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Ingy döt Net 2023-07-01 11:58:00 -04:00
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---
from: http://rosettacode.org/wiki/Deconvolution/1D
note: Mathematical operations

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The convolution of two functions <math>\mathit{F}</math> and <math>\mathit{H}</math> of
an integer variable is defined as the function <math>\mathit{G}</math>
satisfying
:<math> G(n) = \sum_{m=-\infty}^{\infty} F(m) H(n-m) </math>
for all integers <math>\mathit{n}</math>. Assume <math>F(n)</math> can be non-zero only for <math>0</math> &le; <math>\mathit{n}</math> &le; <math>|\mathit{F}|</math>, where <math>|\mathit{F}|</math> is the "length" of <math>\mathit{F}</math>, and similarly for <math>\mathit{G}</math> and <math>\mathit{H}</math>, so that the functions can be modeled as finite sequences by identifying <math>f_0, f_1, f_2, \dots</math> with <math>F(0), F(1), F(2), \dots</math>, etc.
Then for example, values of <math>|\mathit{F}| = 6</math> and <math>|\mathit{H}| = 5</math> would determine the following value of <math>\mathit{g}</math> by definition.
:<math>
\begin{array}{lllllllllll}
g_0 &= &f_0h_0\\
g_1 &= &f_1h_0 &+ &f_0h_1\\
g_2 &= &f_2h_0 &+ &f_1h_1 &+ &f_0h_2\\
g_3 &= &f_3h_0 &+ &f_2h_1 &+ &f_1h_2 &+ &f_0h_3\\
g_4 &= &f_4h_0 &+ &f_3h_1 &+ &f_2h_2 &+ &f_1h_3 &+ &f_0h_4\\
g_5 &= &f_5h_0 &+ &f_4h_1 &+ &f_3h_2 &+ &f_2h_3 &+ &f_1h_4\\
g_6 &= & & &f_5h_1 &+ &f_4h_2 &+ &f_3h_3 &+ &f_2h_4\\
g_7 &= & & & & &f_5h_2 &+ &f_4h_3 &+ &f_3h_4\\
g_8 &= & & & & & & &f_5h_3 &+ &f_4h_4\\
g_9 &= & & & & & & & & &f_5h_4
\end{array}
</math>
We can write this in matrix form as:
:<math>
\left(
\begin{array}{l}
g_0 \\
g_1 \\
g_2 \\
g_3 \\
g_4 \\
g_5 \\
g_6 \\
g_7 \\
g_8 \\
g_9 \\
\end{array}
\right) = \left(
\begin{array}{lllll}
f_0\\
f_1 & f_0\\
f_2 & f_1 & f_0\\
f_3 & f_2 & f_1 & f_0\\
f_4 & f_3 & f_2 & f_1 & f_0\\
f_5 & f_4 & f_3 & f_2 & f_1\\
& f_5 & f_4 & f_3 & f_2\\
& & f_5 & f_4 & f_3\\
& & & f_5 & f_4\\
& & & & f_5
\end{array}
\right) \; \left(
\begin{array}{l}
h_0 \\
h_1 \\
h_2 \\
h_3 \\
h_4 \\
\end{array} \right)
</math>
or
:<math>
g = A \; h
</math>
For this task, implement a function (or method, procedure, subroutine, etc.) <code>deconv</code> to perform ''deconvolution'' (i.e., the ''inverse'' of convolution) by constructing and solving such a system of equations represented by the above matrix <math>A</math> for <math>\mathit{h}</math> given <math>\mathit{f}</math> and <math>\mathit{g}</math>.
* The function should work for <math>\mathit{G}</math> of arbitrary length (i.e., not hard coded or constant) and <math>\mathit{F}</math> of any length up to that of <math>\mathit{G}</math>. Note that <math>|\mathit{H}|</math> will be given by <math>|\mathit{G}| - |\mathit{F}| + 1</math>.
* There may be more equations than unknowns. If convenient, use a function from a [http://www.netlib.org/lapack/lug/node27.html library] that finds the best fitting solution to an overdetermined system of linear equations (as in the [[Multiple regression]] task). Otherwise, prune the set of equations as needed and solve as in the [[Reduced row echelon form]] task.
* Test your solution on the following data. Be sure to verify both that <code>deconv</code><math>(g,f) = h</math> and <code>deconv</code><math>(g,h) = f</math> and display the results in a human readable form.
<code>
h = [-8,-9,-3,-1,-6,7]<br>
f = [-3,-6,-1,8,-6,3,-1,-9,-9,3,-2,5,2,-2,-7,-1]<br>
g = [24,75,71,-34,3,22,-45,23,245,25,52,25,-67,-96,96,31,55,36,29,-43,-7]
</code>

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F deconv(g, f)
V result = [0]*(g.len - f.len + 1)
L(&e) result
V n = L.index
e = g[n]
V lower_bound = I n >= f.len {n - f.len + 1} E 0
L(i) lower_bound .< n
e -= result[i] * f[n - i]
e /= f[0]
R result
V h = [-8,-9,-3,-1,-6,7]
V f = [-3,-6,-1,8,-6,3,-1,-9,-9,3,-2,5,2,-2,-7,-1]
V g = [24,75,71,-34,3,22,-45,23,245,25,52,25,-67,-96,96,31,55,36,29,-43,-7]
print(deconv(g, f))
print(deconv(g, h))

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with Ada.Text_IO; use Ada.Text_IO;
procedure Main is
package real_io is new Float_IO (Long_Float);
use real_io;
type Vector is array (Natural range <>) of Long_Float;
function deconv (g, f : Vector) return Vector is
len : Positive :=
Integer'Max ((g'Length - f'length), (f'length - g'length));
h : Vector (0 .. len);
Lower : Natural := 0;
begin
for n in h'range loop
h (n) := g (n);
if n >= f'length then
Lower := n - f'length + 1;
end if;
for i in Lower .. n - 1 loop
h (n) := h (n) - (h (i) * f (n - i));
end loop;
h (n) := h (n) / f (0);
end loop;
return h;
end deconv;
procedure print (v : Vector) is
begin
Put ("(");
for I in v'range loop
Put (Item => v (I), Fore => 1, Aft => 1, Exp => 0);
if I < v'Last then
Put (" ");
else
Put_Line (")");
end if;
end loop;
end print;
h : Vector := (-8.0, -9.0, -3.0, -1.0, -6.0, 7.0);
f : Vector :=
(-3.0, -6.0, -1.0, 8.0, -6.0, 3.0, -1.0, -9.0, -9.0, 3.0, -2.0, 5.0, 2.0,
-2.0, -7.0, -1.0);
g : Vector :=
(24.0, 75.0, 71.0, -34.0, 3.0, 22.0, -45.0, 23.0, 245.0, 25.0, 52.0, 25.0,
-67.0, -96.0, 96.0, 31.0, 55.0, 36.0, 29.0, -43.0, -7.0);
begin
print (h);
print (deconv (g, f));
print (f);
print (deconv (g, h));
end Main;

