Hi, Rooters:
I have met some problems in my fitting in which the Minuit is used. I really need you help!
my questions are:
1, the output information is copied below. Does my fitting work correctly judged by these output?
2,what is the meaning of “ERR MATRIX NOT POS-DEF” mentioned in the output information ?
3, what is the meaning of " PARAMETER CORRELATION COEFFICIENTS" matrix in the end of the utput?
The values of GLOBAL are very close to 1. what does this imply?
4, why “HESSE” appears in the output? In my code, I haven’t execute the HESSE command. Does it execute automatically after thee MIGRAD command?
5, the most important things: I am seriously interested the parameter errors.
For example, my fitting function is y = f(x,C0,C1…C6), where C0,C1…C6 is 7 parameters.
I want to calculated the error of y. My simple idea is using the errors of C0,C1…C6 given by HESSE to get the propagation error of y。That is: y_Error= sqrt[(dy/dC0)^2Err_C0^2+…(dy/dC6)^2Err_C6^2], in which dy/dCi(i=0,6) is the partial derivative of y respect to Ci.
Is it correct ? Do I need to consider the parameter correlation?
Thank you!!
Ps:The output information:
PARAMETER DEFINITIONS:
NO. NAME VALUE STEP SIZE LIMITS
1 C0 1.91712e+01 1.00000e-02 no limits
2 C1 -3.63544e-02 1.00000e-02 no limits
3 C2 -1.05223e+01 1.00000e-02 no limits
4 C3 -3.63538e-02 1.00000e-02 no limits
5 C4 9.66959e+02 1.00000e-02 no limits
6 C5 4.46961e-01 1.00000e-02 no limits
7 C6 1.03263e+01 1.00000e-02 no limits
** 1 **SET PRINT 2
** 2 **SET STR 1
NOW USING STRATEGY 1: TRY TO BALANCE SPEED AGAINST RELIABILITY
** 3 **MIGRAD 1e+04 0.1
FIRST CALL TO USER FUNCTION AT NEW START POINT, WITH IFLAG=4.
START MIGRAD MINIMIZATION. STRATEGY 1. CONVERGENCE WHEN EDM .LT. 1.00e-04
FCN=4.1513 FROM MIGRAD STATUS=INITIATE 32 CALLS 33 TOTAL
EDM= unknown STRATEGY= 1 NO ERROR MATRIX
EXT PARAMETER CURRENT GUESS STEP FIRST
NO. NAME VALUE ERROR SIZE DERIVATIVE
1 C0 1.91712e+01 1.00000e-02 1.00000e-02 4.82435e-05
2 C1 -3.63544e-02 1.00000e-02 1.00000e-02 3.02295e-02
3 C2 -1.05223e+01 1.00000e-02 1.00000e-02 4.82445e-05
4 C3 -3.63538e-02 1.00000e-02 1.00000e-02 -1.60345e-02
5 C4 9.66959e+02 1.00000e-02 1.00000e-02 -3.48501e-07
6 C5 4.46961e-01 1.00000e-02 1.00000e-02 -2.02234e-04
7 C6 1.03263e+01 1.00000e-02 1.00000e-02 2.98532e-05
NO ERROR MATRIX
FCN=4.1513 FROM MIGRAD STATUS=PROGRESS 48 CALLS 49 TOTAL
EDM=1.94851e-08 STRATEGY= 1 NO ERROR MATRIX
EXT PARAMETER CURRENT GUESS STEP FIRST
NO. NAME VALUE ERROR SIZE DERIVATIVE
1 C0 1.91712e+01 1.00000e-02 -3.59611e-05 2.90554e-07
2 C1 -3.63545e-02 1.00000e-02 -5.60077e-08 -5.31095e-02
3 C2 -1.05223e+01 1.00000e-02 -3.59606e-05 2.88442e-07
4 C3 -3.63537e-02 1.00000e-02 9.82328e-08 2.98281e-02
5 C4 9.66961e+02 1.00000e-02 1.94464e-03 -8.18504e-07
6 C5 4.47015e-01 1.00000e-02 5.35534e-05 -5.22694e-05
7 C6 1.03263e+01 1.00000e-02 -1.90321e-05 7.40282e-05
MIGRAD MINIMIZATION HAS CONVERGED.
MIGRAD WILL VERIFY CONVERGENCE AND ERROR MATRIX.
START COVARIANCE MATRIX CALCULATION.
EIGENVALUES OF SECOND-DERIVATIVE MATRIX:
-7.6801e-06 1.2667e-04 4.0675e-04 1.7475e-02 9.2812e-02 7.2952e-01 6.1597e+00
MINUIT WARNING IN HESSE
============== MATRIX FORCED POS-DEF BY ADDING 0.006167 TO DIAGONAL.
FCN=4.1513 FROM MIGRAD STATUS=CONVERGED 98 CALLS 99 TOTAL
EDM=2.788e-08 STRATEGY= 1 ERR MATRIX NOT POS-DEF
EXT PARAMETER APPROXIMATE STEP FIRST
NO. NAME VALUE ERROR SIZE DERIVATIVE
1 C0 1.91712e+01 8.11910e+00 9.78461e-04 2.90549e-07
2 C1 -3.63545e-02 1.28110e-02 1.54261e-06 -5.31678e-02
3 C2 -1.05223e+01 8.11661e+00 9.78444e-04 2.88443e-07
4 C3 -3.63537e-02 2.24270e-02 2.80509e-06 2.97700e-02
5 C4 9.66961e+02 7.29320e+02 4.61082e-02 -8.18504e-07
6 C5 4.47015e-01 1.94744e+00 5.83193e-04 -5.25352e-05
7 C6 1.03263e+01 7.75123e+00 9.04888e-04 7.42565e-05
EXTERNAL ERROR MATRIX. NDIM= 25 NPAR= 7 ERR DEF=1
6.592e+01 -3.229e-03 -6.050e+01 8.384e-04 -6.482e+01 -1.179e+00 7.227e-01
-3.229e-03 1.641e-04 -1.428e-03 2.480e-04 -9.375e-01 7.379e-03 9.580e-03
-6.050e+01 -1.428e-03 6.588e+01 3.689e-03 -7.289e+01 -1.115e+00 8.052e-01
8.384e-04 2.480e-04 3.689e-03 5.030e-04 9.470e-01 -7.405e-03 -9.679e-03
-6.482e+01 -9.375e-01 -7.289e+01 9.470e-01 5.319e+05 -4.179e+02 4.256e+03
-1.179e+00 7.379e-03 -1.115e+00 -7.405e-03 -4.179e+02 3.793e+00 4.158e+00
7.227e-01 9.580e-03 8.052e-01 -9.679e-03 4.256e+03 4.158e+00 6.008e+01
ERR MATRIX NOT POS-DEF
PARAMETER CORRELATION COEFFICIENTS
NO. GLOBAL 1 2 3 4 5 6 7
1 0.99411 1.000 -0.031 -0.918 0.005 -0.011 -0.075 0.011
2 0.99412 -0.031 1.000 -0.014 0.863 -0.100 0.296 0.096
3 0.99410 -0.918 -0.014 1.000 0.020 -0.012 -0.071 0.013
4 0.99365 0.005 0.863 0.020 1.000 0.058 -0.170 -0.056
5 0.99453 -0.011 -0.100 -0.012 0.058 1.000 -0.294 0.753
6 0.96303 -0.075 0.296 -0.071 -0.170 -0.294 1.000 0.275
7 0.99447 0.011 0.096 0.013 -0.056 0.753 0.275 1.000
ERR MATRIX NOT POS-DEF