Two-dimensional histograms (xfig example) - Revision history

Obst: /* Using two-dimensional histograms */

2018-04-17T12:18:45Z

Using two-dimensional histograms

Obst at 12:17, 17 April 2018

2018-04-17T12:17:24Z

Obst: Obst moved page Example: two-dimensional histograms to Two-dimensional histograms (xfig example) without leaving a redirect

2018-04-17T11:06:27Z

Obst moved page Example: two-dimensional histograms to Two-dimensional histograms (xfig example) without leaving a redirect

Sokolova-lapa at 16:45, 13 April 2018

2018-04-13T16:45:21Z

Sokolova-lapa at 14:13, 13 April 2018

2018-04-13T14:13:09Z

Sokolova-lapa at 13:34, 13 April 2018

2018-04-13T13:34:11Z

Sokolova-lapa at 13:18, 13 April 2018

2018-04-13T13:18:17Z

Sokolova-lapa: Created page with " Category:SLxfig === Plotting two-dimensional histograms using the png and xfig modules === --- //example added by Manfred// --- Similarly to the isis:slxfig:ccmap|..."

2018-04-13T10:34:55Z

Created page with " Category:SLxfig === Plotting two-dimensional histograms using the png and xfig modules === --- //example added by Manfred// --- Similarly to the isis:slxfig:ccmap|..."

New page

[[Category:SLxfig]]

=== Plotting two-dimensional histograms using the png and xfig modules ===

--- //example added by Manfred// ---

Similarly to the [[isis:slxfig:ccmap|first example]] for creating [[isis:slxfig:ccmap|color-coded maps]] with the [[isis:slxfig|SLxfig module]], the goal of this one is to produce a color-coded map,
but this time, the color-scale represents a density of (a possibly large number of) data points.

=== ISIS' histogram2d function ===

==== Usage ====
The ''histogram2d'' function is used in the following way (see also [[http://pulsar.sternwarte.uni-erlangen.de/hanke/science/X-ray/ISIS/cgi/help.cgi?subj=histogram2d|help("histogram2d");]]):
num = histogram2d(A, B, Agrid, Bgrid);
''A'' and ''B'' have to be ''Double_Type'' arrays of the same length,
''Agrid'' and ''Bgrid'' have to be ''Double_Type'' arrays with monotonically increasing elements.

Now, ''num[a,b]'' contains the **number of points** (''A'', ''B'')
falling into each 2d-bin defined by the lower bin boundaries ''Agrid[a]'' and ''Bgrid[b]'', i.e.:
num[a,b] == howmany( (Agrid[a] <= A < Agrid[a+1]) and (Bgrid[b] <= B < Bgrid[b+1]) );

==== Overflow bins ====
The last bin in each row or column is an //**overflow bin**// whose upper limit is at infinity, i.e.,
num[-1,b] == howmany( (Agrid[-1] <= A) and (Bgrid[b] <= B < Bgrid[b+1]) );
num[a,-1] == howmany( (Agrid[a] <= A < Agrid[a+1]) and (Bgrid[-1] <= B) );
and
num[-1,-1] == howmany( (Agrid[-1] <= A) and (Bgrid[-1] <= B) );

If one wants to remove these overflow bins,
one can simply apply the index-array ''[:-2]'' (which means "take all elements up to the second last one")
in both dimensions in order to create a smaller two-dimensional array:
num_ = num[ [:-2], [:-2] ];

The last bins corresponding to the reduced 2d-array ''num_'' //end// now at the same position where the grids //end//, too:
num_[-1,-1] == num[-2,-2] == howmany( (Agrid[-2] <= A < Agrid[-1]) and (Bgrid[-2] <= B < Bgrid[-1]) );
Before, the grids specified always lower bin boundaries,
but now, the grids have one element more than the correpsonding array-dimensions of ''num_''.

Note that ISIS (one-dimensional) ''histogram'' function does not produce an overflow bin.

==== Order of the indices ====
The first index of ''num'' (called ''a'' above) will always correspond
to the first [and third] argument of the ''histogram2d'' function (here called ''A'' [and ''Agrid'']),
and the second index (''b'') to the second [and fourth] argument (''B'' [and ''Bgrid'']).

As most functions that operate on two dimensional arrays (like ''plot_image'', ''png_write'', ''ds9_view'', ...)
expect that the //first index// of the 2d-array to correspond to the y-axis,
whereas only the //second index// to the x-axis,
one will have to pass the y-data [and -grid] before the x-data [and -grid]:
num = histogram2d(Y, X, Xgrid, Ygrid);

=== Using two-dimensional histograms ===

Just as in the [[isis:slxfig:ccmap|previous example]],
these two dimensional histograms can be transformed into a color-coded image,
which can then be included in an [[isis:slxfig|xfig plot]] which adds back the original coordinate system.