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*FLOAT 64
DIM h(5), f(15), g(20)
h() = -8,-9,-3,-1,-6,7
f() = -3,-6,-1,8,-6,3,-1,-9,-9,3,-2,5,2,-2,-7,-1
g() = 24,75,71,-34,3,22,-45,23,245,25,52,25,-67,-96,96,31,55,36,29,-43,-7
PROCdeconv(g(), f(), x())
PRINT "deconv(g,f) = " FNprintarray(x())
x() -= h() : IF SUM(x()) <> 0 PRINT "Error!"
PROCdeconv(g(), h(), y())
PRINT "deconv(g,h) = " FNprintarray(y())
y() -= f() : IF SUM(y()) <> 0 PRINT "Error!"
END
DEF PROCdeconv(g(), f(), RETURN h())
LOCAL f%, g%, i%, l%, n%
f% = DIM(f(),1) + 1
g% = DIM(g(),1) + 1
DIM h(g% - f%)
FOR n% = 0 TO g% - f%
h(n%) = g(n%)
IF n% < f% THEN l% = 0 ELSE l% = n% - f% + 1
IF n% THEN
FOR i% = l% TO n% - 1
h(n%) -= h(i%) * f(n% - i%)
NEXT
ENDIF
h(n%) /= f(0)
NEXT n%
ENDPROC
DEF FNprintarray(a())
LOCAL i%, a$
FOR i% = 0 TO DIM(a(),1)
a$ += STR$(a(i%)) + ", "
NEXT
= LEFT$(LEFT$(a$))

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#include <stdio.h>
#include <stdlib.h>
#include <math.h>
#include <complex.h>
double PI;
typedef double complex cplx;
void _fft(cplx buf[], cplx out[], int n, int step)
{
if (step < n) {
_fft(out, buf, n, step * 2);
_fft(out + step, buf + step, n, step * 2);
for (int i = 0; i < n; i += 2 * step) {
cplx t = cexp(-I * PI * i / n) * out[i + step];
buf[i / 2] = out[i] + t;
buf[(i + n)/2] = out[i] - t;
}
}
}
void fft(cplx buf[], int n)
{
cplx out[n];
for (int i = 0; i < n; i++) out[i] = buf[i];
_fft(buf, out, n, 1);
}
/* pad array length to power of two */
cplx *pad_two(double g[], int len, int *ns)
{
int n = 1;
if (*ns) n = *ns;
else while (n < len) n *= 2;
cplx *buf = calloc(sizeof(cplx), n);
for (int i = 0; i < len; i++) buf[i] = g[i];
*ns = n;
return buf;
}
void deconv(double g[], int lg, double f[], int lf, double out[]) {
int ns = 0;
cplx *g2 = pad_two(g, lg, &ns);
cplx *f2 = pad_two(f, lf, &ns);
fft(g2, ns);
fft(f2, ns);
cplx h[ns];
for (int i = 0; i < ns; i++) h[i] = g2[i] / f2[i];
fft(h, ns);
for (int i = 0; i >= lf - lg; i--)
out[-i] = h[(i + ns) % ns]/32;
free(g2);
free(f2);
}
int main()
{
PI = atan2(1,1) * 4;
double g[] = {24,75,71,-34,3,22,-45,23,245,25,52,25,-67,-96,96,31,55,36,29,-43,-7};
double f[] = { -3,-6,-1,8,-6,3,-1,-9,-9,3,-2,5,2,-2,-7,-1 };
double h[] = { -8,-9,-3,-1,-6,7 };
int lg = sizeof(g)/sizeof(double);
int lf = sizeof(f)/sizeof(double);
int lh = sizeof(h)/sizeof(double);
double h2[lh];
double f2[lf];
printf("f[] data is : ");
for (int i = 0; i < lf; i++) printf(" %g", f[i]);
printf("\n");
printf("deconv(g, h): ");
deconv(g, lg, h, lh, f2);
for (int i = 0; i < lf; i++) printf(" %g", f2[i]);
printf("\n");
printf("h[] data is : ");
for (int i = 0; i < lh; i++) printf(" %g", h[i]);
printf("\n");
printf("deconv(g, f): ");
deconv(g, lg, f, lf, h2);
for (int i = 0; i < lh; i++) printf(" %g", h2[i]);
printf("\n");
}

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;; Assemble the mxn matrix A from the 2D row vector x.
(defun make-conv-matrix (x m n)
(let ((lx (cadr (array-dimensions x)))
(A (make-array `(,m ,n) :initial-element 0)))
(loop for j from 0 to (- n 1) do
(loop for i from 0 to (- m 1) do
(setf (aref A i j)
(cond ((or (< i j) (>= i (+ j lx)))
0)
((and (>= i j) (< i (+ j lx)))
(aref x 0 (- i j)))))))
A))
;; Solve the overdetermined system A(f)*h=g by linear least squares.
(defun deconv (g f)
(let* ((lg (cadr (array-dimensions g)))
(lf (cadr (array-dimensions f)))
(lh (+ (- lg lf) 1))
(A (make-conv-matrix f lg lh)))
(lsqr A (mtp g))))

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(setf f #2A((-3 -6 -1 8 -6 3 -1 -9 -9 3 -2 5 2 -2 -7 -1)))
(setf h #2A((-8 -9 -3 -1 -6 7)))
(setf g #2A((24 75 71 -34 3 22 -45 23 245 25 52 25 -67 -96 96 31 55 36 29 -43 -7)))
(deconv g f)
#2A((-8.0)
(-9.000000000000002)
(-2.999999999999999)
(-0.9999999999999997)
(-6.0)
(7.000000000000002))
(deconv g h)
#2A((-2.999999999999999)
(-6.000000000000001)
(-1.0000000000000002)
(8.0)
(-5.999999999999999)
(3.0000000000000004)
(-1.0000000000000004)
(-9.000000000000002)
(-9.0)
(2.9999999999999996)
(-1.9999999999999991)
(5.0)
(1.9999999999999996)
(-2.0000000000000004)
(-7.000000000000001)
(-0.9999999999999994))

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T[] deconv(T)(in T[] g, in T[] f) pure nothrow {
int flen = f.length;
int glen = g.length;
auto result = new T[glen - flen + 1];
foreach (int n, ref e; result) {
e = g[n];
immutable lowerBound = (n >= flen) ? n - flen + 1 : 0;
foreach (i; lowerBound .. n)
e -= result[i] * f[n - i];
e /= f[0];
}
return result;
}
void main() {
import std.stdio;
immutable h = [-8,-9,-3,-1,-6,7];
immutable f = [-3,-6,-1,8,-6,3,-1,-9,-9,3,-2,5,2,-2,-7,-1];
immutable g = [24,75,71,-34,3,22,-45,23,245,25,52,25,-67,
-96,96,31,55,36,29,-43,-7];
writeln(deconv(g, f) == h, " ", deconv(g, f));
writeln(deconv(g, h) == f, " ", deconv(g, h));
}

