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56 lines
1.5 KiB
56 lines
1.5 KiB
/*Extended Yet Another Curve Fitting Solution (The poor man's RMA)
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An extension of yacfs.mod adding a Weight parameter:
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When set to 1 the model produces best fit by least squares with all error in y and none in x (YonX);
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When set to zero the model produces best fit by least squares with all error in x and none in y (XonY);
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When set to 0.5 the model assumes equal error in x and y producing results similar to fitting by Reduced Major Axis Analysis.
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Nigel_Galloway@operamail.com
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November 5th., 2009
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*/
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set Sample;
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param Sx {z in Sample};
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param Sy {z in Sample};
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param Weight := 0.5;
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var a;
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var b;
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var p;
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var q;
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XonY1 :sum{z in Sample} q*Sy[z]*Sy[z] + sum{z in Sample} p*Sy[z] = sum{z in Sample} Sy[z]*Sx[z];
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XonY2 :sum{z in Sample} q*Sy[z] + sum{z in Sample} p = sum{z in Sample} Sx[z];
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YonX1 :sum{z in Sample} a*Sx[z]*Sx[z] + sum{z in Sample} b*Sx[z] = sum{z in Sample} Sy[z]*Sx[z];
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YonX2 :sum{z in Sample} a*Sx[z] + sum{z in Sample} b = sum{z in Sample} Sy[z];
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solve;
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param W := Weight*a + (1-Weight)*(1/q);
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printf "\nbest linear fit is:\n\ty = %f %s %fx\n\n", b*Weight - (1-Weight)*(p/q), if W < 0 then "-" else "+", abs(W);
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data;
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param:
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Sample: Sx Sy :=
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1 0 1
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2 0.5 0.9
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3 1 0.7
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4 1.5 1.5
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5 1.9 2
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6 2.5 2.4
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7 3 3.2
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8 3.5 2
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9 4 2.7
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10 4.5 3.5
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11 5 1
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12 5.5 4
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13 6 3.6
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14 6.6 2.7
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15 7 5.7
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16 7.6 4.6
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17 8.5 6
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18 9 6.8
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19 10 7.3
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;
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end;
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