Stefan Gerlach <gerlach@mbi-berlin.de>
Revision 1.2.1
Copyright © 2003 Stefan Gerlach
Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.1 or any later version published by the Free Software Foundation; with no Invariant Sections, with no Front-Cover Texts, and with no Back-Cover Texts. A copy of the license is included in the section entitled "GNU Free Documentation License".
LabPlot is a program for two- and three-dimensional function plotting and data analysis.
Table of Contents
Introduction
LabPlot is a program for two- and three-dimensional graphical presentation of data sets and functions. LabPlot allows you to work with multiple plots which each can have multiple graphs. The graphs can be produced from data or from functions.
All settings of a complete set of plots can be saved in a project files. These project files may be chosen by command line parameters, using the File menu, or by drag and drop.
Every object (title, legend, axes) can be dragged with the mouse. A doubleclick on an object opens a corresponding dialog with many options.
The settings of a plot/graph may also be changed using the Appearance menu. With the Edit menu additional data sets and functions (graphs) can be included which can be displayed in the same as well as in different plot.
Version 1.2.1 (October 26, 2003)
much improved GUI
better KDE integration
richtext title and axes label
improved 3d plotting
new analysis functions
better data reading
configure and save user settings
examples
Version 1.2.0 (September 08, 2003)
new improved internal plot structure
parser support for functions with more parameters
new surface plot with contour support and legend
support for jpeg2000 and tiff
user guide (this handbook)
more buxfixes
Version 1.1.1 (July 26, 2003)
matrix-data-reading
paradensity plots from function and data
parser completly rewritten
colored and scaled printing
export plot as graphics
more flexible data reading
improved axis tics label (format and position)
more bugfixes
Version 1.1 (June 22, 2003)
more object attributes (title color, grid color, etc.)
support 2d errorbars
drag and drop of the title, the axes with correct rescaling
improved save and open of all plots in a project file
lots of bug fixes
Version 1.0.3 (May 11, 2003)
Plot list in menubar
improved workspace management
drag and drop of the legend
EditDialog for editing data
Version 1.0.2 (April 4, 2003)
shift plot with toolbuttons
scaling of plot with toolbuttons
opening Dialogs via mouse click
improved print preview
Version 1.0.1 (March 18, 2003)
Print Preview implemented
introduced graph label different from name
Version 1.0 (March 3, 2003; renamed to LabPlot)
support for KDE 3.0 and KDE 2.x
automake and autoconf scripts (./configure)
Version 0.9.x (February 26, 2003)
improved DataDialog
save and open of an Plot
started with i18n (de)
started with migration from QT to KDE
improved ListDialog
changing of data and function graphs in ListDialog
support for grid in 2d and 3d plots
Version 0.4.0 (October 7, 2002)
support for 3D Plots
using GraphList for storing all graph of a plot
better scaling of the whole plot
new class GraphM for matrix-data support
Version 0.2.1 (June 30, 2001)
Legend in Plot
ListDialog for all graphs in a Plot
Version 0.2 (June 16, 2001)
first PlotWidget with single graph
creating data via FunctionDialog
Version 0.1 (May 20, 2001; first release under the name QPlot)
Using LabPlot
When starting LabPlot from the command prompt, you can supply the names of a project file:
LabPlot [file.lpl...]
The following command line help options are available
- LabPlot --help
This lists the most basic options available at the command line.
- LabPlot --help-qt
This lists the options available for changing the way LabPlot interacts with Qt.
- LabPlot --help-kde
This lists the options available for changing the way LabPlot interacts with KDE.
- LabPlot --help-all
This lists all of the command line options.
- LabPlot --author
Lists LabPlot's author in the terminal window
- LabPlot --version
Lists version information for Qt, KDE, and LabPlot. Also available through LabPlot -v
Drag and Drop
LabPlot supports the Drag and Drop protocol of KDE and Qt. This means that you can open a project by dragging their symbols onto the LabPlot window. Project files ahould have the extension .lpl.
Positioning with the Mouse
LabPlotsupports dragging of the axes, title, legend and axes label with the mouse.
To move an item, its area has to be clicked with the left mouse button. When the mouse is moved with the left mouse button pressed, the plot is continously updated to display the new position. After releasing of the mouse button the item is dropped there.
Status Bar
The horizontal and vertical positions of the mouse pointer in the plot area are displayed in data units on the right side of the status bar at the bottom of the LabPlot window.
Command Reference
- File->Open (Ctrl-o)
Opens a LabPlot project file.
In a project file all settings and all plots are stored in ASCII format.
- File->Open Recent
Opens a recent LabPlot project file.
Here the last used 10 project files are listet.
- File->Save (Ctrl-s)
Saves the actual project.
If you haven't saved the project before, you are asked to select a project file name.
- File->Save As (Ctrl-a)
Saves the actual project under a different name.
- File->Save As Image (Ctrl-v)
Saves the active plot as a graphic.
Here you have the possibility to save the active plot under different image formats. Currently supported are : bmp, jpg, jpg2000, pbm, pgm, png, ppm, tiff, xbm and xpm.
- File->Print (Ctrl-p)
Prints the active plot.
Here a print dialog is opened where you can select the printer, different paper sizes, etc.
- File->Print Preview
Open a print preview.
This item opens an embedded print preview of the active plot in A5 landscape. If the print preview is active you can close it with this item.
- File->Quit (Ctrl-q)
Quit LabPlot.
The Edit Menu
- Edit->Graph List (Ctrl-g)
Opens the graph list dialog. In the list dialog you can manipulate the graphs of a plot.
- Edit->2D Function (Ctrl-e)
Opens the 2d function dialog. This item add a new graph to the active 2d plot. If a 3d plot is active or none an empty plot is created.
The graph is created from a 2d function.
- Edit->2D Surface Function (Ctrl-u)
Opens the 2d surface function dialog. This item add a new surface plot. If a 3d plot is active or none an empty plot is created.
The plot is created from a 2d function.
- Edit->2D Data (Ctrl-d)
Opens the 2d data dialog. This item add a new graph to the active 2d plot. If a 3d plot is active or none an empty plot is created.
The plot is created from a given 2d dataset.
