# Module positions¶

In module wcs we provided two methods of the Projection object for transformations between pixels and world coordinates. These methods are wcs.Projection.topixel() and wcs.Projection.toworld() and they allow (only) numbers as their input parameters. These transformation methods apply to the coordinate system for which the Projection object is created and it is not possible to enter world coordinates from other sky systems or with other units.

Often one wants more flexibility. For instance, in interaction with the user, positions can be used to plot markers on a map or to preset the location of labels and graticule lines. But what to do if you have positions that need to be marked and the positions are from a FK5 catalog while your current map is given in Galactic coordinates? Or what to do if you need to know, given a radio velocity, what the optical velocity is for a spectral axis which has frequency as its primary type? For these situations we wrote function str2pos().

This module enables a user/programmer to specify positions in either pixel- or world coordinates. Its functionality is provided by a parser which converts strings with position information into pixel coordinates and world coordinates. Let’s list some options with examples how to use function str2pos() which is the most important method in this module.

Assume we have a projection object pr and you want to know the world coordinates w and the pixels p for a given string. Further, assume u are the units of the world coordinates and e is an error message. Both u and e are output parameters. Here are some examples how to use str2pos(). We will give detailed descriptions of the options in later sections.

• Expressions for the input of numbers.
Example: w,p,u,e = str2pos('[pi**2::3], [1:3]', pr)
• Use of physical constants.
Example: w,p,u,e = str2pos('c_/299792458.0,  G_/6.67428e-11', pr)
• Use of units to set world coordinates
Example: w,p,u,e = str2pos('178.7792 deg  53.655 deg', pr)
• Mix of pixels and world coordinates.
Example: w,p,u,e = str2pos('5.0, 53.655 deg', pr)
• Support of sky definitions.
Example: w,p,u,e = str2pos('{eq, B1950,fk4, J1983.5} 178.12830409  {} 53.93322241', pr)
• Support for spectral translations.
Example: w,p,u,e = str2pos('vopt 1050 km/s', pr)
• Coordinates from text file on disk.
Example: w,p,u,e = str2pos('readcol("test123.txt", col=2)', pr)
• Support for maps with only one spatial axis (e.g. XV maps).
Example: w,p,u,e = str2pos('{} 53.655 1.415418199417E+03 Mhz', pr, mixpix=6)
• Use of sexagesimal notation of spatial world coordinates.
Example: w,p,u,e = str2pos('11h55m07.008s 53d39m18.0s', pr)
• Units, sky definitions and spectral translations are case insensitive and minimal matched to the full names.

Examine next small script that uses the syntax described in this document to set marker positions:

Example: mu_markers.py - Demonstrate the use of strings for a position

from kapteyn import maputils, tabarray
from matplotlib import pyplot as plt
import numpy

f = maputils.FITSimage("m101.fits")
fig = plt.figure()
annim = f.Annotatedimage(frame, cmap="binary")
annim.Image()
grat = annim.Graticule()
#annim.Marker(pos="210.80 deg 54.34 deg", marker='o', color='b')
annim.Marker(pos="pc", marker='o', markersize=10, color='r')
annim.Marker(pos="14h03m30 54d20m", marker='o', color='y')
annim.Marker(pos="ga 102.035415152 ga 59.772512522", marker='+',
markersize=20, markeredgewidth=2, color='m')
annim.Marker(pos="{ecl,fk4,J2000} 174.367462651 {} 59.796173724",
marker='x', markersize=20, markeredgewidth=2, color='g')
annim.Marker(pos="{eq,fk4-no-e,B1950,F24/04/55} 210.360200881 {} 54.587072397",
marker='o', markersize=25, markeredgewidth=2, color='c',
alpha=0.4)

# Use pos= keyword argument to enter sequence of
# positions in pixel coordinates. The syntax is described
# in the module positions.py
pos = "200+20*sin([100:199]/20), range(100,200)"

annim.Marker(pos=pos, marker='o', color='r')

# Use x= and y= keyword arguments to enter sequence of
# positions in pixel coordinates. Note that this is not parsed by
# module positions.py. Here we need list comprehension to
# get the same effect.
xp = [400+20*numpy.sin(x/20.0) for x in range(100,200)]
yp = range(100,200)
annim.Marker(x=xp, y=yp, mode='pixels', marker='o', color='g')

xp = yp = 150
annim.Marker(x=xp, y=yp, mode='pixels', marker='+', color='b')

annim.plot()
annim.interact_imagecolors()
annim.interact_toolbarinfo()
plt.show()


## Introduction¶

Physical quantities, in a data structure which represents a measurement of an astronomical phenomenon, are usually measurements at fixed positions in the sky, sometimes at some spectral value such as a Doppler shift, frequencies or velocity. These positions are examples of so called World Coordinates. To identify a world coordinate in a measured data structure, we use a coordinate system based on the pixels in that structure. Often the data structures are FITS files and the coordinate system is subject to a set of rules. For FITS files the first pixel on an axis is labeled with coordinate 1 and it runs to the value of NAXISn which is a FITS header item that sets the length of the n-th axis in the data structure.

