# solving equation system Classic List Threaded 8 messages Open this post in threaded view
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## solving equation system

 hello, it`s my first time using octave and I want to solve the following equation system: 29.3 = A*124.5^4+B*124.5^3+C*124.5^2+124.5*D+F, 126.7 = A*111^4+B*111^3+C*111^2+D*111+F, 236.4 = A*88.9^4+B*88.9^3+C*88.9^2+D*88.9+F, 284.7 = A*75.5^4+B*75.5^3+C*75.5^2+D*75.5+F, 315.5 = A*63^4+B*63^3+C*63^2+D*63+F }, I need to find the variables {A,B,C,D,F} to get a function like this: y(x)=a*x^4+b*x^3+c*x^2+d*x+e I Don`t know the syntax I have to use with octave to solve this equation system. many thanks in advance. Brigitte ------------------------------------------------------------- Octave is freely available under the terms of the GNU GPL. Octave's home on the web:  http://www.octave.orgHow to fund new projects:  http://www.octave.org/funding.htmlSubscription information:  http://www.octave.org/archive.html-------------------------------------------------------------
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## Re: solving equation system

 Looks simple. Define a coefficient matrix and solve it : octave:6> a=[1,124.5,124.5^2,124.5^3,124.5^4;1,111,111^2,111^3,111^4;1,88.9,88.9^2,88.9^3,88.9^4;1,75.5,75.5^2,75.5^3,75.5^4;1,63,63^2,63^3,63^4] a =    1.0000e+00   1.2450e+02   1.5500e+04   1.9298e+06   2.4026e+08    1.0000e+00   1.1100e+02   1.2321e+04   1.3676e+06   1.5181e+08    1.0000e+00   8.8900e+01   7.9032e+03   7.0260e+05   6.2461e+07    1.0000e+00   7.5500e+01   5.7002e+03   4.3037e+05   3.2493e+07    1.0000e+00   6.3000e+01   3.9690e+03   2.5005e+05   1.5753e+07 octave:7> f=[29.3,126.7,236.4,284.7,315.5]' f =    29.300   126.700   236.400   284.700   315.500 octave:8> a\f ans =    -2.6907e+02     2.9366e+01    -5.0372e-01     3.5786e-03    -1.0222e-05 I hope that someone can point out a shorter way to define the coefficient matrix since all its rows are of the form [1,x,x^2,x^3,x^4]. HTH On Tuesday 19 April 2005 12:15, Brigitte Diekhaus wrote: > hello, > > it`s my first time using octave and I want to solve the following equation > system: > > 29.3 = A*124.5^4+B*124.5^3+C*124.5^2+124.5*D+F, > 126.7 = A*111^4+B*111^3+C*111^2+D*111+F, > 236.4 = A*88.9^4+B*88.9^3+C*88.9^2+D*88.9+F, > 284.7 = A*75.5^4+B*75.5^3+C*75.5^2+D*75.5+F, > 315.5 = A*63^4+B*63^3+C*63^2+D*63+F }, > > I need to find the variables {A,B,C,D,F} > > to get a function like this: > > y(x)=a*x^4+b*x^3+c*x^2+d*x+e > > I Don`t know the syntax I have to use with octave to solve this equation > system. > > many thanks in advance. > > Brigitte > > > > ------------------------------------------------------------- > Octave is freely available under the terms of the GNU GPL. > > Octave's home on the web:  http://www.octave.org> How to fund new projects:  http://www.octave.org/funding.html> Subscription information:  http://www.octave.org/archive.html> ------------------------------------------------------------- ------------------------------------------------------------- Octave is freely available under the terms of the GNU GPL. Octave's home on the web:  http://www.octave.orgHow to fund new projects:  http://www.octave.org/funding.htmlSubscription information:  http://www.octave.org/archive.html-------------------------------------------------------------
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## Re: solving equation system

 Madhusudan Singh wrote: > I hope that someone can point out a shorter way to define the coefficient > matrix since all its rows are of the form [1,x,x^2,x^3,x^4]. > help vander > HTH > Regards, Dmitri. -- ------------------------------------------------------------- Octave is freely available under the terms of the GNU GPL. Octave's home on the web:  http://www.octave.orgHow to fund new projects:  http://www.octave.org/funding.htmlSubscription information:  http://www.octave.org/archive.html-------------------------------------------------------------
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## RE: solving equation system

