Plot graph near zero
I want to plot the following function with TikZ.
begin{tikzpicture}[scale=0.7,
declare function={
func(z) = 1/(2*(abs(z)^3)) * (
(1+abs(z)) - 2*ln(1+abs(z)) - 1/(1+abs(z))
);
}
]
The problem occurs near zero, the function isn't plotted the right way.
tikz-pgf pgfplots plot
edited 10 hours ago
JouleV
10.3k22558
asked 11 hours ago
joejoe
161
New contributor
joe is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
add a comment |
I want to plot the following function with TikZ.
begin{tikzpicture}[scale=0.7,
declare function={
func(z) = 1/(2*(abs(z)^3)) * (
(1+abs(z)) - 2*ln(1+abs(z)) - 1/(1+abs(z))
);
}
]
The problem occurs near zero, the function isn't plotted the right way.
tikz-pgf pgfplots plot
edited 10 hours ago
JouleV
10.3k22558
asked 11 hours ago
joejoe
161
New contributor
joe is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
I edited your question a bit so that it is easier for readers to understand your question.
– JouleV
10 hours ago
add a comment |
I want to plot the following function with TikZ.
begin{tikzpicture}[scale=0.7,
declare function={
func(z) = 1/(2*(abs(z)^3)) * (
(1+abs(z)) - 2*ln(1+abs(z)) - 1/(1+abs(z))
);
}
]
The problem occurs near zero, the function isn't plotted the right way.
tikz-pgf pgfplots plot
edited 10 hours ago
JouleV
10.3k22558
asked 11 hours ago
joejoe
161
New contributor
joe is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
I want to plot the following function with TikZ.
begin{tikzpicture}[scale=0.7,
declare function={
func(z) = 1/(2*(abs(z)^3)) * (
(1+abs(z)) - 2*ln(1+abs(z)) - 1/(1+abs(z))
);
}
]
The problem occurs near zero, the function isn't plotted the right way.
tikz-pgf pgfplots plot
tikz-pgf pgfplots plot
edited 10 hours ago
JouleV
10.3k22558
asked 11 hours ago
joejoe
161
New contributor
joe is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
edited 10 hours ago
JouleV
10.3k22558
asked 11 hours ago
joejoe
161
New contributor
joe is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
edited 10 hours ago
JouleV
10.3k22558
edited 10 hours ago
JouleV
10.3k22558
edited 10 hours ago
JouleV
10.3k22558
10.3k22558
asked 11 hours ago
joejoe
161
New contributor
joe is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked 11 hours ago
joejoe
161
asked 11 hours ago
joejoe
161
161
New contributor
joe is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
New contributor
joe is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
joe is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
I edited your question a bit so that it is easier for readers to understand your question.
– JouleV
10 hours ago
add a comment |
I edited your question a bit so that it is easier for readers to understand your question.
– JouleV
10 hours ago
I edited your question a bit so that it is easier for readers to understand your question.
– JouleV
10 hours ago
I edited your question a bit so that it is easier for readers to understand your question.
– JouleV
10 hours ago
add a comment |
1 Answer
1
active
oldest
votes
One way that produces some plot that is reasonably close to the "true" result is to insert the Taylor expansion of the function for smallish x. Otherwise TikZ will evaluate first the 1/x^3 piece and complain. The Taylor expansion, on the other hand shows that there is no singularity. A true computer algebra system would do the limits on its own, but TeX is not such a computer algebra system.
documentclass[tikz,border=3.14mm]{standalone}
usepackage{pgfplots}
pgfplotsset{compat=1.16}
begin{document}
begin{tikzpicture}[scale=0.7,
declare function={
func(z)=ifthenelse(abs(z)>0.251, 1/(2*(abs(z)^3)) * (
(1+abs(z)) - 2*ln(1+abs(z)) - 1/(1+abs(z))),
1/6 - abs(z)/4 + (3*abs(z)^2)/10 - abs(z)^3/3 + (5*abs(z)^4)/14);
}
]
begin{axis}
addplot[domain=-1:1,samples=31,smooth] {func(x)};
end{axis}
end{tikzpicture}
end{document}
answered 10 hours ago
marmotmarmot
114k5145276
add a comment |
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1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
One way that produces some plot that is reasonably close to the "true" result is to insert the Taylor expansion of the function for smallish x. Otherwise TikZ will evaluate first the 1/x^3 piece and complain. The Taylor expansion, on the other hand shows that there is no singularity. A true computer algebra system would do the limits on its own, but TeX is not such a computer algebra system.