==== A "banana-plot" ====

In an X-ray gratings spectrometer (//Chandra//-HETGS, //XMM//-RGS),
the dispersion is not only proportional to the photon's wavelength, but also to the dispersion order.
Different orders, however, can be separated with the internal energy resolution of the CCD detector.

The following example plots the density of events in a position--energy diagram:

===== Writing the png image =====

<pre>
variable evts = fits_read_table("evt2.fits"); % reading a Chandra level-2 event file

variable x_grid = [2300:5700:#320]; % x position on the detector (320 values)
variable energy_grid = [0:10000:#240]; % energies in eV (240 values from 0 to 10 keV)

variable num = histogram2d(evts.energy, evts.x, % the data (Y, X)
energy_grid, x_grid % the grids (Ygrid, Xgrid)
)[[:-2],[:-2]]; % removing overflow bins

require("png"); % load png module
variable RGB = png_gray_to_rgb(log(1+num), "ds9sls"); % transform num values logarithmically to RGB values, using the ds9sls color map
png_write_flipped("banana.png", RGB); % write RGB values to a png file
% png_write_flipped places RGB[0,0] in the *lower* left corner
</pre>
This produces just the bare image "banana.png":

{{:isis:slxfig:banana.png|bare image "banana.png"}}

With the [[isis:slxfig|S-Lang xfig module]], the coordinate system can, however, be easily added (back again).

===== Plotting the png into an SLxfig plot =====

It is important to set the correct coordinates for the SLxfig plot object,
as this information is no more present in the bare image.
As discussed above (in the section on "overflow bins"),
the last bins of the reduced 2d-array end where the original grids end
-- and obviously the first bins start where the grids start.
This is all the information that needs to be passed to the ''world'' method of an SLxfig plot object:
<pre>
require("xfig");
variable p = xfig_plot_new();
p.world(x_grid[0], x_grid[-1], energy_grid[0]/1000, energy_grid[-1]/1000); % defining the coordinate system; energy in keV instead of eV
p.plot_png("banana.png");
p.xlabel("Sky X Position");
p.ylabel("Energy [keV]");
p.render("banana-plot.pdf");
</pre>
The resulting plot looks like this:

{{:isis:slxfig:banana-plot.png|banana-plot with coordinate system}}

@@ Line 49: / Line 49: @@
 === Using two-dimensional histograms ===
-Just as in the [[Example:_color-coded_maps_with_2d_histograms,_png,_and_xfig|previous example]],
+Just as in the [[Color-coded_maps_with_2d_histograms,_png,_and_xfig_(xfig_example)|previous example]],
 these two dimensional histograms can be transformed into a color-coded image,
 which can then be included in an [[Plotting_with_the_S-Lang_Xfig_module|xfig plot]] which adds back the original coordinate system.

@@ Line 2: / Line 2: @@
 <i>example added by Manfred</i>
-Similarly to the [[Example: color-coded maps with 2d histograms, png, and xfig|first example]] for creating [[Example: color-coded maps with 2d histograms, png, and xfig|color-coded maps]] with the [[Plotting_with_the_S-Lang_Xfig_module|SLxfig module]], the goal of this one is to produce a color-coded map,
+Similarly to the [[Color-coded maps with 2d histograms, png, and xfig (xfig example)|first example]] for creating [[Color-coded maps with 2d histograms, png, and xfig (xfig example)|color-coded maps]] with the [[Plotting_with_the_S-Lang_Xfig_module|SLxfig module]], the goal of this one is to produce a color-coded map,
 but this time, the color-scale represents a density of (a possibly large number of) data points.

@@ Line 59: / Line 59: @@
 Different orders, however, can be separated with the internal energy resolution of the CCD detector.
-The following example plots the density of events in a position &dash energy diagram:
+The following example plots the density of events in a position &ndash; energy diagram:
 ===== Writing the png image =====
@@ Line 90: / Line 90: @@
 As discussed above (in the section on "overflow bins"),
 the last bins of the reduced 2d-array end where the original grids end
-&ndash and obviously the first bins start where the grids start.
+&ndash; and obviously the first bins start where the grids start.
 This is all the information that needs to be passed to the <code>world</code> method of an SLxfig plot object:
 <pre>

← Older revision	Revision as of 11:06, 17 April 2018
(No difference)