- Edit->3D Function (Ctrl-f)
Opens the 3d function dialog. This item add a new graph to the active 3d plot. If a 2d plot is active or none an empty plot is created.
The plot is created from a given 3d function.
- Edit->3D Data (Ctrl-i)
Opens the 3d data dialog. This item add a new graph to the active 3d plot. If a 2d plot is active or none an empty plot is created.
The plot is created from a given 3d dataset.
The Plot Menu
- Plot->New 2D Plot (Ctrl-n)
This is used to open an empty 2D Plot.
- Plot->New 3D Plot (Ctrl-m)
This is used to open an empty 3D Plot.
- Plot->Clear (Ctrl-c)
Clear the active plot. With this item all graphs in the plot are cleared and you get an empty plot like from "New 2D/3D Plot".
- Plot->Close (Ctrl-w)
Closes the active worksheet. With this item you can also close the print preview.
The Analysis Menu
- Plot->Average (Alt-a)
Opens the Average Dialog Here you can create a new graph from the averaged data of any other graph.
- Plot->Smooth (Alt-s)
Opens the Smooth Dialog Here you can create a new graph from the smoothed data of any other graph.
- Plot->Prune (Alt-r)
Opens the Prune Dialog Here you can create a new graph from the pruned data of any other graph.
The Appearance Menu
- Appearance->Plot Settings (Ctrl-j)
Opens the plot dialog. Here you can make the settings that are equal to all graph in a plot.
- Appearance->Axes Settings (Ctrl-b)
Opens the axes dialog. Here you can change the settings of the axes in a plot.
- Appearance->Title Dialog (Ctrl-t)
Opens the title dialog. Here you can change the settings of the title in a plot.
- Appearance->Legend Dialog (Ctrl-l)
Opens the legend dialog. Here you can change the settings of the legend in a plot.
The Worksheet List Menu
The Settings Menu
- Settings->Fullscreen (Ctrl+Shift-f)
Show the workspace in full screen mode.
- Settings->Show Menubar (Ctrl-m)
Toggle the menubar.
- Settings->CConfigure LabPlot
Configure user settings of LabPlot.
- Settings->Save settings
Save all the user settings of LabPlot.
The Help Menu
- Help->Contents (F1)
Here the contents page of the help for LabPlot is available.
- Help->Examples
Here you will find some LabPlot example projects.
- Help->About LabPlot
Displays essential information about LabPlot.
Main Tool Bar
Side Tool Bar
The LabPlot side tool bar contains the following buttons:
| Button | Action |
|---|---|
| X | Autoscale X. |
| Y | Autoscale Y. |
| Z | Autoscale Z. |
| Left | Shift all graphs to the left. |
| Right | Shift all graphs to the right. |
| Up | Shift all graphs up. |
| Down | Shift all graphs to the down. |
| X+ | Increases magnification in X. |
| X- | Decreases magnification in X. |
| Y+ | Increases magnification in Y. |
| Y- | Decreases magnification in Y. |
| Z+ | Increases magnification in Z. |
| Z- | Decreases magnification in Z. |
The Dialogs
The dialog Function is used to create and perform the settings for function plots. It looks the same for 2d, surface and 3d plots. Only a few plot specific things differ. Especially the Style is different for surface plots.
The first lineedit contains the expression for the plot function. The entered expression is evaluated via a powerful parser. For a complete list of supported functions see the parser section.
the second lineedit is for setting the label of the created graph. This is the label which you see in the legend.
In the "Range" and "Number of Points" section you can select the range and the number of points for the created function.
With the remaining style items you can influence the appearance of the function. If you create a normal function the first selection defines the line style (Lines, NoLines, Steps, Boxes, Impulses), the color and if you want to have it filled (with a different color). The other items select the symbol for the plot points, with color, size, if it should be filled and with which color. If you create a surface plot you have the possibility to select whether to show a density or contour plot, or both. Then you can select the number of levels for contour plots and the colorscale for density plots.
For changing the settings of a function you have to select the change button in the list dialog. For changing the style of a surface plot you can also use the "Plot Settings" dialog.
Data
The dialog Data is used to create graphs from data files.
This dialog looks very similar to the function dialog. There are some differences though. You have to select a data file to open in the first lineedit. You can use the "New" button to open a file dialog for this. In the "Read from column" section you can enter from which column you want to read the corresponding values. If unsure use the check button to have a look at the data file. You can select here also from which to which row to read data and what separating character is used. The "auto" separation detectes all number and combination of whitespaces.
The "Read As" section selects the kind of data in the data file. The "Graph Type" selects the type of graph to create. From x-y data you can make only 2 dimensional plots. From x-y-z data you can create error and suface plots (2D data dialog) or density, contour or 3d plots (3D data dialog). From matrix data you can create density or contour plots (2D data dialog) or 3d plots (3D data dialog).
List
The list dialog is the central point for dealing with the different graphs of a plot. Here you have an overview of all graphs and you can manipulate them. You can reach the list dialog via the Edit->Graphs menu or by double clicking inside the plot.
With the buttons "Add Datafile" and "Add Function" you can add a graph from data or function to the plot. (see function dialog or data dialog. ) With "Delete" you can easily delete the seleted graph. With "Change" you can change the settings of the graph.
The "Export" button dumps the graph into a selected data file and the "Edit" button gets you to the edit dialog. Here you can edit the data of the selected graph.
Edit
With the edit dialog you can easily edit the data of a graph. You can reach this dialog via the list dialog.
The table on the top side shows you all the data. Here you can select which rows and columns you want to edit. You can delete or sort selected rows ascending or descending with the buttons under the Table. You can also evaluate an expression to the selected rows and columns. Here the same powerful parser features like in the function dialog can be used. For a list of available functions see the parser section.
Appearance
With the four appearance dialogs you can influence the settings of the active plot. You can reach this dialogs via the "Appearance" menu or by double clicking on the object in the plot.
The graph dialog lets you select the background color, the graph background color (inside the plot) and the ranges for the different axes. The autorange functionality can also be reached from the side tool bar. If you have a surface plot you can also change the style settings here.
The axes dialog lets you change the settings for the different axes. It opens if you click on one of the axes.
