gnuplot-info — For questions and discussion about gnuplot

Re: [Gnuplot-info] Plotting fortran formatted data

[ivana r. <iva...@mf...>]

Hi  Sergei,

although to use external simple filter was intended in such cases,
under unix-like OS e.g. "cut":


gnuplot> plot '<cut -b 11-14,16- --output-delimiter=" " datafile'


you can do this directly by gnuplot as well:


# begin gnuplot code

# replace datafile with real filename
file="datafile"

# set the data separator to a char missed in the file
set datafile separator ";"

# use string functions to extract columns of a given width to a named datablock
set table $mydata
plot file u (stringcolumn(1)[11:14]):(stringcolumn(1)[16:]) w table
unset table

# reset the data separator
set datafile separator

# uncomment to print the preprocessed datablock if you wish
# print $mydata

# plot the preprocessed datablock

plot $mydata w lp t "extracted data"

# end of gnuplot code


sincerely

Iva

[Gnuplot-info] Plotting fortran formatted data

[Sergei N. <vo...@ra...>]

Hi!
I need to plot from a file written by a FORTRAN code with formatted output like
this:

J0023+092311.8D 0.085
J0030+045158.8P 0.861
J0034-0534 6.6D10.255
As you can see the formats here are A10,F4.1,A1,F6.3. The plot needs to be
created as a second column versus the fourth. Plotting as a straight text file
will not work because there are no spaces between the columns. I was reading
about plotting a binary file but this feature does not seem to applicable in this
case.

Can anyone, please, explain whether such data can be plotted by GnuPlot or I
would need to write a filer to convert the data into separate columns?

Thanks in advance,

-- Sergei

Re: [Gnuplot-info] Rearrange data with gnuplot?

[theozh <th...@gm...>]

Hi Iva,
thanks for your reply. I tried again, and voilà... there is a way, although again not very elegant.
Maybe, somebody else might find it useful...

It's really a pitty that gnuplot is not supporting at least very simple table manipulations,
e.g. reversing data, transposing data arrays, copying columns or rows and/or putting columns side by side to arrange new arrays...
Sure, you can use other scripting languages to manipulate data and generate gnuplot scripts.
Well, it would be nice if you can do it "monolithically" without any wrappers...


The intended result of the script below is:
1 10 111 211
1 20 121 221
1 30 131 231
1 40 141 241

2 10 112 212
2 20 122 222
2 30 132 232
2 40 142 242

3 10 113 213
3 20 123 223
3 30 133 233
3 40 142 242


### Merge and rearrange two datablocks or files
reset

$Data1 <<EOD
0	1	2	3
10	111	112	113
20	121	122	123
30	131	132	133
40	141	142	142
EOD

$Data2 <<EOD
0	1	2	3
10	211	212	213
20	221	222	223
30	231	232	233
40	241	242	242
EOD

stats $Data1 nooutput
print "Rows: ".STATS_records."\n"."Columns: ".STATS_columns

set print $Data3
set table $Nowhere    # plot data to "nowhere" to avoid unnecessary plot windows

do for [i=2:STATS_columns] {
  do for [j=1:STATS_records-1] {
    plot $Data1 u (a=column(i),1/0) every ::0::0 with table
    plot $Data1 u (b=column(1),1/0):(c=column(i),1/0) every ::j::j with table
    plot $Data2 u (d=column(i),1/0) every ::j::j with table
    print sprintf("%g\t%g\t%g\t%g",a,b,c,d)
  }
  print ""    # separat blocks by empty line
}  
set print
print $Data3
### end gnuplot code

Re: [Gnuplot-info] Rearrange data with gnuplot?

[ivana r. <iva...@mf...>]

Hi Theo,

probably, you can win building something like you did for "the last
data points of each block" (instead of pipe reversed data to gnuplot),
but the general answer is that gnuplot is not aimed as a data editor.

There are general powerful scripting languages (python, perl, gawk,
...) or smart math-stat languages that can use gnuplot as a graphical
frontend (Octave, R, maxima, ...).

Do not hesitate to explore them. Good luck.

Iva

[Gnuplot-info] Rearrange data with gnuplot?

[theozh <th...@gm...>]

Is there maybe a way in gnuplot to rearrange data of two files into one file according to the scheme below?
The number of columns and rows are variable and unknown but they are the same in File1 and File2.
The number of rows and columns can be found via 'stats File1':
Rows: STATS_records
Cols: STATS_columns

I tried with 
plot ... with table
or 
print table ...
But didn't yet find a solution with gnuplot.
Any ideas?


