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Tau, version 1.50 Copyright © Tim Birks 1993, 1994, 2000, 2001 GPL Freeware: for conditions of use, see the files ReadMe & gpl.txt Current development Peter Killworth 2001-2005 (p.killworth@noc.soton.ac.uk) Desktop graph preparation software. Tau generates publication-quality graphs in the form of Draw files, ready to import into your favourite word-processor, computer presentation, or DTP. A data worksheet (16 columns by 4096 rows) can be filled by keying-in, importing from a file, and/or calculation. You determine line patterns and thicknesses, colours, text positioning and font sizes, etc. The data worksheet can be redimensioned, if you would prefer more rows of data for example. Note that Tau does not (usually) draw graphs on the screen (Acorn's excellent Draw or similar applications will do that). In the following text, all references to 'drawing' or 'plotting' a graph refer to the construction of a Draw file. This file is intended to be some kind of help, but no way is it comprehensive. It assumes some experience with graph drawing packages, common sense, and a willingness to suck-it-and-see. ----------------------------------------------------------------------------- Important changes from version 1.30. A new feature has been added. While !Tau has always been able to plot multiple data with the same x-values, there are occasions, particularly when working with observed data, in which one has several sets of (x, y) data which need plotting on the same graph. In previous versions, the workaround has been to plot each pair separately and superimpose the graphs afterwards, which isn’t very neat. In 1.40 one can turn on "Many Xs" which allows each y column of data to have a specific x column associated with it for all plotting purposes; they can all be plotted simultaneously. An improvement has been made to log scaling, and an obscure bug in data import has been fixed. In 1.41 the ability to specify suffices k, M, G and T for thousands, millions, billions and, er, whatever comes next has been added. In 1.50, the ability to specify colours in 24-bit modes is included. The user can specify colours for the line and/or character and/or fill for each set of y-values (already added in 1.30). In addition, the colour for the frame (axes, labels and annotations), for a possible background fill of the graph, and for the border and fill of the graph key (if selected) can also be chosen and stored in style files. In 256-colour modes, !Tau does what it can to represent the 24-bit colours, like any other application. Important changes from version 1.20. The resizable worksheet has been doubled in size again (assuming most users can cope with a 640k Wimpslot). With an eye towards computer presentations, where colour replaces linestyles, both lines and symbols can be in any desktop colour. Linestyles are now user-definable (lengths and gaps can be specified). The F3 key has been enabled for quick saves to Drawfiles. The best fit option now shows the equation for the fit, and the correlation. A facility for globally editing data has been added (useful if a certain data value has the meaning "no or missing data". The key now has a black rectangle around it, with a white background (so can be moved over the graph without any of the graph showing through). Important changes from version 1.10. Actually, there are quite a few changes, like the resizable worksheet (with twice the previous capacity), and the Plot (many) option. The most significant change is that the TauFile and TauStyle formats are different. Old-type files can be read by Tau 1.20, but the new-type files cannot be read by Tau 1.10 and earlier versions. In other words, if you get rid of your old version of Tau there shouldn't be any problems. ----------------------------------------------------------------------------- Starting Tau. Double-click on the !Tau icon in a filer window, or double-click on the icon of a file of type 082 (TauFile) or 083 (TauStyle). The Tau icon is installed on the icon bar, and the application's main window opens, showing the data worksheet (dark blue background) with labelling (grey background) along the top and left edges. If starting by a double-click on a TauFile or TauStyle, that file is loaded into Tau. If starting by a double-click on the !Tau icon itself, Tau looks for a TauFile or TauStyle called "Default" within the !Tau directory and loads that. If there is no such file, Tau starts with its worksheet empty and with minimal appearance data. Assuming there are no data initially (usually the case), then simply drag in a text file with some data columns. If the first of these represents the x-axis for your plot, and the remainder represent the y-axis (or -axes if you wish to plot more than one simultaneously), then bringing up the save option on the main menu and saving as a drawfile will give you a publishable graph right away. ----------------------------------------------------------------------------- Default settings. There are three ways Tau can get its default settings when it is started. These include the graph style parameters, and also other things like whether the user is prompted if unsaved data is about to be lost (hidden, a little unhelpfully, in the Reduce menu from historical times), and whether Tau automatically scales your graph. 