smooth peaks in gnuplot

I have datapoints f(x_i) at points x_i (function f not known, only numerically) with f(0) = 0. The data show a peaklike structure at small x, to be followed by a slow shoulder-falloff at larger x that sets in half-way down from the maximum. I want to plot smoothed lines through these data points.
If I use bezier then indeed f(0)=0 is ok, but the peak is significantly (by about 25%), lowered. If I use acsplines then the peak looks somewhat better, but f(0) = 0 is not maintained.
How can I smooth that dataset without loosing vital info (f(0)=0) or the peak-height of the distribution?

asked Jun 1 '15 at 18:19

Umo

2112

stats.stackexchange.com

– Andrew Arnold
Jun 1 '15 at 18:34

1

Try cubic splines, smooth csplines or smooth mcsplines

– Christoph
Jun 1 '15 at 19:12

Thanks, indeed cplines or mcsplines maintain the peak much better than the others. However, there is a price: now the rest of the curve (shoulder at high x) looks wiggly if I choose weights such that the peak height is correct. Is there a way to do piecewise smoothing in gnuplot??

– Umo
Jun 2 '15 at 9:40

That's what smooth mcsplines does, so that should work fine. BTW: both csplines and mcsplines don't use weights.

– Christoph
Jun 2 '15 at 11:07

Sorry, I was not clear enough: mcsplines indeed gives a good and smooth reproduction of the peak area, but in the tails wiggles show up. I would like to supress these wiggles.

– Umo
Jun 2 '15 at 18:42

add a comment |

asked Jun 1 '15 at 18:19

Umo

2112

stats.stackexchange.com

– Andrew Arnold
Jun 1 '15 at 18:34

1

Try cubic splines, smooth csplines or smooth mcsplines

– Christoph
Jun 1 '15 at 19:12

Thanks, indeed cplines or mcsplines maintain the peak much better than the others. However, there is a price: now the rest of the curve (shoulder at high x) looks wiggly if I choose weights such that the peak height is correct. Is there a way to do piecewise smoothing in gnuplot??

– Umo
Jun 2 '15 at 9:40

That's what smooth mcsplines does, so that should work fine. BTW: both csplines and mcsplines don't use weights.

– Christoph
Jun 2 '15 at 11:07

Sorry, I was not clear enough: mcsplines indeed gives a good and smooth reproduction of the peak area, but in the tails wiggles show up. I would like to supress these wiggles.

– Umo
Jun 2 '15 at 18:42

add a comment |

asked Jun 1 '15 at 18:19

Umo

2112

gnuplot smoothing

asked Jun 1 '15 at 18:19

Umo

2112

asked Jun 1 '15 at 18:19

Umo

2112

asked Jun 1 '15 at 18:19

Umo

2112

asked Jun 1 '15 at 18:19

Umo

2112

asked Jun 1 '15 at 18:19

Umo

2112

stats.stackexchange.com

– Andrew Arnold
Jun 1 '15 at 18:34

1

Try cubic splines, smooth csplines or smooth mcsplines

– Christoph
Jun 1 '15 at 19:12

Thanks, indeed cplines or mcsplines maintain the peak much better than the others. However, there is a price: now the rest of the curve (shoulder at high x) looks wiggly if I choose weights such that the peak height is correct. Is there a way to do piecewise smoothing in gnuplot??

– Umo
Jun 2 '15 at 9:40

That's what smooth mcsplines does, so that should work fine. BTW: both csplines and mcsplines don't use weights.

– Christoph
Jun 2 '15 at 11:07

Sorry, I was not clear enough: mcsplines indeed gives a good and smooth reproduction of the peak area, but in the tails wiggles show up. I would like to supress these wiggles.

– Umo
Jun 2 '15 at 18:42

add a comment |

stats.stackexchange.com

– Andrew Arnold
Jun 1 '15 at 18:34

1

Try cubic splines, smooth csplines or smooth mcsplines

– Christoph
Jun 1 '15 at 19:12

Thanks, indeed cplines or mcsplines maintain the peak much better than the others. However, there is a price: now the rest of the curve (shoulder at high x) looks wiggly if I choose weights such that the peak height is correct. Is there a way to do piecewise smoothing in gnuplot??

– Umo
Jun 2 '15 at 9:40

That's what smooth mcsplines does, so that should work fine. BTW: both csplines and mcsplines don't use weights.

– Christoph
Jun 2 '15 at 11:07

Sorry, I was not clear enough: mcsplines indeed gives a good and smooth reproduction of the peak area, but in the tails wiggles show up. I would like to supress these wiggles.