# File1:
xxx c01 c02 c03
r01 d11 d12 d13
r02 d21 d22 d23
r03 d31 d32 d33

# File2:
xxx c01 c02 c03
r01 e11 e12 e13
r02 e21 e22 e23
r03 e31 e32 e33

# File3:
c01 r01 d11 e11
c01 r02 d21 e21
c01 r03 d31 e31

c02 r01 d12 e12
c02 r02 d22 e22
c02 r03 d32 e32

c03 r01 d13 e13
c03 r02 d23 e23
c03 r03 d33 e33

[Gnuplot-info] effect with label

[Pedro C. <ped...@gm...>]

Dear Gnuplot Users

I have some strange behavior (or maybe not) using a label on a pm3d map
projection. Example:

set term post enhanced color
set output "spectrum3d.ps"
unset border
f(x)=x-1
set palette color
set pm3d map
set xrange [1:13]
unset ztics
unset ytics
unset xtics
set samples 201
set isosamples 2
set size 0.8,0.2
unset key
unset colorbox
set label 2 "M" font "Helvetica-Bold,12" at 2.15,graph 0.5,graph 1 center
front tc rgb "black"
set palette model RGB defined (1 "green", 1.25 "dark-green", 1.25 "yellow",
1.33 "dark-yellow", 1.33 "red", 4 "dark-red" )
set origin 0.0,0.5
splot f(x)

If I run gnuplot (version 5.1 and 5.2) on the right side of the plot appear
an extra line (see pdf "plot_withlabel.pdf" created from the postscript
file). If I comment

set label 2 "M" font "Helvetica-Bold,12" at 2.15,graph 0.5,graph 1 center
front tc rgb "black"

no such feature appears (file "plot_withnolable.pdf".

Is it something associated to the boxed label option or some bug?

Pedro

Re: [Gnuplot-info] Increase number of digits

[ivana r. <iva...@mf...>]

Hi Patric,

are you sure that you wanna get the fit parameter with higher
precision that the error order?

Anyhow, the precision of gnuplot float variables is (under official
linux distribution) about 10e-15. You can print the variable via
sprintf/gprintf:

gnuplot> pr sprintf("%.20g",1+1e-15)
gnuplot> pr sprintf("%.20g",1+1e-16)

(Contrary to, e.g. gawk's OFMT, you can set global floating precision
for axis only.)

Sincerely

Iva


On 14/12/2017, Patrick Dupre <pd...@gm...> wrote:
> Hello,
>
> How can I increase the number of digits of the values provided
> by a fit?
> For example, I get
> x0              = 61281.3          +/- 5.43         (0.008861%)
>
> I would like to have 1 more digit on x0
>
> Thank.
>
> ===========================================================================
>  Patrick DUPRÉ                                 | | email: pd...@gm...
>  Laboratoire de Physico-Chimie de l'Atmosphère | |
>  Université du Littoral-Côte d'Opale           | |
>  Tel.  (33)-(0)3 28 23 76 12                   | | Fax: 03 28 65 82 44
>  189A, avenue Maurice Schumann                 | | 59140 Dunkerque, France
> ===========================================================================
>
> ------------------------------------------------------------------------------
> Check out the vibrant tech community on one of the world's most
> engaging tech sites, Slashdot.org! http://sdm.link/slashdot
> _______________________________________________
> gnuplot-info mailing list
> gnu...@li...
> Membership management via:
> https://lists.sourceforge.net/lists/listinfo/gnuplot-info
>

[Gnuplot-info] Increase number of digits

[Patrick D. <pd...@gm...>]

Hello,

How can I increase the number of digits of the values provided
by a fit?
For example, I get
x0              = 61281.3          +/- 5.43         (0.008861%)

I would like to have 1 more digit on x0

Thank.

