• file name and/or its path may contain blank spaces
• comments beginning with an exclamation point (!) are ignored
• non-numeric lines are treated as blank lines
• line terminator (the character or sequence of characters that marks the end of a line of text) can be CR (usually Macintosh files), LF (usually Unix files), or CRLF (usually Windows files). All lines in a given file must have the same terminator.
• the different values (columns) in a line can be separated by spaces, tabs, commas, semicolons, or a combination of them

• lines with fewer columns are treated as blank lines
• any additional columns are ignored
• $\left( h_{\mathrm{applied}},h_{\mathrm{reversal}} \right)$ play the role of the independent variables $\left( x,y \right)$, also known as explanatory variables, input, predictor, regressor, feature, etc.
• magnetic_moment plays the role of the dependent variable $f$, also known as output, outcome, response, etc.

• file can have any of the PMC / Lakeshore files formats
• header lines are not mandatory
• each FORC curve must be preceded by the drift field measurement and a blank line
• each FORC must be followed by a blank (non-numeric) line
• the first line from a FORC is the reversal point
• the first FORC does not need to contain a single point

• similar with the PMC format, but without the drift field measurements
• each FORC must be followed by a blank (non-numeric) line
• the first line from a FORC is the reversal point

• the first three columns represent the $\left( x,y,z \right)$ Cartesian coordinates
• blank and non-numeric lines are ignored

• the first three columns represent the $\left( x,y,z \right)$ Cartesian coordinates
• blank and non-numeric lines are ignored

• atol = absolute tolerance
• rtol = tolerance relative to the size of the smallest $h_{\mathrm{applied}},h_{\mathrm{reversal}}$ interval

This feature is useful in the case of missing data or of large gaps in the input data.

A statistic regarding the values of the increment $dx$ on each individual curve and respectively of the increment $dy$ between curves is provided in the Command Prompt window.

This feature is useful in the case of "very close" points in the input data.

The merging procedure may return points that were not input points, and it can even have a "smoothing effect".

The first point corresponding to the smallest value of the $x$ ($h_{\mathrm{applied}}$) coordinate on each individual FORC is not modified.

Smoothing is performed with a local regression around each input point, the size of each neighborhood being chosen so that the neighborhood contains at most nn_iFORC+1 data points.

The individually smoothed curves will be subsequently smoothed with respect to both $h_{\mathrm{applied}}$ and $h_{\mathrm{reversal}}$, in the processing step.

$\;\overline{y}=\dfrac{y}{\mathrm{noncircularity}}$ .

Scale factor changes the shape of the neighborhood, considering the points lying on an ellipse centered at the given point to be equidistant from the given point, and it is useful when the variables have different scales.

After smoothing all the data are transformed back to their original state.

Winsorized mean and standard deviation are robust scale estimators in that extreme values of a variable are discarded (the smallest and largest 5% of the data) before estimating the data scaling.

Standardization changes the shape of the neighborhood and it is useful when the variables have significantly different scales.

• no standardization, the data remain unchanged

• independent variables are divided (scaled) by the same scale factor = $\mathrm{max}\left( \sigma _x,\sigma _y\right) $
  → does NOT change the shape of the neighborhood
• dependent variable is NOT scaled

• independent variables are scaled by $\sigma _x$ and $\sigma _y$, respectively
  → DOES change the shape of the neighborhood
• dependent variable is NOT scaled

• independent variables are scaled by the same scale factor = $\mathrm{max}\left( \sigma _x,\sigma _y\right) $
  → DOES change the shape of the neighborhood
• dependent variable is scaled by $\sigma _z$
  → can affect the statistics

• independent variables are scaled by $\sigma _x$ and $\sigma _y$, respectively
  → DOES change the shape of the neighborhood
• dependent variable is scaled by $\sigma _z$
  → can affect the statistics

• positive integers

• $dy \geq 0$

• extend

The command has three optional subcommands (parts):

• a list of the curves that will be processed given as a list of values, a loop construct start:end:increment where increment is optional (default increment is 1), as a combination of them, or as one of the keywords 'all','odd','even'
• the minimum increment (step) dy between the curves selected according the first subcommand
  
  • the curves for which the value of the increment between them is smaller than dy will not be processed
  • the first two subcommands can restrain (if necessary) the cropped region defined by ha_in_min, ..., ha_min, ..., hc_min, ..., or x_min, ...
  • the cropped region can be extended to the maximum values allowed by the first two subcommands using the third subcommand
• 'extend' or 'ext'

For example, '10:30:2 dy=0.01 extend' will select from the curves 10, 12, ..., 28, 30 those curves for which the value of the increment between them is greater than 0.01, and will extend the cropped region to the maximum allowed values.

