Model

The model
Choosing a curve type
Building the model from the Tools tab
Picking points on the chart
Curve positions
Fit intervals
The background
Subtracting the background
Background fraction
Background variation
The Model tab
The Curve Attributes table
Parameter kinds: fitted, shared, fixed and computed
Deleting a curve
Clearing the model
User-defined curves
Writing the formula of a user-defined curve
Parameter roles and starting values
Selecting and deleting user-defined curves

The model

This software's choice — A decision made by this software rather than by the field's sources; the explanation says why it was made.

The model is what the program fits to the profile: curves of a chosen shape, placed at positions, fitted over intervals, above a background.

It is built from four parts:

The curve type - the shape of every curve placed from a position, chosen from Model > Curve Type or the list at the top of the Tools tab.
The curve positions - one per curve, the argument where that curve is placed. They are listed in the Curve Positions table at the bottom of the window.
The fit intervals - stretches of the profile, each fitted as a problem of its own, marked by pairs of bounds and listed in the Fit Intervals table.
The background - the slowly varying level under the peaks, which can be subtracted from the profile before fitting or varied along with the curves.

Once the model has at least one curve position and at least one fit interval bound, the program builds a curve at every position and draws it, with the computed profile and its difference from the data, before any fit. The curves are listed in the Model tab on the right and their parameters in the Curve Attributes table.

Each part can be picked by hand on the chart or proposed by the program - the Compute Automatically entries of the Model menu and the Auto buttons of the Tools tab. A fit also proposes what is missing: Fit > Minimize Difference computes the fit intervals when fewer than two bounds are set, and the curve positions when there are none.

The curve positions, fit intervals and background points are saved with the project, together with the settings that shape them.

Limitations

Every curve placed from a position has the selected curve type. Choosing another type changes the shape of all of them, and the values an earlier fit found for the old shape are not carried over.

Choosing a curve type

This software's choice — A decision made by this software rather than by the field's sources; the explanation says why it was made.

The curve type is the shape every curve placed from a position takes, and is chosen from Model > Curve Type or from the list at the top of the Tools tab.

Model > Curve Type opens a submenu of groups. Standard holds the types the program ships; a curve pack included in the build may add groups of its own after it; User comes last and holds New User Curve and the curve types you have defined yourself. The type in use is ticked.

The same types are listed at the top of the Tools tab on the left, under the same group names. Click a type to select it; clicking a group name selects the first type under it.

Every curve type explains itself. Rest the pointer on a type in the Tools list to read a one-line summary of it. When you select a type, the Explain pane under the Model tab on the right shows its full explanation - what its formula means, what each parameter controls, where the shape is used and what it does not cover - and every type can also be found under Help > Explain Everything.

A type can be chosen before any data is loaded. While the axis rule is From Curve Type, choosing a type also sets the argument axis.

New User Curve does not name a shape: it opens the dialogs that define one. Cancelling them leaves the previous type in use.

Limitations

The curve types you have defined are listed only in the menu, under Model > Curve Type > User. The Tools list offers New User Curve but not the types already made.

Building the model from the Tools tab

This software's choice — A decision made by this software rather than by the field's sources; the explanation says why it was made.

The Tools tab on the left carries the model-building commands as buttons, so a round of picking, fitting and adjusting needs no trip through the menus.

At the top is the list of curve types. Below it the buttons are grouped in the order the work is done:

Positions: Pick, Auto and Clear run Model > Curve Positions > Start Manual Selection, Compute Automatically and Remove All.
Fit intervals: Pick, Auto and Clear run Model > Fit Intervals > Start Manual Selection, Compute Automatically and Remove All.
Background: Pick, Auto and Clear run Model > Background > Points > Start Manual Selection, Compute Automatically and Remove All; Subtract runs Model > Background > Subtract > Automatically.
Fit: Fit and Stop run Fit > Minimize Difference and Fit > Stop.

A button runs exactly the command of its menu entry, shows the same hint, and is greyed whenever that entry is. A Pick button stays pressed while its picking mode runs; pressing it again ends the mode.

Each heading counts what the model holds - Positions (3) means three curve positions. A zero is shown rather than hidden.

A curve pack included in the build may add buttons of its own, under its own heading. The bar between the list and the buttons can be dragged to give either more room.

Limitations

Subtract always subtracts automatically, ignoring the background points you picked. To subtract through your own points use Model > Background > Subtract > By Selected Points.