Assume you have a data structure representing an optical image of a part of the sky and you need to mark a certain feature in the image or need to retrieve the intensity of a pixel at a certain location. Then it is possible to identify the pixel using pixel coordinates. But when you have positions from external sources like catalogs, then these are not related to a FITS file and therefore given in world coordinates coupled to a certain coordinate system (e.g. a sky system). Then it would be convenient if you could specify positions exactly in those coordinates.

This module uses two other modules from the Kapteyn Package: Module wcs provides methods for conversions between pixel coordinates and world coordinates given a description of the world coordinate system as defined in a (FITS) header). Module celestial converts world coordinates between different sky- and reference systems and/or epochs. In this module we combine the functionality of wcs and celestial to write a coordinate parser to convert world coordinates to pixel coordinates (and back) given a header that describes the WCS. Note that a description of a world coordinate system can be either derived from a FITS header or a Python dictionary with FITS keywords.

## How to use this module¶

This module is used in several modules of the Kapteyn Package, but it can also be imported in your own scripts so that you are able to convert positions (given as a string) to pixel- and world coordinates. It is also possible to use this module as a test application. If you want to see the test run then type: python positions.py on the command line. The source of the test strings with positions can be found in function dotest() in this module.

To get the idea, we list a short example starting with the definition of a header:

from kapteyn import wcs, positions

header = { 'NAXIS'  : 2,
'CDELT1' : -1.200000000000E-03, 'CDELT2' : 1.497160000000E-03,
'CRPIX1' : 5, 'CRPIX2' : 6,
'CRVAL1' : 1.787792000000E+02, 'CRVAL2' : 5.365500000000E+01,
'CTYPE1' : 'RA---NCP', 'CTYPE2' : 'DEC--NCP',
'CUNIT1' : 'DEGREE', 'CUNIT2' : 'DEGREE',
'NAXIS1' : 10, 'NAXIS2' : 10,
}

w,p,u,e = positions.str2pos('5, 6', pr)
if e == '':
print "pixels:", p
print "world coordinates:", w, u


Its output (which is always a NumPy array) is:

pixels: [[ 5.  6.]]
world coordinates: [[ 178.7792   53.655 ]] ('deg', 'deg')


Remember, p are the pixel coordinates, w the world coordinates and u is a tuple with units. We have valid coordinates if the string e is empty. If it is not empty then there is an error condition and the string is an error message. The parser does not raise exceptions but it stores a message after an exception in the error message. This is to simplify the use of str2pos(). If you want to extract just one position then give the index in the output array, for example W0 = w[0]. The x and y coordinates are in this case: wx = W0[0]; wy = W0[1].

Structure of output

The function str2pos() returns a tuple with four items:

• w: an array with positions in world coordinates. One position has n coordinates and n is the dimension of your data structure which 1 for structure with one axis, 2 for a map, 3 for a cube etc.
• p: an array with positions in pixel coordinates. It has the same structure as w.
• u: an array with the units of the world coordinates These units are derived from the projection object with an optional alternative sky system and/or an optional spectral translation. The number of units in the list is the number of coordinates in a position.
• e: an error message. If the length of this string is not 0, then it represents an error message and the arrays w and p are empty.

## Position syntax¶

### Number of coordinates¶

A position has the same number of coordinates as the number of axes that are defined by the Projection object. So each position in a 2-dim map has two coordinates. One can enter 1 position or a sequence of positions as in:

>>> pos="0,1  4,5  2,3"


Numbers are separated either by a space or a comma.

So also:

>>> pos="0 1 4 5 2 3"
>>> pos="0,1,4,5,2,3"


give the same result.

### Numbers in expressions¶

Numbers can be given as valid (Python) expressions. A selection of functions and operators known to module NumPy can be used. The functions are:

• abs, arccos, arccosh, arcsin, arcsinh, arctan, arctan2, arctanh, cos, cosh, degrees, exp, log2, log10, mean, median, min, max, pi, radians, sin, sinc, sqrt, sum, tan, tanh, rand, randn, ranf, randint, sign
• Aliases: acos = arccos, acosh = arccosh, asin = arcsin, asinh = arcsinh, atan = arctan, atan2 = arctan2, atanh = arctanh, ln = log10(x)/log10(e), log=log10, deg=degrees, rad=radians
• arange, linspace

The functions allow a NumPy array as argument. Here its definition starts and ends with a square bracket. Its elements are separated by a comma. But note, it is not a Python list. In addition to the selection of mathematical functions we also include the functions arange() and linspace() from NumPy to be able to generate arrays.