===========================================================================
 Patrick DUPRÉ                                 | | email: pd...@gm...
 Laboratoire de Physico-Chimie de l'Atmosphère | |
 Université du Littoral-Côte d'Opale           | |
 Tel.  (33)-(0)3 28 23 76 12                   | | Fax: 03 28 65 82 44
 189A, avenue Maurice Schumann                 | | 59140 Dunkerque, France
===========================================================================

Re: [Gnuplot-info] Outputs of fit: details of how they're defined

[Daniel H. <vi5...@ya...>]

Am 28.11.2017 um 00:34 schrieb Dan via gnuplot-info:

>> - in the variable L_err, the value (presumably calculated in a
>> finite-difference way) of
>> \sqrt{\frac{2}{\left(\partial\!^{2}\!\left(\chi^2\right)/\partial 
>> L\!^{2}\right)_{L = l,M = 
>> m}-\left(\left(\partial\!^{2}\!\left(\chi^2\right)/\left(\partial\!\!L\!\partial\!\!M\right)\right)_{L 
>> = l,M = m}\right)^2/\left(\partial\!^{2}\!\left(\chi^2\right)/\partial 

>> M\!^{2}\right)_{L = l,M = m}}}

On Saturday, 2 December 2017, 17:35, Hans-Bernhard Bröker <HBB...@t-...> wrote:

> The algorithm never actually computes it just like that.  What actually 
> happens is that the code builds a matrix of all the second partial 
> derivatives of \chi^2 with respect to the given parameters.  This 
> matrix is inverted, to yield the covariance matrix.  The roots of the 
> diagonal elements of that matrix form the error values.  These get 
> divided out of each column and row, to form the correlation matrix that 
> is printed out.

> For the special case of just two parameters the formulae you found may 
> well be correct... I didn't compute it through to check one way or the 
> other.


No worries: you'd given me enough information that I could turn the handle on the formula for the inverse of a 2\times 2 matrix myself.  I can confirm that the formula, which I originally conjectured was used to provide the value that Gnuplot puts in the variable L_err, is indeed the square root of twice the "LL" diagonal element of the inverse of the Hessian of \chi^2, evaluated at the L and M values that minimize \chi^2.  That matches your description of what's going on except for the "twice".  (And similarly for M_err).

Similarly, the formula, which I originally conjectured was used to provide the value that Gnuplot puts in the variable FIT_COV_M_L, is minus twice (either one of) the off-diagonal element(s) of the inverse of the Hessian of \chi^2, evaluated at the L and M values that minimize \chi^2.  That matches your description of what's going on except for the "minus twice", and the fact that my formula hadn't had the diagonal elements 'divided out of each column and row' (but the latter may just be because I'd done "set fit noerrorscaling").  Incidentally, something I'd already observed is that the value that gets stored in FIT_COV_M_L is not the same as the off-diagonal element of the "covariance matrix" that gets printed to the screen at the end of the fit process.

> There's really nothing special about that method.  It's basically the 
> definition of what all fitting tools do for asymptotic error estimation. 
> They're "asymptotic" because they're derived from the second 
> derivatives, i.e. just lowest-order term describing the shape of the 

> \chi^2 function "landscape" near the discovered minimum

On the contrary, there's something _very_ special about it - namely that, if one gets the detailed handle-turning right, the integral over all (parameter) space that formally defines the standard error belongs to a class of problems whereby there is a rigorous upper bound on the magnitude of the error of (one particular variant of) the method based on the second derivatives evaluated at the discovered minimum, when used as an approximation to that integral (see Olver, 1997, _Asymptotics and special functions_, CRC Press, Boca Raton, section 3.7).  The reason I keep prodding away about published sources is that I'd like to confirm that I _have_ got the detailed handle-turning right by finding someone else who's done it (and preferably got it through peer review).

Re: [Gnuplot-info] plot with x from file

[Patrick D. <pd...@gm...>]

OK

Actually 
plot $DATA using (x=$1): (my_function(x))

is OK

===========================================================================
 Patrick DUPRÉ                                 | | email: pd...@gm...
 Laboratoire de Physico-Chimie de l'Atmosphère | |
 Université du Littoral-Côte d'Opale           | |
 Tel.  (33)-(0)3 28 23 76 12                   | | Fax: 03 28 65 82 44
 189A, avenue Maurice Schumann                 | | 59140 Dunkerque, France
===========================================================================


> Sent: Thursday, December 07, 2017 at 11:51 PM
> From: "Hans-Bernhard Bröker" <HBB...@t-...>
> To: "Patrick Dupre" <pd...@gm...>, gnuplot <gnu...@li...>
> Subject: Re: [Gnuplot-info] plot with x from file
>
> Am 07.12.2017 um 23:37 schrieb Patrick Dupre:
> > Hello,
> > 
> > I would like to plot, something like:
> > plot $DATA using (x=$1): my_function(x)
> > 
> > but it does not work.
> 
> You're trying way too hard.  What you appear to be looking for is
> 
> 	plot $DATA using 1:(my_function($1))
> 
>

Re: [Gnuplot-info] plot with x from file

[Patrick D. <pd...@gm...>]

> > Hello,
> > 
> > I would like to plot, something like:
> > plot $DATA using (x=$1): my_function(x)
> > 
> > but it does not work.
> 
> You're trying way too hard.  What you appear to be looking for is
> 
> 	plot $DATA using 1:(my_function($1))
> 
Thank
Humm, my problem is that my_function(x) is a multiple function of x.
Can I define x=$1 ? 

