FOR NUMERICAL POSTPROCESSING AND RESULT VISUALIZATION USING PGFPLOTS AND PGFPLOTSTABLE. Christian Feuersänger

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1 A COMPLETE WORK-FLOW FOR NUMERICAL POSTPROCESSING AND RESULT VISUALIZATION USING PGFPLOTS AND PGFPLOTSTABLE Christian Feuersänger Institute for Numerical Simulation University of Bonn Seminar Technische Numerik 2009

2 OUTLINE INTRODUCTION Computer Experiments and Postprocessing Installation of PGFPLOTS 2 A SAMPLE WORK FLOW WITH PGFPLOTS Visualizing the plots Table postprocessing 3 CONCLUSION AND OUTLOOK

3 OUTLINE INTRODUCTION Computer Experiments and Postprocessing Installation of PGFPLOTS 2 A SAMPLE WORK FLOW WITH PGFPLOTS Visualizing the plots Table postprocessing 3 CONCLUSION AND OUTLOOK

4 COMPUTER EXPERIMENTS AND POSTPROCESSING Realizes algorithm Visualize result Measures quality and cost Prototype Computer Experiment Detailed cost and errors Produces data for result visualization Visualize data tables Show Measures as Plots Often: log-log scaling Involves number printing Show Measures as Tables Compute gradients Functional relations error = cost α

5 COMPUTER EXPERIMENTS AND POSTPROCESSING Realizes algorithm Visualize result Measures quality and cost Prototype Computer Experiment Detailed cost and errors Produces data for result visualization Visualize data tables Often: log-log scaling Involves number printing Show Measures as Tables Present all results in.tex Showdocument. Two approaches: Measures as Plots External graphics (.eps/.pdf) + \includegraphics 2 Graphics with LAT E X package PGFPLOTS. Compute gradients Functional relations error = cost α

6 WELL-KNOWN PROBLEMS OF EXTERNAL GRAPHICS In External graphics: Font sizes are good relative to the figure. Font sizes are bad relative to the embedding document. Font types need to be adjusted problematic with LAT E X + Matlab, tricky with LAT E X + gnuplot tricky with overlay.eps + LAT E X descriptions Math axis descriptions problematic ( L 2 error ; tick labels 0 5 ) More than one graphics attention for consistency of line styles, colors, markers,...

7 WELL-KNOWN PROBLEMS OF EXTERNAL GRAPHICS fixed. fixed. fixed. fixed. fixed. With PGFPLOTS: Font sizes are good relative to the figure. Font sizes are bad relative to the embedding document. Font types need to be adjusted problematic with LAT E X + Matlab, tricky with LAT E X + gnuplot tricky with overlay.eps + LAT E X descriptions Math axis descriptions problematic ( L 2 error ; tick labels 0 5 ) More than one graphics attention for consistency of line styles, colors, markers,...

8 OUTLINE INTRODUCTION Computer Experiments and Postprocessing Installation of PGFPLOTS 2 A SAMPLE WORK FLOW WITH PGFPLOTS Visualizing the plots Table postprocessing 3 CONCLUSION AND OUTLOOK

9 INSTALLATION OF PGFPLOTS Usage at the INS: set the environment variables export TEXINPUTS=.:~feuersae/share/texmf//: export TEXDOCS=.:~feuersae/share/texmf//: This activates the latest developer versions of PGFPLOTS and TikZ. in MikT E X: \usepackage{pgfplots} uses the latest stable. on Linux: wait for official Ubuntu Package or use inofficial websites for package repositories See the PGFPLOTS manual for installation advice (or use environment variables above)

10 OUTLINE INTRODUCTION Computer Experiments and Postprocessing Installation of PGFPLOTS 2 A SAMPLE WORK FLOW WITH PGFPLOTS Visualizing the plots Table postprocessing 3 CONCLUSION AND OUTLOOK