@@ Line 59: / Line 59: @@
 Different orders, however, can be separated with the internal energy resolution of the CCD detector.
-The following example plots the density of events in a position - energy diagram:
+The following example plots the density of events in a position &dash energy diagram:
 ===== Writing the png image =====
@@ Line 80: / Line 80: @@
 This produces just the bare image "banana.png":
-{{:isis:slxfig:banana.png|bare image "banana.png"}}
+[[File:banana.png|bare image "banana.png"]]
 With the [[Plotting_with_the_S-Lang_Xfig_module|S-Lang xfig module]], the coordinate system can, however, be easily added (back again).
@@ Line 90: / Line 90: @@
 As discussed above (in the section on "overflow bins"),
 the last bins of the reduced 2d-array end where the original grids end
--- and obviously the first bins start where the grids start.
+&ndash and obviously the first bins start where the grids start.
-This is all the information that needs to be passed to the ''world'' method of an SLxfig plot object:
+This is all the information that needs to be passed to the <code>world</code> method of an SLxfig plot object:
 <pre>
 require("xfig");
@@ Line 103: / Line 103: @@
 The resulting plot looks like this:
-{{:isis:slxfig:banana-plot.png|banana-plot with coordinate system}}
+[[File:banana-plot.png|banana-plot with coordinate system]]

@@ Line 1: / Line 1: @@
 [[Category:SLxfig]]
 <i>example added by Manfred</i>
@@ Line 12: / Line 8: @@
 ==== Usage ====
-The <code>histogram2d</code> function is used in the following way (see also [http://pulsar.sternwarte.uni-erlangen.de/hanke/science/X-ray/ISIS/cgi/help.cgi?subj=histogram2d|help("histogram2d");]):
+The <code>histogram2d</code> function is used in the following way (see also [http://pulsar.sternwarte.uni-erlangen.de/hanke/science/X-ray/ISIS/cgi/help.cgi?subj=histogram2d help("histogram2d")]):
    num = histogram2d(A, B, Agrid, Bgrid);
-''A'' and ''B'' have to be ''Double_Type'' arrays of the same length,
+<code>A</code> and <code>B</code> have to be <code>Double_Type</code> arrays of the same length,
-''Agrid'' and ''Bgrid'' have to be ''Double_Type'' arrays with monotonically increasing elements.
+<code>Agrid</code> and <code>Bgrid</code> have to be <code>Double_Type</code> arrays with monotonically increasing elements.
 Now, <code>num[a,b]</code> contains the <strong>number of points</strong> (<code>A</code>, <code>B</code>)
@@ Line 22: / Line 18: @@
 ==== Overflow bins ====
-The last bin in each row or column is an //**overflow bin**// whose upper limit is at infinity, i.e.,
+The last bin in each row or column is an <strong>overflow bin</strong> whose upper limit is at infinity, i.e.,
    num[-1,b]  ==  howmany( (Agrid[-1] <= A) and (Bgrid[b] <= B < Bgrid[b+1]) );
    num[a,-1]  ==  howmany( (Agrid[a] <= A < Agrid[a+1]) and (Bgrid[-1] <= B) );
@@ Line 29: / Line 25: @@
 If one wants to remove these overflow bins,
-one can simply apply the index-array ''[:-2]'' (which means "take all elements up to the second last one")
+one can simply apply the index-array <code>[:-2]</code> (which means "take all elements up to the second last one")
 in both dimensions in order to create a smaller two-dimensional array:
    num_ = num[ [:-2], [:-2] ];
-The last bins corresponding to the reduced 2d-array ''num_'' //end// now at the same position where the grids //end//, too:
+The last bins corresponding to the reduced 2d-array <code>num_</code> <i>end</i> now at the same position where the grids <i>end</i>, too:
    num_[-1,-1]  ==  num[-2,-2]  ==  howmany( (Agrid[-2] <= A < Agrid[-1]) and (Bgrid[-2] <= B < Bgrid[-1]) );
 Before, the grids specified always lower bin boundaries,
-but now, the grids have one element more than the correpsonding array-dimensions of ''num_''.
+but now, the grids have one element more than the correpsonding array-dimensions of <code>num_</code>.
-Note that ISIS (one-dimensional) ''histogram'' function does not produce an overflow bin.
+Note that ISIS (one-dimensional) <code>histogram</code> function does not produce an overflow bin.
 ==== Order of the indices ====
-The first index of ''num'' (called ''a'' above) will always correspond
+The first index of <code>num</code> (called <code>a</code> above) will always correspond
-to the first [and third] argument of the ''histogram2d'' function (here called ''A'' [and ''Agrid'']),
+to the first [and third] argument of the <code>histogram2d</code> function (here called <code>A</code> [and <code>Agrid</code>]),
-and the second index (''b'') to the second [and fourth] argument (''B'' [and ''Bgrid'']).
+and the second index (<code>b</code>) to the second [and fourth] argument (<code>B</code> [and <code>Bgrid</code>]).
-As most functions that operate on two dimensional arrays (like ''plot_image'', ''png_write'', ''ds9_view'', ...)
+As most functions that operate on two dimensional arrays (like <code>plot_image</code>, <code>png_write</code>, <code>ds9_view</code>, ...)
-expect that the //first index// of the 2d-array to correspond to the y-axis,
+expect that the <i>first index</i> of the 2d-array to correspond to the y-axis,
-whereas only the //second index// to the x-axis,
+whereas only the <i>second index</i> to the x-axis,
 one will have to pass the y-data [and -grid] before the x-data [and -grid]:
    num = histogram2d(Y, X, Xgrid, Ygrid);
 === Using two-dimensional histograms ===
-Just as in the [[isis:slxfig:ccmap|previous example]],
+Just as in the [[Example:_color-coded_maps_with_2d_histograms,_png,_and_xfig|previous example]],
 these two dimensional histograms can be transformed into a color-coded image,
-which can then be included in an [[isis:slxfig|xfig plot]] which adds back the original coordinate system.
+which can then be included in an [[Plotting_with_the_S-Lang_Xfig_module|xfig plot]] which adds back the original coordinate system.
 ==== A "banana-plot" ====
-In an X-ray gratings spectrometer (//Chandra//-HETGS, //XMM//-RGS),
+In an X-ray gratings spectrometer (<i>Chandra</i>-HETGS, <i>XMM</i>-RGS),
 the dispersion is not only proportional to the photon's wavelength, but also to the dispersion order.
 Different orders, however, can be separated with the internal energy resolution of the CCD detector.
-The following example plots the density of events in a position--energy diagram:
+The following example plots the density of events in a position - energy diagram:
 ===== Writing the png image =====
@@ Line 87: / Line 82: @@
 {{:isis:slxfig:banana.png|bare image "banana.png"}}
-With the [[isis:slxfig|S-Lang xfig module]], the coordinate system can, however, be easily added (back again).
+With the [[Plotting_with_the_S-Lang_Xfig_module|S-Lang xfig module]], the coordinate system can, however, be easily added (back again).
 ===== Plotting the png into an SLxfig plot =====