In the upper region you have a list of all axes. Here you can select the axis to change. To enable or disable the axis use the checkbutton at the top of the dialog. Under the axes list you have a tab widget where you can change a lot of different settings (color, tics, grid, etc.).
In the title dialog you can change parameters of the title (label, size and font). The dialog open with double clicking on the title.
Parser functions
The LabPlot parser allows you to use following functions:
| Function | Description |
|---|---|
| acos(x) | Arc cosine |
| acosh(x) | Arc hyperbolic cosine |
| asin(x) | Arcsine |
| asinh(x) | Arc hyperbolic sine |
| atan(x) | Arctangent |
| atan2(y,x) | arc tangent function of two variables |
| atanh(x) | Arc hyperbolic tangent |
| beta(a,b) | Beta |
| cbrt(x) | Cube root |
| ceil(x) | Truncate upward to integer |
| chbevl(x, coef, N) | Evaluate Chebyshev series |
| chdtrc(df,x) | Complemented Chi square |
| chdtr(df,x) | Chi square distribution |
| chdtri(df,y) | Inverse Chi square |
| cos(x) | Cosine |
| cosh(x) | Hyperbolic cosine |
| cosm1(x) | cos(x)-1 |
| dawsn(x) | Dawson's integral |
| ellie(phi,m) | Incomplete elliptic integral (E) |
| ellik(phi,m) | Incomplete elliptic integral (E) |
| ellpe(x) | Complete elliptic integral (E) |
| ellpk(x) | Complete elliptic integral (K) |
| exp(x) | Exponential, base e |
| expm1(x) | exp(x)-1 |
| expn(n,x) | Exponential integral |
| fabs(x) | Absolute value |
| fac(i) | Factorial |
| fdtrc(ia,ib,x) | Complemented F |
| fdtr(ia,ib,x) | F distribution |
| fdtri(ia,ib,y) | Inverse F distribution |
| gdtr(a,b,x) | Gamma distribution |
| gdtrc(a,b,x) | Complemented gamma |
| hyp2f1(a,b,c,x) | Gauss hypergeometric function |
| hyperg(a,b,x) | Confluent hypergeometric 1F1 |
| i0(x) | Modified Bessel, order 0 |
| i0e(x) | Exponentially scaled i0 |
| i1(x) | Modified Bessel, order 1 |
| i1e(x) | Exponentially scaled i1 |
| igamc(a,x) | Complemented gamma integral |
| igam(a,x) | Incomplete gamma integral |
| igami(a,y0) | Inverse gamma integral |
| incbet(aa,bb,xx) | Incomplete beta integral |
| incbi(aa,bb,yy0) | Inverse beta integral |
| iv(v,x) | Modified Bessel, nonint. order |
| j0(x) | Bessel, order 0 |
| j1(x) | Bessel, order 1 |
| jn(n,x) | Bessel, order n |
| jv(n,x) | Bessel, noninteger order |
| k0(x) | Mod. Bessel, 3rd kind, order 0 |
| k0e(x) | Exponentially scaled k0 |
| k1(x) | Mod. Bessel, 3rd kind, order 1 |
| k1e(x) | Exponentially scaled k1 |
| kn(nn,x) | Mod. Bessel, 3rd kind, order n |
| lbeta(a,b) | Natural log of |beta| |
| ldexp(x,exp) | multiply floating-point number by integral power of 2 |
| log(x) | Logarithm, base e |
| log10(x) | Logarithm, base 10 |
| logb(x) | ?? |
| log1p(x) | log(1+x) |
| ndtr(x) | Normal distribution |
| ndtri(x) | Inverse normal distribution |
| pdtrc(k,m) | Complemented Poisson |
| pdtr(k,m) | Poisson distribution |
| pdtri(k,y) | Inverse Poisson distribution |
| pow(x,y) | power function |
| psi(x) | Psi (digamma) function |
| rgamma(x) | Reciprocal Gamma |
| rint(x) | round to nearest integer |
| sin(x) | Sine |
| sinh(x) | Hyperbolic sine |
| spence(x) | Dilogarithm |
| sqrt(x) | Square root |
| stdtr(k,t) | Student's t distribution |
| stdtri(k,p) | Inverse student's t distribution |
| struve(v,x) | Struve function |
| tan(x) | Tangent |
| tanh(x) | Hyperbolic tangent |
| true_gamma(x) | ?? |
| y0(x) | Bessel, second kind, order 0 |
| y1(x) | Bessel, second kind, order 1 |
| yn(n,x) | Bessel, second kind, order n |
| yv(v,x) | Bessel, noninteger order |
| zeta(x,y) | Riemann Zeta function |
| zetac(x) | Two argument zeta function |
GSL special function
For more information about the functions see the documentation of GSL.
