Deconvolution/2D+: Difference between revisions

</pre>

 

 

=={{header|J}}==

Actually it is a matter of setting up the linear equations and then solving them.

 

sz =. x >:@-&$ y NB. shape of z

poi =. ,<"1 ($y) ,"0/&(,@i.) sz NB. pair of indexes

sz $ 1e_8 round ({:"1 %. }:"1) T1

)

 

 

 

 

 

 

my @h;

}

}

 

 

my @row;

}

}

return @row;

 

}

 

}

}

 

 

}

 

for ^$rows -> $r {

my $i = $r;

$i = $r;

}

for ^$rows -> $n {

next if $n == $r;

}

++$lead;

}

 

}

}

 

if @array[0] ~~ Array {

say ' ' x $indent,"[";

say ' ' x $indent, "]{$indent??','!!''}";

} else {

}

 

}

 

[

],

[

],

[

]

);

 

[

[ 54, 42, 53, -42, 85, -72 ],

);

 

say "h =";

 

Output:

[ 9, 9, 4, -4 ],

[ -3, 7, -2, -3 ],

],

]</pre>

The trick to doing this (without using a library to do all the legwork for you) is to recast the higher-order solutions into solutions in the 1D case. This is done by regarding an ''n''-dimensional address as a coding of a 1-D address.

 

namespace path {::tcl::mathfunc ::tcl::mathop}

 

 

return $h

Demonstrating how to use for the 3-D case:

proc pretty matrix {

set size [rank $matrix]

 

# Now do the deconvolution and print it out

Output:

<pre>

the [http://www.netlib.org/lapack/lug/node27.html <code>dgelsd</code>] function from the Lapack library.

The <code>break</code> function breaks a long list into a sequence of sublists according to a given template, and the <code>band</code> function is taken from the [[Deconvolution/1D]] solution.

#import nat

 

lapack..dgelsd^^(

(~&||0.!**+ ~&B^?a\~&Y@a ^lriFhNSS2iDrlYSK7LS2SL2rQ/~&alt band@alh2faltPrDPMX)^|\~&+ gang,

The equations tend to become increasingly sparse in higher dimensions,

so the following alternative implementation uses the sparse matrix

instead of Lapack, which is also callable in Ursala, adjusted as shown for the different

[http://www.basis.uklinux.net/avram/refman/umf-input-parameters.html calling convention].

 

~&?\math..div! iota; ~&!*; @h|\; -+

~&rFS+ num*rSS+ zipt^*D/~&r ^lrrSPT/~&ltK33tx zipt^/~&r ~&lSNyCK33+ zipp0,

^/~&rx ~&B->NlNSPC ~&bt+-+-+-,

UMFPACK doesn't solve systems with more equations than unknowns, so

the system is pruned to a square matrix by first selecting an equation

However, some improvement may be possible by averaging the results over several runs.

Here is a test program.

f = <<<-9.,5.,-8.>,<3.,5.,1.>>,<<-1.,-7.,2.>,<-5.,-6.,6.>>,<<8.,5.,8.>,<-2.,-6.,-4.>>>

 

'h': deconv3(g,f),

'f': deconv3(g,h)>

output:

<pre style="height:25ex;overflow:scroll">

<8.000000e+00,5.000000e+00,8.000000e+00>,

<-2.000000e+00,-6.000000e+00,-4.000000e+00>>>>

</pre>