@@ Line 3: / Line 3: @@
 [[Category:SLxfig]]
-=== Plotting two-dimensional histograms using the png and xfig modules ===
+<p style="font-size:15px"><b>Plotting two-dimensional histograms using the png and xfig modules</b></p style="font-size:15px"><br/>
---- //example added by Manfred// ---
+Similarly to the [[Example: color-coded maps with 2d histograms, png, and xfig|first example]] for creating [[Example: color-coded maps with 2d histograms, png, and xfig|color-coded maps]] with the [[Plotting_with_the_S-Lang_Xfig_module|SLxfig module]], the goal of this one is to produce a color-coded map,
 but this time, the color-scale represents a density of (a possibly large number of) data points.
@@ Line 14: / Line 12: @@
 ==== Usage ====
-The ''histogram2d'' function is used in the following way (see also [[http://pulsar.sternwarte.uni-erlangen.de/hanke/science/X-ray/ISIS/cgi/help.cgi?subj=histogram2d|help("histogram2d");]]):
+The <code>histogram2d</code> function is used in the following way (see also [http://pulsar.sternwarte.uni-erlangen.de/hanke/science/X-ray/ISIS/cgi/help.cgi?subj=histogram2d|help("histogram2d");]):
    num = histogram2d(A, B, Agrid, Bgrid);
 ''A'' and ''B'' have to be ''Double_Type'' arrays of the same length,
 ''Agrid'' and ''Bgrid'' have to be ''Double_Type'' arrays with monotonically increasing elements.
-Now, ''num[a,b]'' contains the **number of points** (''A'', ''B'')
+Now, <code>num[a,b]</code> contains the <strong>number of points</strong> (<code>A</code>, <code>B</code>)
-falling into each 2d-bin defined by the lower bin boundaries ''Agrid[a]'' and ''Bgrid[b]'', i.e.:
+falling into each 2d-bin defined by the lower bin boundaries <code>Agrid[a]</code> and <code>Bgrid[b]</code>, i.e.:
    num[a,b]  ==  howmany( (Agrid[a] <= A < Agrid[a+1]) and (Bgrid[b] <= B < Bgrid[b+1]) );