– Umo
Jun 2 '15 at 18:42

stats.stackexchange.com

– Andrew Arnold
Jun 1 '15 at 18:34

Try cubic splines, smooth csplines or smooth mcsplines

– Christoph
Jun 1 '15 at 19:12

Thanks, indeed cplines or mcsplines maintain the peak much better than the others. However, there is a price: now the rest of the curve (shoulder at high x) looks wiggly if I choose weights such that the peak height is correct. Is there a way to do piecewise smoothing in gnuplot??

– Umo
Jun 2 '15 at 9:40

That's what smooth mcsplines does, so that should work fine. BTW: both csplines and mcsplines don't use weights.

– Christoph
Jun 2 '15 at 11:07

Sorry, I was not clear enough: mcsplines indeed gives a good and smooth reproduction of the peak area, but in the tails wiggles show up. I would like to supress these wiggles.

– Umo
Jun 2 '15 at 18:42

add a comment |

1 Answer
1

active

oldest

votes

Smoothing with acsplines draws an approximating cubic spline, which doesn't go through your original data points.

A better approach could be to use cubic splines smooth csplines, which go through all data points but may show overshoots for sharp peaks.

The probably best solution in your case is to use monotonic cubic splines, smooth mcsplines, which maintain the monotonicity and convexity of the original data points (see F.N. Fritsch and R.E. Carlson, "Monotone Piecewise Cubic Interpolation", SIAM Journal on Numerical Analysis 17, pp. 238-246 (1980)).

Here is a short example which shows these differences:

The test.dat file contains the points

And the script to plot them is

set xzeroaxis

set style data lines

set samples 500

plot 'test.dat' u 1:2 smooth acsplines title 'acsplines', 

     '' u 1:2 smooth csplines title 'csplines', 

     '' u 1:2 smooth mcsplines lw 2 title 'mcsplines',

     '' u 1:2 w p pt 7 title 'data points'

enter image description here

answered Jun 2 '15 at 11:24

Christoph

38.9k847120

Thanks for these extended explanations. Now I understand why mcsplines is not ideal for me. The data points that I work with have some numerical noise so that the smoothed curve should NOT go through the points. acsplines does that quite well in the area to the right of the peak, if the weights are chosen right, but it also smoothes the peak away ( it lowers the maximum significantly). This is why I would like to apply different smoothing algorithms for different parts of the curve. In your little example give some scatter to the 6 rightmost points and then find a smooth curve through all.

– Umo
Jun 2 '15 at 18:58

For what do you need the smoothed curve? You could plot the data around the peak with mcsplines, and the tail with acsplines. Restrict the areas using every then you could read the peaks fwhm, but you'll get a discontinuity where the two curves meet

– Christoph
Jun 2 '15 at 19:15

I need the smoothed curve for a publication. All I was looking for is a smoothed curve that removes the statistical noise from the data points and retains the peak (which has a clear physics justification) with approximately (within 5% let's say) the correct maximum value. A discontinuity is thus a not so desirable feature.

– Umo
Jun 3 '15 at 9:06

Well, those requirements are contradicting, I don't think that you can find a single suitable smoothing method without questionable hacks.My question aimed more at whether the line should be a guide to the eye, or if you want to estimate e.g. the peak width, or the fall down time etc. If you have some model for your data you could also do a fit.

– Christoph
Jun 3 '15 at 16:15

add a comment |

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1 Answer
1

active

oldest

votes

1 Answer
1

active

oldest

votes

Smoothing with acsplines draws an approximating cubic spline, which doesn't go through your original data points.

A better approach could be to use cubic splines smooth csplines, which go through all data points but may show overshoots for sharp peaks.

Here is a short example which shows these differences:

The test.dat file contains the points

And the script to plot them is

set xzeroaxis

set style data lines

set samples 500

plot 'test.dat' u 1:2 smooth acsplines title 'acsplines', 

     '' u 1:2 smooth csplines title 'csplines', 

     '' u 1:2 smooth mcsplines lw 2 title 'mcsplines',

     '' u 1:2 w p pt 7 title 'data points'

enter image description here

answered Jun 2 '15 at 11:24

Christoph

38.9k847120

Thanks for these extended explanations. Now I understand why mcsplines is not ideal for me. The data points that I work with have some numerical noise so that the smoothed curve should NOT go through the points. acsplines does that quite well in the area to the right of the peak, if the weights are chosen right, but it also smoothes the peak away ( it lowers the maximum significantly). This is why I would like to apply different smoothing algorithms for different parts of the curve. In your little example give some scatter to the 6 rightmost points and then find a smooth curve through all.