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! Build
! Windows: ifort /I "%IFORT_COMPILER11%\mkl\include\ia32" deconv1d.f90 "%IFORT_COMPILER11%\mkl\ia32\lib\*.lib"
! Linux:
program deconv
! Use gelsd from LAPACK95.
use mkl95_lapack, only : gelsd
implicit none
real(8), allocatable :: g(:), href(:), A(:,:), f(:)
real(8), pointer :: h(:), r(:)
integer :: N
character(len=16) :: cbuff
integer :: i
intrinsic :: nint
! Allocate data arrays
allocate(g(21),f(16))
g = [24,75,71,-34,3,22,-45,23,245,25,52,25,-67,-96,96,31,55,36,29,-43,-7]
f = [-3,-6,-1,8,-6,3,-1,-9,-9,3,-2,5,2,-2,-7,-1]
! Calculate deconvolution
h => deco(f, g)
! Check result against reference
N = size(h)
allocate(href(N))
href = [-8,-9,-3,-1,-6,7]
cbuff = ' '
write(cbuff,'(a,i0,a)') '(a,',N,'(i0,a),i0)'
if (any(abs(h-href) > 1.0d-4)) then
write(*,'(a)') 'deconv(f, g) - FAILED'
else
write(*,cbuff) 'deconv(f, g) = ',(nint(h(i)),', ',i=1,N-1),nint(h(N))
end if
! Calculate deconvolution
r => deco(h, g)
cbuff = ' '
N = size(r)
write(cbuff,'(a,i0,a)') '(a,',N,'(i0,a),i0)'
if (any(abs(r-f) > 1.0d-4)) then
write(*,'(a)') 'deconv(h, g) - FAILED'
else
write(*,cbuff) 'deconv(h, g) = ',(nint(r(i)),', ',i=1,N-1),nint(r(N))
end if
contains
function deco(p, q)
real(8), pointer :: deco(:)
real(8), intent(in) :: p(:), q(:)
real(8), allocatable, target :: r(:)
real(8), allocatable :: A(:,:)
integer :: N
! Construct derived arrays
N = size(q) - size(p) + 1
allocate(A(size(q),N),r(size(q)))
A = 0.0d0
do i=1,N
A(i:i+size(p)-1,i) = p
end do
! Invoke the LAPACK routine to do the work
r = q
call gelsd(A, r)
deco => r(1:N)
end function deco
end program deconv

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deconv(f, g) = -8, -9, -3, -1, -6, 7
deconv(h, g) = -3, -6, -1, 8, -6, 3, -1, -9, -9, 3, -2, 5, 2, -2, -7, -1

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package main
import "fmt"
func main() {
h := []float64{-8, -9, -3, -1, -6, 7}
f := []float64{-3, -6, -1, 8, -6, 3, -1, -9, -9, 3, -2, 5, 2, -2, -7, -1}
g := []float64{24, 75, 71, -34, 3, 22, -45, 23, 245, 25, 52, 25, -67, -96,
96, 31, 55, 36, 29, -43, -7}
fmt.Println(h)
fmt.Println(deconv(g, f))
fmt.Println(f)
fmt.Println(deconv(g, h))
}
func deconv(g, f []float64) []float64 {
h := make([]float64, len(g)-len(f)+1)
for n := range h {
h[n] = g[n]
var lower int
if n >= len(f) {
lower = n - len(f) + 1
}
for i := lower; i < n; i++ {
h[n] -= h[i] * f[n-i]
}
h[n] /= f[0]
}
return h
}

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package main
import (
"fmt"
"math"
"math/cmplx"
)
func main() {
h := []float64{-8, -9, -3, -1, -6, 7}
f := []float64{-3, -6, -1, 8, -6, 3, -1, -9, -9, 3, -2, 5, 2, -2, -7, -1}
g := []float64{24, 75, 71, -34, 3, 22, -45, 23, 245, 25, 52, 25, -67, -96,
96, 31, 55, 36, 29, -43, -7}
fmt.Printf("%.1f\n", h)
fmt.Printf("%.1f\n", deconv(g, f))
fmt.Printf("%.1f\n", f)
fmt.Printf("%.1f\n", deconv(g, h))
}
func deconv(g, f []float64) []float64 {
n := 1
for n < len(g) {
n *= 2
}
g2 := make([]complex128, n)
for i, x := range g {
g2[i] = complex(x, 0)
}
f2 := make([]complex128, n)
for i, x := range f {
f2[i] = complex(x, 0)
}
gt := fft(g2)
ft := fft(f2)
for i := range gt {
gt[i] /= ft[i]
}
ht := fft(gt)
it := 1 / float64(n)
out := make([]float64, len(g)-len(f)+1)
out[0] = real(ht[0]) * it
for i := 1; i < len(out); i++ {
out[i] = real(ht[n-i]) * it
}
return out
}
func fft(in []complex128) []complex128 {
out := make([]complex128, len(in))
ditfft2(in, out, len(in), 1)
return out
}
func ditfft2(x, y []complex128, n, s int) {
if n == 1 {
y[0] = x[0]
return
}
ditfft2(x, y, n/2, 2*s)
ditfft2(x[s:], y[n/2:], n/2, 2*s)
for k := 0; k < n/2; k++ {
tf := cmplx.Rect(1, -2*math.Pi*float64(k)/float64(n)) * y[k+n/2]
y[k], y[k+n/2] = y[k]+tf, y[k]-tf
}
}

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package main
import (
"fmt"
"gonum.org/v1/gonum/mat"
)
var (
h = []float64{-8, -9, -3, -1, -6, 7}
f = []float64{-3, -6, -1, 8, -6, 3, -1, -9, -9, 3, -2, 5, 2, -2, -7, -1}
g = []float64{24, 75, 71, -34, 3, 22, -45, 23, 245, 25, 52, 25, -67, -96,
96, 31, 55, 36, 29, -43, -7}
)
func band(g, f []float64) *mat.Dense {
nh := len(g) - len(f) + 1
b := mat.NewDense(len(g), nh, nil)
for j := 0; j < nh; j++ {
for i, fi := range f {
b.Set(i+j, j, fi)
}
}
return b
}
func deconv(g, f []float64) mat.Matrix {
z := mat.NewDense(len(g)-len(f)+1, 1, nil)
z.Solve(band(g, f), mat.NewVecDense(len(g), g))
return z
}
func main() {
fmt.Printf("deconv(g, f) =\n%.1f\n\n", mat.Formatted(deconv(g, f)))
fmt.Printf("deconv(g, h) =\n%.1f\n", mat.Formatted(deconv(g, h)))
}

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deconv1d :: [Double] -> [Double] -> [Double]
deconv1d xs ys = takeWhile (/= 0) $ deconv xs ys
where
[] `deconv` _ = []
(0:xs) `deconv` (0:ys) = xs `deconv` ys
(x:xs) `deconv` (y:ys) =
let q = x / y
in q : zipWith (-) xs (scale q ys ++ repeat 0) `deconv` (y : ys)
scale :: Double -> [Double] -> [Double]
scale = map . (*)
h, f, g :: [Double]
h = [-8, -9, -3, -1, -6, 7]
f = [-3, -6, -1, 8, -6, 3, -1, -9, -9, 3, -2, 5, 2, -2, -7, -1]
g =
[ 24
, 75
, 71
, -34
, 3
, 22
, -45
, 23
, 245
, 25
, 52
, 25
, -67
, -96
, 96
, 31
, 55
, 36
, 29
, -43
, -7
]
main :: IO ()
main = print $ (h == deconv1d g f) && (f == deconv1d g h)

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Ai=: (i.@] =/ i.@[ -/ i.@>:@-)&#
divide=: [ +/ .*~ [:%.&.x: ] +/ .* Ai

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h=: _8 _9 _3 _1 _6 7
f=: _3 _6 _1 8 _6 3 _1 _9 _9 3 _2 5 2 _2 _7 _1
g=: 24 75 71 _34 3 22 _45 23 245 25 52 25 _67 _96 96 31 55 36 29