11 A SAMPLE WORK FLOW WITH PGFPLOTS Example scenario given program prototype which approximates f : [0, ] d R in dimension d up to ɛ../prototype -d 2 --eps visualizeto output --measuresto table_d2.dat --parameters... Output: a table row (append) Dof L2_error rel_l2_error Lmax_error rel_lmax_error eps to table.dat. Iteration convergence table Visualization: output.dat will contain a full grid interpolation a function output_grid.dat will contain the evaluated coordinates a grid

12 THE OUTPUT OF OUR EXPERIMENTS Scenario: fix all input parameters but one, change one (here: ɛ) result output: table.dat of the form dof L2_error rel_l2_error Lmax_error rel_lmax_error eps e e e e e e e e e e e e e e e e e e e e Visualization output: output.dat and output_grid.dat (here: comments; tuples (x 0, x, f (x 0, x )); and more) # ordering=colwise, basis=basis_nodal, number points=4225, (max)level(s): (6,6), domain=[0,]^2 # x_i : coordinates; (l_i,i_i): multiindex coords; scalaridx_i: linearized multiindex coords x_0 x_ f(x) l_0 i_0 scalaridx_0 l_ i_ Goal: visualize table.dat and output.dat

13 RESULT.tex FILE \documentclass[a4paper]{article} 2 \usepackage{pgfplots} 3 \pgfplotsset{compat=newest} 4 5 \title{approximation results} 6 \author{christian Feuers\"anger} 7 8 \begin{document} 9 \maketitle 0 \tableofcontents 2 \section{first set of parameters} 3 We use routine XYZ with parameters a-b-c. 4 5 \begin{tikzpicture} 6 \begin{loglogaxis}[ 7 title=xyz with a-b-c, 8 ylabel=relative $L_2$ error, 9 xlabel=\textsc{dof}, 20 ] 2 \addplot table[x=dof,y=rel_l2_error] {XYZ_abc/d2/table.dat}; 22 \end{loglogaxis} 23 \end{tikzpicture} 24 \end{document}

14 RESULT.tex FILE Approximation results Christian Feuersänger \documentclass[a4paper]{article} January 4, \usepackage{pgfplots} 3 \pgfplotsset{compat=newest} 4 Contents 5 \title{approximation results} First set of parameters 6 \author{christian Feuers\"anger} 7 8 \begin{document} First set of parameters 9 \maketitle We use routine XYZ with parameters a-b-c. 0 \tableofcontents XYZ with a-b-c 0 2 \section{first set of parameters} 3 We use routine XYZ with parameters a-b-c \begin{tikzpicture} \begin{loglogaxis}[ 0 7 title=xyz with a-b-c, 8 ylabel=relative $L_2$ error, xlabel=\textsc{dof}, 20 ] \addplot table[x=dof,y=rel_l2_error] {XYZ_abc/d2/table.dat}; \end{loglogaxis} Dof 23 \end{tikzpicture} 24 \end{document} relative L2 error

15 RESULT.tex FILE Advice: always make Title page \maketitle Approximation results 2 Table of contents 3 One \section for each set of parameters Christian Feuersänger \documentclass[a4paper]{article} January 4, \usepackage{pgfplots} 3 \pgfplotsset{compat=newest} 4 PGFPLOTS: Contents 5 \title{approximation results} First set of parameters 6 \author{christian Feuers\"anger} \usepackage{pgfplots} 7 8 \begin{document} 2 \begin{tikzpicture} First set of parameters... 9 \maketitle \end{tikzpicture} We use routine XYZ with parameters a-b-c. 0 \tableofcontents XYZ with a-b-c 0 2 \section{first set of parameters} 3 We use routine XYZ with parameters4 \addplot... ; a-b-c \begin{tikzpicture} Descriptions with 0 title, xlabel, ylabel 3 0 use, 4 after last option xlabel=\textsc{dof}, so you won t forget it for next option 20 ] \addplot table[x=dof,y=rel_l2_error] {XYZ_abc/d2/table.dat}; \end{loglogaxis} Dof 23 \end{tikzpicture} 24 \end{document} 6 \begin{loglogaxis}[ 7 title=xyz with a-b-c, Advice: 8 ylabel=relative $L_2$ error, 3 \begin{loglogaxis}... \end{loglogaxis} relative L2 error