– Umo
Jun 2 '15 at 18:58

For what do you need the smoothed curve? You could plot the data around the peak with mcsplines, and the tail with acsplines. Restrict the areas using every then you could read the peaks fwhm, but you'll get a discontinuity where the two curves meet

– Christoph
Jun 2 '15 at 19:15

I need the smoothed curve for a publication. All I was looking for is a smoothed curve that removes the statistical noise from the data points and retains the peak (which has a clear physics justification) with approximately (within 5% let's say) the correct maximum value. A discontinuity is thus a not so desirable feature.

– Umo
Jun 3 '15 at 9:06

Well, those requirements are contradicting, I don't think that you can find a single suitable smoothing method without questionable hacks.My question aimed more at whether the line should be a guide to the eye, or if you want to estimate e.g. the peak width, or the fall down time etc. If you have some model for your data you could also do a fit.

– Christoph
Jun 3 '15 at 16:15

add a comment |

Smoothing with acsplines draws an approximating cubic spline, which doesn't go through your original data points.

A better approach could be to use cubic splines smooth csplines, which go through all data points but may show overshoots for sharp peaks.

Here is a short example which shows these differences:

The test.dat file contains the points

And the script to plot them is

set xzeroaxis

set style data lines

set samples 500

plot 'test.dat' u 1:2 smooth acsplines title 'acsplines', 

     '' u 1:2 smooth csplines title 'csplines', 

     '' u 1:2 smooth mcsplines lw 2 title 'mcsplines',

     '' u 1:2 w p pt 7 title 'data points'

enter image description here

answered Jun 2 '15 at 11:24

Christoph

38.9k847120

Thanks for these extended explanations. Now I understand why mcsplines is not ideal for me. The data points that I work with have some numerical noise so that the smoothed curve should NOT go through the points. acsplines does that quite well in the area to the right of the peak, if the weights are chosen right, but it also smoothes the peak away ( it lowers the maximum significantly). This is why I would like to apply different smoothing algorithms for different parts of the curve. In your little example give some scatter to the 6 rightmost points and then find a smooth curve through all.

– Umo
Jun 2 '15 at 18:58

For what do you need the smoothed curve? You could plot the data around the peak with mcsplines, and the tail with acsplines. Restrict the areas using every then you could read the peaks fwhm, but you'll get a discontinuity where the two curves meet

– Christoph
Jun 2 '15 at 19:15

I need the smoothed curve for a publication. All I was looking for is a smoothed curve that removes the statistical noise from the data points and retains the peak (which has a clear physics justification) with approximately (within 5% let's say) the correct maximum value. A discontinuity is thus a not so desirable feature.

– Umo
Jun 3 '15 at 9:06

Well, those requirements are contradicting, I don't think that you can find a single suitable smoothing method without questionable hacks.My question aimed more at whether the line should be a guide to the eye, or if you want to estimate e.g. the peak width, or the fall down time etc. If you have some model for your data you could also do a fit.

– Christoph
Jun 3 '15 at 16:15

add a comment |

Smoothing with acsplines draws an approximating cubic spline, which doesn't go through your original data points.

A better approach could be to use cubic splines smooth csplines, which go through all data points but may show overshoots for sharp peaks.

Here is a short example which shows these differences:

The test.dat file contains the points

And the script to plot them is

set xzeroaxis

set style data lines

set samples 500

plot 'test.dat' u 1:2 smooth acsplines title 'acsplines', 

     '' u 1:2 smooth csplines title 'csplines', 

     '' u 1:2 smooth mcsplines lw 2 title 'mcsplines',

     '' u 1:2 w p pt 7 title 'data points'

enter image description here

answered Jun 2 '15 at 11:24

Christoph

38.9k847120

Smoothing with acsplines draws an approximating cubic spline, which doesn't go through your original data points.

A better approach could be to use cubic splines smooth csplines, which go through all data points but may show overshoots for sharp peaks.