Re: [Gnuplot-info] plot with x from file

[Hans-Bernhard B. <HBB...@t-...>]

Am 07.12.2017 um 23:37 schrieb Patrick Dupre:
> Hello,
> 
> I would like to plot, something like:
> plot $DATA using (x=$1): my_function(x)
> 
> but it does not work.

You're trying way too hard.  What you appear to be looking for is

	plot $DATA using 1:(my_function($1))

[Gnuplot-info] plot with x from file

[Patrick D. <pd...@gm...>]

Hello,

I would like to plot, something like:
plot $DATA using (x=$1): my_function(x)

but it does not work.
I can do:
plot $DATA using (x=$1):2, (my_function(x))

but it plot my_function(x) and $2
while I do not want $2

Some ideas?

Thank

===========================================================================
 Patrick DUPRÉ                                 | | email: pd...@gm...
 Laboratoire de Physico-Chimie de l'Atmosphère | |
 Université du Littoral-Côte d'Opale           | |
 Tel.  (33)-(0)3 28 23 76 12                   | | Fax: 03 28 65 82 44
 189A, avenue Maurice Schumann                 | | 59140 Dunkerque, France
===========================================================================

Re: [Gnuplot-info] Setting dash length for individual lines

[Ethan M. <eam...@gm...>]

See "set dashtype".
You can definitely a new dash pattern in terms of numerical length and then
choose it for a particular line.

set dashtype 5 (10, 2, 10, 2)
set dashtype 6 (20,4,20,4)
plot foo dt 5, baz dt 6



On Dec 7, 2017 09:08, "Nunzio Losacco" <nun...@gm...> wrote:

> Hi,
>
> thanks for your reply and sorry I wasn't clear enough. I wish to know if
> there is any way to scale dash lengths other than dl as a terminal option.
> I would like to use, say, the same dash type but different dash length for
> some functions (or arrows or whatever) in the same plot.
> Is that more clear?
>
> Best,
>
> N
>
> Il 6 dic 2017 21:49, "theozh" <th...@gm...> ha scritto:
>
> I'm not sure whether I understand your question correctly.
> A single line with different dash lengths along this line?
>
> Probably, you're not looking for something like:
> plot x*x dashtype ". - _ "
>
> So, what should the dash length depend on?
> The x- or y-value or some tabulated values?
>
>
> ------------------------------------------------------------
> ------------------
> Check out the vibrant tech community on one of the world's most
> engaging tech sites, Slashdot.org! http://sdm.link/slashdot
> _______________________________________________
> gnuplot-info mailing list
> gnu...@li...
> Membership management via: https://lists.sourceforge.net/
> lists/listinfo/gnuplot-info
> ------------------------------------------------------------
> ------------------
> Check out the vibrant tech community on one of the world's most
> engaging tech sites, Slashdot.org! http://sdm.link/slashdot
> _______________________________________________
> gnuplot-info mailing list
> gnu...@li...
> Membership management via: https://lists.sourceforge.net/
> lists/listinfo/gnuplot-info
>

Re: [Gnuplot-info] Setting dash length for individual lines

[Nunzio L. <nun...@gm...>]

Hi,

thanks for your reply and sorry I wasn't clear enough. I wish to know if
there is any way to scale dash lengths other than dl as a terminal option.
I would like to use, say, the same dash type but different dash length for
some functions (or arrows or whatever) in the same plot.
Is that more clear?

Best,

N

Il 6 dic 2017 21:49, "theozh" <th...@gm...> ha scritto:

I'm not sure whether I understand your question correctly.
A single line with different dash lengths along this line?

Probably, you're not looking for something like:
plot x*x dashtype ". - _ "

So, what should the dash length depend on?
The x- or y-value or some tabulated values?


