Jacobian-matrix-generator

Input: Takes n dimension function and variables as input along with the point(vector) at which the jacobian is to be calculated.

Output: outputs the jacobian matrix along with its determinant.

General form of the function:

f:Rn->Rm

f(x1, x2, x3, ..., xn) = (f1, f2, f3, ..., fm)

n = dimension of domain

m = dimension of co-domain

variables = {x1, x2, x3, ..., xn}

vector components = {f1, f2, f3, ..., fm}

order of jacobian matrix = m * n

Jacobian matrix:

| df1/dx1 df1/dx2 ... df1/dxn |
| df2/dx1 df2/dx2 ... df2/dxn |
| .       .       ... .       |
| .       .       ... .       |
| dfm/dx1 dfm/dx2 ... dfm/dxn | m * n

Example1:

fuction: f(x) = sin(cos(x)*sin(x))+1

Enter the dimension of the domain: 1

Enter the dimension of the codomain: 1

Enter the function: sin(sin(x)*cos(x))+1

Enter the variables symbols: x

Enter the point: 1

Jacobian matrix:

-0.373873

Determinant of the Jacobian matrix: -0.373873

Example2:

function: f(x, y) = (x^4+3y^2x, 5y^2-2x*y+1)

Enter the dimension of the domain: 2

Enter the dimension of the codomain: 2

Enter the function f1: x^4+3y^2x

Enter the function f2: 5y^2-2x*y+1

Enter the variables symbols: x y

Enter the point: 1 2

Jacobian matrix:

16 12 
-4 18 

Determinant of the Jacobian matrix: 336