1) If Tau is started by double-clicking on a TauFile or TauStyle icon, the defaults are set to the values stored in the file. 2) If Tau is started "empty", by double-clicking on the !Tau icon, the defaults are obtained from a file called "Default" within the !Tau directory. If you would like to use your own set of defaults, just put them in a TauStyle file and save it as "Default" in the !Tau directory. 3) If there is no file "Default" in the !Tau directory and Tau is started by double-clicking on the !Tau icon, a set of default defaults from within the program is used. ----------------------------------------------------------------------------- Editing data. The data worksheet is arranged in 16 columns, each containing 4096 rows of cells. The cells can be filled with data by importing from a file (see below), by calculation (see below), or from the keyboard. Click on the appropriate cell with Select to set the caret and highlight. You can then edit the contents of the cell. Valid contents are: a number (use 'E' for exponential notation; 'D' and lowercase are also understood); no contents (blank cell); or the special entry 'M'(for 'move') which will cause any eventual line graph to have a break at that position. If you click on a cell with Adjust, the caret does not move, but all the cells in a rectangle between the caret-cell and the cell you clicked on will highlight. Any action performed at the caret (followed by RETURN when entering a number) will then affect all these cells. Tau keeps a note of the maximum row and column numbers for which data are held. If you double-click on a cell, that cell gains the caret and the whole column (down to the maximum row) will highlight. Double-click with SHIFT to highlight a whole row instead. Values are displayed in cells to six significant figures. ----------------------------------------------------------------------------- Special key presses. RETURN - Reflect the value in the current cell in all highlit cells, then move the caret down one row. SHIFT-RETURN - As RETURN, but move the caret right one column. CTRL-RETURN - Carriage return, move down one row, and to leftmost column. LEFT/RIGHT - Move caret one character left/right. BACKSPACE - Delete the character to the left of the caret within a cell. DOWN/UP - Move caret down/up one cell. SHIFT-DOWN/UP/LEFT/RIGHT - Extend or contract the highlit block of cells. CTRL-DOWN/UP - Move caret to the last/first cell in a column. TAB - Move caret right one cell, perform 'carriage return' if at the last column. SHIFT-TAB - Move caret left one cell, perform 'reverse carriage return' if at the first column. HOME - Move caret to the first cell in the worksheet. SHIFT-COPY (ie, END) - Move caret to the bottom-right-most cell of a rectangle enclosing all cells containing data. CTRL-U - Blank all highlit cells. DELETE - Same action as BACKSPACE. SHIFT-DELETE - All highlit cells in the same row as the caret are blanked, then all the values in the cells below these are scrolled up to 'fill the hole'. INSERT - The values in all highlit cells in the same row as the caret, and the cells below these, are scrolled down. A row of blank cells is inserted. F3 - Does a quick save to a Drawfile. ----------------------------------------------------------------------------- Dragging files onto the main window (or the icon bar icon). This starts a load action which depends on the filetype of the file dragged: 082 (TauFile) - A TauFile file is a complete record of a previous state of Tau, and includes all the data in a worksheet and the variables governing the appearance of a graph. Dragging a TauFile onto Tau will restore the saved state, overwriting all of the current state. 083 (TauStyle) - A TauStyle file is a TauFile file without any worksheet data. It replaces the variables governing the appearance of a graph, without overwriting the current data. It's like the 'template' files in other graph software, but the word 'template' already has a very particular meaning in RISC OS. ffb (BASIC) - Has no immediate effect. Tau assumes any imported BASIC file to be a function library. You can then perform calculations on worksheet data using your own defined functions. A simple example, Sinc, is provided with Tau - this contains a function FNsinc(x) which returns SIN(x)/x without generating an error at x=0. To avoid clashes with the program's internal FN definitions, do not use FN names beginning with capital 'T'. fff (Text), dfe (CSV) - Tau assumes files of these types contain textual data for import, either separated by spaces or commas, with row endings marked by one or more control characters (such a linefeed or carriage-return). Import *starts at the caret*; data in cells not explicitly overwritten by new data are retained. Incidentally, Tau treats these files identically on import - eg the contents of a Text file can be