------------------------------------------------------------
------------------
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engaging tech sites, Slashdot.org! http://sdm.link/slashdot
_______________________________________________
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Membership management via: https://lists.sourceforge.net/
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Re: [Gnuplot-info] Setting dash length for individual lines

[theozh <th...@gm...>]

I'm not sure whether I understand your question correctly.
A single line with different dash lengths along this line?

Probably, you're not looking for something like:
plot x*x dashtype ". - _ "

So, what should the dash length depend on?
The x- or y-value or some tabulated values?

Re: [Gnuplot-info] Outputs of fit: details of how they're defined

[Hans-Bernhard B. <HBB...@t-...>]

Am 28.11.2017 um 00:34 schrieb Dan via gnuplot-info:

> - in the variables L and M, the values l and m of the L and M
> parameters respectively, which, among all the (L,M) pairs that the
> Marquardt-Levenberg algorithm has tried, produce the lowest value of
> the \chi^2 statistic;

Yes.

> - in the variable FIT_WSSR, the value \Chi^2 of the \chi^2 statistic
> that is achieved by setting L = l and M = m;

Yes.

> - in the variable L_err, the value (presumably calculated in a
> finite-difference way) of
> \sqrt{\frac{2}{\left(\partial\!^{2}\!\left(\chi^2\right)/\partial 
> L\!^{2}\right)_{L = l,M = 
> m}-\left(\left(\partial\!^{2}\!\left(\chi^2\right)/\left(\partial\!\!L\!\partial\!\!M\right)\right)_{L 
> = l,M = m}\right)^2/\left(\partial\!^{2}\!\left(\chi^2\right)/\partial 
> M\!^{2}\right)_{L = l,M = m}}}

The algorithm never actually computes it just like that.  What actually 
happens is that the code builds a matrix of all the second partial 
derivatives of \chi^2 with resepect to the given parameters.  This 
matrix is inverted, to yield the covariance matrix.  The roots of the 
diagonal elements of that matrix form the error values.  These get 
divided out of each column and row, to form the correlation matrix that 
is printed out.

For the special case of just two parameters the formulae you found may 
well be correct... I didn't compute it through to check one way or the 
other.

There's really nothing special about that method.  It's basically the 
definition of what all fitting tools do for asymptotic error estimation. 
  They're "asymptotic" because they're derived from the second 
derivatives, i.e. just lowest-order term describing the shape of the 
\chi^2 function "landscape" near the discovered minimum, which is only 
truly accurate asymptotically close to the point of evaluation.

If memory serves, the non-asymptotic approach would try to actually 
trace the contour of \chi^2 at a value of <minimum> + 1, instead.

Re: [Gnuplot-info] How to plot the last data points of each block?

[BBands <bb...@gm...>]

Probably not what you want, but I preprocess the data in VisualBasic or
Python and then pass just the data to be plotted to gnuplot.

Best,

      John

On Fri, Dec 1, 2017 at 3:26 PM, theozh <th...@gm...> wrote:

> still nobody has an idea...?
>
> Well, since the construct
>   plot $Data u 1:2 every ::-1::-1
> does not exist... here is an ugly workaround (see below).
> It basically reverses a dataset and plots the first datapoint of each
> datablock.
> Maybe someone else might find it useful or even knows a better and more
> elegant way to achieve this.
> If it can be done easier using awk, gawk, sed, etc. please let me know how.
> But the following is a pure gnuplot solution.
>
> ### plot the last point of each datablock
> reset
> $Data <<EOD
> 11 1
> 22 4
> 33 9
>
> 44 16
> 55 25
> 66 36
> 77 49
>
> 88 64
> 99 81
> 110 100
> 121 121
> 132 144
> EOD
>
> print $Data
> stats $Data
> print STATS_records    # number of datapoints
>
> array A[STATS_records]   # helper array
> array B[STATS_records]   # helper array
> array C[STATS_records]   # helper array
>
> # puttig the dataset into arrays
> set table $Data2
> plot $Data u (A[$0+1]=column(-1),column(-1)):(B[$0+1]=$1,$1):(C[$0+1]=$2,$2)
> with table
> unset table
> print $Data2
>
> # reverse the dataset
> set print $Data3
> G = A[STATS_records] # initialize block indicator
> do for [i=STATS_records:1:-1] {
>   if (A[i] != G) { print "" }  # if different insert empty line / start
> new block
>   G = A[i]
>   print sprintf("%g %g", B[i], C[i])
> }
> set print
> print $Data3
>
> # plot the original values
> set key top left
> plot $Data u 1:2 w lp
>
> # plot the first datapoints of each datablock of the reversed dataset
> replot $Data3 u 1:2 every ::0::0 w p pt 6 ps 3 t "last point of each
> datablock"
>
> ### end gnuplot code
>
>
>
> ------------------------------------------------------------
> ------------------
> Check out the vibrant tech community on one of the world's most
> engaging tech sites, Slashdot.org! http://sdm.link/slashdot
> _______________________________________________
> gnuplot-info mailing list
> gnu...@li...
> Membership management via: https://lists.sourceforge.net/
> lists/listinfo/gnuplot-info
>