| Function | Description |
|---|---|
| gsl_log1p(x) | log(1+x) |
| gsl_expm1(x) | exp(x)-1 |
| gsl_hypot(x,y) | sqrt{x^2 + y^2} |
| gsl_acosh(x) | arccosh(x) |
| gsl_asinh(x) | arcsinh(x) |
| gsl_atanh(x) | arctanh(x) |
| airy_Ai(x) | Airy function Ai(x) |
| airy_Bi(x) | Airy function Bi(x) |
| airy_Ais(x) | scaled version of the Airy function S_A(x) Ai(x) |
| airy_Bis(x) | scaled version of the Airy function S_B(x) Bi(x) |
| airy_Aid(x) | Airy function derivative Ai'(x) |
| airy_Bid(x) | Airy function derivative Bi'(x) |
| airy_Aids(x) | derivative of the scaled Airy function S_A(x) Ai(x) |
| airy_Bids(x) | derivative of the scaled Airy function S_B(x) Bi(x) |
| airy_0_Ai(s) | s-th zero of the Airy function Ai(x) |
| airy_0_Bi(s) | s-th zero of the Airy function Bi(x) |
| airy_0_Aid(s) | s-th zero of the Airy function derivative Ai'(x) |
| airy_0_Bid(s) | s-th zero of the Airy function derivative Bi'(x) |
| bessel_J0(x) | regular cylindrical Bessel function of zeroth order, J_0(x) |
| bessel_J1(x) | regular cylindrical Bessel function of first order, J_1(x) |
| bessel_Jn(n,x) | regular cylindrical Bessel function of order n, J_n(x) |
| bessel_Y0(x) | irregular cylindrical Bessel function of zeroth order, Y_0(x) |
| bessel_Y1(x) | irregular cylindrical Bessel function of first order, Y_1(x) |
| bessel_Yn(n,x) | irregular cylindrical Bessel function of order n, Y_n(x) |
| bessel_I0(x) | regular modified cylindrical Bessel function of zeroth order, I_0(x) |
| bessel_I1(x) | regular modified cylindrical Bessel function of first order, I_1(x) |
| bessel_In(n,x) | regular modified cylindrical Bessel function of order n, I_n(x) |
| bessel_I0s(x) | scaled regular modified cylindrical Bessel function of zeroth order, exp (-|x|) I_0(x) |
| bessel_I1s(x) | scaled regular modified cylindrical Bessel function of first order, exp(-|x|) I_1(x) |
| bessel_Ins(n,x) | scaled regular modified cylindrical Bessel function of order n, exp(-|x|) I_n(x) |
| bessel_K0(x) | irregular modified cylindrical Bessel function of zeroth order, K_0(x) |
| bessel_K1(x) | irregular modified cylindrical Bessel function of first order, K_1(x) |
| bessel_Kn(n,x) | irregular modified cylindrical Bessel function of order n, K_n(x) |
| bessel_K0s(x) | scaled irregular modified cylindrical Bessel function of zeroth order, exp (x) K_0(x) |
| bessel_K1s(x) | scaled irregular modified cylindrical Bessel function of first order, exp(x) K_1(x) |
| bessel_Kns(n,x) | scaled irregular modified cylindrical Bessel function of order n, exp(x) K_n(x) |
| bessel_j0(x) | regular spherical Bessel function of zeroth order, j_0(x) |
| bessel_j1(x) | regular spherical Bessel function of first order, j_1(x) |
| bessel_j2(x) | regular spherical Bessel function of second order, j_2(x) |
| bessel_jl(l,x) | regular spherical Bessel function of order l, j_l(x) |
| bessel_y0(x) | irregular spherical Bessel function of zeroth order, y_0(x) |
| bessel_y1(x) | irregular spherical Bessel function of first order, y_1(x) |
| bessel_y2(x) | irregular spherical Bessel function of second order, y_2(x) |
| bessel_yl(l,x) | irregular spherical Bessel function of order l, y_l(x) |
| bessel_i0s(x) | scaled regular modified spherical Bessel function of zeroth order, exp(-|x|) i_0(x) |
| bessel_i1s(x) | scaled regular modified spherical Bessel function of first order, exp(-|x|) i_1(x) |
| bessel_i2s(x) | scaled regular modified spherical Bessel function of second order, exp(-|x|) i_2(x) |
| bessel_ils(l,x) | scaled regular modified spherical Bessel function of order l, exp(-|x|) i_l(x) |
| bessel_k0s(x) | scaled irregular modified spherical Bessel function of zeroth order, exp(x) k_0(x) |
| bessel_k1s(x) | scaled irregular modified spherical Bessel function of first order, exp(x) k_1(x) |
| bessel_k2s(x) | scaled irregular modified spherical Bessel function of second order, exp(x) k_2(x) |
| bessel_kls(l,x) | scaled irregular modified spherical Bessel function of order l, exp(x) k_l(x) |
| bessel_Jnu(nu,x) | regular cylindrical Bessel function of fractional order nu, J_\nu(x) |
| bessel_Ynu(nu,x) | irregular cylindrical Bessel function of fractional order nu, Y_\nu(x) |
| bessel_Inu(nu,x) | regular modified Bessel function of fractional order nu, I_\nu(x) |
| bessel_Inus(nu,x) | scaled regular modified Bessel function of fractional order nu, exp(-|x|) I_\nu(x) |
| bessel_Knu(nu,x) | irregular modified Bessel function of fractional order nu, K_\nu(x) |
| bessel_lnKnu(nu,x) | logarithm of the irregular modified Bessel function of fractional order nu,ln(K_\nu(x)) |
| bessel_Knus(nu,x) | scaled irregular modified Bessel function of fractional order nu, exp(|x|) K_\nu(x) |
| bessel_0_J0(s) | s-th positive zero of the Bessel function J_0(x) |
| bessel_0_J1(s) | s-th positive zero of the Bessel function J_1(x) |
| bessel_0_Jnu(nu,s) | s-th positive zero of the Bessel function J_nu(x) |
| clausen(x) | Clausen integral Cl_2(x) |