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g divide f
_8 _9 _3 _1 _6 7
g divide h
_3 _6 _1 8 _6 3 _1 _9 _9 3 _2 5 2 _2 _7 _1

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divide=: [ +/ .*~ [:%. ] +/ .* Ai

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import java.util.Arrays;
public class Deconvolution1D {
public static int[] deconv(int[] g, int[] f) {
int[] h = new int[g.length - f.length + 1];
for (int n = 0; n < h.length; n++) {
h[n] = g[n];
int lower = Math.max(n - f.length + 1, 0);
for (int i = lower; i < n; i++)
h[n] -= h[i] * f[n - i];
h[n] /= f[0];
}
return h;
}
public static void main(String[] args) {
int[] h = { -8, -9, -3, -1, -6, 7 };
int[] f = { -3, -6, -1, 8, -6, 3, -1, -9, -9, 3, -2, 5, 2, -2, -7, -1 };
int[] g = { 24, 75, 71, -34, 3, 22, -45, 23, 245, 25, 52, 25, -67, -96,
96, 31, 55, 36, 29, -43, -7 };
StringBuilder sb = new StringBuilder();
sb.append("h = " + Arrays.toString(h) + "\n");
sb.append("deconv(g, f) = " + Arrays.toString(deconv(g, f)) + "\n");
sb.append("f = " + Arrays.toString(f) + "\n");
sb.append("deconv(g, h) = " + Arrays.toString(deconv(g, h)) + "\n");
System.out.println(sb.toString());
}
}

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@ -0,0 +1,9 @@
h = [-8, -9, -3, -1, -6, 7]
g = [24, 75, 71, -34, 3, 22, -45, 23, 245, 25, 52, 25, -67, -96, 96, 31, 55, 36, 29, -43, -7]
f = [-3, -6, -1, 8, -6, 3, -1, -9, -9, 3, -2, 5, 2, -2, -7, -1]
hanswer = deconv(float.(g), float.(f))
println("The deconvolution deconv(g, f) is $hanswer, which is the same as h = $h\n")
fanswer = deconv(float.(g), float.(h))
println("The deconvolution deconv(g, h) is $fanswer, which is the same as f = $f\n")

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@ -0,0 +1,27 @@
// version 1.1.3
fun deconv(g: DoubleArray, f: DoubleArray): DoubleArray {
val fs = f.size
val h = DoubleArray(g.size - fs + 1)
for (n in h.indices) {
h[n] = g[n]
val lower = if (n >= fs) n - fs + 1 else 0
for (i in lower until n) h[n] -= h[i] * f[n -i]
h[n] /= f[0]
}
return h
}
fun main(args: Array<String>) {
val h = doubleArrayOf(-8.0, -9.0, -3.0, -1.0, -6.0, 7.0)
val f = doubleArrayOf(-3.0, -6.0, -1.0, 8.0, -6.0, 3.0, -1.0, -9.0,
-9.0, 3.0, -2.0, 5.0, 2.0, -2.0, -7.0, -1.0)
val g = doubleArrayOf(24.0, 75.0, 71.0, -34.0, 3.0, 22.0, -45.0,
23.0, 245.0, 25.0, 52.0, 25.0, -67.0, -96.0,
96.0, 31.0, 55.0, 36.0, 29.0, -43.0, -7.0)
println("${h.map { it.toInt() }}")
println("${deconv(g, f).map { it.toInt() }}")
println()
println("${f.map { it.toInt() }}")
println("${deconv(g, h).map { it.toInt() }}")
}

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function deconvolve(f, g)
local h = setmetatable({}, {__index = function(self, n)
if n == 1 then self[1] = g[1] / f[1]
else
self[n] = g[n]
for i = 1, n - 1 do
self[n] = self[n] - self[i] * (f[n - i + 1] or 0)
end
self[n] = self[n] / f[1]
end
return self[n]
end})
local _ = h[#g - #f + 1]
return setmetatable(h, nil)
end

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@ -0,0 +1,5 @@
local f = {-3,-6,-1,8,-6,3,-1,-9,-9,3,-2,5,2,-2,-7,-1}
local g = {24,75,71,-34,3,22,-45,23,245,25,52,25,-67,-96,96,31,55,36,29,-43,-7}
local h = {-8,-9,-3,-1,-6,7}
print(unpack(deconvolve(f, g))) --> -8 -9 -3 -1 -6 7
print(unpack(deconvolve(h, g))) --> -3 -6 -1 8 -6 3 -1 -9 -9 3 -2 5 2 -2 -7 -1

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@ -0,0 +1,14 @@
>> h = [-8,-9,-3,-1,-6,7];
>> g = [24,75,71,-34,3,22,-45,23,245,25,52,25,-67,-96,96,31,55,36,29,-43,-7];
>> f = [-3,-6,-1,8,-6,3,-1,-9,-9,3,-2,5,2,-2,-7,-1];
>> deconv(g,f)
ans =
-8.0000 -9.0000 -3.0000 -1.0000 -6.0000 7.0000
>> deconv(g,h)
ans =
-3 -6 -1 8 -6 3 -1 -9 -9 3 -2 5 2 -2 -7 -1

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deconv[f_List, g_List] :=
Module[{A =
SparseArray[
Table[Band[{n, 1}] -> f[[n]], {n, 1, Length[f]}], {Length[g], Length[f] - 1}]},
Take[LinearSolve[A, g], Length[g] - Length[f] + 1]]

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proc deconv(g, f: openArray[float]): seq[float] =
var h: seq[float] = newSeq[float](len(g) - len(f) + 1)
for n in 0..<len(h):
h[n] = g[n]
var lower: int
if n >= len(f):
lower = n - len(f) + 1
for i in lower..<n:
h[n] -= h[i] * f[n - i]
h[n] /= f[0]
h
let h = [-8'f64, -9, -3, -1, -6, 7]
let f = [-3'f64, -6, -1, 8, -6, 3, -1, -9, -9, 3, -2, 5, 2, -2, -7, -1]
let g = [24'f64, 75, 71, -34, 3, 22, -45, 23, 245, 25, 52, 25, -67, -96,
96, 31, 55, 36, 29, -43, -7]
echo h
echo deconv(g, f)
echo f
echo deconv(g, h)