Here is a short example which shows these differences:

The test.dat file contains the points

And the script to plot them is

set xzeroaxis

set style data lines

set samples 500

plot 'test.dat' u 1:2 smooth acsplines title 'acsplines', 

     '' u 1:2 smooth csplines title 'csplines', 

     '' u 1:2 smooth mcsplines lw 2 title 'mcsplines',

     '' u 1:2 w p pt 7 title 'data points'

enter image description here

answered Jun 2 '15 at 11:24

Christoph

38.9k847120

answered Jun 2 '15 at 11:24

Christoph

38.9k847120

answered Jun 2 '15 at 11:24

Christoph

38.9k847120

answered Jun 2 '15 at 11:24

Christoph

38.9k847120

Thanks for these extended explanations. Now I understand why mcsplines is not ideal for me. The data points that I work with have some numerical noise so that the smoothed curve should NOT go through the points. acsplines does that quite well in the area to the right of the peak, if the weights are chosen right, but it also smoothes the peak away ( it lowers the maximum significantly). This is why I would like to apply different smoothing algorithms for different parts of the curve. In your little example give some scatter to the 6 rightmost points and then find a smooth curve through all.

– Umo
Jun 2 '15 at 18:58

For what do you need the smoothed curve? You could plot the data around the peak with mcsplines, and the tail with acsplines. Restrict the areas using every then you could read the peaks fwhm, but you'll get a discontinuity where the two curves meet

– Christoph
Jun 2 '15 at 19:15

I need the smoothed curve for a publication. All I was looking for is a smoothed curve that removes the statistical noise from the data points and retains the peak (which has a clear physics justification) with approximately (within 5% let's say) the correct maximum value. A discontinuity is thus a not so desirable feature.

– Umo
Jun 3 '15 at 9:06

Well, those requirements are contradicting, I don't think that you can find a single suitable smoothing method without questionable hacks.My question aimed more at whether the line should be a guide to the eye, or if you want to estimate e.g. the peak width, or the fall down time etc. If you have some model for your data you could also do a fit.

– Christoph
Jun 3 '15 at 16:15

add a comment |

Thanks for these extended explanations. Now I understand why mcsplines is not ideal for me. The data points that I work with have some numerical noise so that the smoothed curve should NOT go through the points. acsplines does that quite well in the area to the right of the peak, if the weights are chosen right, but it also smoothes the peak away ( it lowers the maximum significantly). This is why I would like to apply different smoothing algorithms for different parts of the curve. In your little example give some scatter to the 6 rightmost points and then find a smooth curve through all.

– Umo
Jun 2 '15 at 18:58

For what do you need the smoothed curve? You could plot the data around the peak with mcsplines, and the tail with acsplines. Restrict the areas using every then you could read the peaks fwhm, but you'll get a discontinuity where the two curves meet

– Christoph
Jun 2 '15 at 19:15

I need the smoothed curve for a publication. All I was looking for is a smoothed curve that removes the statistical noise from the data points and retains the peak (which has a clear physics justification) with approximately (within 5% let's say) the correct maximum value. A discontinuity is thus a not so desirable feature.

– Umo
Jun 3 '15 at 9:06

Well, those requirements are contradicting, I don't think that you can find a single suitable smoothing method without questionable hacks.My question aimed more at whether the line should be a guide to the eye, or if you want to estimate e.g. the peak width, or the fall down time etc. If you have some model for your data you could also do a fit.

– Christoph
Jun 3 '15 at 16:15

Thanks for these extended explanations. Now I understand why mcsplines is not ideal for me. The data points that I work with have some numerical noise so that the smoothed curve should NOT go through the points. acsplines does that quite well in the area to the right of the peak, if the weights are chosen right, but it also smoothes the peak away ( it lowers the maximum significantly). This is why I would like to apply different smoothing algorithms for different parts of the curve. In your little example give some scatter to the 6 rightmost points and then find a smooth curve through all.

– Umo
Jun 2 '15 at 18:58

For what do you need the smoothed curve? You could plot the data around the peak with mcsplines, and the tail with acsplines. Restrict the areas using every then you could read the peaks fwhm, but you'll get a discontinuity where the two curves meet

– Christoph
Jun 2 '15 at 19:15

I need the smoothed curve for a publication. All I was looking for is a smoothed curve that removes the statistical noise from the data points and retains the peak (which has a clear physics justification) with approximately (within 5% let's say) the correct maximum value. A discontinuity is thus a not so desirable feature.

– Umo
Jun 3 '15 at 9:06

Well, those requirements are contradicting, I don't think that you can find a single suitable smoothing method without questionable hacks.My question aimed more at whether the line should be a guide to the eye, or if you want to estimate e.g. the peak width, or the fall down time etc. If you have some model for your data you could also do a fit.

– Christoph
Jun 3 '15 at 16:15

add a comment |

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