| hydrogenicR_1(Z,R) | lowest-order normalized hydrogenic bound state radial wavefunction R_1 := 2Z \sqrt{Z} \exp(-Z r) |
| hydrogenicR(n,l,Z,R) | n-th normalized hydrogenic bound state radial wavefunction |
| dawson(x) | Dawson's integral |
| debye_1(x) | first-order Debye function D_1(x) = (1/x) \int_0^x dt (t/(e^t - 1)) |
| debye_2(x) | second-order Debye function D_2(x) = (2/x^2) \int_0^x dt (t^2/(e^t - 1)) |
| debye_3(x) | third-order Debye function D_3(x) = (3/x^3) \int_0^x dt (t^3/(e^t - 1)) |
| debye_4(x) | fourth-order Debye function D_4(x) = (4/x^4) \int_0^x dt (t^4/(e^t - 1)) |
| dilog(x) | dilogarithm |
| ellint_Kc(k) | complete elliptic integral K(k) |
| ellint_Ec(k) | complete elliptic integral E(k) |
| ellint_F(phi,k) | incomplete elliptic integral F(phi,k) |
| ellint_E(phi,k) | incomplete elliptic integral E(phi,k) |
| ellint_P(phi,k,n) | incomplete elliptic integral P(phi,k,n) |
| ellint_D(phi,k,n) | incomplete elliptic integral D(phi,k,n) |
| ellint_RC(x,y) | incomplete elliptic integral RC(x,y) |
| ellint_RD(x,y,z) | incomplete elliptic integral RD(x,y,z) |
| ellint_RF(x,y,z) | incomplete elliptic integral RF(x,y,z) |
| ellint_RJ(x,y,z) | incomplete elliptic integral RJ(x,y,z,p) |
| gsl_erf(x) | error function erf(x) = (2/\sqrt(\pi)) \int_0^x dt \exp(-t^2) |
| gsl_erfc(x) | complementary error function erfc(x) = 1 - erf(x) = (2/\sqrt(\pi)) \int_x^\infty \exp(-t^2) |
| log_erfc(x) | logarithm of the complementary error function \log(\erfc(x)) |
| erf_Z(x) | Gaussian probability function Z(x) = (1/(2\pi)) \exp(-x^2/2) |
| erf_Q(x) | upper tail of the Gaussian probability function Q(x) = (1/(2\pi)) \int_x^\infty dt \exp(-t^2/2) |
| gsl_exp(x) | exponential function |
| exprel(x) | (exp(x)-1)/x using an algorithm that is accurate for small x |
| exprel_2(x) | 2(exp(x)-1-x)/x^2 using an algorithm that is accurate for small x |
| exprel_n(n,x) | n-relative exponential, which is the n-th generalization of the functions `gsl_sf_exprel' |
| exp_int_E1(x) | exponential integral E_1(x), E_1(x) := Re \int_1^\infty dt \exp(-xt)/t |
| exp_int_E2(x) | second-order exponential integral E_2(x), E_2(x) := \Re \int_1^\infty dt \exp(-xt)/t^2 |
| exp_int_Ei(x) | exponential integral E_i(x), Ei(x) := PV(\int_{-x}^\infty dt \exp(-t)/t) |
| shi(x) | Shi(x) = \int_0^x dt sinh(t)/t |
| chi(x) | integral Chi(x) := Re[ gamma_E + log(x) + \int_0^x dt (cosh[t]-1)/t] |
| expint_3(x) | exponential integral Ei_3(x) = \int_0^x dt exp(-t^3) for x >= 0 |
| si(x) | Sine integral Si(x) = \int_0^x dt sin(t)/t |
| ci(x) | Cosine integral Ci(x) = -\int_x^\infty dt cos(t)/t for x > 0 |
| atanint(x) | Arctangent integral AtanInt(x) = \int_0^x dt arctan(t)/t |
| fermi_dirac_m1(x) | complete Fermi-Dirac integral with an index of -1, F_{-1}(x) = e^x / (1 + e^x) |
| fermi_dirac_0(x) | complete Fermi-Dirac integral with an index of 0, F_0(x) = \ln(1 + e^x) |
| fermi_dirac_1(x) | complete Fermi-Dirac integral with an index of 1, F_1(x) = \int_0^\infty dt (t /(\exp(t-x)+1)) |
| fermi_dirac_2(x) | complete Fermi-Dirac integral with an index of 2, F_2(x) = (1/2) \int_0^\infty dt (t^2 /(\exp(t-x)+1)) |
| fermi_dirac_int(j,x) | complete Fermi-Dirac integral with an index of j, F_j(x) = (1/Gamma(j+1)) \int_0^\infty dt (t^j /(exp(t-x)+1)) |
| fermi_dirac_mhalf(x) | complete Fermi-Dirac integral F_{-1/2}(x) |
| fermi_dirac_half(x) | complete Fermi-Dirac integral F_{1/2}(x) |
| fermi_dirac_3half(x) | complete Fermi-Dirac integral F_{3/2}(x) |
| fermi_dirac_inc_0(x,b) | incomplete Fermi-Dirac integral with an index of zero, F_0(x,b) = \ln(1 + e^{b-x}) - (b-x) |
| gamma(x) | Gamma function |
| lngamma(x) | logarithm of the Gamma function |
| gammastar(x) | regulated Gamma Function \Gamma^*(x) for x > 0 |
| gammainv(x) | reciprocal of the gamma function, 1/Gamma(x) using the real Lanczos method. |
| taylorcoeff(n,x) | Taylor coefficient x^n / n! for x >= 0 |
| fact(n) | factorial n! |
| doublefact(n) | double factorial n!! = n(n-2)(n-4)... |
| lnfact(n) | logarithm of the factorial of n, log(n!) |
| lndoublefact(n) | logarithm of the double factorial n!! = n(n-2)(n-4)... |
| choose(n,m) | combinatorial factor `n choose m' = n!/(m!(n-m)!) |
| lnchoose(n,m) | logarithm of `n choose m' |
| poch(a,x) | Pochhammer symbol (a)_x := \Gamma(a + x)/\Gamma(x) |
| lnpoch(a,x) | logarithm of the Pochhammer symbol (a)_x := \Gamma(a + x)/\Gamma(x) |
| pochrel(a,x) | relative Pochhammer symbol ((a,x) - 1)/x where (a,x) = (a)_x := \Gamma(a + x)/\Gamma(a) |
| gamma_inc_Q(a,x) | normalized incomplete Gamma Function P(a,x) = 1/Gamma(a) \int_x\infty dt t^{a-1} exp(-t) for a > 0, x >= 0 |
| gamma_inc_P(a,x) | complementary normalized incomplete Gamma Function P(a,x) = 1/Gamma(a) \int_0^x dt t^{a-1} exp(-t) for a > 0, x >= 0 |
| gsl_beta(a,b) | Beta Function, B(a,b) = Gamma(a) Gamma(b)/Gamma(a+b) for a > 0, b > 0 |
| lnbeta(a,b) | logarithm of the Beta Function, log(B(a,b)) for a > 0, b > 0 |