comma- separated. A blank cell can be marked by an isolated decimal '.', and a 'move' cell by 'M'. The Global Edit feature (below) allows for a specific value to be replaced by another throughout the data, which is useful if 999, or 1.E20, etc. are defined as "missing data". The fact that import starts at the caret means that several datasets (presumably occupying separate columns!) can easily be imported by positioning the caret accordingly before dragging them into !Tau. Other filetypes - action is normally as for fff (Text). But Tau first investigates whether the file might contain non-textual numerical data ("Binary data"). Such a file would be generated by, for example, the Basic PRINT# statement. Tau assumes that your file is "Binary data" if the first byte in the file is ascii &40, &80 or &88; no self-respecting file of textual data should contain any of these characters. Because there is no row-ending marker in such a file, Tau expects a special first datum in the file to be an integer specifying the number of data columns in one row. However, you can instead specify the number of columns in the Import dbox. Import starts at the caret; data not overwritten are retained. ----------------------------------------------------------------------------- ----------------------------------------------------------------------------- Main menu. Click Menu over the main window, gives the following items: Paper - Leads to a submenu controlling the size and shape of a graph on the paper. Graph - Leads to a submenu controlling the appearance of the whole graph. This includes such attributes as its scaling and the appearance of ticks and labels, and the number of rows and columns in the worksheet. Column - Leads to a submenu controlling the treatment of an individual column of data. This includes control of the meaning of a column (use as X data, Y data, error bar data, or ignore), the appearance of a plot (whether to draw points, lines between points, etc), and actions such as calculation and sort. Save - Leads to a submenu allowing the saving of data in various ways. Clicking on the Save item in the Main menu will save the current Tau state as a TauFile, or generate an error if no pathname is specified yet. (F3 will do a quick save as a Drawfile.) Import - Leads to a dialogue box. The first part governs the import of a file of Binary data (see above). The second part allows you to "weed" data being imported, reading in only 1 row of data for each n rows of data in the file. Cells - A submenu, various ways of highlighting parts of the worksheet. Reduce - A submenu, various ways to shrink your data, and disable the warning Tau gives when edited data is about to be lost or over-written. View - Equivalent to clicking on the Tau icon in the left-hand corner, and produces a quick graph of the data. Many Xs – A tickable item (click on the item to choose/unchoose it). When unticked, a single column of data (the leftmost one labelled “X”, in fact) serves as the x values for all current plots. When ticked, each set of y data can (and must) have an x-column associated with it, so that several datasets with different x values can be plotted simultaneously. k,M,G labels - Setting this changes labels to use k (for thousands), M (for millions) and G (for billions) instead of E powers. Global Edit - Leads to a dialogue box. The user can specify a data value and a replacement value, which are changed globally within the data when "OK" is clicked. Values can be changed to missing by specifying full stop (period) or leaving the value blank; values can also be set to "m" or "M" with the standard meaning (break the plot at this point). ----------------------------------------------------------------------------- Paper submenu. The items in this submenu lead to dialogue boxes. All dimensions are in points (1/72 inch) unless otherwise specified. + Size dbox. This governs the size and positioning, on paper, of the three main separate structures in a Tau graph. All sizes are in INCHES. (Aside, to any Euro-freaks: the 'inch' is a special Tau unit of length defined to be equal to 72 points. Happy now?) Graph - This is actually the size and position of the graph's viewport, ie the frame if one is being drawn. Border - You can have a border to make your graph look pretty. However, the main reason for having one is for grid-locking in !Draw. The average graph will have a well-defined frame, but also all sorts of labels and text hanging off it. The Draw bounding box of the graph will therefore not be simply related to the frame, and will vary from graph to graph. This causes problems when trying to arrange two or more graphs to line up nicely when using gridlock in Draw. So Tau can draw a big well-defined border around the whole lot. Then you can line your graphs up in Draw, then delete the frames afterwards. Since the border is meant to be a throw-away structure, it will always be 'thin'. That's the theory anyway; shame it doesn't work. Key - A simple key to the graph can be drawn. The key is a list of the Y plots drawn, showing the line pattern, the point shape, and a bit of