Jacobian of a Matrix

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Jacobian of a Matrix - salvomic - 05-15-2015 03:20 PM

hi all,
here there is a CAS program to calc the Jacobian of a Matrix.

Input: [f(1), f(2), ...], [x,y,...]

Enjoy!

Salvo Micciché

Code:

#cas
jacob(args):=
// Jacobian Matrix by Salvo Micciché
// input vectorial expression, vector of variables
BEGIN
local argv, argc, mat, f, var, fn, j, k,  gr, vd;
argv:=[args];
argc:=size(argv);
IF argc !=2 THEN
return "Input:[f1(x),f1(y),f1(z)...], [x,y,z,...]"; 
ELSE
f:=argv(1);
var:=argv(2);
fn:=size(f);
vd:=size(var);
mat:=makemat(0,fn,vd);
FOR j FROM 1 TO fn DO // gradients
gr:=grad(f(j),var);
FOR k FROM 1 TO vd DO // items
mat[j,k]:=gr(k);
END; // for k
END; // for j
return mat;
END; // if-else

END;
#end


RE: Jacobian of a Matrix - Rudi - 03-25-2017 09:51 AM

hi all,
I've improved the Code of the Jacobian Matrix by salvomic - 15.05.2015 21:20

Enjoy!

Rudi Steeger

For Example:

jacob(grad([e^(x*y^2)*sin(z)],[x,y,z]),[x,y,z]);

The same Example with the new Feature in this Code:
jacob2([e^(x*y^2)*sin(z)],[x,y,z])
==>
[[[y^4*e^(x*y^2)*sin(z)],[2*y*(x*y^2+1)*e^(x*y^2)*sin(z)],[y^2*cos(z)*e^(x*y^2)]],[[2*y*(x*y^2+1)*e^(x*y^2)*sin(z)],[2*x*(2*x*y^2+1)*e^(x*y^2)*sin(z)],[2*x*y*cos(z)*e^(x*y^2)]],[[y^2*cos(z)*e^(x*y^2)],[2*x*y*cos(z)*e^(x*y^2)],[-e^(x*y^2)*sin(z)]]];

Code:
#cas
jacob2(args):=
// Jacobian Matrix by Salvo Micciché
// input vectorial expression, vector of variables
BEGIN
local argv, argc, mat, f, var, fn, fg, j, k, gr, vd;
argv:=args;
argc:=size(argv);
IF argc !=2 THEN
return "Input:[f1(x),f1(y),f1(z)...], [x,y,z,...]";
ELSE
f:=argv(1);
var:=argv(2);
fn:=size(f);
vd:=size(var);
IF fn:=1 THEN
fg:=grad(f(1),var);
f:=fg;
fn:=size(f);
END;
mat:=makemat(0,fn,vd);
FOR j FROM 1 TO fn DO // gradients
gr:=grad(f(j),var);
FOR k FROM 1 TO vd DO // items
mat[j,k]:=factor(gr(k));
END; // for k
END; // for j
return mat;
END; // if-else
END;
#end

RE: Jacobian of a Matrix - Han - 03-25-2017 10:23 AM

A slightly shorter program:

Code:

#cas
jacob(args):=
begin
local argv, argc, mat, f, var, fn, j, k,  gr, vd;
argv:=[args];
argc:=size(argv);
IF argc !=2 THEN
return "Input:[f1(x1,...,xn),...,fm(x1,...,xn)], [x1,...,xn]"; 
ELSE
return transpose(diff(argv[1],argv[2]));
END;
end;
#end

Basically, the Jacobian is: transpose(diff([f1,f2,...,fm], [x1,x2,...,xn]))

RE: Jacobian of a Matrix - Arno K - 04-09-2018 05:16 PM

I improved Han's program a little bit, now you can enter what you desire, with and without substitution:
Code:
#cas
 jacob(args):=
 begin
 local argv,argc,mat,f;
 LOCAL var,fn,j,k,gr,vd;
 argv:=[args];
 argc:=size(argv);
 IF argc == 3 THEN
   return subst(transpose(diff(argv[1],argv[2])),argv[3]);
  END;
 IF argc == 2 THEN
   return transpose(diff(argv[1],argv[2]));
  END;
 return "Input:[f1(x1,...,xn),...,fm(x1,...,xn)], [x1,...,xn][,[x1=a1,...xn=an]]"; 
 end;
#end
For its usage see the following picture.
Hope that helps
Arno