| betainc(a,b,x) | normalize incomplete Beta function B_x(a,b)/B(a,b) for a > 0, b > 0 |
| gegenpoly_1(lambda,x) | Gegenbauer polynomial C^{lambda}_1(x) |
| gegenpoly_2(lambda,x) | Gegenbauer polynomial C^{lambda}_2(x) |
| gegenpoly_3(lambda,x) | Gegenbauer polynomial C^{lambda}_3(x) |
| gegenpoly_n(n,lambda,x) | Gegenbauer polynomial C^{lambda}_n(x) |
| hyperg_0F1(c,x) | hypergeometric function 0F1(c,x) |
| hyperg_1F1i(m,n,x) | confluent hypergeometric function 1F1(m,n,x) = M(m,n,x) for integer parameters m, n |
| hyperg_1F1(a,b,x) | confluent hypergeometric function 1F1(m,n,x) = M(m,n,x) for general parameters a,b |
| hyperg_Ui(m,n,x) | confluent hypergeometric function U(m,n,x) for integer parameters m,n |
| hyperg_U(a,b,x) | confluent hypergeometric function U(a,b,x) |
| hyperg_2F1(a,b,c,x) | Gauss hypergeometric function 2F1(a,b,c,x) for |
| hyperg_2F1c(ar,ai,c,x) | Gauss hypergeometric function 2F1(a_R + i a_I, a_R - i a_I, c, x) with complex parameters |
| hyperg_2F1r(ar,ai,c,x) | renormalized Gauss hypergeometric function 2F1(a,b,c,x) / Gamma(c) |
| hyperg_2F1cr(ar,ai,c,x) | renormalized Gauss hypergeometric function 2F1(a_R + i a_I, a_R - i a_I, c, x) / Gamma(c) |
| hyperg_2F0(a,b,x) | hypergeometric function 2F0(a,b,x) |
| laguerre_1(a,x) | generalized Laguerre polynomials L^a_1(x) |
| laguerre_2(a,x) | generalized Laguerre polynomials L^a_2(x) |
| laguerre_3(a,x) | generalized Laguerre polynomials L^a_3(x) |
| lambert_W0(x) | principal branch of the Lambert W function, W_0(x) |
| lambert_Wm1(x) | secondary real-valued branch of the Lambert W function, W_{-1}(x) |
| legendre_P1(x) | Legendre polynomials P_1(x) |
| legendre_P2(x) | Legendre polynomials P_2(x) |
| legendre_P3(x) | Legendre polynomials P_3(x) |
| legendre_Pl(l,x) | Legendre polynomials P_l(x) |
| legendre_Q0(x) | Legendre polynomials Q_0(x) |
| legendre_Q1(x) | Legendre polynomials Q_1(x) |
| legendre_Ql(l,x) | Legendre polynomials Q_l(x) |
| legendre_Plm(l,m,x) | associated Legendre polynomial P_l^m(x) |
| legendre_sphPlm(l,m,x) | normalized associated Legendre polynomial $\sqrt{(2l+1)/(4\pi)} \sqrt{(l-m)!/(l+m)!} P_l^m(x)$ suitable for use in spherical harmonics |
| conicalP_half(lambda,x) | irregular Spherical Conical Function P^{1/2}_{-1/2 + i \lambda}(x) for x > -1 |
| conicalP_mhalf(lambda,x) | regular Spherical Conical Function P^{-1/2}_{-1/2 + i \lambda}(x) for x > -1 |
| conicalP_0(lambda,x) | conical function P^0_{-1/2 + i \lambda}(x) for x > -1 |
| conicalP_1(lambda,x) | conical function P^1_{-1/2 + i \lambda}(x) for x > -1 |
| conicalP_sphreg(l,lambda,x) | Regular Spherical Conical Function P^{-1/2-l}_{-1/2 + i \lambda}(x) for x > -1, l >= -1 |
| conicalP_cylreg(l,lambda,x) | Regular Cylindrical Conical Function P^{-m}_{-1/2 + i \lambda}(x) for x > -1, m >= -1 |
| legendre_H3d_0(lambda,eta) | zeroth radial eigenfunction of the Laplacian on the 3-dimensional hyperbolic space, L^{H3d}_0(lambda,eta) := sin(lambda eta)/(lambda sinh(eta)) for eta >= 0 |
| legendre_H3d_1(lambda,eta) | zeroth radial eigenfunction of the Laplacian on the 3-dimensional hyperbolic space, L^{H3d}_1(lambda,eta) := 1/sqrt{lambda^2 + 1} sin(lambda eta)/(lambda sinh(eta)) (coth(eta) - lambda cot(lambda eta)) for eta >= 0 |
| legendre_H3d(l,lambda,eta) | L'th radial eigenfunction of the Laplacian on the 3-dimensional hyperbolic space eta >= 0, l >= 0 |
| gsl_log(x) | logarithm of X |
| loga(x) | logarithm of the magnitude of X, log(|x|) |
| logp(x) | log(1 + x) for x > -1 using an algorithm that is accurate for small x |
| logm(x) | log(1 + x) - x for x > -1 using an algorithm that is accurate for small x |
| gsl_pow(x,n) | power x^n for integer N |
| psii(n) | digamma function psi(n) for positive integer n |
| psi(x) | digamma function psi(n) for general x |
| psiy(y) | real part of the digamma function on the line 1+i y, Re[psi(1 + i y)] |
| ps1i(n) | Trigamma function psi'(n) for positive integer n |
| ps_n(m,x) | polygamma function psi^{(m)}(x) for m >= 0, x > 0 |
| synchrotron_1(x) | first synchrotron function x \int_x^\infty dt K_{5/3}(t) for x >= 0 |
| synchrotron_2(x) | second synchrotron function x K_{2/3}(x) for x >= 0 |
| transport_2(x) | transport function J(2,x) |
| transport_3(x) | transport function J(3,x) |
| transport_4(x) | transport function J(4,x) |
| transport_5(x) | transport function J(5,x) |
| hypot(x,y) | hypotenuse function \sqrt{x^2 + y^2} |
| sinc(x) | sinc(x) = sin(pi x) / (pi x) |
| lnsinh(x) | log(sinh(x)) for x > 0 |
| lncosh(x) | log(cosh(x)) |
| zetai(n) | Riemann zeta function zeta(n) for integer N |
| gsl_zeta(s) | Riemann zeta function zeta(s) for arbitrary s |
| hzeta(s,q) | Hurwitz zeta function zeta(s,q) for s > 1, q > 0 |
| etai(n) | eta function eta(n) for integer n |
| eta(s) | eta function eta(s) for arbitrary s |
GSL random number distributions
For more information about the functions see the documentation of GSL.