Examples:

• arange(4) -> [0, 1, 2, 3]
• max(arange(4)) -> 3
• linspace(1,2,5) -> [1., 1.25, 1.5, 1.75, 2.]
• randint(0,10,3) -> [6, 4, 3]
• sin(ranf(4)) -> [0.66019925, 0.24063844, 0.28068498, 0.23582177]
• median([-1,3,5,-2,5,1]) -> 2.0
• mean(arange(4)) -> 1.5
• log(10**[1,2,3]) -> [1, 2, 3]
• log(100) log10(100) -> [2, 2]
• log2(e), ln(e) -> [1.44269504, 1.]
• log2(2**[1,2,3,4]) -> [1, 2, 3, 4]

Note the difference between the result of [pi]*3 when [pi] is a Python list (then a new list is created with elements [pi,pi,pi]), and the array [pi]. The array in our context is multiplied (element-wise) by 3. This is also true for other operators. So it is also valid to write:

• [1,2,3,4] -> [1, 2, 3, 4]
• pi*[1,2,3] -> [3.14159265, 6.28318531, 9.42477796]
• [1,2,3]**2 -> [1., 4., 9.]
• [1,2,3]-100 -> [-99., -98., -97.]
• [1,2,3]/0.3 -> [ 3.33333333, 6.66666667, 10.]

The array syntax also allows for the generation of ranges. A range follows the syntax start:end:step and start may be smaller than end. Here we deviate also from Python. That is, we include always the values start and end in the result: Some examples:

• [1:4] -> [ 1., 2., 3., 4.]
• [-1:-5] -> [-1., -2., -3., -4., -5.]
• [-1:-5:-2] -> [-1., -3., -5.]
• [5:1:1] -> [] # Note that increment is positive
• [1:3, 10:12, 100] -> [1., 2., 3., 10., 11., 12., 100.]
• [1*pi:2*pi] -> [3.14159265, 4.14159265, 5.14159265, 6.14159265, 7.14159265]

If one prefers the non-inclusive Python style ranges, then function arange() is available. Another function is linspace() which generates a (given) number of equidistant samples between a start and end value.

• arange(). For example arange(1,4)**3 results in an array with elements 1, 2, 3 and all these elements are taken to the power of 3
• linspace(). The arguments for ‘linspace’ are a start value, an end value and and the number of samples. For example linspace(1,3,4) results in an array with elements 1, 1.66666667, 2.33333333, 3

A range with a number of identical elements is created using a syntax with two subsequent colons:

• [1::3] -> [1, 1, 1]
• [1**2::2, pi::2] -> [1, 1, 3.14159265, 3.14159265]

Note

• Functions can have scalars, lists and arrays as arguments.
• Mathematical expressions can be applied on all array elements at the same time.
• Note that x to the power of y is written as x**y and not as x^y (which is a bitwise or).

To get information about NumPy functions you have to read the Python documentation (e.g. on the command line in a terminal, type: ipython. On the ipython command line type: import numpy; help(numpy.linspace)). Here are some examples how to use ranges in the input of positions:

>>> pos = "degrees(pi) e"                 # pixel coordinates: 180, 2.71828183
>>> pos = "degrees(atan2(1,1)) abs(-10)"  # pixel coordinates: 45, 10.
>>> pos = "[pi::3]**2, [1:3]**3"
>>> pos = "[1,6/3,3,4]**3, pi*[1,2,3,4]"
>>> pos = "[1:10], [10,1]"
>>> pos = "[sin(pi):-10:-2]  range(6)"


### Grouping of numbers¶

Coordinates can also be grouped. Elements in a group are processed in one pass and they represent only one coordinate in a position. A group of numbers can be prepended by a sky definition or spectral translation or be appended by a unit. Then the unit applies to all the elements in the group. We will see examples of this in one of the next sections. For the first example we could have grouped the coordinates as follows:

>>> pos="'0,4,2' '1,5,3'"


or, using the more powerful array generator, as:

>>> pos="[0,4,2] [1,5,3]"


Coordinates enclosed by single quotes or square brackets are parsed by Python’s expression evaluator eval() as one expression. The elements in a group can also be expressions. If square brackets are part of the expression, the expression represents a Python list and not an array! Examine the next expressions:

>>> pos = "'[pi]+[1,2]' range(3)"   # [pi, 1, 2]  [0, 1, 2]
>>> pos = "'[pi]*3' range(3)"       # [pi, pi, pi]  [0, 1, 2]
>>> pos = "'[sin(x) for x in range(4)]' range(4)"


In this context the square brackets define a list. In the examples we demonstrate the list operator ‘+’ which concatenates lists, ‘*’ which repeats the elements in a list and list comprehension. Note that Python’s eval() function requires that the elements in an expression are separated by a comma.

It is important to remember that without quotes, the square brackets define an array. The list operators ‘+’ and ‘*’ have a different meaning for lists and arrays. For arrays they add or multiply element-wise as shown in:

>>> pos = "[0,4,2]+10 [1,5,3]*2"  # is equivalent with "[10,14,12]  [2,10,6]"


Other examples of grouping are listed in the section about reading data from disk with readcol() and in the section about the eval() function.