text. Around these is a black rectangle with a white background (which ensures the key is visible if it is later positioned over the graph). The key is a separate group within the Drawfile, so if you wish to move its position within !Draw or any other drawing package, ungroup the whole picture and select the key area. Colours for the graph key (its border and background) can be chosen here. + Magnify dbox. The whole graph can be magnified (or shrunk) uniformly when saved as a Draw file. Enter the magnification factor here. ----------------------------------------------------------------------------- Graph submenu. The items in this submenu lead to dialogue boxes. All dimensions are in points (1/72 inch) unless otherwise specified. + Scaling dbox. Governs the scaling of the graph. All dimensions refer to the data in the worksheet. Auto scale - When selected, Tau takes a look at the worksheet and your other choices, and automatically scales the graph. Deselect it if you want to make any changes yourself. Bound - When selected, the graph will include only data points and line segments within the frame of the graph. Otherwise points and lines outside the frame will be drawn also. (The 'fill' option is disabled when bounding is active, as it is unlikely to be useful.) X/Y log scale - Whether or not a log scale is selected governs the type of scaling information required, below. Beware negative or zero values! X/Y values - Determines the range of the graph's viewport, and the positioning of axes within it. Format - Determines the appearance of numerical axis labels. The choices follow BASIC's @% format. X/Y tick spacing - Tau supports two sets of ticks on each axis, major ticks usually being more prominent than minor ticks. The anchor is any one value where a major tick is to lie. Hence if the tick spacing is '2' and the anchor is '5', then major ticks will be drawn at 1,3,5,7,... If a log scale is selected, you have several choices. Choosing any of the top four choices (“1, 1000”; “1, 10”; “1, 3, 10”; or “1, 2, 5, 10”) gives you a logarithmic tick distribution. For example, if ‘1, 3, 10’ is selected then ticks will be drawn at 0.1, 0.3, 1,3, 10,30... and so on. In all these cases labels only occur at 1, 10, 100 etc. Alternatively, choose the ‘linear’ settings, which put ticks at 1, 2, 3, 4, ..., 8, 9, 10, 20, 30, 40, ..., 80, 90, 100, 200, and so on. In this case, labels are put at 1, 2, and 5 in each decade. + Frame dbox. Governs the axis structures to be drawn. All dimensions are in points. A frame is a rectangular box at the edge of the graph's viewport, and carries ticks on all four sides. An X/Y axis is a horizontal/vertical bar which stretches the whole length/height of the viewport and can be positioned anywhere vertically/horizontally (as defined in the Scaling dbox). The colour of the axis structures (lines, labels, ticks) can be chosen. A background colour for the whole graph can also be chosen, provided the "background" box is selected. This dbox can be used to produce a graph with two sets of data, each with their own y-axes, for example. Generate one file with an axis at the left, containing one set of data; then generate another with an axis at the right, with the other set of data. Finally, superimpose the two. Mind you, the multiple X option is simpler... + Ticks dbox. Governs the appearance of axis/frame ticks. All dimensions in points. Tau supports two sets of ticks on each axis; major ticks usually being more prominent than minor ticks. Ticks on an X axis extend up and/or down. Ticks on a Y axis extend left and/or right. Ticks on a frame extend in and/or out. You can choose whether to plot a certain family of ticks at all. + Grids dbox. Governs the appearance of grid lines. All dimensions in points. Grid lines are usually broken or dashed, so you choose the dash pattern. Grid lines are anchored to ticks, but can omit the minor ticks. + Labels dbox. Governs the appearance and positioning of numerical labels on axes/frame. Labels can appear on axes and/or the frame. Below ? - When selected, labels are placed below the X axis or frame bottom edge. Otherwise labels are placed above the X axis or frame top edge. Left ? - Analogous to Below ? but for Y values. Minors ? - When selected, labels are placed at minor ticks as well as major ticks. Rotate ? - When selected, Y labels are written 'sideways' parallel to the axis or frame edge. THIS OPTION FAILS IN RISC OS 2 !!! Offset - The distance between the axis or frame and the label, as a fraction of the font height/width. Font Size - In points. The label font is determined in the Fonts dbox. + Texts dbox. Governs the appearance of textual labels on axes/frames, such as a description of the quantity plotted along an axis. plot? - Whether to draw at all. on Frame? - When selected, plot along the frame, else along the axis. below?/left?