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@ -0,0 +1,69 @@
use v5.36;
use Math::Cartesian::Product;
sub deconvolve($g,$f) {
my @g = @{$g};
my @f = @{$f};
my(@m,@d);
my $h = 1 + @g - @f;
push @m, [(0) x $h, $g[$_]] for 0..$#g;
for my $j (0..$h-1) {
for my $k (0..$#f) {
$m[$j + $k][$j] = $f[$k]
}
}
rref(\@m);
push @d, @{ $m[$_] }[$h] for 0..$h-1;
@d;
}
sub convolve($f,$h) {
my @f = @{$f};
my @h = @{$h};
my @i;
for my $x (cartesian {@_} [0..$#f], [0..$#h]) {
push @i, @$x[0]+@$x[1];
}
my $cnt = 0;
my @g = (0) x (@f + @h - 1);
for my $x (cartesian {@_} [@f], [@h]) {
$g[$i[$cnt++]] += @$x[0]*@$x[1];
}
@g;
}
sub rref($m) {
my @m = @{$m};
@m or return;
my ($lead, $rows, $cols) = (0, scalar(@m), scalar(@{$m[0]}));
for my $r (0 .. $rows - 1) {
$lead < $cols or return;
my $i = $r;
until ($m[$i][$lead]) {
++$i == $rows or next;
$i = $r;
++$lead == $cols and return;
}
@m[$i, $r] = @m[$r, $i];
my $lv = $m[$r][$lead];
$_ /= $lv foreach @{ $m[$r] };
my @mr = @{ $m[$r] };
for my $i (0 .. $rows - 1) {
$i == $r and next;
($lv, my $n) = ($m[$i][$lead], -1);
$_ -= $lv * $mr[++$n] foreach @{ $m[$i] };
}
++$lead;
}
}
my @h = qw<-8 -9 -3 -1 -6 7>;
my @f = qw<-3 -6 -1 8 -6 3 -1 -9 -9 3 -2 5 2 -2 -7 -1>;
print ' conv(f,h) = g = ' . join(' ', my @g = convolve(\@f, \@h)) . "\n";
print 'deconv(g,f) = h = ' . join(' ', deconvolve(\@g, \@f)) . "\n";
print 'deconv(g,h) = f = ' . join(' ', deconvolve(\@g, \@h)) . "\n";

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@ -0,0 +1,39 @@
(phixonline)-->
<span style="color: #008080;">with</span> <span style="color: #008080;">javascript_semantics</span>
<span style="color: #008080;">function</span> <span style="color: #000000;">deconv</span><span style="color: #0000FF;">(</span><span style="color: #004080;">sequence</span> <span style="color: #000000;">g</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">f</span><span style="color: #0000FF;">)</span>
<span style="color: #004080;">integer</span> <span style="color: #000000;">lf</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">f</span><span style="color: #0000FF;">),</span> <span style="color: #000000;">lg</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">g</span><span style="color: #0000FF;">),</span> <span style="color: #000000;">lh</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">lg</span><span style="color: #0000FF;">-</span><span style="color: #000000;">lf</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span>
<span style="color: #004080;">sequence</span> <span style="color: #000000;">h</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">repeat</span><span style="color: #0000FF;">(</span><span style="color: #000000;">0</span><span style="color: #0000FF;">,</span><span style="color: #000000;">lh</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">n</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #000000;">lh</span> <span style="color: #008080;">do</span>
<span style="color: #004080;">atom</span> <span style="color: #000000;">e</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">g</span><span style="color: #0000FF;">[</span><span style="color: #000000;">n</span><span style="color: #0000FF;">]</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #7060A8;">max</span><span style="color: #0000FF;">(</span><span style="color: #000000;">n</span><span style="color: #0000FF;">-</span><span style="color: #000000;">lf</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">to</span> <span style="color: #000000;">n</span><span style="color: #0000FF;">-</span><span style="color: #000000;">2</span> <span style="color: #008080;">do</span>
<span style="color: #000000;">e</span> <span style="color: #0000FF;">-=</span> <span style="color: #000000;">h</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">*</span> <span style="color: #000000;">f</span><span style="color: #0000FF;">[</span><span style="color: #000000;">n</span><span style="color: #0000FF;">-</span><span style="color: #000000;">i</span><span style="color: #0000FF;">]</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #000000;">h</span><span style="color: #0000FF;">[</span><span style="color: #000000;">n</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">e</span><span style="color: #0000FF;">/</span><span style="color: #000000;">f</span><span style="color: #0000FF;">[</span><span style="color: #000000;">1</span><span style="color: #0000FF;">]</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #008080;">return</span> <span style="color: #000000;">h</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
<span style="color: #008080;">function</span> <span style="color: #000000;">conv</span><span style="color: #0000FF;">(</span><span style="color: #004080;">sequence</span> <span style="color: #000000;">f</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">h</span><span style="color: #0000FF;">)</span>
<span style="color: #004080;">integer</span> <span style="color: #000000;">lf</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">f</span><span style="color: #0000FF;">),</span> <span style="color: #000000;">lh</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">h</span><span style="color: #0000FF;">),</span> <span style="color: #000000;">lg</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">lf</span><span style="color: #0000FF;">+</span><span style="color: #000000;">lh</span><span style="color: #0000FF;">-</span><span style="color: #000000;">1</span>
<span style="color: #004080;">sequence</span> <span style="color: #000000;">g</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">repeat</span><span style="color: #0000FF;">(</span><span style="color: #000000;">0</span><span style="color: #0000FF;">,</span><span style="color: #000000;">lg</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #000000;">lh</span> <span style="color: #008080;">do</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">j</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #000000;">lf</span> <span style="color: #008080;">do</span>
<span style="color: #004080;">integer</span> <span style="color: #000000;">k</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">+</span><span style="color: #000000;">j</span><span style="color: #0000FF;">-</span><span style="color: #000000;">1</span>
<span style="color: #000000;">g</span><span style="color: #0000FF;">[</span><span style="color: #000000;">k</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">f</span><span style="color: #0000FF;">[</span><span style="color: #000000;">j</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">*</span> <span style="color: #000000;">h</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">]</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #008080;">return</span> <span style="color: #000000;">g</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
<span style="color: #008080;">constant</span> <span style="color: #000000;">h</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{-</span><span style="color: #000000;">8</span><span style="color: #0000FF;">,-</span><span style="color: #000000;">9</span><span style="color: #0000FF;">,-</span><span style="color: #000000;">3</span><span style="color: #0000FF;">,-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,-</span><span style="color: #000000;">6</span><span style="color: #0000FF;">,</span><span style="color: #000000;">7</span><span style="color: #0000FF;">},</span>
<span style="color: #000000;">f</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{-</span><span style="color: #000000;">3</span><span style="color: #0000FF;">,-</span><span style="color: #000000;">6</span><span style="color: #0000FF;">,-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">8</span><span style="color: #0000FF;">,-</span><span style="color: #000000;">6</span><span style="color: #0000FF;">,</span><span style="color: #000000;">3</span><span style="color: #0000FF;">,-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,-</span><span style="color: #000000;">9</span><span style="color: #0000FF;">,-</span><span style="color: #000000;">9</span><span style="color: #0000FF;">,</span><span style="color: #000000;">3</span><span style="color: #0000FF;">,-</span><span style="color: #000000;">2</span><span style="color: #0000FF;">,</span><span style="color: #000000;">5</span><span style="color: #0000FF;">,</span><span style="color: #000000;">2</span><span style="color: #0000FF;">,-</span><span style="color: #000000;">2</span><span style="color: #0000FF;">,-</span><span style="color: #000000;">7</span><span style="color: #0000FF;">,-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">},</span>
<span style="color: #000000;">g</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">24</span><span style="color: #0000FF;">,</span><span style="color: #000000;">75</span><span style="color: #0000FF;">,</span><span style="color: #000000;">71</span><span style="color: #0000FF;">,-</span><span style="color: #000000;">34</span><span style="color: #0000FF;">,</span><span style="color: #000000;">3</span><span style="color: #0000FF;">,</span><span style="color: #000000;">22</span><span style="color: #0000FF;">,-</span><span style="color: #000000;">45</span><span style="color: #0000FF;">,</span><span style="color: #000000;">23</span><span style="color: #0000FF;">,</span><span style="color: #000000;">245</span><span style="color: #0000FF;">,</span><span style="color: #000000;">25</span><span style="color: #0000FF;">,</span><span style="color: #000000;">52</span><span style="color: #0000FF;">,</span><span style="color: #000000;">25</span><span style="color: #0000FF;">,-</span><span style="color: #000000;">67</span><span style="color: #0000FF;">,-</span><span style="color: #000000;">96</span><span style="color: #0000FF;">,</span><span style="color: #000000;">96</span><span style="color: #0000FF;">,</span><span style="color: #000000;">31</span><span style="color: #0000FF;">,</span><span style="color: #000000;">55</span><span style="color: #0000FF;">,</span><span style="color: #000000;">36</span><span style="color: #0000FF;">,</span><span style="color: #000000;">29</span><span style="color: #0000FF;">,-</span><span style="color: #000000;">43</span><span style="color: #0000FF;">,-</span><span style="color: #000000;">7</span><span style="color: #0000FF;">}</span>
<span style="color: #008080;">procedure</span> <span style="color: #000000;">test</span><span style="color: #0000FF;">(</span><span style="color: #004080;">string</span> <span style="color: #000000;">desc</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">eq</span><span style="color: #0000FF;">,</span> <span style="color: #004080;">sequence</span> <span style="color: #000000;">r</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">e</span><span style="color: #0000FF;">)</span>
<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"%s (%ssame as %s): %V\n"</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">desc</span><span style="color: #0000FF;">,</span><span style="color: #008080;">iff</span><span style="color: #0000FF;">(</span><span style="color: #000000;">r</span><span style="color: #0000FF;">==</span><span style="color: #000000;">e</span><span style="color: #0000FF;">?</span><span style="color: #008000;">""</span><span style="color: #0000FF;">:</span><span style="color: #008000;">"**NOT** "</span><span style="color: #0000FF;">),</span><span style="color: #000000;">eq</span><span style="color: #0000FF;">,</span><span style="color: #000000;">r</span><span style="color: #0000FF;">})</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">procedure</span>
<span style="color: #000000;">test</span><span style="color: #0000FF;">(</span><span style="color: #008000;">" conv(h,f)"</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"g"</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">conv</span><span style="color: #0000FF;">(</span><span style="color: #000000;">h</span><span style="color: #0000FF;">,</span><span style="color: #000000;">f</span><span style="color: #0000FF;">),</span><span style="color: #000000;">g</span><span style="color: #0000FF;">)</span>
<span style="color: #000000;">test</span><span style="color: #0000FF;">(</span><span style="color: #008000;">"deconv(g,f)"</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"h"</span><span style="color: #0000FF;">,</span><span style="color: #000000;">deconv</span><span style="color: #0000FF;">(</span><span style="color: #000000;">g</span><span style="color: #0000FF;">,</span><span style="color: #000000;">f</span><span style="color: #0000FF;">),</span><span style="color: #000000;">h</span><span style="color: #0000FF;">)</span>
<span style="color: #000000;">test</span><span style="color: #0000FF;">(</span><span style="color: #008000;">"deconv(g,h)"</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"f"</span><span style="color: #0000FF;">,</span><span style="color: #000000;">deconv</span><span style="color: #0000FF;">(</span><span style="color: #000000;">g</span><span style="color: #0000FF;">,</span><span style="color: #000000;">h</span><span style="color: #0000FF;">),</span><span style="color: #000000;">f</span><span style="color: #0000FF;">)</span>
<!--