### Pixel coordinates¶

All numbers, in a string representing a position, which are not recognized as world coordinates are returned as pixel coordinates. The first pixel on an axis has coordinate 1. Header value CRPIX sets the position of the reference pixel. If this is an integer number, the reference is located at the center of a pixel. This reference sets the location of of the world coordinate given in the (FITS) header in keyword CRVAL.

For the examples below you should use function str2pos() to test the conversions. However, for this function you need a (FITS) header. In the description at str2pos() you will find an example of its use.

Examples of two pixel coordinates in a two dimensional world coordinate system (wcs):

>>> pos = "10 20"       # Pixel position 10, 20
>>> pos = "10 20 10 30" # Two pixel positions
>>> pos = "(3*4)-5 1/5*(7-2)"
>>> pos = "abs(-10), sqrt(3)"
>>> pos = "pi, tan(radians(45))-0.5, 3*4,0"        # 2 positions
>>> pos = "atan2(2,3), 192"
>>> pos = "[pi::3], [e**2::3]*3"   # [pi, pi, pi], [3*e**2, 3*e**2, 3*e**2]


### Special pixel coordinates¶

For the reference position in a map we can use symbol ‘PC’ (Projection center). The center of your data structure is set with symbol ‘AC’. You can use either one symbol or the same number of symbols as there are axes in your data structure.

>>> pos = "pc"     # Pixel coordinates of the reference pixel
>>> pos = "PC pc"  # Same as previous. Note case insensitive parsing
>>> pos = "AC"     # Center of the map in pixel coordinates


### Constants¶

A number of global constants are defined and these can be used in the expressions for positions. The constants are case sensitive. These constants are:

c_ = 299792458.0             # Speed of light in m/s
h_ = 6.62606896e-34          # Planck constant in J.s
k_ = 1.3806504e-23           # Boltzmann in J.K^-1
G_ = 6.67428e-11             # Gravitation in m^3. kg^-1.s^-2
s_ = 5.6704e-8               # Stefan-Boltzmann in J.s^-1.m^-2.K^-4
M_ = 1.9891e+30              # Mass of Sun in kg
P_ = 3.08567758066631e+16    # Parsec in m


### World coordinates¶

World coordinates can be distinguished from pixel coordinates. A world coordinate is:

• a coordinate followed by a (compatible) unit. Note that the units of the world coordinate are given in the (FITS) header in keyword CUNIT. If there is no CUNIT in the header or it is an empty string or you don’t remember the units, then use either:

• The wildcard symbol ‘?’
• A case insensitive minimal match for the string ‘UNITS’
• a coordinate prepended by a definition for a sky system or a spectral system.

• a coordinate entered in sexagesimal notation. (hms/dms)

Note

One can mix pixel- and world coordinates in a position.

#### Units¶

For a two dimensional data structure (e.g. an optical image of part of the sky) we can enter a position in world coordinates as:

>>> pos = 178.7792 deg  53.655 deg


But we can also use compatible units:

>>> pos = "178.7792*60 arcmin  53.655 deg"    # Use of a compatible unit if CUNIT is "DEGREE"
>>> pos = "10 1.41541820e+09 Hz"              # Mix of pixel coordinate and world coordinate
>>> pos = "10 1.41541820 GHz"                 # Same position as previous using a compatible unit


Units are minimal matched against a list with known units. The parsing of units is case insensitive. The list with known units is:

• angles: ‘DEGREE’,’ARCMIN’, ‘ARCSEC’, ‘MAS’, ‘RADIAN’ ‘CIRCLE’, ‘DMSSEC’, ‘DMSMIN’, ‘DMSDEG’, ‘HMSSEC’, ‘HMSMIN’, ‘HMSHOUR’
• distances: ‘METER’, ‘ANGSTROM’, ‘NM’, ‘MICRON’, ‘MM’, ‘CM’, ‘INCH’, ‘FOOT’, ‘YARD’, ‘M’, ‘KM’, ‘MILE’, ‘PC’, ‘KPC’, ‘MPC’, ‘AU’, ‘LYR’
• time: ‘TICK’, ‘SECOND’, ‘MINUTE’, ‘HOUR’, ‘DAY’, ‘YR’
• frequency: ‘HZ’, ‘KHZ’,’MHZ’, ‘GHZ’
• velocity: ‘M/S’, ‘MM/S’, ‘CM/S’, ‘KM/S’
• temperature: ‘K’, ‘MK’
• flux (radio astr.): ‘W/M2/HZ’, ‘JY’, ‘MJY’
• energy: ‘J’, ‘EV’, ‘ERG’, ‘RY’

It is also possible to convert between inverse units like the wave number’s 1/m which, for example, can be converted to 1/cm.

For a unit, one can also substitute the wildcard symbol ‘?’. This is the same as setting the units from the header (conversion factor is 1.0). The symbol is handy to set coordinates to world coordinates. But it is essential if there are no units in the header like the unitless STOKES axis. One can also use the string units which has the same role as ‘?’.