16 ADDING A FURTHER EXPERIMENT AND A LEGEND 4 5 \begin{tikzpicture} 6 \begin{loglogaxis}[ 7 title=xyz with a-b-c, 8 ylabel=relative $L_2$ error, 9 xlabel=\textsc{dof}, 20 legend entries={$d=2$,$d=3$}, 2 ] 22 \addplot table[x=dof,y=rel_l2_error] {XYZ_abc/d2/table.dat}; 23 \addplot table[x=dof,y=rel_l2_error] {XYZ_abc/d3/table.dat}; 24 \end{loglogaxis} 25 \end{tikzpicture} legend entries={... } a further \addplot

17 ADDING A FURTHER EXPERIMENT AND A LEGEND 4 5 \begin{tikzpicture} Approximation results Christian Feuersänger 6 \begin{loglogaxis}[ 7 title=xyz with a-b-c, January 4, ylabel=relative $L_2$ error, 9 xlabel=\textsc{dof}, 20 legend entries={$d=2$,$d=3$}, Contents 2 ] First set of parameters 22 \addplot table[x=dof,y=rel_l2_error] {XYZ_abc/d2/table.dat}; 23 \addplot table[x=dof,y=rel_l2_error] {XYZ_abc/d3/table.dat}; First set of parameters 24 \end{loglogaxis} We use routine XYZ with parameters a-b-c. 25 \end{tikzpicture} XYZ with a-b-c legend entries={... } a further \addplot relative L2 error d = 2 d = Dof

18 VISUALIZATION FOR THE FUNCTION \begin{tikzpicture} 28 \begin{axis}[ 29 title=the function $f(x)$, 30 xlabel=$x$, 3 ylabel=$y$, 32 zlabel=$f(x)$, 33 ] 34 \addplot3[surf] table {XYZ_abc/d2/output.dat}; 35 \end{axis} 36 \end{tikzpicture} \begin{tikzpicture} 39 \begin{axis}[ 40 title=its grid, 4 enlargelimits=false, 42 xlabel=$x$, 43 ylabel=$y$, 44 ] 45 \addplot[only marks,mark=*,blue] 46 table {XYZ_abc/d2/output_grid.dat}; 47 \end{axis} 48 \end{tikzpicture} 49 \end{document}

19 VISUALIZATION FOR \begin{axis} THE FUNCTION... \end{axis} instead of loglogaxis \begin{tikzpicture} 28 \begin{axis}[ 29 title=the function $f(x)$, 30 xlabel=$x$, 3 ylabel=$y$, 32 zlabel=$f(x)$, 33 ] 34 \addplot3[surf] table {XYZ_abc/d2/output.dat}; 35 \end{axis} 36 \end{tikzpicture} \begin{tikzpicture} 39 \begin{axis}[ 40 title=its grid, 4 enlargelimits=false, 42 xlabel=$x$, 43 ylabel=$y$, 44 ] 45 \addplot[only marks,mark=*,blue] 46 table {XYZ_abc/d2/output_grid.dat}; 47 \end{axis} 48 \end{tikzpicture} 49 \end{document} Styles as \addplot[options] without [options]: cyle list

20 y VISUALIZATION FOR THE FUNCTION \begin{tikzpicture} Approximation results 28 \begin{axis}[ 29 title=the function Christian Feuersänger $f(x)$, 30 xlabel=$x$, January 4, ylabel=$y$, 32 zlabel=$f(x)$, Contents 33 ] 34 First \addplot3[surf] set of parameters table {XYZ_abc/d2/output.dat}; 35 \end{axis} 36 \end{tikzpicture} First set of parameters 37 We use routine XYZ with parameters a-b-c. XYZ with a-b-c 38 \begin{tikzpicture} 39 \begin{axis}[ d = title=its grid, d = 3 4 enlargelimits=false, xlabel=$x$, 0 43 ylabel=$y$, 44 ] \addplot[only marks,mark=*,blue] table {XYZ_abc/d2/output_grid.dat}; 47 \end{axis} \end{tikzpicture} \end{document} Dof relative L2 error f(x) x The function f(x) 0.6 Its grid x y