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@ -0,0 +1,10 @@
(load "@lib/math.l")
(de deconv (G F)
(let A (pop 'F)
(make
(for (N . H) (head (- (length F)) G)
(for (I . M) (made)
(dec 'H
(*/ M (get F (- N I)) 1.0) ) )
(link (*/ H 1.0 A)) ) ) ) )

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@ -0,0 +1,7 @@
(setq
F (-3. -6. -1. 8. -6. 3. -1. -9. -9. 3. -2. 5. 2. -2. -7. -1.)
G (24. 75. 71. -34. 3. 22. -45. 23. 245. 25. 52. 25. -67. -96. 96. 31. 55. 36. 29. -43. -7.)
H (-8. -9. -3. -1. -6. 7.) )
(test H (deconv G F))
(test F (deconv G H))

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@ -0,0 +1,54 @@
def ToReducedRowEchelonForm( M ):
if not M: return
lead = 0
rowCount = len(M)
columnCount = len(M[0])
for r in range(rowCount):
if lead >= columnCount:
return
i = r
while M[i][lead] == 0:
i += 1
if i == rowCount:
i = r
lead += 1
if columnCount == lead:
return
M[i],M[r] = M[r],M[i]
lv = M[r][lead]
M[r] = [ mrx / lv for mrx in M[r]]
for i in range(rowCount):
if i != r:
lv = M[i][lead]
M[i] = [ iv - lv*rv for rv,iv in zip(M[r],M[i])]
lead += 1
return M
def pmtx(mtx):
print ('\n'.join(''.join(' %4s' % col for col in row) for row in mtx))
def convolve(f, h):
g = [0] * (len(f) + len(h) - 1)
for hindex, hval in enumerate(h):
for findex, fval in enumerate(f):
g[hindex + findex] += fval * hval
return g
def deconvolve(g, f):
lenh = len(g) - len(f) + 1
mtx = [[0 for x in range(lenh+1)] for y in g]
for hindex in range(lenh):
for findex, fval in enumerate(f):
gindex = hindex + findex
mtx[gindex][hindex] = fval
for gindex, gval in enumerate(g):
mtx[gindex][lenh] = gval
ToReducedRowEchelonForm( mtx )
return [mtx[i][lenh] for i in range(lenh)] # h
if __name__ == '__main__':
h = [-8,-9,-3,-1,-6,7]
f = [-3,-6,-1,8,-6,3,-1,-9,-9,3,-2,5,2,-2,-7,-1]
g = [24,75,71,-34,3,22,-45,23,245,25,52,25,-67,-96,96,31,55,36,29,-43,-7]
assert convolve(f,h) == g
assert deconvolve(g, f) == h

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import numpy
h = [-8,-9,-3,-1,-6,7]
f = [-3,-6,-1,8,-6,3,-1,-9,-9,3,-2,5,2,-2,-7,-1]
g = [24,75,71,-34,3,22,-45,23,245,25,52,25,-67,-96,96,31,55,36,29,-43,-7]
# https://stackoverflow.com/questions/14267555/find-the-smallest-power-of-2-greater-than-n-in-python
def shift_bit_length(x):
return 1<<(x-1).bit_length()
def conv(a, b):
p = len(a)
q = len(b)
n = p + q - 1
r = shift_bit_length(n)
y = numpy.fft.ifft(numpy.fft.fft(a,r) * numpy.fft.fft(b,r),r)
return numpy.trim_zeros(numpy.around(numpy.real(y),decimals=6))
def deconv(a, b):
p = len(a)
q = len(b)
n = p - q + 1
r = shift_bit_length(max(p, q))
y = numpy.fft.ifft(numpy.fft.fft(a,r) / numpy.fft.fft(b,r), r)
return numpy.trim_zeros(numpy.around(numpy.real(y),decimals=6))
# should return g
print(conv(h,f))
# should return h
print(deconv(g,f))
# should return f
print(deconv(g,h))

