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XMM-Newton Science Analysis System Page: 1
The XMM Selector library
July 1, 2008
Abstract
selectlib provides functionality to perform table and array processing with boolean
and arithmetic expressions
1 Introduction
The selector library selectlib provides functionality to perform table and array processing driven by
boolean and arithmetic expressions. The notion of table and array is that of the Data Model dened
in the SAS Data Access Layer package dal. Other dal terms such as table column, data set, block, and
attribute are likewise used throughout the following sections. Readers not familiar with these notions are
therefore advised to consult the dal documentation prior to reading any further.
2 Description
Table and array processing in selectlib is controlled via user-specied boolean and arithmetic expres-
sions. These take the form of single character strings which are composed of a variety of elements
including numerical and logical constants, operators, functions, and attributes. The following operations
are supported by selectlib:
operation required
expression
comment
table ltering logic can contain names of other columns (see Sect. 2.15.1)
construction of new table column arithmetic can contain names of other columns (see Sect. 2.15.2)
construction of new array arithmetic can contain symbolic references to other arrays (see
Sect. 2.15.3)
The following sections detail the syntax and semantics of the expressions driving the above operations
and give sample expressions to demonstrate typical usage scenarios.
2.1 Boolean operators and functions
Table ltering requires the specication of a single boolean expression which must evaluate to either true
or false for all rows of the table. Rows are selected if the expression evaluates to true, otherwise they are
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not selected. The notion of a valid boolean expression is identical to the one in the programming languages
C/C++ and Fortran: An expression is comprised of a sequence of sub-expressions combined with the
logical operators && (and) and || (or). Sub-expressions are constructed from table column names (the
equivalent of variable names in C/C++/Fortran), boolean operators, and symbolic or numeric constants
or other arithmetic expressions. The following table lists the available operators which can be used in
their C/C++ or Fortran form:
description C/C++ form Fortran form
equal == .eq.
not equal != .ne.
less than < .lt.
less than or equal <= .le.
greater than > .gt.
greater than or equal >= .ge.
or || .or.
and && .and.
logical negation ! .not.
inclusion test in (see Sect. 2.13)
Operator precedences are as in C/C++ and parentheses may be used as necessary to group sub-expressions.
Case is insignicant, i.e., .and., .AND., and .aNd. are all valid specications for the logical and-operator.
The C/C++ forms and Fortran forms can be mixed within a single expression.
In addition to the above operators, a limited set of boolean functions is available as well. These take
a number of arguments and return either true or false. The following table lists the available boolean
functions:
function name meaning comment
ifthenelse(expr1, expr2, expr3) if expr1 is true value of con-
struct is value of expr2, other-
wise value of expr3
all three arguments must
be boolean expressions
near(val1,val2,tol) true if jval1 val2j
jval1j <= tol
point(...), line(...), : : : point-in-gure test see Sect. 2.10
gti(...), mask(...), region(...) value-in-GTI/point in region
tests
see Sect. 2.12
selected() or selected selection status test see Sect. 2.14
2.2 Arithmetic constants and identiers
Boolean and arithmetic expressions may contain integer and oating point constants which can be
specied as in C/C++ or Fortran, e.g. 1.234E-12, -23, .111222, 1e2. The value of an integer con-
stant can be given in binary, octal, or hexadecimal by prepending b, o, and h or 0x respectively, i.e.,
32482 = b111111011100010 = o77342 = 0x7ee2 = h7ee2. Some frequently used constants are available
as symbolic names:
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name type value comment
#PI real  = 3:1415926535 : : :
#E real e = 2:718281828 : : : Euler number
#RAD real =180 = 0:017453 : : : for deg ! rad conversion
#DEG real 180= = 57:29577 : : : for rad ! deg conversion
#ARCSEC real =180=3600 = 4:8481 : : : 6 1 arcsec expressed in rad
#ARCMIN real =180=60 = 2:9088 : : : 4 1 arcmin expressed in rad
TRUE boolean true
FALSE boolean false
2.2.1 Angles
Angles can be regarded as ordinary real numbers in units of radians. In addition angles may be expressed
in terms of hours, minutes, and second of arc or time (e.g. for Right Ascension, Declination):
format comment evaluates to example
(+|-)xxdxxmxx[.xxx]s degrees + minutes and seconds of arc angle in radians -45d23m59.9s
xxhxxmxx[.xxx]s hours + minutes and seconds of time angle in radians 23h59m24.1s
x stands for a single decimal digit, d, h, m, s are literal characters and square brackets denote optional
items. The number of shown digits after the decimal point is not signicant.