21 VISUALIZATION READY! Summary: input: data tables styles defined in T E X document key-value options for descriptions / fine tuning output: readily usable plot. Outlook (refer to manual): other input (math expressions,... ) more plot styles (line, scatter, bar, mesh, surf,... ) loops to include files Advice: speed improvement by \usepackage{pgfplots} \usepgfplotslibrary{external} \tikzexternalize{<name-of-tex-file>} % without.tex pdflatex -shell-escape <name-of-tex-file>: auto-generates separate.pdf for each picture

22 VISUALIZATION READY! Summary: input: data tables styles defined in T E X document key-value options for descriptions / fine tuning output: readily Forusable those who plot. are satisfied with Outlook (refer toplots: manual): relax! other input (math Rest of expressions, talk:... ) more plot styles (line, tablescatter, typesetting bar, mesh, (number surf,... ) loops to include formatting files in T E X) Advice: speed improvement compute convergence by rates automatically \usepackage{pgfplots} \usepgfplotslibrary{external} \tikzexternalize{<name-of-tex-file>} % without.tex pdflatex -shell-escape <name-of-tex-file>: auto-generates separate.pdf for each picture

23 OUTLINE INTRODUCTION Computer Experiments and Postprocessing Installation of PGFPLOTS 2 A SAMPLE WORK FLOW WITH PGFPLOTS Visualizing the plots Table postprocessing 3 CONCLUSION AND OUTLOOK

24 TYPESETTING THE DATA TABLES We can simply write \pgfplotstabletypeset{xyz_abc/d2/table.dat} which leads to dof L2 e rror rel L 2 e rror Lmax e rror rel L max e rror eps , , , underscores 2, _ , ,745provide names for2.64 the 0columns , and a lot of Missing $ inserted due to the

25 TYPESETTING THE DATA TABLES \documentclass[a4paper]{article} 2 \usepackage{pgfplots} 3 \usepackage{pgfplotstable} 4 \pgfplotsset{compat=newest} 5 6 % this configures document-wide styles for table typesetting. 7 \pgfplotstableset{ 8 columns={dof,rel_l2_error,rel_lmax_error}, % choose columns 9 columns/rel_l2_error/.style={ % tell how rel_l2_error shall be typeset 0 column name={$l_2$ rel}, }, 2 columns/rel_lmax_error/.style={ % tell how rel_lmax_error shall be typeset 3 column name={$l_\infty$ rel}, 4 }, 5 } 6 7 \title{approximation results} 8 \author{christian Feuers\"anger} 9 20 \begin{document} 2 \maketitle 22 \tableofcontents 39 \pgfplotstabletypeset{xyz_abc/d2/table.dat}

26 TYPESETTING THE DATA TABLES \documentclass[a4paper]{article} Contents 2 \usepackage{pgfplots} First set of parameters 3 \usepackage{pgfplotstable} 4 \pgfplotsset{compat=newest} 5 First set of parameters We use routine XYZ with parameters a-b-c. 6 % this configures document-wide styles for table typesetting. XYZ with a-b-c 7 \pgfplotstableset{ d = 2 8 columns={dof,rel_l2_error,rel_lmax_error}, % choose0 columns 9 columns/rel_l2_error/.style={ d = 3 % tell how rel_l2_error shall be typeset 0 column name={$l_2$ rel}, 0 2 }, columns/rel_lmax_error/.style={ % tell how rel_lmax_error shall be typeset 3 column name={$l_\infty$ rel}, 4 }, 5 } 6 7 \title{approximation results} 8 \author{christian Feuers\"anger} 9 20 \begin{document} 2 \maketitle 22 \tableofcontents 39 \pgfplotstabletypeset{xyz_abc/d2/table.dat} relative L2 error Approximation results Christian Feuersänger January 4, Dof dof L2 rel L rel , , , , , , ,