Re: [Gnuplot-info] How to plot the last data points of each block?

[theozh <th...@gm...>]

still nobody has an idea...?

Well, since the construct
  plot $Data u 1:2 every ::-1::-1
does not exist... here is an ugly workaround (see below).
It basically reverses a dataset and plots the first datapoint of each datablock. 
Maybe someone else might find it useful or even knows a better and more elegant way to achieve this.
If it can be done easier using awk, gawk, sed, etc. please let me know how.
But the following is a pure gnuplot solution.

### plot the last point of each datablock
reset
$Data <<EOD
11 1
22 4
33 9

44 16
55 25
66 36
77 49

88 64
99 81
110 100
121 121
132 144
EOD

print $Data
stats $Data
print STATS_records    # number of datapoints

array A[STATS_records]   # helper array
array B[STATS_records]   # helper array
array C[STATS_records]   # helper array

# puttig the dataset into arrays
set table $Data2
plot $Data u (A[$0+1]=column(-1),column(-1)):(B[$0+1]=$1,$1):(C[$0+1]=$2,$2) with table
unset table
print $Data2

# reverse the dataset
set print $Data3
G = A[STATS_records] # initialize block indicator
do for [i=STATS_records:1:-1] { 
  if (A[i] != G) { print "" }  # if different insert empty line / start new block
  G = A[i] 
  print sprintf("%g %g", B[i], C[i])
}
set print
print $Data3

# plot the original values 
set key top left
plot $Data u 1:2 w lp

# plot the first datapoints of each datablock of the reversed dataset
replot $Data3 u 1:2 every ::0::0 w p pt 6 ps 3 t "last point of each datablock"

### end gnuplot code

[Gnuplot-info] Setting dash length for individual lines

[Nunzio L. <nun...@gm...>]

Hi all,

is it possible in the latest versions of gnuplot to set a different dash
length for a single line?
If that is not the case, did anyone find a workaround for that?

best,

Nunzio

Re: [Gnuplot-info] Outputs of fit: details of how they're defined

[Dan <vi5...@ya...>]

> Am 20.11.2017 um 16:32 schrieb Daniel Hatton via gnuplot-info:
>
>> Please can anyone confirm whether I've correctly assessed what the fit
>> routine is putting in those output variables?

On Tue, 21 Nov 2017, Hans-Bernhard Bröker wrote:

> Not from those Unicode jungles I can't, sorry.

Thanks for trying, Hans-Bernhard.  I'll try and say the same things in
LaTeX, then...

Let's say that I have run

set fit noerrorscaling
set fit errorvariables
set fit covariancevariables

fit some_equation(L,M,x) 'some_data_set.dat' using ($1):($3):($2):($4)
errors x,z via L,M

where some_equation(L,M,x) is a theoretical formula, with adjustable
parameters L and M, which is supposed to predict the quantity in the
third column of the data file, when the value of the quantity in the
first column of the data file is x; the second column of the data file
contains the standard uncertainties in the measured values in the
first column of the data file 'some_data_set.dat'; and the fourth
column of the data file contains the standard uncertainties in the
measured values in the third column of the data file
'some_data_set.dat'.

Then I _think_ I expect to find:

