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CalculateInverse

Guides

  • Guide to ZigangPan`CalculateInverse`

Symbols

  • FormulaToCPFunction
  • FormulaToFunction
  • inversefunction
  • updatenames
ZigangPan`CalculateInverse`
inversefunction
​
inversefunction
[f,xc,xt,xt0]
{g,yt,yt0}=inversefunction[f,xc,xt,xt0], where
f
is a n (n>0) dimensional pure function with n+m number of independent variables which are listed in
xt
,and
xc
is a sublist of n variables of
xt
that we would like to inverse
f
with respect to.
xt0
is the value of
xt
that we are interested in, around which the inverse function is sought.
xt0
takes the default value of
Table
[0,{i,
Length
[xt]}]
if it is not specified. We assume that the inverse function exists.
y=f[xt]
. The return of the function is {
g
,
yt
,
yt0
}, where
g
is a pure function with n+m variables, where the first n variables are
y
and the rest of m variables are those in
xt
but not in
xc
listed in order of
xt
, and
yt
is the list of independent variables in
g
, and
yt0
is the value of
yt
that we are interested in, around which the inverse function is valid.
​
Examples  
(1)
Basic Examples  
(1)
In[1]:=
fx={x1+x2+x4,x2+x3+x4,x3+x4^2-x2};xc={x1,x2,x3};xt={x1,x2,x3,x4};
In[2]:=
f=
FormulaToFunction
[xt,fx]
Out[2]=
Function[{x1,x2,x3,x4},{x1+x2+x4,x2+x3+x4,-x2+x3+
2
x4
}]
In[3]:=
{g,yt,yt0}=
inversefunction
[f,xc,xt]
Out[3]=
Function{y1,y2,y3,x4},y1-y2+
1
2
(-x4-
2
x4
+y2+y3),-x4+y2+
1
2
(x4+
2
x4
-y2-y3),
1
2
(-x4-
2
x4
+y2+y3),{y1,y2,y3,x4},{0,0,0,0}
In[4]:=
Simplify[Apply[g,Join[Apply[f,xt],yt〚4;;4〛]]]
Out[4]=
{x1,x2,x3}
SeeAlso
InverseFunction
 
▪
InverseFunctions
RelatedGuides
▪
Guide to ZigangPan`CalculateInverse`
""

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