27 Approximation results TYPESETTING THE DATA TABLES Christian Feuersänger Advice: use preamble config with January 4, 200 \pgfplotstableset \documentclass[a4paper]{article} Contents 2 \usepackage{pgfplots} 3 \usepackage{pgfplotstable} 4 \pgfplotsset{compat=newest} 5 6 % this configures document-wide styles for table typesetting. We use routine XYZ with parameters a-b-c. XYZ with a-b-c 7 \pgfplotstableset{ d = 2 8 columns={dof,rel_l2_error,rel_lmax_error}, preamble% config: choose0 columns d = 3 9 columns/rel_l2_error/.style={ % tell how rel_l2_error shall be typeset 0 column name={$l_2$ rel}, 0 select relevant 2 columns }, columns/rel_lmax_error/.style={ % tell how rel_lmax_error shall be typeset 3 column name={$l_\infty$ rel}, 4 }, 5 } 6 7 \title{approximation results} 8 \author{christian Feuers\"anger} 9 20 \begin{document} 2 \maketitle 22 \tableofcontents 39 \pgfplotstabletypeset{xyz_abc/d2/table.dat} in document: First\pgfplotstabletypeset set of parameters (without [options]) First set of parameters pretty printed tables, consistent format relative L2 error define styles (column names here) Dof dof L2 rel L rel , , , , , , ,

28 CHANGE NUMBER FORMATTING We provide some fine-tuning of the display to the preamble: 6 % this configures document-wide styles for table typesetting. 7 \pgfplotstableset{ 8 columns={dof,rel_l2_error,rel_lmax_error}, % choose columns 9 columns/rel_l2_error/.style={ % tell how rel_l2_error shall be typeset 0 column name={$l_2$ rel}, sci,sci zerofill, % scientific format 2 sci sep align, % align at \cdot 0^ 3 }, 4 columns/rel_lmax_error/.style={ % tell how rel_lmax_error shall be typeset 5 column name={$l_\infty$ rel}, 6 sci,sci zerofill, 7 sci sep align, 8 sci subscript, %... just to demonstrate different sci formats 9 }, 20 } 44 \pgfplotstabletypeset{xyz_abc/d2/table.dat}

29 CHANGE NUMBER FORMATTING Approximation results Christian Feuersänger January 4, 200 Contents First set of parameters We provide some fine-tuning of the First set display of parameters to the We use routine XYZ with parameters a-b-c. preamble: XYZ with a-b-c d = 2 6 % this configures document-wide styles for table typesetting. 0 d = 3 7 \pgfplotstableset{ 8 columns={dof,rel_l2_error,rel_lmax_error}, % choose0 columns 9 columns/rel_l2_error/.style={ % tell how 0 rel_l2_error shall be typeset 0 column name={$l_2$ rel}, sci,sci zerofill, % scientific format sci sep align, % align at \cdot 0^ }, 4 columns/rel_lmax_error/.style={ % tell how 0 rel_lmax_error shall be typeset 5 column name={$l_\infty$ rel}, Dof 6 sci,sci zerofill, dof L2 rel L rel sci sep align, %... just to demonstrate different.0 sci formats sci subscript, 9 }, } , , , \pgfplotstabletypeset{xyz_abc/d2/table.dat} , , , , relative L2 error

30 COMPUTE PIECEWISE GRADIENTS We want postprocessing columns containing piecewise gradients: 6 % this configures document-wide styles for table typesetting. 7 \pgfplotstableset{ 8 columns={dof,rel_l2_error,grad_l2,rel_lmax_error,grad_lmax}, 9 % define how to create grad_l2 : 0 create on use/grad_l2/.style={ create col/gradient loglog={dof}{rel_l2_error} 2 }, 3 % define how to create grad_lmax : 4 create on use/grad_lmax/.style={ 5 create col/gradient loglog={dof}{rel_lmax_error} 6 }, 7 % tell it how to format grad_l2 and grad_lmax 8 columns/grad_lmax/.style={ 9 column name={$l_\infty$ grad}, 20 fixed,fixed zerofill, 2 precision=, 22 multiply with=-, 23 dec sep align, 24 }, 66 \pgfplotstabletypeset{xyz_abc/d2/table.dat}