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conv <- function(a, b) {
p <- length(a)
q <- length(b)
n <- p + q - 1
r <- nextn(n, f=2)
y <- fft(fft(c(a, rep(0, r-p))) * fft(c(b, rep(0, r-q))), inverse=TRUE)/r
y[1:n]
}
deconv <- function(a, b) {
p <- length(a)
q <- length(b)
n <- p - q + 1
r <- nextn(max(p, q), f=2)
y <- fft(fft(c(a, rep(0, r-p))) / fft(c(b, rep(0, r-q))), inverse=TRUE)/r
return(y[1:n])
}

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h <- c(-8,-9,-3,-1,-6,7)
f <- c(-3,-6,-1,8,-6,3,-1,-9,-9,3,-2,5,2,-2,-7,-1)
g <- c(24,75,71,-34,3,22,-45,23,245,25,52,25,-67,-96,96,31,55,36,29,-43,-7)
max(abs(conv(f,h) - g))
max(abs(deconv(g,f) - h))
max(abs(deconv(g,h) - f))

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conv(a, b) == convolve(a, rev(b), type="open")

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/*REXX pgm performs deconvolution of two arrays: deconv(g,f)=h and deconv(g,h)=f */
call make 'H', "-8 -9 -3 -1 -6 7"
call make 'F', "-3 -6 -1 8 -6 3 -1 -9 -9 3 -2 5 2 -2 -7 -1"
call make 'G', "24 75 71 -34 3 22 -45 23 245 25 52 25 -67 -96 96 31 55 36 29 -43 -7"
call show 'H' /*display the elements of array H. */
call show 'F' /* " " " " " F. */
call show 'G' /* " " " " " G. */
call deco 'G', "F", 'X' /*deconvolution of G and F ───► X */
call test 'X', "H" /*test: is array H equal to array X?*/
call deco 'G', "H", 'Y' /*deconvolution of G and H ───► Y */
call test 'F', "Y" /*test: is array F equal to array Y?*/
exit 0 /*stick a fork in it, we're all done. */
/*──────────────────────────────────────────────────────────────────────────────────────*/
deco: parse arg $1,$2,$r; b= @.$2.# + 1; a= @.$1.# + 1 /*get sizes of array 1&2*/
@.$r.#= a - b /*size of return array. */
do n=0 to a-b /*define return array. */
@.$r.n= @.$1.n /*define RETURN element.*/
if n<b then L= 0 /*define the variable L.*/
else L= n - b + 1 /* " " " " */
if n>0 then do j=L to n-1; _= n-j /*define elements > 0. */
@.$r.n= @.$r.n - @.$r.j * @.$2._ /*compute " " " */
end /*j*/ /* [↑] subtract product.*/
@.$r.n= @.$r.n / @.$2.0 /*divide array element. */
end /*n*/; return
/*──────────────────────────────────────────────────────────────────────────────────────*/
make: parse arg $,z; @.$.#= words(z) - 1 /*obtain args; set size.*/
do k=0 to @.$.#; @.$.k= word(z, k + 1) /*define array element. */
end /*k*/; return /*array starts at unity.*/
/*──────────────────────────────────────────────────────────────────────────────────────*/
show: parse arg $,z,_; do s=0 to @.$.#; _= strip(_ @.$.s) /*obtain the arguments. */
end /*s*/ /* [↑] build the list. */
say 'array' $": " _; return /*show the list; return*/
/*──────────────────────────────────────────────────────────────────────────────────────*/
test: parse arg $1,$2; do t=0 to max(@.$1.#, @.$2.#) /*obtain the arguments. */
if @.$1.t= @.$2.t then iterate /*create array list. */
say "***error*** arrays" $1 ' and ' $2 "aren't equal."
end /*t*/; return /* [↑] build the list. */

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#lang racket
(require math/matrix)
(define T matrix-transpose)
(define (convolution-matrix f m n)
(define l (matrix-num-rows f))
(for*/matrix m n ([i (in-range 0 m)] [j (in-range 0 n)])
(cond [(or (< i j) (>= i (+ j l))) 0]
[(matrix-ref f (- i j) 0)])))
(define (least-square X y)
(matrix-solve (matrix* (T X) X) (matrix* (T X) y)))
(define (deconvolve g f)
(define lg (matrix-num-rows g))
(define lf (matrix-num-rows f))
(define lh (+ (- lg lf) 1))
(least-square (convolution-matrix f lg lh) g))

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(define f (col-matrix [-3 -6 -1 8 -6 3 -1 -9 -9 3 -2 5 2 -2 -7 -1]))
(define h (col-matrix [-8 -9 -3 -1 -6 7]))
(define g (col-matrix [24 75 71 -34 3 22 -45 23 245 25 52 25 -67 -96 96 31 55 36 29 -43 -7]))
(deconvolve g f)
(deconvolve g h)

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#<array '#(6 1) #[-8 -9 -3 -1 -6 7]>
#<array '#(16 1) #[-3 -6 -1 8 -6 3 -1 -9 -9 3 -2 5 2 -2 -7 -1]>

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sub deconvolve (@g, @f) {
my \h = 1 + @g - @f;
my @m;
@m[^@g;^h] »+=» 0;
@m[^@g; h] »=« @g;
for ^h -> \j { for @f.kv -> \k, \v { @m[j+k;j] = v } }
(rref @m)[^h;h]
}
sub convolve (@f, @h) {
my @g = 0 xx + @f + @h - 1;
@g[^@f X+ ^@h] »+=« (@f X× @h);
@g
}
# Reduced Row Echelon Form simultaneous equation solver
# Can handle over-specified systems of equations (N unknowns in N + M equations)
sub rref (@m) {
@m = trim-system @m;
my ($lead, $rows, $cols) = 0, @m, @m[0];
for ^$rows -> $r {
return @m unless $lead < $cols;
my $i = $r;
until @m[$i;$lead] {
next unless ++$i == $rows;
$i = $r;
return @m if ++$lead == $cols;
}
@m[$i, $r] = @m[$r, $i] if $r != $i;
@m[$r] »/=» $ = @m[$r;$lead];
for ^$rows -> $n {
next if $n == $r;
@m[$n] »-=» @m[$r] »×» (@m[$n;$lead] // 0);
}
++$lead;
}
@m
}
# Reduce to N equations in N unknowns; a no-op unless rows > cols
sub trim-system (@m) {
return @m unless @m @m[0];
my (\vars, @t) = @m[0] - 1;
for ^vars -> \lead {
for ^@m -> \row {
@t.append: @m.splice(row, 1) and last if @m[row;lead];
}
}
while @t < vars and @m { @t.push: shift @m }
@t
}
my @h = (-8,-9,-3,-1,-6,7);
my @f = (-3,-6,-1,8,-6,3,-1,-9,-9,3,-2,5,2,-2,-7,-1);
my @g = (24,75,71,-34,3,22,-45,23,245,25,52,25,-67,-96,96,31,55,36,29,-43,-7);
.say for ~@g, ~convolve(@f, @h),'';
.say for ~@h, ~deconvolve(@g, @f),'';
.say for ~@f, ~deconvolve(@g, @h),'';