2.2.2 Times
Times can be expressed in either of the following ways:
form comment example
xxxx-xx-xxTxx:xx:xx[.xxx] combined date-time string 2002-06-03T18:59:01.1
jdxxxxxx.xxx Julian date jd2450850.5
mjdxxxxx.xxx Modied Julian Day mjd50850.5
yxxxx.xxx decimal year number y2002.5
xxx xxx x xx:xx:xx xxxx calendar date Mon Jun 3 18:21:19 2002
x stands for a single decimal digit, jd, mjd, y, T are literal character strings and square brackets denote
optional items. The number of shown digits after the decimal point is not signicant. In an arithmetic
context all given times evaluate to the number of elapsed seconds since the xed time 1998-01-01T00:00:00
TT.
2.2.3 Identiers
Identiers are alphanumeric strings which can contain letters, digits and the underscore character ( ).
They must start with a letter | case is signicant. An identier must match a name of an existing
column in the input table unless it is prexed by a hash mark (#). In this case it must match any of
the above names for symbolic constants or is otherwise interpreted as a reference to a to numerical or
textual attribute in the currently processed table. The identier #ROW has a special meaning: It stands
for the current row number (starting from one) in the processed table.
Examples: #PI (the numerical value of ), #ROW (the current row number), ROWPI (a table column with
name ROWPI), #ROWPI (value of the numerical attribute ROWPI).
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2.3 Arithmetic operators and functions
Boolean and arithmetic expression can contain arithmetic sub-expressions consisting of operators, func-
tions and constants. The following operators and functions are available:
description symbol/name
arithmetic negation -
addition/subtraction +/-
multiplication/division *//
modulus %
exponentiation **, pow(x, y)
absolute value abs(x)
sine/cosine/tangent sin(x)/cos(x)/tan(x)
arc sine/arc cosine arcsin(x)/arccos(x)
arc tan arctan(x)/arctan2(x, y) = arctan(x/y)
hyperbolic sine/cosine/tangent sinh(x)/cosh(x)/tanh(x)
exponential exp(x)
natural log log(x)
common log log10(x)
square root sqrt(x)
integral part int(x)
fractional part modf(x)
smallest integral value not less than x ceil(x)
largest integral value not greater than x floor(x)
oating point remainder of x=y fmod(x, y)
The argument of the trigonometric functions and the result of their respective inverses are angles in
units of radians. For required conversions between radians and decimal degrees please avail the symbolic
constants #RAD and #DEG (see Sect. 2.2). Example: sin(ANGLE*#RAD), #DEG*arcsin(VAL).