Picking points on the chart

This software's choice — A decision made by this software rather than by the field's sources; the explanation says why it was made.

In a picking mode each left click on the chart adds the data point nearest the pointer to the set being built, and a click on a point already in the set takes it out.

Several commands start a picking mode: the Start Manual Selection entries for curve positions, fit intervals, background points and the data range, and the Pick buttons of the Tools tab. Only one mode runs at a time: starting another ends the first, and choosing the same entry or button again ends it.

The entries for curve positions, fit intervals and background points say whether their mode is on. They read Start Visual Position Selection or Start Visual Selection, and Stop Visual Position Selection or Stop Visual Selection while it runs; the matching Pick button stays pressed. The other picking entries are ticked instead.

A pick is made with the left button, and only if the mouse does not move between press and release; a drag zooms the chart instead. The pick goes to the data point nearest the pointer, measured on the screen in both directions, so every pick is a real point of the profile. A click that lands on a curve or another series drawn over the data is taken as a click on the data beneath it.

Clicking a point already in the set removes it. For curve positions this also removes the curve placed there. In a mode that takes a set number of picks - two ends of a range, three points of a peak - clicks after the last one are ignored.

The right button never picks: it opens the chart's menu of axis rules. The status line at the bottom of the window says what to pick next.

A curve position or a fit interval bound can also be moved, by typing its new position into the Curve Positions or the Fit Intervals table. A moved position keeps what a fit found for its curve; taking a position out with a click and picking another places a new curve, which starts again from the data.

Limitations

A pick cannot be dragged on the chart.
Picks are refused while a fit or another calculation is running, with a message saying a calculation is already in progress.

Curve positions

This software's choice — A decision made by this software rather than by the field's sources; the explanation says why it was made.

A curve position is the argument where one curve of the model is placed; positions can be picked on the chart, proposed by the program or put at every data point.

Each position seeds one curve: the curve is placed there, and its height is taken from the data at that point. The Model > Curve Positions submenu offers four ways to set them:

Model > Curve Positions > Start Manual Selection, shown as Start Visual Position Selection, or the Pick button under Positions - pick positions on the chart. The status line invites the next pick or a fit.
Model > Curve Positions > Compute Automatically, or Auto - replaces the positions with ones the program finds. Working down from the highest point, it takes every peak that stands above the background fraction of that point and places a position at each local maximum - or minimum, or both, as the curve type asks.
Model > Curve Positions > At Every Point - puts a position at every point of the profile, or of the data interval in force. It is a starting point for Fit > Minimize Number of Curves, which removes the curves that are not needed. A curve type placed from its own markup refuses it with a message.
Model > Curve Positions > Remove All, or Clear - removes every position, and with them the curves built from them: with nothing picked there is no model.

The positions are listed in the Curve Positions table (Position and Amplitude) and drawn as the Curve positions series. After a fit a second series, Fitted positions, shows where each curve ended up; your picks never move. When nothing was picked - a model placed from a curve type's own markup - the table lists where the model's curves are instead.

The submenu and the Positions buttons are greyed until a profile is loaded, and while a fit runs.

Limitations

At Every Point makes one curve per data point, which on a long profile is a great many curves to fit.

Fit intervals

This software's choice — A decision made by this software rather than by the field's sources; the explanation says why it was made.

A fit interval is a stretch of the profile fitted as a problem of its own, marked by a pair of bounds.

Bounds come in pairs, and each pair encloses one interval. Splitting a profile into intervals keeps each fit small, and lets a stretch with no peaks in it be left out.

Model > Fit Intervals > Start Manual Selection, shown as Start Visual Selection, or the Pick button under Fit intervals - pick bounds on the chart. The status line asks for the left and the right point of each peak in turn.
Model > Fit Intervals > Compute Automatically, or Auto - enters the same picking mode and adds bounds around every peak it finds, with the search the automatic curve positions use: each stretch standing above the background fraction of the highest point gets a bound at each end. Bounds you picked are kept.
Model > Fit Intervals > Remove All, or Clear - removes every bound. Without a fit interval nothing can be built, so the model is emptied too; your curve positions are kept, and picking bounds again rebuilds the curves from them.

The intervals are listed in the Fit Intervals table (Starting Position and Final Position) and drawn as the Fit intervals series. An interval with only one bound picked so far shows its second cell empty.

A fit started with fewer than two bounds computes the intervals itself, as Compute Automatically does.

The background

This software's choice — A decision made by this software rather than by the field's sources; the explanation says why it was made.