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object Deconvolution1D extends App {
val (h, f) = (Array(-8, -9, -3, -1, -6, 7), Array(-3, -6, -1, 8, -6, 3, -1, -9, -9, 3, -2, 5, 2, -2, -7, -1))
val g = Array(24, 75, 71, -34, 3, 22, -45, 23, 245, 25, 52, 25, -67, -96, 96, 31, 55, 36, 29, -43, -7)
val sb = new StringBuilder
private def deconv(g: Array[Int], f: Array[Int]) = {
val h = Array.ofDim[Int](g.length - f.length + 1)
for (n <- h.indices) {
h(n) = g(n)
for (i <- math.max(n - f.length + 1, 0) until n) h(n) -= h(i) * f(n - i)
h(n) /= f(0)
}
h
}
sb.append(s"h = ${h.mkString("[", ", ", "]")}\n")
.append(s"deconv(g, f) = ${deconv(g, f).mkString("[", ", ", "]")}\n")
.append(s"f = ${f.mkString("[", ", ", "]")}\n")
.append(s"deconv(g, h) = ${deconv(g, h).mkString("[", ", ", "]")}")
println(sb.result())
}

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func deconv(g: [Double], f: [Double]) -> [Double] {
let fs = f.count
var ret = [Double](repeating: 0, count: g.count - fs + 1)
for n in 0..<ret.count {
ret[n] = g[n]
let lower = n >= fs ? n - fs + 1 : 0
for i in lower..<n {
ret[n] -= ret[i] * f[n - i]
}
ret[n] /= f[0]
}
return ret
}
let h = [-8.0, -9.0, -3.0, -1.0, -6.0, 7.0]
let f = [-3.0, -6.0, -1.0, 8.0, -6.0, 3.0, -1.0, -9.0,
-9.0, 3.0, -2.0, 5.0, 2.0, -2.0, -7.0, -1.0]
let g = [24.0, 75.0, 71.0, -34.0, 3.0, 22.0, -45.0,
23.0, 245.0, 25.0, 52.0, 25.0, -67.0, -96.0,
96.0, 31.0, 55.0, 36.0, 29.0, -43.0, -7.0]
print("\(h.map({ Int($0) }))")
print("\(deconv(g: g, f: f).map({ Int($0) }))\n")
print("\(f.map({ Int($0) }))")
print("\(deconv(g: g, f: h).map({ Int($0) }))")

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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
}
}

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# Simple pretty-printer
proc pp {name nlist} {
set sep ""
puts -nonewline "$name = \["
foreach n $nlist {
puts -nonewline [format %s%g $sep $n]
set sep ,
}
puts "\]"
}
set h {-8 -9 -3 -1 -6 7}
set f {-3 -6 -1 8 -6 3 -1 -9 -9 3 -2 5 2 -2 -7 -1}
set g {24 75 71 -34 3 22 -45 23 245 25 52 25 -67 -96 96 31 55 36 29 -43 -7}
pp "deconv(g,f) = h" [1D deconvolve $g $f]
pp "deconv(g,h) = f" [1D deconvolve $g $h]
pp " conv(f,h) = g" [1D convolve $f $h]

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#import std
#import nat
band = pad0+ ~&rSS+ zipt^*D(~&r,^lrrSPT/~&ltK33tx zipt^/~&r ~&lSNyCK33+ zipp0)^/~&rx ~&B->NlNSPC ~&bt
deconv = lapack..dgelsd^\~&l ~&||0.!**+ band

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h = <-8.,-9.,-3.,-1.,-6.,7.>
f = <-3.,-6.,-1.,8.,-6.,3.,-1.,-9.,-9.,3.,-2.,5.,2.,-2.,-7.,-1.>
g = <24.,75.,71.,-34.,3.,22.,-45.,23.,245.,25.,52.,25.,-67.,-96.,96.,31.,55.,36.,29.,-43.,-7.>
#cast %eLm
test =
<
'h': deconv(g,f),
'f': deconv(g,h)>

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fn main() {
h := [f64(-8), -9, -3, -1, -6, 7]
f := [f64(-3), -6, -1, 8, -6, 3, -1, -9, -9, 3, -2, 5, 2, -2, -7, -1]
g := [f64(24), 75, 71, -34, 3, 22, -45, 23, 245, 25, 52, 25, -67, -96,
96, 31, 55, 36, 29, -43, -7]
println(h)
println(deconv(g, f))
println(f)
println(deconv(g, h))
}
fn deconv(g []f64, f []f64) []f64 {
mut h := []f64{len: g.len-f.len+1}
for n in 0..h.len {
h[n] = g[n]
mut lower := 0
if n >= f.len {
lower = n - f.len + 1
}
for i in lower..n {
h[n] -= h[i] * f[n-i]
}
h[n] /= f[0]
}
return h
}

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var deconv = Fn.new { |g, f|
var h = List.filled(g.count - f.count + 1, 0)
for (n in 0...h.count) {
h[n] = g[n]
var lower = (n >= f.count) ? n - f.count + 1 : 0
var i = lower
while (i < n) {
h[n] = h[n] - h[i]*f[n-i]
i = i + 1
}
h[n] = h[n] / f[0]
}
return h
}
var h = [-8, -9, -3, -1, -6, 7]
var f = [-3, -6, -1, 8, -6, 3, -1, -9, -9, 3, -2, 5, 2, -2, -7, -1]
var g = [24, 75, 71, -34, 3, 22, -45, 23, 245, 25, 52, 25, -67, -96, 96, 31, 55, 36, 29, -43, -7]
System.print(h)
System.print(deconv.call(g, f))
System.print(f)
System.print(deconv.call(g, h))

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var [const] GSL=Import("zklGSL"); // libGSL (GNU Scientific Library)
fcn dconv1D(f,g){
fsz,hsz:=f.len(), g.len() - fsz +1;
A:=GSL.Matrix(g.len(),hsz);
foreach n,fn in ([0..].zip(f)){ foreach rc in (hsz){ A[rc+n,rc]=fn } }
h:=A.AxEQb(g);
h
}

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f:=GSL.VectorFromData(-3,-6,-1,8,-6,3,-1,-9,-9,3,-2,5,2,-2,-7,-1);
g:=GSL.VectorFromData(24,75,71,-34,3,22,-45,23,245,25,52,25,-67,-96,96,31,55,36,29,-43,-7);
h:=dconv1D(f,g);
h.format().println();
f:=dconv1D(h,g);
f.format().println();

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fcn deconv(g,f){
flen, glen, delta:=f.len(), g.len(), glen - flen + 1;
result:=List.createLong(delta); // allocate list with space for items
foreach n in (delta){
e:=g[n];
lowerBound:=(if (n>=flen) n - flen + 1 else 0);
foreach i in ([lowerBound .. n-1]){ e-=result[i]*f[n - i]; }
result.append(e/f[0]);
}
result;
}

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h:=T(-8,-9,-3,-1,-6,7);
f:=T(-3,-6,-1,8,-6,3,-1,-9,-9,3,-2,5,2,-2,-7,-1);
g:=T(24,75,71,-34,3,22,-45,23,245,25,52,25,-67,
-96,96,31,55,36,29,-43,-7);
println(deconv(g, f) == h, " ", deconv(g, f));
println(deconv(g, h) == f, " ", deconv(g, h));