| Model Curve
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MODEL curvea ! linear regressions for L1 and L (infinity) norms |
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SET |
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nopts = {1 .. 19}; |
! number of data points |
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DATA |
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xvalue[nopts] << "xfile.dat", |
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yvalue[nopts] << "yfile.dat"; |
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VARIABLES |
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a free, |
! coefficients in |
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b free, |
! linear relation |
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maxdev, |
! maximum deviation variable |
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slack[nopts], |
! negative error |
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surp[nopts]; |
! positive error |
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OBJECTIVE |
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MINIMIZE sumdev = sum{i in nopts} (slack[i] + surp[i]); |
! minimise L1 norm |
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! MINIMIZE minmax = maxdev; |
! minimise L (infinity) norm |
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CONSTRAINTS |
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dev{i in nopts} : xvalue[i]*b + a + slack[i] |
! linear relation |
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- surp[i] = yvalue[i], |
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ula{i in nopts} : maxdev-slack[i] >= 0, |
! maximum deviation >= absolute deviations |
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ulb{i in nopts} : maxdev-surp[i] >= 0; |
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END MODEL |
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solve curvea; |
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print solution for curvea >> "curvea.sol"; |
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quit; |
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MODEL curveb ! quadratic regressions for L1 and L (infinity) norms |
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SET |
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nopts = {1 .. 19}; |
! number of data points |
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DATA |
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xvalue[nopts] << "xfile.dat", |
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yvalue[nopts] << "yfile.dat"; |
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VARIABLES |
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a free, |
! coefficients |
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b free, |
! in quadratic |
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c free, |
! relation |
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maxdev, |
! maximum deviation variable |
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slack[nopts], |
! negative error |
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surp[nopts]; |
! positive error |
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OBJECTIVE |
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! MINIMIZE sumdev = sum{i in nopts} (slack[i] + surp[i]); |
! minimise L1 norm |
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MINIMIZE minmax = maxdev; |
! minimise L (infinity) norm |
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CONSTRAINTS |
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dev{i in nopts} : (xvalue[i]*xvalue[i])*c + xvalue[i]*b |
! quadratic relation |
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+ a + slack[i] - surp[i] = yvalue[i], |
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ula{i in nopts} : maxdev-slack[i] >= 0, |
! maximum deviation >=absolute deviations |
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ulb{i in nopts} : maxdev-surp[i] >= 0; |
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END MODEL |
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solve curveb; |
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print solution for curveb >> "curveb.sol"; |
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quit; |
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xfile.dat |
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[0.0,0.5,1.0,1.5,1.9,2.5,3.0,3.5,4.0,4.5,5.0,5.5,6.0,6.6,7.0,7.6,8.5,9.0,10.0] |
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yfile.dat |
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[1.0,0.9,0.7,1.5,2.0,2.4,3.2,2.0,2.7,3.5,1.0,4.0,3.6,2.7,5.7,4.6,6.0,6.8,7.3] |
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