The background is the slowly varying level under the peaks; the program marks it with background points, which you can pick or have proposed.

Background points are points of the profile that lie on the background rather than on a peak. Once they are marked, the background they describe can be subtracted from the profile. The Model > Background > Points submenu sets them:

Model > Background > Points > Start Manual Selection, shown as Start Visual Selection, or the Pick button under Background - pick background points on the chart, as many as you like.
Model > Background > Points > Compute Automatically, or Auto - enters the same picking mode and replaces the background points with ones the program proposes. It starts from the lowest point of the profile and walks outwards in both directions, each step taking the lowest point not below the last one taken. You can then add or remove points by clicking.
Model > Background > Points > Remove All, or Clear - discards the background points.

The points are listed in the Background Points table (Position and Amplitude) and drawn as the Background points series. The small toolbar above that table has buttons for computing the points, subtracting automatically, subtracting by the selected points and removing them all. Typing into the table does not change the points.

The Background submenu and the Background buttons are greyed until a profile is loaded, and while a fit runs.

Limitations

The automatic proposal assumes a background that is lowest in one place and rises on either side of it, as in a neutron diffractogram. On a background of another shape it still proposes points, but they need not lie on the background; look at them on the chart before subtracting.

Subtracting the background

This software's choice — A decision made by this software rather than by the field's sources; the explanation says why it was made.

Model > Background > Subtract joins the background points by straight lines and subtracts those lines from the profile.

Model > Background > Subtract > By Selected Points uses the background points you picked or had proposed. It needs at least two; with fewer it says so and does nothing.
Model > Background > Subtract > Automatically ignores any points you picked, proposes its own as Compute Automatically does, and subtracts through them. The Subtract button under Background in the Tools tab runs this one.

Between each two neighbouring background points the straight line through them is subtracted from the amplitudes, so every background point itself ends at zero. The profile on the chart and in the Data table is replaced by the result and the background points are cleared. With a data interval selected, only that interval is changed.

Subtract is greyed until a profile is loaded, and while a fit runs.

Limitations

Points outside the outermost background points are left as they were, so place background points near both ends of the stretch you fit.
Subtraction cannot be undone, and it can be repeated: each run subtracts again from what the last one left. File > Reload Profile brings back the data as measured.

Background fraction

This software's choice — A decision made by this software rather than by the field's sources; the explanation says why it was made.

The background fraction decides how small a peak the automatic searches still count: a point below 1/N of the highest point, for the factor N you set, is treated as background.

Model > Background > Set Background Fraction opens the Background Factor dialog, whose field is labelled Background factor value 1 /. It must be a number greater than 1; anything else is refused with a message. The default is 30, so anything lower than one thirtieth of the highest point is not searched for peaks.

The factor is used by Model > Curve Positions > Compute Automatically, by Model > Fit Intervals > Compute Automatically, and by a fit that proposes positions or intervals itself, Fit > Automatically included. A larger factor finds smaller peaks; a smaller one keeps only the tall ones.

The factor is saved with the project.

Limitations

Despite its name, the factor has no effect on the automatic background points, which are proposed without it.
The threshold is a fraction of the highest point, not a level above the background: where the background is high, the background itself may stand above it. Subtract the background first.

Background variation

This software's choice — A decision made by this software rather than by the field's sources; the explanation says why it was made.

With Model > Background > Enable Variation ticked, a fit also adjusts a smooth background of its own alongside the curves.

The background the fit varies is a quadratic curve about a centre, described by four coefficients: curvature, slope, offset and centre. The curvature and the offset are kept from going negative, so the background never bends downwards and never sits below zero.

It is off until you turn it on. Choosing the entry turns it on or off, and a tick shows that it is on. The setting is saved with the project.

Use it when a background is left under the peaks that subtraction did not remove, or when you would rather fit the background than subtract it.

Limitations

The varied background is always a quadratic. A background of another shape - one with a step or a separate hump - cannot be described by it.

The Model tab

This software's choice — A decision made by this software rather than by the field's sources; the explanation says why it was made.

The Model tab on the right lists the curves of the model, one row per curve with where it sits, and is where one curve is chosen to be explained or deleted.

Each row names a curve and its position. For a curve type placed from its own markup the tab shows that structure instead, as the curve pack describes it.

When there is nothing to list, the tab says why: no data file is open, no curve has been placed yet, or the selected curve type is placed from its own markup and none has been made.