/rotate? - As in the Labels dbox. Offset - The distance between the frame/axis and the nearest part of the text, as a fraction of the font height/width. Spacing - The line spacing between successive lines of the text, as a fraction of the font height/width. Text - Any text you like. Include backslash characters '\' to force a line break. Font size - In points. Uses the same font as the numerical labels, but can be a different size. + Fonts dbox. There are usually two fonts in use in a Tau graph. You have to enter in their full names in this dbox. Font for data points - This should be some kind of symbolic font to supply circles, squares, triangles, stars, etc for data points. Specifically use the Selwyn font. However, maybe Selwyn only comes with RISC OS 3, I don't know. So you can choose to use another font instead if you like. The public domain Dingbats font should do the trick. Font for graph labels - This serves for all labelling tasks. + Worksheet dbox. This displays the current number of rows and columns in the data worksheet, and invites you to enter new values for either or both. If you enter a new value for just one, then the other will be given the maximum possible range. If you specify fewer rows than the current data, or if you change the number of columns at all, the current data will be forgotten! The maximum number of columns is 64. ----------------------------------------------------------------------------- Column submenu. All but one of the items in this submenu lead to dialogue boxes. + Plot dbox. Governs the appearance of a column of Y data points. All dimensions in points. Acts only on the column which includes the caret. Plot this Column - When deselected, Tau ignores the column of data completely. Draw Line - When selected, draw straight lines between successive X,Y points. Define your own dash patterns: click 'Menu' on Line Style and choose between a continuous line, a dashed line, or a dash-dotted line. In the last two of these cases, the lengths and gaps can be entered numerically. If a value 'M' is encountered on either the X or Y data, the line will be broken by a 'move' operation; line drawing resumes from the next numerical value. Draw Error Bars - If selected, when drawing the graph, Tau looks for any columns designated Ln, Rn, Un, Dn, Hn and Vn, for the appropriate n, to supply error bar data to the graph. If none are found, no error bars are drawn. Key Text - The text to appear in the graph key (if plotted). Fill - Fill the area between the graph line (which of course is not plotted if Draw Line is deselected) and the X axis, in the selected Desktop colour. This is not done if a Y log scale is selected or if Bound ? is selected. Expect peculiar effects if your plot includes moves (an 'M' in the worksheet). Draw Points - When selected, mark data points with characters from the font selected in the Fonts dbox. You choose the character size and ascii code - an enlarged picture of the character is shown. Colours - Fill, Line and Character colours can be chosen; click any key over the appropriate box and select from the list. (The appropriate option must be activated for a colour to be chosen.) Plotting with X - This is usually greyed out (and always is for a column of Xs). If “Many Xs” is set, then the label of the X-column associated with the Y-column in the plot box can be set. The y-data will then be plotted with those x-data (assuming the “plot this column” flag is set for both!), autoscaling will include the relevant x-range, and a best fit to the y-data will use the relevant x-data. + Meaning dbox. You decide the meaning to attach to the data in the column. A string summarising your choice is shown along the top of the worksheet for your information. Valid designations are: X - The column is to supply the X data for a graph. You need one of these somewhere to get a graph! The ‘tag’ entry is greyed out for X values unless the “Many Xs” option is selected, when a tag may be entered. A null value is taken as zero. Yn (where n is any digit or pair of digits) - The column is to supply a set of Y data. Since many sets of Y data can be plotted in Tau, each is distinguished by the tag n. Ln/Rn/Un/Dn - Error bar length left/right/up/down, to attach to the series of data points given by the selected X and Yn. For example, a column designated U3 supplies 'up' error bar information for use with the column designated Y3. Hn/Vn - Combines Ln & Rn / Un & Dn designations; that is, provides horizontal/vertical error bar lengths in both directions. When constructing a graph, Tau looks for the first occurrence of a given column meaning and ignores any others. For example, if you have two columns both designated 'X", (if “Many Xs” is not selected) or two designated ‘X13’ (if “Many Xs” is selected) the second will be ignored. + Plot (many) dbox. This performs the actions of the "Plot" dbox on a number of columns, the parameters being set to the values for the current column (the one the caret is sitting in). To determine which columns to act upon, type an appropriate string into the writable icon. This string can be either: 1) A list of column numbers separated by commas, including ranges. For example, "3,6-9,11" will act on columns 3, 6, 7, 9 and 11; or 2) A BASIC logical expression which includes the "#" character. The program substitutes the # for each column number in