RosettaCodeData/Task/Deconvolution-1D/Tcl/deconvolution-1d-1.tcl

101 lines
2.4 KiB
Tcl

package require Tcl 8.5
namespace eval 1D {
namespace ensemble create; # Will be same name as namespace
namespace export convolve deconvolve
# Access core language math utility commands
namespace path {::tcl::mathfunc ::tcl::mathop}
# Utility for converting a matrix to Reduced Row Echelon Form
# From http://rosettacode.org/wiki/Reduced_row_echelon_form#Tcl
proc toRREF {m} {
set lead 0
set rows [llength $m]
set cols [llength [lindex $m 0]]
for {set r 0} {$r < $rows} {incr r} {
if {$cols <= $lead} {
break
}
set i $r
while {[lindex $m $i $lead] == 0} {
incr i
if {$rows == $i} {
set i $r
incr lead
if {$cols == $lead} {
# Tcl can't break out of nested loops
return $m
}
}
}
# swap rows i and r
foreach j [list $i $r] row [list [lindex $m $r] [lindex $m $i]] {
lset m $j $row
}
# divide row r by m(r,lead)
set val [lindex $m $r $lead]
for {set j 0} {$j < $cols} {incr j} {
lset m $r $j [/ [double [lindex $m $r $j]] $val]
}
for {set i 0} {$i < $rows} {incr i} {
if {$i != $r} {
# subtract m(i,lead) multiplied by row r from row i
set val [lindex $m $i $lead]
for {set j 0} {$j < $cols} {incr j} {
lset m $i $j \
[- [lindex $m $i $j] [* $val [lindex $m $r $j]]]
}
}
}
incr lead
}
return $m
}
# How to apply a 1D convolution of two "functions"
proc convolve {f h} {
set g [lrepeat [+ [llength $f] [llength $h] -1] 0]
set fi -1
foreach fv $f {
incr fi
set hi -1
foreach hv $h {
set gi [+ $fi [incr hi]]
lset g $gi [+ [lindex $g $gi] [* $fv $hv]]
}
}
return $g
}
# How to apply a 1D deconvolution of two "functions"
proc deconvolve {g f} {
# Compute the length of the result vector
set hlen [- [llength $g] [llength $f] -1]
# Build a matrix of equations to solve
set matrix {}
set i -1
foreach gv $g {
lappend matrix [list {*}[lrepeat $hlen 0] $gv]
set j [incr i]
foreach fv $f {
if {$j < 0} {
break
} elseif {$j < $hlen} {
lset matrix $i $j $fv
}
incr j -1
}
}
# Convert to RREF, solving the system of simultaneous equations
set reduced [toRREF $matrix]
# Extract the deconvolution from the last column of the reduced matrix
for {set i 0} {$i<$hlen} {incr i} {
lappend result [lindex $reduced $i end]
}
return $result
}
}