>>> pos = "[0, 3, 4] ?"
>>> pos = "7 units"
>>> pos = "[5, 6.3] U"


#### Sky definitions¶

The detailed information about sky definitions can be found in:

If a coordinate is associated with a sky definition it is parsed as a world coordinate. A sky definition is either a case insensitive minimal match from the list:

'EQUATORIAL','ECLIPTIC','GALACTIC','SUPERGALACTIC'


or it is a definition between curly brackets which can contain one or more items from the following list: sky system, reference system, equinox and epoch of observation.

An empty string between curly brackets e.g. {}, followed by a number, implies a world coordinate in the native sky system.

Examples:

>>> pos = "{eq} 178.7792  {} 53.655"
# As a sky definition between curly brackets
>>> pos = "{} 178.7792 {} 53.655"
# A world coordinate in the native sky system
>>> pos = "{eq,B1950,fk4} 178.12830409  {} 53.93322241"
# With sky system, reference system and equinox
>>> pos = "{fk4} 178.12830409  {} 53.93322241"
# With reference system only.
>>> pos = "{eq, B1950,fk4, J1983.5} 178.1283  {} 53.933"
# With epoch of observation (FK4 only)
>>> pos = "{eq B1950 fk4 J1983.5} 178.1283  {} 53.933"
# With space as separator
>>> pos = "ga 140.52382927 ga 61.50745891"
# Galactic coordinates
>>> pos = "ga 140.52382927 {} 61.50745891"
# Second definition copies from first
>>> pos = "su 61.4767412, su 4.0520188"
# Supergalactic
>>> pos = "ec 150.73844942 ec 47.22071243"
# Ecliptic
>>> pos = "{} 178.7792 6.0"
# Mix world- and pixel coordinate
>>> pos = "5.0, {} 53.655"
# Mix with world coordinate in native system


Note

• Mixing sky definitions for one position is not allowed i.e. one cannot enter pos = “ga 140.52382927 eq 53.655”
• If you mix a pixel- and a world coordinate in a spatial system then this world coordinate must be defined in the native system, i.e. {}

We can also specify positions in data structures with only one spatial axis and a non-spatial axis (e.g. position velocity diagrams). The conversion function str2pos() needs a pixel coordinate for the missing spatial axis. If one of the axes is a spectral axis, then one can enter world coordinates in a compatible spectral system:

>>> pos = "{} 53.655 1.415418199417E+09 hz"
# Spatial and spectral world coordinate
>>> pos = "{} 53.655 1.415418199417E+03 Mhz"
# Change Hz to MHz
>>> pos = "53.655 deg 1.415418199417 Ghz"
# to GHz
>>> pos = "{} 53.655 vopt 1.05000000e+06"
# Use spectral translation to enter optical velocity
>>> pos = "{} 53.655 , vopt 1050 km/s"
# Change units
>>> pos = "10.0 , vopt 1050000 m/s"
# Combine with a pixel position
>>> pos = "{} 53.655 vrad 1.05000000e+06"
>>> pos = "{} 53.655 vrad 1.05000000e+03 km/s"
# Radio velocity with different unit
>>> pos = "{} 53.655 FREQ 1.41541820e+09"
# A Frequency
>>> pos = "{} 53.655 wave 21.2 cm"
# A wave length with alternative unit
>>> pos = "{} 53.655 vopt c_/285.51662
# Use speed of light constant to get number in m/s


Note

For positions in a data structure with one spatial axis, the other (missing) spatial axis is identified by a pixel coordinate. Usually it’s a slice). This restricts the spatial world coordinates to their native wcs. We define a world coordinate in its native sky system with {}

Note

A sky definition needs not to be repeated. Only one definition is allowed in a position. The second definition therefore can be empty as in {}.

Note

World coordinates followed by a unit, are supposed to be compatible with the Projection object. So if you have a header with spectral type FREQ but with a spectral translation set to VOPT, then "{} 53.655 1.415418199417E+09 hz" is invalid, "10.0 , vopt 1050000 m/s" is ok and also "{} 53.655 FREQ 1.415418199417e+09" is correct.

#### Sexagesimal notation¶

Read the documentation at parsehmsdms() for the details. Here are some examples:

>>> pos = "11h55m07.008s 53d39m18.0s"
>>> pos = "{B1983.5} 11h55m07.008s {} -53d39m18.0s"
>>> pos = -33d 0d


Often one wants to plot markers at positions that are stored in a text file (Ascii) on disk.