| Function | Description |
|---|---|
| gaussian(x,sigma) | probability density p(x) at X for a Gaussian distribution with standard deviation SIGMA |
| ugaussian(x) | unit Gaussian distribution. They are equivalent to the functions above with a standard deviation of one, SIGMA = 1 |
| gaussian_tail(x,a,sigma) | probability density p(x) at X for a Gaussian tail distribution with standard deviation SIGMA and lower limit A |
| ugaussian_tail(x,a) | tail of a unit Gaussian distribution. They are equivalent to the functions above with a standard deviation of one, SIGMA = 1 |
| bivariate_gaussian(x,y,sigma_x,sigma_y,rho) | probability density p(x,y) at (X,Y) for a bivariate gaussian distribution with standard deviations SIGMA_X, SIGMA_Y and correlation coefficient RHO |
| exponential(x,mu) | probability density p(x) at X for an exponential distribution with mean MU |
| laplace(x,a) | probability density p(x) at X for a Laplace distribution with mean A |
| exppow(x,a,b) | probability density p(x) at X for an exponential power distribution with scale parameter A and exponent B |
| cauchy(x,a) | probability density p(x) at X for a Cauchy distribution with scale parameter A |
| rayleigh(x,sigma) | robability density p(x) at X for a Rayleigh distribution with scale parameter SIGMA |
| rayleigh_tail(x,a,sigma) | probability density p(x) at X for a Rayleigh tail distribution with scale parameter SIGMA and lower limit A |
| landau(x) | probability density p(x) at X for the Landau distribution |
| gamma_pdf(x,a,b) | probability density p(x) at X for a gamma distribution with parameters A and B |
| flat(x,a,b) | probability density p(x) at X for a uniform distribution from A to B |
| lognormal(x,zeta,sigma) | probability density p(x) at X for a lognormal distribution with parameters ZETA and SIGMA |
| chisq(x,nu) | probability density p(x) at X for a chi-squared distribution with NU degrees of freedom |
| fdist(x,nu1,nu2) | probability density p(x) at X for an F-distribution with NU1 and NU2 degrees of freedom |
| tdist(x,nu) | probability density p(x) at X for a t-distribution with NU degrees of freedom |
| beta_pdf(x,a,b) | probability density p(x) at X for a beta distribution with parameters A and B |
| logistic(x,a) | probability density p(x) at X for a logistic distribution with scale parameter A |
| pareto(x,a,b) | probability density p(x) at X for a Pareto distribution with exponent A and scale B |
| weibull(x,a,b) | probability density p(x) at X for a Weibull distribution with scale A and exponent B |
| gumbel1(x,a,b) | probability density p(x) at X for a Type-1 Gumbel distribution with parameters A and B |
| gumbel2(x,a,b) | probability density p(x) at X for a Type-2 Gumbel distribution with parameters A and B |
| poisson(k,mu) | probability p(k) of obtaining K from a Poisson distribution with mean mu |
| bernoulli(k,p) | probability p(k) of obtaining K from a Bernoulli distribution with probability parameter P |
| binomial(k,p,n) | probability p(k) of obtaining K from a binomial distribution with parameters P and N |
| negative_binomial(k,p,n) | probability p(k) of obtaining K from a negative binomial distribution with parameters P and N |
| pascal(k,p,n) | probability p(k) of obtaining K from a Pascal distribution with parameters P and N |
| geometric(k,p) | probability p(k) of obtaining K from a geometric distribution with probability parameter P |
| hypergeometric(k,n1,n2,t) | probability p(k) of obtaining K from a hypergeometric distribution with parameters N1, N2, N3 |
| logarithmic(k,p) | probability p(k) of obtaining K from a logarithmic distribution with probability parameter P |
constants
| Constant | Description |
|---|---|
| PI1 | 1/pi |
| PI2 | 2/pi |
| PISQRT2 | 2/sqrt(pi) |
| E | e |
| LN2 | log_e 2 |
| LN10 | log_e 10 |
| LOG2E | log_2 e |
| LOG10E | log_10 e |
| PI | pi |
| PI_2 | pi/2 |
| PI_4 | pi/4 |
| SQRT2 | sqrt(2) |
| SQRT1_2 | 1/sqrt(2) |
GSL constants
For more information about this constants see the documentation of GSL.
| Constant | Description |
|---|---|
| c | The speed of light in vacuum |
| mu0 | The permeability of free space |
| e0 | The permittivity of free space |
| Na | Avogadro's number |
| F | The molar charge of 1 Faraday |
| k | The Boltzmann constant |
| R0 | The molar gas constant |
| V0 | The standard gas volume |
| Gauss | The magnetic field of 1 Gauss |
| mu | The length of 1 micron |
| ha | The area of 1 hectare |
| mph | The speed of 1 mile per hour |
| kmh | The speed of 1 kilometer per hour |
| au | The length of 1 astronomical unit (mean earth-sun distance) |
| G | The gravitational constant |
| ly | The distance of 1 light-year |
| pc | The distance of 1 parsec |
| g | The standard gravitational acceleration on Earth |
| ms | The mass of the Sun |
| e | The charge of the electron |
| eV | The energy of 1 electron volt |
| amu | The unified atomic mass |
| me | The mass of the electron |
| mmu | The mass of the muon |
| mp | The mass of the proton |
| mn | The mass of the neutron |
| alpha | The electromagnetic fine structure constant |
| Ry | The Rydberg constant |
| a0 | The Bohr radius |
| A | The length of 1 angstrom |
| barn | The area of 1 barn |
| muB | The Bohr Magneton |
| muN | The Nuclear Magneton |
| mue | The magnetic moment of the electron |
| mup | The magnetic moment of the proton |
| min | The number of seconds in 1 minute |
| h | The number of seconds in 1 hour |
| d | The number of seconds in 1 day |
| week | The number of seconds in 1 week |
| in | The length of 1 inch |
| ft | The length of 1 foot |
| yard | The length of 1 yard |
