17 March 1995 13:18  |
orbach
Messages: 9
Registered: June 1994
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Junior Member |
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Greetings all.
I need to find the inner product between a single floating point
image (of size 64*48; let's call it specialimage) and several
thousands of integer-type images (all with same 64*48 size).
The integer images are stored in files, each of which consists
of a stack of approximately 100 images (so the file structure
is int(64, 48, 100). My task is to, as efficiently as possible,
read in specialimage, read in the integer files, perform the inner
product operation, and store the output into an array of floats.
In order to avoid performing a multiplication for every individual
snapshot, I've been replicating specialimage 100 times (so that it's
now a floating point array of dim 64*48*100), reading
in an entire image file into a variable (of size integer(64*48*100)),
and then simply multipliying the two large arrays. This leaves me
with a new array of size 64*48*100 (call it productarray).
Here's the question: In order to extract the inner products from this
big array, I've been looping over the z-variable and doing a "total()"
operation: for i = 0, 99 do output(i)=total(productarray(*,*,i)).
This process seems highly inefficient, and since I'm doing this
hundreds of times every time I need the series of inner products,
I'm looking for a better method. Is there a function analogous to
total(), which can be directed to act over a specified dimension without
looping over every element of that dimension? If it's at all relevant,
I'm using PV-WAVE Advantage 5.0.
Thanks in advance.
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| Re: efficient matrix multiplication [message #3943 is a reply to message #3817] |
Tue, 21 March 1995 13:49  |
amaravad
Messages: 11
Registered: September 1994
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Junior Member |
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In article <D5LsIF.417@rockyd.rockefeller.edu>,
Darren Orbach <orbach@rockvax.rockefeller.edu> wrote:
> Greetings all.
>
> I need to find the inner product between a single floating point
> image (of size 64*48; let's call it specialimage) and several
> thousands of integer-type images (all with same 64*48 size).
> The integer images are stored in files, each of which consists
> of a stack of approximately 100 images (so the file structure
> is int(64, 48, 100). My task is to, as efficiently as possible,
> read in specialimage, read in the integer files, perform the inner
> product operation, and store the output into an array of floats.
>
> In order to avoid performing a multiplication for every individual
> snapshot, I've been replicating specialimage 100 times (so that it's
> now a floating point array of dim 64*48*100), reading
> in an entire image file into a variable (of size integer(64*48*100)),
> and then simply multipliying the two large arrays. This leaves me
> with a new array of size 64*48*100 (call it productarray).
>
> Here's the question: In order to extract the inner products from this
> big array, I've been looping over the z-variable and doing a "total()"
> operation: for i = 0, 99 do output(i)=total(productarray(*,*,i)).
> This process seems highly inefficient, and since I'm doing this
> hundreds of times every time I need the series of inner products,
> I'm looking for a better method. Is there a function analogous to
> total(), which can be directed to act over a specified dimension without
> looping over every element of that dimension? If it's at all relevant,
> I'm using PV-WAVE Advantage 5.0.
>
> Thanks in advance.
One thing you can do to reduce the number of float point operations,
is to quantize special image, ie factor specialimage into a floating
point constant times an integer array. Let SI = specialimage array.
FI = any of the integer arrays in file.
ie SI = q*NEWSI (q is the floating point quantization factor)
SI*FI = q*NEWSI*FI
total(SI*FI)=total(q*NEWSI*FI)=q*total(NEWSI*FI)
You are now doing only one fp op for each array, ofcourse
at the cost of some quantization error.
hope this helps. comments welcome.
--
Ratnakar Amaravadi Software/Hardware Engineer
Department of Radiology I.U. School of Medicine
(317)274-1843 (w) amaravad@indiana.edu
(317)274-4074 (fax) ratty@foyt.indyrad.iupui.edu
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