In practice one can encounter many formats for coordinates in text files. Usually these coordinates are written in columns. For example one can expect longitudes in degrees in the first column and latitudes in degrees in the second. But what do these coordinates represent? Are they galactic or ecliptic positions? If your current plot represents an equatorial system can we still plot the markers from the file if these are given in the galactic sky system? And there are more questions:

• Assume you have a file with three columns with hours, minutes and seconds as longitude and three columns with degrees, minutes and seconds as latitude. Is it possible to read these columns and combine them into longitudes and latitudes? Assume you have a file and the Right Ascensions are given in decimal hours, is it possible to convert those to degrees?
• Assume your file has numbers that are in a unit that is not the same unit as the axis unit in your plot. Is it possible to change the units of the data of the column in the text file?
• Assume you have several (hundreds of) thousands marker positions. Is reading the marker positions fast?
• If a file has comment lines that start with another symbol than ‘!’ or ‘#’, can one still skip the comment lines?
• If a file has columns separated by something else than whitespace, is it still possible then to read a column?

syntax

>>> readcol(filename, col=1, fromline=None, toline=None, rows=None, comment="!#",
sepchar=', t', bad=999.999, fromrow=None, torow=None, rowstep=None)

>>> readhms(filename, col1=1, col2=2, col3=3,
fromline=None, toline=None, rows=None, comment="!#",
fromrow=None, torow=None, rowstep=None)


The parameters are:

• filename - a string with the name of a text file containing the table. The string must be entered with double quotes. Single quotes have a different function in this parser (grouping).
• col - a scalar that sets the column number.
• fromline - Start line to be read from file (first is 1).
• toline - Last line to be read from file. If not specified, the end of the file is assumed.
• comment - a string with characters which are used to designate comments in the input file. The occurrence of any of these characters on a line causes the rest of the line to be ignored. Empty lines and lines containing only a comment are also ignored.
• sepchar - a string containing the column separation characters to be used. Columns are separated by any combination of these characters.
• rows - a tuple or list containing the row numbers to be extracted.
• bad - a number to be substituted for any field which cannot be decoded as a number. The default value is 999.999
• fromrow - number of row from the set of lines with real data to start reading
• torow - number of row from the set of lines with real data to end reading. The torow line is included.
• rowstep - Step size in rows. Works also if no values are given for fromrow and torow.

There is a difference between the rows= and the fromline= , toline= keywords. The first reads the specified rows from the parsed contents of the file( (parsed contents are lines that are not comment lines), while the line keywords specify which lines you want to read from file. Usually comment characters ‘#’ and ‘!’ are used. If you expect another comment character then change this keyword. Keyword sepchar= sets the separation character. The default is a comma, a space and a tab. bad= is the value that is substituted for values that could not be parsed so that they can be easily identified.

Note

• The result is an array so it can be used in an expression

Some examples:

Assume a text file on disk with a number of rows with 2 dimensional marker positions in pixel coordinates. The text file is called pixmarks.txt. Then the simplest line to read this data is:

>>> pos = 'readcol("pixmarks.txt") readcol("pixmarks.txt",2)'
>>> annim.Marker(pos=pos, marker='o', markersize=10, color='r')


All parameters have defaults except the filename parameter. The default column is 1, i.e. the first column. For readability we prefer to write the positions as:

>>> pos = 'readcol("pixmarks.txt", col=1) readcol("pixmarks.txt",col=2)'


If you want all the data up to line 30 (and line 30 including) you should write:

>>> pos = 'readcol("pixmarks.txt", col=1, toline=30) readcol("pixmarks.txt",col=2, toline=30)'


If your file has relevant data from line 30 to the end of the file, one should write:

>>> pos = 'readcol("pixmarks.txt", col=1, fromline=30) readcol("pixmarks.txt",col=2, fromline=30)'


As stated earlier, we distinguish lines and rows in a file. Lines are also those which are empty or which start with a comment. Rows are only those lines with data. So if you want to read only the first 5 rows of data, then use:

>>> pos = 'readcol("pixmarks.txt", col=1, torow=5) readcol("pixmarks.txt",col=2, torow=5)'


Note that the parameters toline and torow include the given value. You can specify a range of rows including a step size with:

>>> pos = 'readcol("pixmarks.txt", col=1, fromrow=10, torow=44, rowstep=2), .....'


to get row number 10, 12, ..., 44. Note that it is not possible to set a step size if you use the fromline or toline parameter.

In some special circumstances you want to be able to read only preselected rows from the data lines. Assume a user needs rows 1,3,7,12,44. Then the position string should be:

>>> pos = 'readcol("pixmarks.txt", col=1, rows=[1,3,7,12,44]), .....'


Perhaps you wonder why you need to repeat the readcol() function for each coordinate. It is easier to use it once and specify two columns instead of one. We did not implement this feature because usually one will read world coordinates from file and often we want to add units or a sky- or spectral conversion. Then you must be able to read the data for each column separately. Assume we have a file on disk called ‘lasfootprint’ which stores two sets of 2 dimensional positions (i.e. 4 coordinates) separated by an empty line.

#  RA J2000  Dec      l         b         eta     lambda
8.330    -1.874   225.624    19.107   -36.250   300.000
8.663    -2.150   228.598    23.268   -36.250   305.000
8.996    -2.409   231.763    27.369   -36.250   310.000
9.329    -2.651   235.170    31.394   -36.250   315.000
9.663    -2.872   238.878    35.320   -36.250   320.000
.....     ......
.....