Selecting a row shows the explanation of that curve's type in the Explain pane below the list. Right-clicking a row selects it and opens the commands that act on one curve, such as Delete curve.

The Curve Attributes table

This software's choice — A decision made by this software rather than by the field's sources; the explanation says why it was made.

The Curve Attributes tab at the bottom of the window lists every curve of the model with the value of each of its parameters.

There is one row per curve and one column per parameter name. When curves of different types share the model, the columns cover every parameter any of them has, and a cell is blank where a curve has no such parameter.

Values are shown with four decimals. Where the engine estimated an uncertainty it follows the value after a plus-minus sign; the built-in engine does not estimate one. Positions are shown on the argument axis in force, as on the chart.

Colour shows how each value is treated, and the row under the table names the colours: Fitted, Shared, Fixed and Computed. Rest the pointer on one to read what it means.

Select whole rows and choose Edit > Delete to remove those curves. A button above the table copies what is selected to the clipboard.

A value the fit varies can be typed over: click the cell, type the number and leave it. The engine rebuilds the model with it and the table and the chart are redrawn, so the next fit starts from there. A value shown in the table's units - an angle, for instance - is typed in those units.

Limitations

A parameter computed from the others cannot be typed, and text that is not a number is refused; a message says which.
Edit > Delete acts only on whole rows. A selection that does not span every column deletes nothing.

Parameter kinds: fitted, shared, fixed and computed

This software's choice — A decision made by this software rather than by the field's sources; the explanation says why it was made.

Each parameter value in the Curve Attributes table is one of four kinds, which say whether and how the fit moves it.

Fitted - varied by the fit to match the data. The ordinary case and most of the table; it keeps the table's own row colour.
Shared - varied by the fit, but held to one value across the curves of an interval.
Fixed - set when the curve was placed and not varied; for a wave pattern, the points you picked.
Computed - neither fitted nor entered: it follows from the other parameters and is recomputed whenever they change.

The engine tells more kinds apart - which parameter is the amplitude, which the width, which the position - but to a reader of the table those differ only in how the fit starts them, so they are all shown as Fitted.

For the program's own curve types the kinds are part of the type. For a user-defined curve you choose them yourself when you define it.

Deleting a curve

This software's choice — A decision made by this software rather than by the field's sources; the explanation says why it was made.

Right-click a curve in the Model tab and choose Delete curve to remove it, together with the position it was placed from.

In the Model tab on the right, right-click the curve's row - the click also selects it - and choose Delete curve. The entry is greyed when the row does not stand for a curve, and while a fit runs.

There is no Model > Delete Curve entry in the menu bar: deleting one curve needs a curve to act on, and the selected row of the Model tab is what names it.

The position the curve was placed from goes with it - the model is rebuilt from the positions, so a position left behind would put the curve straight back. The other curves keep what the last fit found for them.

There are two other ways to remove curves: select whole rows of the Curve Attributes table and choose Edit > Delete, or, while picking curve positions, click a curve's position on the chart.

If the engine cannot remove a curve on its own - one a curve pack placed from its markup, for example - it refuses, and the message says why.

Limitations

There is no undo. Save the project first if you may want the curve back.

Clearing the model

This software's choice — A decision made by this software rather than by the field's sources; the explanation says why it was made.

Model > Clear Model removes every curve from the model at once, after asking.

It is the last entry of the Model menu. It asks whether to remove all the curves, naming how many, says that their picks go with them and that this cannot be undone, and does nothing unless you answer Yes.

Each curve is removed as Delete curve removes one, its position included, so you start again from an empty model on the same data. The fit intervals, the background points and the curve type are kept.

The entry is greyed while the model holds no curve, until a profile is loaded, and while a fit runs.

A curve the engine keeps stays where it is: one that the curve type builds per fit interval rather than from a position is rebuilt at once, and a curve pack may decline to give one up. A single message then says how many curves stayed and why.

Limitations

There is no undo. Save the project first if you may want the model back.

User-defined curves

This software's choice — A decision made by this software rather than by the field's sources; the explanation says why it was made.

You can fit a shape of your own by typing its formula; the program turns it into a curve type that is saved and offered like the built-in ones.

Choose Model > Curve Type > User > New User Curve, or New User Curve in the Tools list. Two dialogs follow: Create New Curve Type, where you name the curve and write its formula, and Set Curve Type Properties, where you say which parameter plays which role and give starting values.

When you press Done the curve type is saved and selected. It appears under Model > Curve Type > User, below New User Curve, and is ticked while it is in use. It is kept between sessions: each one is stored as a file in the program's settings folder.