turn. Those columns for which the expression is TRUE are acted upon. For example, the string "(# MOD2)=0" acts only on the even numbered columns, and "#>5 AND #<9" acts only on columns 6, 7 and 8. The column's tag number can also be changed. Specify a BASIC expression with the "#" character again specifying the column number. + Calculate dbox. To fill the highlit area of the column with the caret with the results of a calculation, enter a valid BASIC expression. To use values from worksheet column n as arguments, use #n; to use values from the selected column, use #@; to use the row number (the number shown down the left side of the worksheet), use ##. For example, if you want to plot a graph of EXP(X) versus X, from -5 to 5 in 50 steps. Start with an empty worksheet. Highlight rows 0 to 50 in column 0. In the Calculate dbox, enter the expression: (##-25)/5, to give values from -5 to 5. Double-click on column 1 to highlight rows 0 to 50, then calculate: EXP(#0). Designate column 0 as 'X' and column 1 as, for example, 'Y1'. You can define your own functions for use in calculations: write a BASIC library containing the FN definition, then drag the BASIC file onto the Tau main window. Tau will install the library. Make sure the function name doesn't begin FNT..., to guarantee no conflict with Tau's internal FN definitions. A simple example 'Sinc' is included. You can also use Calculate to copy or move data from one column to another - for example, to copy column 3, use the expression: #3. + Best fit dbox. Performs linear/log regression (depending on whether X/Y log scales are currently selected) on X,Y data. If “many Xs” is not selected, these data are supplied by the selected rows of the data columns designated X and Yn respectively. If “Many Xs” is selected, the x-data relevant for Yn are used. You select the Yn to use - note this is NOT the column number, but the Y tag. The Y values given by the regression are then inserted into the highlit columns. You can force the regression to pass through a given point (usually the origin). A window is opened for information showing the equation of the fit, and the correlation if this is relevant (i.e., if the regression has not been forced to pass through a given point). Note that the best fit can be used to fit: a straight line y = mx + c (use linear-linear in the scale db) an exponential fit y = a.exp(bx) (use linear x, log y in the scale db) a log fit y = a.log x + b (use log x, linear y in the scale db) a power law (use log x and log y in the scale db) + Normalise. Finds the maximum absolute value in the highlit area, then divides all highlit cells by that value. + Sort. When the item is clicked, the highlit rows across all columns are sorted in ascending order of the values in the highlit column. ----------------------------------------------------------------------------- Save submenu. All items but one lead to a Save dialogue box. + Draw file THIS IS THE PRIMARY OUTPUT OF TAU !!! Saving a Draw file initiates the construction of the graph as defined by the values in the worksheet and the various style variables. The resultant Draw file can be imported directly into other applications, or edited using !Draw; for example, if you want to combine several graphs onto one diagram. F3 does a quick save to a Draw file also. + Tau file Makes a copy of the complete state of Tau in a file of type 082 (TauFile). However, information about any user function libraries currently in place is not saved. + Tau style The Tau equivalent of a graphics template file, to make it easier to produce a batch of graphs with the same style. + CSV data Export data from the worksheet in the form of textual CSV (comma separated values). Export is influenced by the selections made in the Options dbox (see below). + Text data Export data in the form of spaced text. Also uses Options dbox. + Binary data Export numerical data in BASIC PRINT# format. This saves space. The first datum in the file is an integer indicating the number of columns the data spans. Also uses Options dbox. + Options dbox This is a dbox of data export options. Choose to use an isolated point character '.' to mark blank cells, an 'M' character to mark 'move' cells, whether to export data in order of meaning (Y1, Y2, etc) or not, whether to export the whole worksheet or just a highlit selection, and whether to export the number of columns as the first datum when saving a Binary file. ----------------------------------------------------------------------------- View option. If you click on "View" in the main menu, or on the Tau icon in the top left corner, a window will open that displays the graph. This window has its own menu, which should be self-explanatory. Dragging any drawfile into Tau will open the View window to display that file. Tau thus acts as a drawfile viewer. ----------------------------------------------------------------------------- Quitting Tau. If you click on the Close icon of the main window, you do not actually leave Tau: clicking on the icon bar icon restores the main window unchanged. To quit Tau, select Quit from the icon bar menu.