2.4 Vector operators and functions
A limited set of operators and functions to perform vector algebra in three-dimensional Eucledian space
is available. The following table provides an overview over the available constructs:
description symbol/name type comment
vector construction vector(x, y, z) vector x/y/z can be arithmetic expressions
unit vector construction unitvector(x, y, z) vector norm(unitvector(x, y, z))==1
construction sky vector in
J2000 reference frame
skyvector(ra, dec) vector ra/dec Right Ascension/Declination in
rad
unary minus v vector v vector
vector addition v1+v2 vector v1/v2 vectors
vector subtraction v1 v2 vector v1/v2 vectors
multiplication with scalar sv vector v vector, s arithmetic expression
division by scalar v=s vector v vector, s arithmetic expression 6= 0
cross product cross(v1, v2) vector v1/v2 vectors
vector component v[i] scalar 0 <= i <= 2
vector norm norm(v) scalar equivalent to
sqrt(v[0]**2+v[1]**2+v[2]**2)
scalar product v1v2 scalar equivalent to
v1[0]*v2[0]+v1[1]*v2[1]+v1[2]*v2[2]
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Example expressions involving vector algebra:
 norm(vector(1,2,3)-4*vector(8,9,10))
 cross(skyvector(0,0), skyvector(#PI/2, 0))
 norm(vector(3,4,5)*unitvector(-2,3,4))-1
 5*vector(1,2,3)[0]
2.5 Character string constants, operators and functions
Boolean subexpressions may also be formed from character string constants, identiers that refer to text
columns, and a limited set of associated operators and functions. As in C/C++ a string constant is a
list of characters enclosed in double quotes ("). A double quote as part of the string must be preceded
by a backslash. In addition, string constants may also be given as single-quoted text in which case they
may contain un-escaped double quotes but no other single quote. Examples of valid string constants are:
"XMM", "", "The double quote:n"", 'A single-quoted string with a double quote (")'.
The following string operators and functions are available:
description symbol/name true example expression comment
equality ==, != "X"=="X", "XMM"!="XTE"
relational operators <, <=, >, >= "a"<"b", "a"<="b", lexicographical order
"b">"a", "b">="a"
change case upper/lower upper("Xmm")=="XMM"
lower("XMM")=="xmm"
length strlen strlen("XMM")==3,
strlen("")==0
ASCII value ascii ascii(" ")==32,
ascii("Z")-ascii("A")+1==26
concatenation + "Coca-"+"Cola"=="Coca-Cola"
range operator [:], [:hi], "XMM"[0:1]=="XM" rst character has index 0;
[lo:], [lo:hi] "FREDDY"[2:]=="EDDY" omitted lower/upper bound
expands to 0/actual length-1
Please note: The name of a string column can be used everywhere where a string constant is syntactically
correct. An error condition will be raised if a numeric column is used in a textual context. All of the
above string operators and functions can be arbitrarily nested to form more complex expressions, e.g.
(upper(STRCOL1)[:3]+STRCOL2)[5:]==upper(STRCOL3).
2.6 Null value function
Numerical columns in tables can optionally have associated null values. The usual convention is that
data entries that are set to a column's special null value are to be interpreted as 'not applicable/available'
by the application. The operator function
isnull(COLNAME)
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selects all rows in which the value of COLNAME is equal to the column's null value. If the column has no
associated null value dened the function evaluates to false. Please note:
1. The isnull() function can only be used in the above manner, i.e., with the name of a
numerical table column as argument. Attempts to use it in any other way will lead to an
error condition.
2. Unlike integer-valued columns there is always an implicit null value for oating point data,
viz. the special IEEE value NaN (Not-A-Number). It is not possible to dene any other real
value to serve as 'null' for real-valued columns.
2.7 Table column names
Column identiers can refer to table columns of scalar integral, oating point, boolean, or string type.
Mixed-type arithmetic is supported with the exception that names of boolean and string columns must not
be used in arithmetic sub-expressions. Names of boolean columns are valid logical sub-expressions, i.e.,
they do not need to be used in conjunction with the equality operators ==/!= and constants true/false
to form valid logical sub-expressions, e.g. BOOLCOL==true is equivalent to BOOLCOL.
Vector columns are not yet supported.