- in the variables L and M, the values l and m of the L and M
parameters respectively, which, among all the (L,M) pairs that the
Marquardt-Levenberg algorithm has tried, produce the lowest value of
the \chi^2 statistic;
- in the variable FIT_WSSR, the value \Chi^2 of the \chi^2 statistic
that is achieved by setting L = l and M = m;
- in the variable L_err, the value (presumably calculated in a
finite-difference way) of
\sqrt{\frac{2}{\left(\partial\!^{2}\!\left(\chi^2\right)/\partial L\!^{2}\right)_{L = l,M = m}-\left(\left(\partial\!^{2}\!\left(\chi^2\right)/\left(\partial\!\!L\!\partial\!\!M\right)\right)_{L = l,M = m}\right)^2/\left(\partial\!^{2}\!\left(\chi^2\right)/\partial M\!^{2}\right)_{L = l,M = m}}}
- in the variable M_err, the value (presumably calculated in a
finite-difference way) of
\sqrt{\frac{2}{\left(\partial\!^{2}\!\left(\chi^2\right)/\partial M\!^{2}\right)_{L = l,M = m}-\left(\left(\partial\!^{2}\!\left(\chi^2\right)/\left(\partial\!\!L\!\partial\!\!M\right)\right)_{L = l,M = m}\right)^2/\left(\partial\!^{2}\!\left(\chi^2\right)/\partial L\!^{2}\right)_{L = l,M = m}}}
- in the variable FIT_COV_M_L, the value (presumably calculated in a
finite-difference way) of
\frac{2\left(\partial\!^{2}\!\left(\chi^2\right)/\left(\partial\!\!L\!\partial\!\!M\right)\right)_{L = l,M = m}}{\left(\partial\!^{2}\!\left(\chi^2\right)/\partial L\!^{2}\right)_{L = l,M = m}\left(\partial\!^{2}\!\left(\chi^2\right)/\partial M\!^{2}\right)_{L = l,M = m}-\left(\left(\partial\!^{2}\!\left(\chi^2\right)/\left(\partial\!\!L\!\partial\!\!M\right)\right)_{L = l,M = m}\right)^2}

Please can anyone confirm whether I've correctly assessed what the fit
routine is putting in those output variables?

> Had you found and considered the documentation under "help 
> statistical_overview"?

I've now had a look, but it doesn't tell me any more than the manual
did.

> You can rest assured that no Bayesian-style reasoning whatsoever was
> used in the design or implementation of this function.  This is
> strictly classical statistics and optimization theory, assuming
> normal-distributed inputs etc.

OK... but irrespective of whether the author of the relevant section
of the manual (and of "help statistical_overview") was a Bayesian or a
frequentist, his/her use of the word 'asymptotic' (in 'asymptotic
standard error') strongly suggests that s/he has seen a relevant
integral approximated using Laplace's method.  What I'm after is a
reference to a published source where that Laplace's method
approximation to a relevant integral took place.  (A Bayesian would
have had a subtly different integrand from a frequentist, but in many
ways, the real magic is that I'd expect the leading-order Laplace's
method approximation to the Bayesian's integral to be exactly the same
as the leading-order Laplace's method approximation to the
frequentist's integral.)

Thanks again.

-- 

Kind regards,

Dan

[Gnuplot-info] How to plot the last data points of each block?

[theozh <th...@gm...>]

In the following simplified dataset I just want to plot the last point of each block, here: 7, 4, 1.
How can I do that? 
Isn't there anything like: plot $Data u 0:1 every ::-1::-1

$Data <<EOD
9
8
7

6
5
4

3
2
1
EOD

# With the following:

stats $Data using 1
plot $Data index STATS_blocks-1 w lp

I could plot the complete last block (3,2,1), but ONLY if there were 2 empty lines between the blocks.
But I need to plot the last point of each block, i.e. 7, 4, 1

Re: [Gnuplot-info] Outputs of fit: details of how they're defined

[Hans-Bernhard B. <HBB...@t-...>]

Am 20.11.2017 um 16:32 schrieb Daniel Hatton via gnuplot-info:

> Please can anyone confirm whether I've correctly assessed what the fit
> routine is putting in those output variables?

Not from those Unicode jungles I can't, sorry.

Had you found and considered the documentation under "help 
statistical_overview"?

> As an aside, I believe the following two statements to be true when
> this least-squares fitting process is done in a Bayesian framework:
[...]

You can rest assured that no Bayesian-style reasoning whatsoever was 
used in the design or implementation of this function.  This is strictly 
classical statistics and optimization theory, assuming 
normal-distributed inputs etc.

[Gnuplot-info] Outputs of fit: details of how they're defined

[Daniel H. <vi5...@ya...>]

Dear All,

I find myself using Gnuplot (5.0 patchlevel 3) in teaching
least-squares fitting in a Bayesian framework.  As such, I need to
know some of the details of how the various outputs from the fit
command are defined.