31 COMPUTE PIECEWISE GRADIENTS We want postprocessing columns containing piecewise Contents gradients: 6 % this configures document-wide styles for table typesetting. First set of parameters 7 \pgfplotstableset{ We use routine XYZ with parameters a-b-c. 8 columns={dof,rel_l2_error,grad_l2,rel_lmax_error,grad_lmax}, XYZ with a-b-c 9 % define how to create grad_l2 : d = 2 0 create on use/grad_l2/.style={ 0 d = 3 create col/gradient loglog={dof}{rel_l2_error} 2 }, % define how to create grad_lmax : create on use/grad_lmax/.style={ 5 create col/gradient loglog={dof}{rel_lmax_error} }, % tell it how to format grad_l2 and grad_lmax 8 columns/grad_lmax/.style={ column name={$l_\infty$ grad}, Dof dof L2 rel L2 grad L rel L grad fixed,fixed zerofill, 2 precision=, 22 multiply with=-, 23 dec sep align, 24 }, 66 \pgfplotstabletypeset{xyz_abc/d2/table.dat} Approximation results Christian Feuersänger January 4, 200 First set of parameters relative L2 error , , , , , , ,

32 COMPUTE PIECEWISE GRADIENTS Approximation results Christian Feuersänger create on use: used for column names January 4, 200 We want postprocessing which columns do not exist. containing piecewise Contents gradients: here: computes First set oflog log parameters gradient 6 % this configures document-widebetween styles for table successive typesetting. First set of parameters rows 7 \pgfplotstableset{ 8 columns={dof,rel_l2_error,grad_l2,rel_lmax_error,grad_lmax}, 9 % define how to create grad_l2 : 0 create on use/grad_l2/.style={ create col/gradient loglog={dof}{rel_l2_error} 2 }, 3 % define how to create grad_lmax : 4 create on use/grad_lmax/.style={ 5 create col/gradient loglog={dof}{rel_lmax_error} 6 }, 7 % tell it how to format grad_l2 and grad_lmax 8 columns/grad_lmax/.style={ 9 column name={$l_\infty$ grad}, 20 fixed,fixed zerofill, 2 precision=, 22 multiply with=-, 23 dec sep align, 24 }, 66 \pgfplotstabletypeset{xyz_abc/d2/table.dat} We use routine XYZ with parameters a-b-c. XYZ with a-b-c relative L2 error d = 2 d = Dof dof L2 rel L2 grad L rel L grad , , , , , , ,

33 PUTTING IT ALL TOGETHER I \documentclass[a4paper]{article} 2 \usepackage{pgfplots} 3 \usepackage{pgfplotstable} 4 \pgfplotsset{compat=newest} 5 \usepgfplotslibrary{clickable} 6 7 \usepackage{booktabs} % to allow nicer tables 8 9 % this configures document-wide styles for table typesetting. 0 \pgfplotstableset{ % select columns: 2 columns={dof,rel_l2_error,grad_l2,rel_lmax_error,grad_lmax}, 3 % define how to create grad_l2 : 4 create on use/grad_l2/.style={ 5 create col/gradient loglog={dof}{rel_l2_error}}, 6 % define how to create grad_lmax : 7 create on use/grad_lmax/.style={ 8 create col/gradient loglog={dof}{rel_lmax_error}}, 9 % we define a new style named gradient style which can be used below: 20 gradient style/.style={ 2 fixed,fixed zerofill, 22 precision=, 23 multiply with=-, 24 dec sep align}, 25 error style/.style={ %... and we define error style for use below