It has a blank line at line 63. The first column represents Right Ascensions in decimal hours. If we want to read the positions given by column 1 and 2 of the second segment (starting with line 66) and column 1 is given in decimal hours, then you need the command:

>>> pos=  'readcol("lasfootprint", col=1,fromline=64)


The first coordinate is followed by a unit, so it is a world coordinate. We have a special unit that converts from decimal hours to degrees (HMSHOUR). The last coordinate is followed by a unit (deg) so it is a world coordinate. It was also possible to prepend the second coordinate with {} and omit the unit as in: Between the brackets there is nothing specified. This means that we assume the coordinates in the file (J2000) match the sky system of the world coordinate system of your map.

>>> pos=  'readcol("lasfootprint", 1,64) HMShour {} readcol("lasfootprint", 2,64)'


Note that the third parameter is the fromline parameter. If columns 3 and 4 in the file are galactic longitudes and latitudes, but our basemap is equatorial, then we could have read the positions with an alternative sky system as in (now we read the first data segment):

>>> pos=  '{ga} readcol("lasfootprint", 3, toline=63)  {} readcol("lasfootprint", 4, toline=63)'


The second sky definition is empty which implies a copy of the first definition (i.e. {ga}).

Note

The sky definition must describe the world coordinate system of the data on disk. It will be automatically converted to a position in the sky system of the Projection object which is associated with your map or axis.

Some files have separate columns for hour, degrees, minutes and seconds. Assume you have an ASCII file on disk with 6 columns representing sexagesimal coordinates. For example:

! Test file for Ascii data and the READHMS/READDMS command
11 57 .008 53 39 18.0
11 58 .008 53 39 17.0
11 59 .008 53 39 16.0
....


Assume that this file is called hmsdms.txt and it contains equatorial coordinates in ‘hours minutes seconds degrees minutes seconds’ format, then read this data with:

>>> pos= '{} readhms("hmsdms.txt",1,2,3) {} readdms("hmsdms.txt",4,5,6)'


Or with explicit choice of which lines to read:

>>> pos= '{} readhms("hmsdms.txt",1,2,3,toline=63) {} readdms("hmsdms.txt",4,5,6,toline=63)'


The data is automatically converted to degrees. What if the format is ‘d m s d m s’ and the coordinates are galactic. Then we should enter;

>>> pos= 'ga readdms("hmsdms.txt",1,2,3) ga readdms("hmsdms.txt",4,5,6)'


if your current sky system is galactic then it also possible to enter:

>>> pos= 'readdms("hmsdms.txt",1,2,3) deg  readdms("hmsdms.txt",4,5,6) deg'


If the columns are not in the required order use the keyword names:

>>> pos= 'readdms("hmsdms.txt",col3=0,col2=1,col3=2) deg  readdms("hmsdms.txt",4,5,6) deg'


The result of one of the functions described in this section is an array and therefore suitable to use in combination with functions and operators:

>>> pos='1.1*readhms("hmsdms.txt",1,2,3)-5 sin(readdms("hmsdms.txt",4,5,6)-10.1)'


Command header reads an item from the header that was used to create the Projection object. The header item must represent a number.

>>> pos= 'header("crpix1") header("crpix2")'


Note

• Header keys are case insensitive
• A key must be given with double quotes

### Parser errors messages¶

The position parser is flexible but there are some rules. If the input cannot be transformed into coordinates then an appropriate message will be returned. In some cases the error message seems not to be related to the problem but that seems often the case with parsers. If a number is wrong, the parser tries to parse it as a sky system or a unit. If it fails, it will complain about the sky system or the unit and not about the number.

### Testing the parser¶

You can run the module’s ‘main’ (i.e. execute the module) to test pre installed expressions and to experiment with your own positions entered at a prompt. Please copy the module positions.py to your working directory first! The program will display a couple of examples before it prompts for user input. Then your are prompted to enter a string (no need to enclose it with quotes because it is read as a string). Enter positions for a two dimensional data structure with axes R.A. and Dec. Start the test with:

>>> python positions.py


### GIPSY’s grids mode¶

FITS pixel coordinates start with number one and the last pixel for axis n is the value of header item NAXISn. Pixel value CRPIXn is the pixel that corresponds to CRVALn. The value of CRPIXn can be non-integer. There are also systems that implement a different numbering. For example the Groningen Image Processing SYstem (GIPSY) uses an offset. There we call pixel CRPIXn grid 0, so grid 0 corresponds to CRVALn. It has the advantage that these grid coordinates are still valid after cropping the input data. For FITS data we need to change the value for CRPIXn after slicing the data and writing it to a new FITS file. But then your original pixel coordinates for the same positions need to be shifted too. The Projection object can be set into GIPSY’s grid mode using attribute gridmode (True or False).

## Functions¶

positions.str2pos(postxt, subproj, mixpix=None, gridmode=False)

This function accepts a string that represents a position in the world coordinate system defined by subproj. If the string contains a valid position, it returns a tuple with numbers that are the corresponding pixel coordinates and a tuple with world coordinates in the system of subproj. One can also enter a number of positions. If a position could not be converted then an error message is returned.