>From a mixture of reading the manual and experimenting with running
various commands, I've come to the following tentative view of what's
happening:

Let's say that I have run

set fit noerrorscaling
set fit errorvariables
set fit covariancevariables

fit some_equation(L,M,x) 'some_data_set.dat' using ($1):($3):($2):($4) errors x,z via L,M

where some_equation(L,M,x) is a theoretical formula, with adjustable
parameters L and M, which is supposed to predict the quantity in the
third column of the data file, when the value of the quantity in the
first column of the data file is x; the second column of the data file
contains the standard uncertainties in the measured values in the
first column of the data file 'some_data_set.dat'; and the fourth
column of the data file contains the standard uncertainties in the
measured values in the third column of the data file
'some_data_set.dat'.

Then I _think_ I expect to find (with apologies if my Unicode
equations don't display correctly):

- in the variables L and M, the values l and m of the L and M
parameters respectively, which, among all the (L,M) pairs that the
Marquardt-Levenberg algorithm has tried, produce the lowest value of
the χ⁲ statistic;
- in the variable FIT_WSSR, the value Χ⁲ of the χ⁲ statistic that is
achieved by setting L = l and M = m;
- in the variable L_err, the value (presumably calculated in a
finite-difference way) of
√(2/((∂⁲(χ⁲)/∂L⁲)ₗ¸ₘ-((∂⁲(χ⁲)/(∂L∂M))ₗ¸ₘ)⁲/(∂⁲(χ⁲)/∂M⁲)ₗ¸ₘ));
- in the variable M_err, the value (presumably calculated in a
finite-difference way) of
√(2/((∂⁲(χ⁲)/∂M⁲)ₗ¸ₘ-((∂⁲(χ⁲)/(∂L∂M))ₗ¸ₘ)⁲/(∂⁲(χ⁲)/∂L⁲)ₗ¸ₘ)); and
- in the variable FIT_COV_M_L, the value (presumably calculated in a
finite-difference way) of
2(∂⁲(χ⁲)/(∂L∂M))ₗ¸ₘ/((∂⁲(χ⁲)/∂L⁲)ₗ¸ₘ(∂⁲(χ⁲)/∂M⁲)ₗ¸ₘ-((∂⁲(χ⁲)/(∂L∂M))ₗ¸ₘ)⁲).

Please can anyone confirm whether I've correctly assessed what the fit
routine is putting in those output variables?

As an aside, I believe the following two statements to be true when
this least-squares fitting process is done in a Bayesian framework:

- As long as the prior probability density over parameter space,
evaluated at the point (L,M) = (l,m), is non-zero, the leading-order
Laplace's method approximation to the standard deviation of the
posterior probability distribution for L, marginalized over M, is
√(2/((∂⁲(χ⁲)/∂L⁲)ₗ¸ₘ-((∂⁲(χ⁲)/(∂L∂M))ₗ¸ₘ)⁲/(∂⁲(χ⁲)/∂M⁲)ₗ¸ₘ)).

- As long as the prior probability density over parameter space,
evaluated at the point (L,M) = (l,m), is non-zero, the leading-order
Laplace's method approximation to the standard deviation of the
posterior probability distribution for M, marginalized over L, is
√(2/((∂⁲(χ⁲)/∂M⁲)ₗ¸ₘ-((∂⁲(χ⁲)/(∂L∂M))ₗ¸ₘ)⁲/(∂⁲(χ⁲)/∂L⁲)ₗ¸ₘ)).

I had to (re)invent those two statements myself, by means of an
enormously long-winded derivation: I haven't seen them in any
published source.  However, I can't believe that I'm the first to make
those statements, and I have a sneaking suspicion that the person who
wrote the phrase "asymptotic standard error", both in the Gnuplot
manual and in the comments of file <src/fit.c>, in the Gnuplot source
code tree, _has_ seen those two statements or something very like them
in a published source.  If that person is on this mailing list, it'd
be great if s/he could provide a reference, please.

Thanks very much.

-- 

Kind regards,

Dan

Re: [Gnuplot-info] integer vs. floating point division

[David K. <da...@gn...>]

Ethan Merritt <eam...@gm...> writes:

> [now I'm nit-picking...]
>
> Lua doesn't have integer variables, so there the question is moot.

That nit, by the way, is dead.

dak@lola:/usr/local/tmp/lilypond$ lua5.3 
Lua 5.3.3  Copyright (C) 1994-2016 Lua.org, PUC-Rio
> =math.type(4.0)
float
> =math.type(4)
integer
> 


-- 
David Kastrup