more functions

tikz/discontinuity-jump/Readme.md

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+Compiled example
+----------------
+![Example](discontinuity-jump.png)

tikz/hard-limit-function/Makefile

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+SOURCE = hard-limit-function
+DELAY = 80
+DENSITY = 300
+WIDTH = 500
+
+make:
+	pdflatex $(SOURCE).tex -output-format=pdf
+	make clean
+
+clean:
+	rm -rf  $(TARGET) *.class *.html *.log *.aux *.data *.gnuplot
+
+gif:
+	pdfcrop $(SOURCE).pdf
+	convert -verbose -delay $(DELAY) -loop 0 -density $(DENSITY) $(SOURCE)-crop.pdf $(SOURCE).gif
+	make clean
+
+png:
+	make
+	make svg
+	inkscape $(SOURCE).svg -w $(WIDTH) --export-png=$(SOURCE).png
+
+transparentGif:
+	convert $(SOURCE).pdf -transparent white result.gif
+	make clean
+
+svg:
+	#inkscape $(SOURCE).pdf --export-plain-svg=$(SOURCE).svg
+	pdf2svg $(SOURCE).pdf $(SOURCE).svg
+	# Necessary, as pdf2svg does not always create valid svgs:
+	inkscape $(SOURCE).svg --export-plain-svg=$(SOURCE).svg

tikz/hard-limit-function/Readme.md

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+Compiled example
+----------------
+![Example](hard-limit-function.png)

tikz/hard-limit-function/hard-limit-function.tex

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+\documentclass[varwidth=false, border=2pt]{standalone}
+
+\usepackage{pgfplots}
+\usepackage{tikz}
+
+\begin{document}
+\begin{tikzpicture}
+    \begin{axis}[
+        axis x line=middle,
+        axis y line=middle,
+        grid = major,
+        width=16cm,
+        height=8cm,
+        grid style={dashed, gray!30},
+        xmin=-1,     % start the diagram at this x-coordinate
+        xmax= 1,    % end   the diagram at this x-coordinate
+        ymin= 0,     % start the diagram at this y-coordinate
+        ymax= 1.2,   % end   the diagram at this y-coordinate
+        xlabel=x,
+        ylabel=y,
+		/pgfplots/xtick={-1, -0.5, ..., 1}, % make steps of length 0.5
+		/pgfplots/ytick={0, 0.5, ..., 1}, % make steps of length 0.5
+        tick align=outside,
+        enlargelimits=false]
+      % plot the function
+	  \addplot[domain=-1:1, blue, ultra thick,samples=500] {x < 0 ? 0 : 1}; 
+    \end{axis} 
+\end{tikzpicture}
+\end{document}

tikz/piecewise-linear-function/Makefile

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+SOURCE = piecewise-linear-function
+DELAY = 80
+DENSITY = 300
+WIDTH = 500
+
+make:
+	pdflatex $(SOURCE).tex -output-format=pdf
+	make clean
+
+clean:
+	rm -rf  $(TARGET) *.class *.html *.log *.aux *.data *.gnuplot
+
+gif:
+	pdfcrop $(SOURCE).pdf
+	convert -verbose -delay $(DELAY) -loop 0 -density $(DENSITY) $(SOURCE)-crop.pdf $(SOURCE).gif
+	make clean
+
+png:
+	make
+	make svg
+	inkscape $(SOURCE).svg -w $(WIDTH) --export-png=$(SOURCE).png
+
+transparentGif:
+	convert $(SOURCE).pdf -transparent white result.gif
+	make clean
+
+svg:
+	#inkscape $(SOURCE).pdf --export-plain-svg=$(SOURCE).svg
+	pdf2svg $(SOURCE).pdf $(SOURCE).svg
+	# Necessary, as pdf2svg does not always create valid svgs:
+	inkscape $(SOURCE).svg --export-plain-svg=$(SOURCE).svg

tikz/piecewise-linear-function/Readme.md

@@ -0,0 +1,3 @@
+Compiled example
+----------------
+![Example](piecewise-linear-function.png)

tikz/piecewise-linear-function/piecewise-linear-function.tex

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+\documentclass[varwidth=false, border=2pt]{standalone}
+
+\usepackage{pgfplots}
+\usepackage{tikz}
+
+\begin{document}
+\begin{tikzpicture}
+    \begin{axis}[
+        axis x line=middle,
+        axis y line=middle,
+        grid = major,
+        width=16cm,
+        height=8cm,
+        grid style={dashed, gray!30},
+        xmin=-1,     % start the diagram at this x-coordinate
+        xmax= 1,    % end   the diagram at this x-coordinate
+        ymin= 0,     % start the diagram at this y-coordinate
+        ymax= 1.2,   % end   the diagram at this y-coordinate
+        xlabel=x,
+        ylabel=y,
+		/pgfplots/xtick={-1, -0.5, ..., 1}, % make steps of length 0.5
+		/pgfplots/ytick={0, 0.5, ..., 1}, % make steps of length 0.5
+        tick align=outside,
+        enlargelimits=false]
+      % plot the function
+	  \addplot[domain=-1:1, blue, ultra thick,samples=500] {x < -0.5 ? 0 : (x < 0.5 ? x +0.5 : 1)}; 
+    \end{axis} 
+\end{tikzpicture}
+\end{document}

tikz/sigmoid-function/sigmoid-function.tex

@@ -2,8 +2,6 @@
 
 \usepackage{pgfplots}
 \usepackage{tikz}
-\usepackage{tkz-fct}
-\usetikzlibrary{arrows}
 
 \begin{document}
 \begin{tikzpicture}