A user-defined curve is fitted like any other: place positions, set fit intervals, fit. Its formula is saved with the project. Under the From Curve Type axis rule it is shown against a plain Position.

Cancelling either dialog creates nothing: a curve type saved when its formula was accepted is removed again if you then cancel the second dialog.

Writing the formula of a user-defined curve

This software's choice — A decision made by this software rather than by the field's sources; the explanation says why it was made.

In the Create New Curve Type dialog you give the curve a name and a formula in x; every other name in the formula becomes a parameter.

Name is what the curve type is called in the menu (MyCurve until you change it). Expression is the formula, filled in with a bell curve to start from: A*exp(-((x-x0)/SIGMA)^2).

x is the argument, the variable running along the axis. Some names mean something, whatever their case: x0 is the position, where the curve is placed, and the fit does not move it; A is taken as the amplitude and SIGMA as the width, and SIGMA starts at 0.25 rather than 0 so that a formula dividing by it can be evaluated. Every other name is an ordinary fitted value starting at 0. The next dialog can change all of this.

The keypad inserts at the cursor. A function is inserted with its brackets, and the cursor left between them. It offers Sin, Cos, Tg, Ctg, the hyperbolic Sh, Ch, Th, Cth, Sch and Csch, the inverses Arcsin, Arccos, Arctg, Arcctg, Arsh, Arch, Arth and Arcth, Ln (natural logarithm), Log (base 10), Exp, Abs and Sqrt, the digits, the operators + - * / ^, brackets and a decimal point. Names are not case-sensitive, a comma typed on the keyboard becomes a decimal point, and sqr and pi can be typed though they have no button.

Continue >> checks the formula before anything is saved. If it cannot be used a message says why and the dialog opens again for you to correct it:

the Expression is empty;
the formula could not be understood - a typo, an unmatched bracket or an unknown function;
the formula does not use x as its argument;
the formula cannot be evaluated at its starting values - most often a parameter used as a denominator left at 0.

Cancel abandons the definition.

Limitations

Pressing a function button while text is selected replaces the selection with an empty call rather than wrapping it: the selected text is lost.

Parameter roles and starting values

This software's choice — A decision made by this software rather than by the field's sources; the explanation says why it was made.

The Set Curve Type Properties dialog says which parameter of a user-defined curve is its argument, position, amplitude and width, which are held, and where each starts.

Expression shows the formula. Four lists give the roles, and each role is held by at most one parameter - giving it to one takes it from any other:

Argument - the variable along the axis, x unless you choose another.
Position parameter - the one that places the curve at a pick. The parameter chosen here starts out held.
Amplitude parameter - the height, started from the data peak.
Width parameter - the width, started from the fit interval.

Amplitude and Width offer (none), which leaves the role unheld.

Shared parameters lists the position and the ordinary parameters - not the argument, the amplitude or the width. Ticking the position parameter makes the fit leave it where it was picked; unticking it lets the fit move it. Ticking any other parameter makes it shared: one value, varied by the fit and held equal across the curves of an interval.

Held parameters lists the shared and the ordinary parameters. Ticking one holds it at its starting value: the fit does not vary it. The tick is kept with the curve and in the project.

To give a starting value, select a parameter in Shared parameters, type the value in Initial value and press Apply. A value that is not a number is refused with a message.

Done saves the roles and selects the curve type. << Backtrack discards this draft and returns to the formula dialog. Cancel closes the dialog and removes the draft.

Once the curves are placed, a value can also be typed into the Curve Attributes table.

Selecting and deleting user-defined curves

This software's choice — A decision made by this software rather than by the field's sources; the explanation says why it was made.

The curve types you have defined are chosen and deleted under Model > Curve Type > User.

Below New User Curve and a separator, the User group lists every curve type you have defined. Choosing one selects it, and it is ticked while in use. New User Curve itself is never ticked: it names no curve, it makes one.

Model > Curve Type > User > Delete User Curve opens a list of the same curve types. Choosing one deletes it, and its file, at once and without asking. The entry is there only while at least one curve type of your own exists.

If you delete the curve type in use, the program says so: the model is left with no curve type, and a fit is refused until you choose another under Model > Curve Type.

A curve type saved without a formula - by an older version, or by a session interrupted while defining it - cannot be selected; choosing it says so and suggests deleting it and making it again.

Limitations

Deleting cannot be undone.

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