Parameters: postxt (String) – The position(s) which must be parsed. subproj (wcs.Projection object) – A projection object (see wcs). Often this projection object will describe a subset of the data structure (e.g. a channel map in a radio data cube). mixpix (Float) – For a world coordinate system with one spatial axis we need a pixel coordinate for the missing spatial axis to be able to convert between world- and pixel coordinates. gridmode (Boolean) – If True, correct pixel position for CRPIX to get grid coordinates where the pixel at CRPIX is 0

This method returns a tuple with four elements:

• a NumPy array with the parsed positions in world coordinates
• a NumPy array with the parsed positions in pixel coordinates
• A tuple with the units that correspond to the axes in your world coordinate system.
• An error message when a position could not be parsed

Each position in the input string is returned in the output as an element of a numpy array with parsed positions. A position has the same number of coordinates are there are axes in the data defined by the projection object.

Examples: from kapteyn import wcs, positions header = { 'NAXIS' : 2, 'BUNIT' :'w.u.', 'CDELT1' : -1.200000000000E-03, 'CDELT2' : 1.497160000000E-03, 'CRPIX1' : 5, 'CRPIX2' : 6, 'CRVAL1' : 1.787792000000E+02, 'CRVAL2' : 5.365500000000E+01, 'CTYPE1' :'RA---NCP', 'CTYPE2' :'DEC--NCP', 'CUNIT1' :'DEGREE', 'CUNIT2' :'DEGREE'} proj = wcs.Projection(header) position = [] position.append("0 0") position.append("eq 178.7792 eq 53.655") position.append("{eq} 178.7792 {} 53.655") position.append("{} 178.7792 {} 53.655") position.append("178.7792 deg 53.655 deg") position.append("11h55m07.008s 53d39m18.0s") position.append("{eq, B1950,fk4} 178.7792 {} 53.655") position.append("{eq, B1950,fk4} 178.12830409 {} 53.93322241") position.append("{fk4} 178.12830409 {} 53.93322241") position.append("{B1983.5} 11h55m07.008s {} 53d39m18.0s") position.append("{eq, B1950,fk4, J1983.5} 178.12830409 {} 53.93322241") position.append("ga 140.52382927 ga 61.50745891") position.append("su 61.4767412, su 4.0520188") position.append("ec 150.73844942 ec 47.22071243") position.append("eq 178.7792 0.0") position.append("0.0, eq 53.655") for pos in position: poswp = positions.str2pos(pos, proj) if poswp[3] != "": raise Exception, poswp[3] world = poswp[0][0] pixel = poswp[1][0] units = poswp[2] print pos, "=", pixel, '->', world , units 
positions.parsehmsdms(hmsdms, axtyp=None)

Given a string, this routine tries to parse its contents as if it was a spatial world coordinate either in hours/minutes/seconds format or degrees/minutes/seconds format.

Parameters: hmsdms (String) – A string containing at least a number followed by the character ‘h’ or ‘d’ (case insensitive) followed by a number and character ‘m’. This check must be performed in the calling environment. The number can be a negative value. The string cannot contain any white space. axtype (String) – Distinguish formatted coordinates for longitude and latitude. The parsed world coordinate in degrees and an empty error message or None and an error message that the parsing failed. A distinction has been made between longitude axes and latitude axes. The hms format can only be used on longitude axes. However there is no check on the sky system (it should be equatorial). The input is flexible (see examples), even expressions are allowed. >>> hmsdms = '20h34m52.2997s' >>> hmsdms = '60d9m13.996s' >>> hmsdms = '20h34m52.2997' # Omit 's' for seconds >>> hmsdms = '60d9m13.996' >>> hmsdms = '20h34m60-7.7003' # Expression NOT allowed >>> hmsdms = '-51.28208458d0m' # Negative value for latitude  The ‘s’ for seconds is optional Expressions in numbers are not allowed because we cannot use Python’s eval() function, because this function interprets expressions like ‘08’ differently (octal). dms format always allowed, hms only for longitude axes. Both minutes and seconds are optional. The numbers need not to be integer.
positions.unitfactor(unitfrom, unitto)

Return the conversion factor between two units.

Parameters: unitfrom (String) – Units to convert from. Strings with ‘1/unit’ or ‘/unit’ are also allowed. If this parameter is ‘?’ then the incoming unit is a wildcard character and the conversion factor 1.0 is returned. The same holds for a case insensitive minimum match of the string ‘UNITS’. This option is necessary for the option to use world coordinates when there are no units given in the header of the data (i.e. there is no CUNITn keyword or its contents is empty). unitto – Units to convert to. Strings with ‘1/unit’ or ‘/unit’ are also allowed. The conversion factor to convert a number in ‘unitsfrom’ to a number in ‘unitsto’. >>> print unitfactor('1/m', '1/km') (1000.0, '') >>> print positions.unitfactor('1/mile', '1/km') (0.62137119223733395, '') >>> print positions.unitfactor('mile', 'km') (1.6093440000000001, '')