documentclass[tikz,border=3.14mm]{standalone}
usepackage{pgfplots}
pgfplotsset{compat=1.16}
begin{document}
begin{tikzpicture}[scale=0.7,
declare function={
func(z)=ifthenelse(abs(z)>0.251, 1/(2*(abs(z)^3)) * (
(1+abs(z)) - 2*ln(1+abs(z)) - 1/(1+abs(z))),
1/6 - abs(z)/4 + (3*abs(z)^2)/10 - abs(z)^3/3 + (5*abs(z)^4)/14);
}
]
begin{axis}
addplot[domain=-1:1,samples=31,smooth] {func(x)};
end{axis}
end{tikzpicture}
end{document}
answered 10 hours ago
marmotmarmot
114k5145276
add a comment |
One way that produces some plot that is reasonably close to the "true" result is to insert the Taylor expansion of the function for smallish x. Otherwise TikZ will evaluate first the 1/x^3 piece and complain. The Taylor expansion, on the other hand shows that there is no singularity. A true computer algebra system would do the limits on its own, but TeX is not such a computer algebra system.
documentclass[tikz,border=3.14mm]{standalone}
usepackage{pgfplots}
pgfplotsset{compat=1.16}
begin{document}
begin{tikzpicture}[scale=0.7,
declare function={
func(z)=ifthenelse(abs(z)>0.251, 1/(2*(abs(z)^3)) * (
(1+abs(z)) - 2*ln(1+abs(z)) - 1/(1+abs(z))),
1/6 - abs(z)/4 + (3*abs(z)^2)/10 - abs(z)^3/3 + (5*abs(z)^4)/14);
}
]
begin{axis}
addplot[domain=-1:1,samples=31,smooth] {func(x)};
end{axis}
end{tikzpicture}
end{document}
answered 10 hours ago
marmotmarmot
114k5145276
add a comment |
One way that produces some plot that is reasonably close to the "true" result is to insert the Taylor expansion of the function for smallish x. Otherwise TikZ will evaluate first the 1/x^3 piece and complain. The Taylor expansion, on the other hand shows that there is no singularity. A true computer algebra system would do the limits on its own, but TeX is not such a computer algebra system.
documentclass[tikz,border=3.14mm]{standalone}
usepackage{pgfplots}
pgfplotsset{compat=1.16}
begin{document}
begin{tikzpicture}[scale=0.7,
declare function={
func(z)=ifthenelse(abs(z)>0.251, 1/(2*(abs(z)^3)) * (
(1+abs(z)) - 2*ln(1+abs(z)) - 1/(1+abs(z))),
1/6 - abs(z)/4 + (3*abs(z)^2)/10 - abs(z)^3/3 + (5*abs(z)^4)/14);
}
]
begin{axis}
addplot[domain=-1:1,samples=31,smooth] {func(x)};
end{axis}
end{tikzpicture}
end{document}
answered 10 hours ago
marmotmarmot
114k5145276
One way that produces some plot that is reasonably close to the "true" result is to insert the Taylor expansion of the function for smallish x. Otherwise TikZ will evaluate first the 1/x^3 piece and complain. The Taylor expansion, on the other hand shows that there is no singularity. A true computer algebra system would do the limits on its own, but TeX is not such a computer algebra system.
documentclass[tikz,border=3.14mm]{standalone}
usepackage{pgfplots}
pgfplotsset{compat=1.16}
begin{document}
begin{tikzpicture}[scale=0.7,
declare function={
func(z)=ifthenelse(abs(z)>0.251, 1/(2*(abs(z)^3)) * (
(1+abs(z)) - 2*ln(1+abs(z)) - 1/(1+abs(z))),
1/6 - abs(z)/4 + (3*abs(z)^2)/10 - abs(z)^3/3 + (5*abs(z)^4)/14);
}
]
begin{axis}
addplot[domain=-1:1,samples=31,smooth] {func(x)};
end{axis}
end{tikzpicture}
end{document}
answered 10 hours ago
marmotmarmot
114k5145276
edited 7 hours ago
answered 10 hours ago
marmotmarmot
114k5145276
answered 10 hours ago
marmotmarmot
114k5145276
answered 10 hours ago
marmotmarmot
114k5145276
114k5145276
add a comment |
add a comment |
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I edited your question a bit so that it is easier for readers to understand your question.
– JouleV
10 hours ago