Re: Partial derviatives in mathematica
- To: mathgroup at smc.vnet.net
- Subject: [mg95777] Re: Partial derviatives in mathematica
- From: xareon at gmail.com
- Date: Tue, 27 Jan 2009 06:57:23 -0500 (EST)
- References: <glk1na$los$1@smc.vnet.net> <glk80p$o86$1@smc.vnet.net>
On Jan 26, 12:49 pm, Jean-Marc Gulliet <jeanmarc.gull... at gmail.com> wrote: > In article <glk1na$lo... at smc.vnet.net>, xar... at gmail.com wrote: > > [snip] > > > jacobian[{x_, y_}] = Transpose[{\[PartialD]x F[{x, y}], \[PartialD]y = F > > [{x, y}]}]; > > > Mathematica's kernel warns me with this message when i try to insert > > it: > > > Code: > > > Syntax::sntxf: "jacobian[{x_, y_}] = Transpose[{" cannot be followed > > by > > "\[PartialD]x F[{x, y}], \[PartialD]y F[{x, y}]}];". > > [snip] > > On my system (v6.0), I have got the more meaningful message: > > "Derivative::novar: x cannot be interpreted. A partial derivative \ > requires a subscript differentiation variable. >>" > > The variable must passed as a *subscript* (shortcut Ctrl+-, control + > dash keys) to the symbol partial d. > > In[1]:= F[{x_, y_}] = {f1[{x, y}], f2[{x, y}]}; > > In[2]:= jacobian[{x_,y_}]=Transpose[{\!\( > \*SubscriptBox[\( \), \(x\)]\ \(F[{x, y}]\)\),\!\( > \*SubscriptBox[\( \), \(y\)]\ \(F[{x, y}]\)\)}]; > > (* jacobian[{x_, y_}] = Transpose[{D[F[{x, y}], x], D[F[{x, y}], y]}]; = *) > > In[3]:= MatrixForm[jacobian[{x, y}]] > > Out[3]//MatrixForm= > > ({1, 0}) ({0, 1}) > f1 [{x, y}] f1 [{x, y}] > > ({1, 0}) ({0, 1}) > f2 [{x, y}] f2 [{x, y}] > > Regards, > --Jean-Marc thank you for your support, with your hints i've finally managed it to work. What does it mean that i get this output? In[46]:= NewtonSystem[{60, 0.0001251648904560967}, 30]; F[{60, 0.000125165}]={-0.0798194, -32172.1} Inverse::luc: Result for Inverse of badly conditioned matrix 8 {{-0.0138889, -2725.54}, {-2725.54, -9.88747 10 }} may contain significant numerical errors. F[{61.3904, 0.0000887939}]={0.0295066, 20324.7} Inverse::luc: Result for Inverse of badly conditioned matrix 9 {{-0.0132669, -4474.06}, {-4474.06, -2.56154 10 }} may contain significant numerical errors. F[{60.2913, 0.0000986483}]={0.00312061, 3127.01} Inverse::luc: Result for Inverse of badly conditioned matrix 9 {{-0.013755, -3907.89}, {-3907.89, -1.91112 10 }} may contain significant numerical errors. General::stop: Further output of Inverse::luc will be suppressed during this calculation. F[{59.7233, 0.000101446}]={0.000280961, 135.783} -7 F[{59.7225, 0.000101523}]={1.55248 10 , 0.153813} -13 -7 F[{59.7225, 0.000101524}]={7.17371 10 , 3.37372 10 } I can't understand the error i'm getting: Inverse::luc: Result for Inverse of badly conditioned matrix It seems like a warning, is it relevant?