 In reply to this post by Brigitte Diekhaus It looks like you're trying to fit a 4th-order polynomial to the data xx = [124.5; 111;    88.9;  75.5;  63  ]; yy = [ 29.3; 126.7; 236.4; 284.7; 315.5]; which you can do using polyfit coeffs = polyfit( xx, yy, 4 ) coeffs =    -1.0222e-05     3.5786e-03    -5.0372e-01     2.9366e+01    -2.6907e+02 -----Original Message----- From: Madhusudan Singh [mailto:[hidden email]] Sent: Tuesday, April 19, 2005 1:52 PM To: [hidden email] Cc: [hidden email] Subject: Re: solving equation system Looks simple. Define a coefficient matrix and solve it : octave:6> a=[1,124.5,124.5^2,124.5^3,124.5^4;1,111,111^2,111^3,111^4;1,88.9,88.9^2,88. 9^3,88.9^4;1,75.5,75.5^2,75.5^3,75.5^4;1,63,63^2,63^3,63^4] a =    1.0000e+00   1.2450e+02   1.5500e+04   1.9298e+06   2.4026e+08    1.0000e+00   1.1100e+02   1.2321e+04   1.3676e+06   1.5181e+08    1.0000e+00   8.8900e+01   7.9032e+03   7.0260e+05   6.2461e+07    1.0000e+00   7.5500e+01   5.7002e+03   4.3037e+05   3.2493e+07    1.0000e+00   6.3000e+01   3.9690e+03   2.5005e+05   1.5753e+07 octave:7> f=[29.3,126.7,236.4,284.7,315.5]' f =    29.300   126.700   236.400   284.700   315.500 octave:8> a\f ans =    -2.6907e+02     2.9366e+01    -5.0372e-01     3.5786e-03    -1.0222e-05 I hope that someone can point out a shorter way to define the coefficient matrix since all its rows are of the form [1,x,x^2,x^3,x^4]. HTH On Tuesday 19 April 2005 12:15, Brigitte Diekhaus wrote: > hello, > > it`s my first time using octave and I want to solve the following equation > system: > > 29.3 = A*124.5^4+B*124.5^3+C*124.5^2+124.5*D+F, > 126.7 = A*111^4+B*111^3+C*111^2+D*111+F, > 236.4 = A*88.9^4+B*88.9^3+C*88.9^2+D*88.9+F, > 284.7 = A*75.5^4+B*75.5^3+C*75.5^2+D*75.5+F, > 315.5 = A*63^4+B*63^3+C*63^2+D*63+F }, > > I need to find the variables {A,B,C,D,F} > > to get a function like this: > > y(x)=a*x^4+b*x^3+c*x^2+d*x+e > > I Don`t know the syntax I have to use with octave to solve this equation > system. > > many thanks in advance. > > Brigitte > > > > ------------------------------------------------------------- > Octave is freely available under the terms of the GNU GPL. > > Octave's home on the web:  http://www.octave.org> How to fund new projects:  http://www.octave.org/funding.html> Subscription information:  http://www.octave.org/archive.html> ------------------------------------------------------------- ------------------------------------------------------------- Octave is freely available under the terms of the GNU GPL. Octave's home on the web:  http://www.octave.orgHow to fund new projects:  http://www.octave.org/funding.htmlSubscription information:  http://www.octave.org/archive.html------------------------------------------------------------- ------------------------------------------------------------- Octave is freely available under the terms of the GNU GPL. Octave's home on the web:  http://www.octave.orgHow to fund new projects:  http://www.octave.org/funding.htmlSubscription information:  http://www.octave.org/archive.html-------------------------------------------------------------
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## Re: solving equation system

 In reply to this post by M Singh > I hope that someone can point out a shorter way to define the coefficient > matrix since all its rows are of the form [1,x,x^2,x^3,x^4]. here, a is a vandermonde matrix a=vander([124.5 111 88.9 75.5 63]); octave:1> a=vander([124.5 111 88.9 75.5 63]) a =    2.4026e+08   1.9298e+06   1.5500e+04   1.2450e+02   1.0000e+00    1.5181e+08   1.3676e+06   1.2321e+04   1.1100e+02   1.0000e+00    6.2461e+07   7.0260e+05   7.9032e+03   8.8900e+01   1.0000e+00    3.2493e+07   4.3037e+05   5.7002e+03   7.5500e+01   1.0000e+00    1.5753e+07   2.5005e+05   3.9690e+03   6.3000e+01   1.0000e+00 you need to flip it to choose the same coordinate system as you did: a=fliplr(a); > octave:6> > a=[1,124.5,124.5^2,124.5^3,124.5^4;1,111,111^2,111^3,111^4;1,88.9,88.9^2,88.9^3,88.9^4;1,75.5,75.5^2,75.5^3,75.5^4;1,63,63^2,63^3,63^4] > a = > >    1.0000e+00   1.2450e+02   1.5500e+04   1.9298e+06   2.4026e+08 >    1.0000e+00   1.1100e+02   1.2321e+04   1.3676e+06   1.5181e+08 >    1.0000e+00   8.8900e+01   7.9032e+03   7.0260e+05   6.2461e+07 >    1.0000e+00   7.5500e+01   5.7002e+03   4.3037e+05   3.2493e+07 >    1.0000e+00   6.3000e+01   3.9690e+03   2.5005e+05   1.5753e+07 eric. ------------------------------------------------------------- Octave is freely available under the terms of the GNU GPL. Octave's home on the web:  http://www.octave.orgHow to fund new projects:  http://www.octave.org/funding.htmlSubscription information:  http://www.octave.org/archive.html-------------------------------------------------------------
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## Re: solving equation system

 In reply to this post by M Singh    I hope that someone can point out a shorter way to define the coefficient    matrix since all its rows are of the form [1,x,x^2,x^3,x^4]. You are right---there's a shorter way. That's a form of VanDerMonde matrix: c =   124.500   111.000    88.900    75.500    63.000 octave:67> vander (c) ans =    2.4026e+08   1.9298e+06   1.5500e+04   1.2450e+02   1.0000e+00    1.5181e+08   1.3676e+06   1.2321e+04   1.1100e+02   1.0000e+00    6.2461e+07   7.0260e+05   7.9032e+03   8.8900e+01   1.0000e+00    3.2493e+07   4.3037e+05   5.7002e+03   7.5500e+01   1.0000e+00    1.5753e+07   2.5005e+05   3.9690e+03   6.3000e+01   1.0000e+00 vander (c)\b  does indeed give the same result as the full matrix    -1.0222e-05     3.5786e-03    -5.0372e-01     2.9366e+01    -2.6907e+02 ------------------------------------------------------------- Octave is freely available under the terms of the GNU GPL. Octave's home on the web:  http://www.octave.orgHow to fund new projects:  http://www.octave.org/funding.htmlSubscription information:  http://www.octave.org/archive.html-------------------------------------------------------------