Section 2: Running multiexp

1. Write a file with instructions for creating fcn (see section 3)
2. run:
   multiexp fcn_file_name
3. write commands at the minuit prompt (see section 4)

Section 3: FCN file

scale = scale_value

where scale_value is the distance (in ps) from consecutive bins. For example:
scale = 2.44


maxdelta = max_delta_value
The F can be displaced with respect to its IRF. The program looks for the best fit displacing the functions by an amount δ, less than max_delta_value in ps.

lambda_corr λ0 c0 c1 c2 ...

The measured amplitude can be dependent on wave length λ. lambda_corr defines a correction for this. The amplitude will be multiplied by:
c₀ + c₁(λ-λ₀) + c₂*(λ-λ₀)² + ...

save data "filename"

The program can output some data on a file. Writing to files is performed when the user calls the standard command at the minuit prompt. But the definition of the file names must be performed in FCN file. data can be graph, tau, gpfile. By default, files are not saved; they are not saved also if file name is a null string "". graph generates a file with one block for each F, with four columns: λ, F value, best fit, IRF. tau contains all the parameter values. gpfile is a gnuplot command file, that can read "tau" and generate a graph with the DAS.

load decay "filename" [ (from-to) ] lambda time

load IRF "filename" [ (from-to) ]

These commands load the F and the IRF. Since each decay can have a different IRF, a load IRF command must be issued before all the load decay" that have that IRF. For example:
load IRF "irfA.txt"
load decay "decay1_irfA.txt" 650 100
load decay "decay2_irfA.txt" 670 100
load decay "decay3_irfA.txt" 690 100
load IRF "irfB.txt"
load decay "decay1_irfB.txt" 650 100
load decay "decay2_irfB.txt" 670 100
load decay "decay3_irfB.txt" 690 100


The first group of decays has been measured with a given setup, and its IRF has been saved as "irfA.txt". Then, a second group of measures has been performed, with a different setup, and its IRF has been saved as "irfB.txt".

The (from-to) can be optionally appended to the command, in order to define which lines must be processed.

For "decay" measurements, "lambda" and "time" must be defined. "lambda" will be used for lambda_corr (if any), while "time" will be used to normalize the resulting A.

The files with data must contain a column of numbers, representin the counts in each bin. Negative values are excluded from the fit. It's worth noting that a poissonian error is assumed for every count in a bin, and is evaluated as the square root of the counts. So do not normalize or multiply the counts by any amount.

basename "base_name"

has effect on all the subsequent load commands. It adds a base name to the file name. For example:
basename "data/"
load decay "d1.txt" 680 10
loads the file "data/d1.txt". This command can be issued anywhere; it has effect until another basename command is issued. To stop the effect of a basename command, use basename ""

Section 4: Minuit commands

tau1

decay time constants. Adding a tauN adds an exponential to the fit, along with all the A, b, δ

tauR

decay time of the fluorophore used to measure the IRF. It should be fixed if known. If it is not present, it is assumed 0.

A3-4

amplitude of 4th decay, with tau4, in 3rd fluorescence measurement.

b3

background of 3rd fluorescence measurement.

delta2

displacement of 2nd fluorescence measurement with respect to IRF.

null4

this parameter is accepted but not used by fcn

When a new tauN is defined, an exponential is added to the fitting function. It is not necessary to define A, b and δ. If they are defined, they can be fixed to any value, and error evaluation can be performed. Anyhow, their value is always calculated, also if the parameter doesn't appear anywhere.

If a parameter has been defined but it is no more needed, it can be overwritten with a new parameter. For example, if parameter 3 is A2-3, you can do:
> param
> 3 'A2-1' 0.02 0.01
> (remember to press <ENTER> in this line before writing other commands)


If no other parameter is needed, minuit gives no way to delete it. Multiexp gives a way to make it harmless: it must be overwritten with a new parameter called 'null1' or similar; the value is not important; moreover, the parameter must be set 'fix'. For example, if parameter 3 is no more needed:
> param
> 3 'null1' 2 1
> (remember to press <ENTER> in this line before writing other commands)
> fix 3


Multiexp accepts parameters like 'null1', 'null2' and so on, and neglects their value; setting them 'fix' prevents minuit from performing any calculation on them.

The parameters τ must be always different from one another. If you define two of them with the same value, you will likely obtain a "singular matrix" error, that means you have a manifold of solutions.

The parameters A are the amplitude of the exponential function in which the measured function is decomposed, with a normalization constant. The normalization constant contains the following terms:

• integration time
• wave length dependent sensitivity

The user should never define UP with "set err 13.5" or similar. The correct value of UP is defined by the program in order to give the 68% confidence.

The command standard performs the following operations:

• saves some data, as defined by save command in FCN file.
• runs make in a shell.