• nha × nhr points

• $\mathrm{ha\_min} \leq h \, _{\mathrm{applied}}^{\mathrm{grid}} \leq \mathrm{ha\_max}$

• $\mathrm{hr\_min} \leq h \, _{\mathrm{reversal}}^{\mathrm{grid}} \leq \mathrm{hr\_max}$

• ignore $h \, _{\mathrm{applied}}^{\mathrm{grid}} < h \, _{\mathrm{reversal}}^{\mathrm{grid}}$ points

• nhc × nhu points

• $\mathrm{hc\_min} \leq h \, _{\mathrm{coercive}}^{\mathrm{grid}} \leq \mathrm{hc\_max}$

• $\mathrm{hu\_min} \leq h \, _{\mathrm{interaction}}^{\mathrm{grid}} \leq \mathrm{hu\_max}$

• nx × ny points

• $\mathrm{x\_min} \leq x^{\mathrm{grid}} \leq \mathrm{x\_max}$

• $\mathrm{y\_min} \leq y^{\mathrm{grid}} \leq \mathrm{y\_max}$

Crop input points, ignoring the points that are outside the domain:

$\; \left[ \mathrm{ha\_in\_min},\,\mathrm{ha\_in\_max}\right] \times \left[ \mathrm{hr\_in\_min},\,\mathrm{hr\_in\_max}\right] $.

$\left[ \mathrm{ha\_in\_min-}\Delta h_{a},\,\mathrm{ha\_in\_max+}\Delta h_{a}\right] \times \left[ \mathrm{hr\_in\_min-}\Delta h_{r},\,\mathrm{hr\_in\_max+}\Delta h_{r}\right], $

In order to diminish the boundary effects (numerical artifacts), the processing is accomplished (if there are input points) on a larger domain:

$\left[ \mathrm{ha\_min}-\Delta h_{a},\,\mathrm{ha\_max}+\Delta h_{a}\right] \times \left[ \mathrm{hr\_min}-\Delta h_{r},\,\mathrm{hr\_max}+\Delta h_{r}\right] $,

In order to diminish the boundary effects (numerical artifacts), the processing is accomplished (if there are input points) on a larger domain:

$\left[ \mathrm{hc\_min}-\Delta h_{c},\,\mathrm{hc\_max}+\Delta h_{c}\right] \times \left[ \mathrm{hu\_min}-\Delta h_{u},\,\mathrm{hu\_max}+\Delta h_{u}\right] $,

In order to diminish the boundary effects (numerical artifacts), the processing is accomplished (if there are input points) on a larger domain:

$\left[ \mathrm{x\_min}-\Delta x,\,\mathrm{x\_max}+\Delta x\right] \times \left[ \mathrm{y\_min}-\Delta y,\,\mathrm{y\_max}+\Delta y\right] $,

These points are only omitted in the output data, not in the calculations.

w = number of positions to be used to write a number including its sign, decimal point, decimal places, exponent part and leading spaces between two consecutive numbers on a line

d = number of digits to the right of the decimal point

e = number of digits in the exponent part without its sign

Specifies the quadratic monomials to exclude from the local quadratic fits.

A large weight can be used to force interpolation.

Such iterations are appropriate when there are outliers in the data or when the error distribution is a symmetric long-tailed distribution.

• nn_list should be provided also
• no CRITERION (or DEFAULT) should be provided
• only (nn, RSS, RSSm) is provided as statistics

• radius of each neighborhood is chosen so that the neighborhood contains a specified number of the data points
• nn in each local neighborhood controls the smoothness of the estimated surface
• minimum value of nn: loess: 7, qshep: 6, cshep: 10, tshep: 10 (each of drop_x2 and drop_y2 decreases by one unit the minimum value of nn required by the loess and qshep methods respectively)
• one of nn_list or nn_range options is required
• only one of nn_list and nn_range options can be used

• a list of values, separated by spaces or by commas
• a loop construct start : end : increment, where increment is optional (default increment is 1)
• a combination of the above methods
• for example, '10 20:30:5 50' will return the values '10,20,25,30,50'

- if no CRITERION is specified → a separate fit is provided for each nn value

• the two values must be separated by spaces or by comma
• only the values lower ≤ nn ≤ upper are examined, and the value that minimizes the specified CRITERION is selected
• golden section search method is used to find a local minimum of the specified CRITERION in the [lower, upper] range

Only for 'shep' methods and only for output_points ≠ input_points.

• determines how the statistical quantities are computed
• can be decreased by the 'nrr' option
• can be increased if necessary by the CRITERION parameter

• exact delta
• use only for testing
• it is not meant for routine usage because computation time can be horrendous

• regardless of 'istat' value, no approximations are used in the statistics computation
• can be decreased by the 'nrr' option
• can be increased if necessary by the CRITERION parameter