34 PUTTING IT ALL TOGETHER II 26 sci,sci zerofill, 27 sci sep align}, 28 % tell it how to format grad_l2 and grad_lmax 29 columns/grad_lmax/.style={ 30 column name={$l_\infty$ grad}, 3 gradient style}, 32 columns/grad_l2/.style={ 33 column name={$l_2$ grad}, 34 gradient style}, 35 columns/rel_l2_error/.style={ 36 column name={$l_2$ rel}, 37 error style}, 38 columns/rel_lmax_error/.style={ 39 column name={$l_\infty$ rel}, 40 error style}, 4 every head row/.style={ 42 before row=\toprule,after row=\midrule}, 43 every last row/.style={ 44 after row=\bottomrule}, 45 } \title{approximation results} 48 \author{christian Feuers\"anger} 49

35 PUTTING IT ALL TOGETHER III 50 \begin{document} 5 \maketitle 52 \tableofcontents \section{first set of parameters} 55 We use routine XYZ with parameters a-b-c \begin{tikzpicture} 58 \begin{loglogaxis}[ 59 title=xyz with a-b-c, 60 ylabel=relative $L_2$ error, 6 xlabel=\textsc{dof}, 62 legend entries={$d=2$,$d=3$}, 63 ] 64 \addplot table[x=dof,y=rel_l2_error] {XYZ_abc/d2/table.dat}; 65 \addplot table[x=dof,y=rel_l2_error] {XYZ_abc/d3/table.dat}; 66 \end{loglogaxis} 67 \end{tikzpicture} \pgfplotstabletypeset{xyz_abc/d2/table.dat} 70 7 \begin{tikzpicture} 72 \begin{axis}[ 73 title=the function $f(x)$,

36 PUTTING IT ALL TOGETHER IV 74 xlabel=$x$, 75 ylabel=$y$, 76 zlabel=$f(x)$, 77 ] 78 \addplot3[surf] table {XYZ_abc/d2/output.dat}; 79 \end{axis} 80 \end{tikzpicture} 8 82 \begin{tikzpicture} 83 \begin{axis}[ 84 title=its grid, 85 enlargelimits=false, 86 xlabel=$x$, 87 ylabel=$y$, 88 ] 89 \addplot[only marks,mark=*,blue] 90 table {XYZ_abc/d2/output_grid.dat}; 9 \end{axis} 92 \end{tikzpicture} 93 \end{document}

37 y PUTTING IT ALL TOGETHER V Approximation results Christian Feuersänger January 4, 200 Contents First set of parameters First set of parameters We use routine XYZ with parameters a-b-c. XYZ with a-b-c dof L2 rel L2 grad L rel L grad , , , , , , , The function f(x) 0 d = 2 d = 3 relative L2 error f(x) x y Dof 0.8 Its grid

38 CONCLUSION AND SUMMARY Solves old problems with graphics and yields: High Quality output of Graphics High Quality embedding in document Styles consistent document wide no third party tool or script necessary (only T E X) Browse illustrated manual for scatter, line, bar, piece const, mesh plots, math expressions,... Limitations: Increased time for pdflatex or latex. Possibility: compile graphics once and re-use them (\usepgfplotslibrary{external}) The plot complexity should not exceed 0.000

39 Using Coordinate Filters to fix z =.4 φxφy φx φy min load nodes cpus processes 0 7 f(x, y) = x y x y Population Far Near tan(x) 5 l3 3 3 l l π π/2 π/2 3 2 π 5 L2 Error d = 2 d = 3 d = 4 d = 5 d = 6 3,000 model estimate 2,000,000 0, Degrees of freedom 2,000 3, Class Class 2 0. Class 3 Line

40 REFERENCES Chr. Feuersänger PGFPLOTS manual. $ texdoc pgfplots $ texdoc pgfplotstable T. Tantau PGF / TikZ manual. $ texdoc pgfmanual

TikZ & PGF(plots) Daniel Knittl-Frank. May This work is licensed under the Creative Commons Attribution-ShareAlike 3.

TikZ & PGF(plots) Daniel Knittl-Frank May 2015 This work is licensed under the Creative Commons Attribution-ShareAlike 3.0 Austria license (CC-BY-SA) 2D value plot Bitstamp USD 20,000 Weighted Price High