| mile | The length of 1 mile |
| mil | The length of 1 mil (1/1000th of an inch) |
| nmile | The length of 1 nautical mile |
| fathom | The length of 1 fathom |
| knot | The speed of 1 knot |
| pt | The length of 1 printer's point (1/72 inch) |
| texpt | The length of 1 TeX point (1/72.27 inch) |
| acre | The area of 1 acre |
| ltr | The volume of 1 liter |
| us_gallon | The volume of 1 US gallon |
| can_gallon | The volume of 1 Canadian gallon |
| uk_gallon | The volume of 1 UK gallon |
| quart | The volume of 1 quart |
| pint | The volume of 1 pint |
| pound | The mass of 1 pound |
| ounce | The mass of 1 ounce |
| ton | The mass of 1 ton |
| mton | The mass of 1 metric ton (1000 kg) |
| uk_ton | The mass of 1 UK ton |
| troy_ounce | The mass of 1 troy ounce |
| carat | The mass of 1 carat |
| gram_force | The force of 1 gram weight |
| pound_force | The force of 1 pound weight |
| kilepound_force | The force of 1 kilopound weight |
| poundal | The force of 1 poundal |
| cal | The energy of 1 calorie |
| btu | The energy of 1 British Thermal Unit |
| therm | The energy of 1 Therm |
| hp | The power of 1 horsepower |
| bar | The pressure of 1 bar |
| atm | The pressure of 1 standard atmosphere |
| torr | The pressure of 1 torr |
| mhg | The pressure of 1 meter of mercury |
| inhg | The pressure of 1 inch of mercury |
| inh2o | The pressure of 1 inch of water |
| psi | The pressure of 1 pound per square inch |
| poise | The dynamic viscosity of 1 poise |
| stokes | The kinematic viscosity of 1 stokes |
| stilb | The luminance of 1 stilb |
| lumen | The luminous flux of 1 lumen |
| lux | The illuminance of 1 lux |
| phot | The illuminance of 1 phot |
| ftcandle | The illuminance of 1 footcandle |
| lambert | The luminance of 1 lambert |
| ftlambert | The luminance of 1 footlambert |
| curie | The activity of 1 curie |
| roentgen | The exposure of 1 roentgen |
| rad | The absorbed dose of 1 rad |
The following constants are the same constants in cgs system :
| Constant | Description |
|---|---|
| c_cgs | |
| G_cgs | |
| h_cgs | |
| hbar_cgs | |
| mu0_cgs | |
| au_cgs | |
| ly_cgs | |
| pc_cgs | |
| g_cgs | |
| eV_cgs | |
| me_cgs | |
| mmu_cgs | |
| mp_cgs | |
| mn_cgs | |
| Ry_cgs | |
| k_cgs | |
| muB_cgs | |
| muN_cgs | |
| mue_cgs | |
| mup_cgs | |
| R0_cgs | |
| V0_cgs | |
| in_cgs | |
| ft_cgs | |
| yard_cgs | |
| mile_cgs | |
| nile_cgs | |
| fathom_cgs | |
| mil_cgs | |
| pt_cgs | |
| texpt_cgs | |
| mu_cgs | |
| A_cgs | |
| ha_cgs | |
| acre_cgs | |
| barn_cgs | |
| ltr_cgs | |
| us_gallon-cgs | |
| quart_cgs | |
| pint_cgs | |
| cup_cgs | |
| fluid_ouncs_cgs | |
| tablespoon_cgs | |
| teaspoon_cgs | |
| can_gallon_cgs | |
| uk_gallon_cgs | |
| mph_cgs | |
| kmh_cgs | |
| knot_cgs | |
| pound_cgs | |
| ouncs_cgs | |
| ton_cgs | |
| mton_cgs | |
| uk_ton_cgs | |
| troy_ounce_cgs | |
| carat_cgs | |
| amu_cgs | |
| gram_cgs | |
| pound_force_cgs | |
| kilopound_force_cgs | |
| poundal_cgs | |
| cal_cgs | |
| btu_cgs | |
| therm_cgs | |
| hp_cgs | |
| bar_cgs | |
| atm_cgs | |
| torr_cgs | |
| mhg_cgs | |
| inhg_cgs | |
| inh2o_cgs | |
| psi_cgs | |
| poise_cgs | |
| stokes_cgs | |
| F_cgs | |
| e_cgs | |
| G_cgs | |
| stilb_cgs | |
| lumen_cgs | |
| lux_cgs | |
| phot_cgs | |
| ftcandle_cgs | |
| lambert_cgs | |
| ftlambert_cgs | |
| curie_cgs | |
| roentgen_cgs | |
| rad_cgs | |
| sm_cgs | |
| a0_cgs | |
| e0_cgs |
Questions and Answers
Credits and License
LabPlot
Program copyright 2003 Stefan Gerlach <gerlach@mbi-berlin.de>
Thanks to
Edgar <egs@saltillo.cinvestav.mx> for suggestions and screenshots
Ron Crouch <va3rcc@bellnet.ca> for providing and supporting packages for SuSE 8.2.
Remember : LabPlot is under active development. So don't expect everything to work correct. Also there is a long list of missing features that will be included in later versions of LabPlot.
Because there are a lot things to do, i need every help i can get. Any contribution like wishes, corrections, patches, bug reports or screen shots is welcome.
Documentation copyright 2003 Stefan Gerlach <gerlach@mbi-berlin.de>
This documentation is licensed under the terms of the GNU Free Documentation License.
This program is licensed under the terms of the GNU General Public License.
Installation
LabPlot can be found on its homepage http://mitarbeiter.mbi-berlin.de/gerlach/Linux/LabPlot/.
Requirements
In order to successfully use LabPlot, you need at least a standard KDE 3.0 installation.
The following libraries are included in LabPlot :
Cephes Math Library Release 2.3: June, 1995 : adapted from Grace for using of powerful mathematical functions (parser)
qjp2io with JasPer Library : support for JPEG 2000 image format
qtiffio Library : support for tiff image format
Optional are following programs/libraries :
pstoedit : For exporting to *.eps,*.dxf,*.fig, etc. via pstoedit you need pstoedit installed.
Imagemagick/ImageMagick-c++ : For exporting to more than 100 image formats you need ImageMagick++ installed.
GNU scientific library (GSL) : if you want to use more special functions in the parser.
Compilation and Installation
In order to compile and LabPlot on your system, type the following in the base directory of LabPlot distribution:
% ./configure % make % make install
Since LabPlot uses autoconf and automake you should have not trouble compiling it. For RedHat 8 + 9 systems there are RPM packages available. There are binary executables for linux_x86, linux_x86_64 and solaris_sparc platforms. Use the "install" script to install on one of the selected platforms. Should you run into problems please report them to the author of LabPlot.