2.8 Subexpressions in table attributes
Table attributes being referred to in the selection expression via their names preceded by a hash mark
('#') are actually not restricted to contain numeric constants only. In fact the values interpreted as
strings can contain anything (including references to other attributes), for instance, to dene convenient
abbreviations for frequently used constructs. All table attributes will get replaced by their respective
values which must yield a valid boolean selection expression. Otherwise a fatal error condition will be
raised. Example: If a table contains the attributes:
RAWXSQ = '(RAWX-1)**2' / RAWX squared
RAWYSQ = '(RAWY-1)**2' / RAWY squared
DIST = 'sqrt(#RAWXSQ + #RAWYSQ)' / distance from center
DISTSEL = '#DIST <= 128' / select events in circle r=128
the selection expression
#DISTSEL
can be used as an alternative to the full form
sqrt((RAWX-1)**2 + (RAWY-1)**2) <= 128
2.9 Bitwise operators
For bit manipulations the following six operators are provided:
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description operand example
bitwise AND & b001110110 & b0111 = b110
bitwise OR | b001110110 | b0101 = b1110111
bitwise exclusive OR ^ b001110110 ^ b0111 = b1110001
left shift << b111 << 2 = b11100
right shift >> b111 >> 2 = b1
one's complement (32 bit)  b111000 = b111...000111
2.10 Special region lter functions
The following functions evaluate to true if a given point lies inside or on the border of the specied
geometric gure:
 point(x0,y0,Xcolumn,Ycolumn)
 line(x0,y0,x1,y1,Xcolumn,Ycolumn)
 circle(xCenter,yCenter,radius,Xcolumn,Ycolumn)
 sector(xCenter,yCenter,fromAngle,toAngle,Xcolumn,Ycolumn) or
pie(xCenter,yCenter,fromAngle,toAngle,Xcolumn,Ycolumn)
 ring(xCenter,yCenter,radius1,radius2,Xcolumn,Ycolumn) or
annulus(xCenter,yCenter,radius1,radius2,Xcolumn,Ycolumn)
 ellipse(xCenter,yCenter,xHalfWidth,yHalfWidth,rotation,Xcolumn,Ycolumn)
 elliptannulus(xCenter,yCenter,xHalfWidthInner,yHalfWidthInner
xHalfWidthOuter,yHalfWidthOuter,rotationInner,rotationOuter,Xcolumn,Ycolumn)
or
elliptring(xCenter,yCenter,xHalfWidthInner,yHalfWidthInner
xHalfWidthOuter,yHalfWidthOuter,rotationInner,rotationOuter,Xcolumn,Ycolumn)
 box(xCenter,yCenter,xHalfWidth,yHalfWidth,rotation,Xcolumn,Ycolumn)
 rectangle(xLoLeft,yLoLeft,xUpRight,yUpRight,rotation,Xcolumn,Ycolumn)
 rhombus(xCenter,yCenter,xHalfWidth,yHalfWidth,rotation,Xcolumn,Ycolumn) or
diamond(xCenter,yCenter,xHalfWidth,yHalfWidth,rotation,Xcolumn,Ycolumn)
 polygon(x1,y1,x2,y2,x3,y3,x4,y4,...,Xcolumn,Ycolumn)
 polygon2(x1,y1,x2,y2,x3,y3,x4,y4,...,Xcolumn,Ycolumn)
where
(x0,y0) : a coordinate pair dening a point - the two points given by (x0,y0) and
(Xcolumn,yColumn) (see below) must coincide for the point function to
return true
(x0,y0,x1,y1) : two points dening a line - the test point (Xcolumn,Ycolumn) (see below)
must lie on the line to within 0.5 units for the line function to return
true
(x1,y1,x2,y2,...) : the corner points of a polygon
(xCenter,yCenter) : the (x,y) position of the center of the region
(xHalfWidth,yHalfWidth) : the (x,y) half widths of the region - for elliptannulus: values for the
inner and outer ellipse respectively
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(xLoLeft,yLoLeft,
xUpRight,yUpRight)
: the coordinates of the lower left and upper right corner of the rectangle
(radius) : the half the diameter of the circle
(radius1,radius2) : the inner and outer half diameters of the annulus
(fromAngle,toAngle) : two angles in decimal degrees dening a sector; fromAngle must be lower
than or equal to toAngle
(rotation) : the angle in decimal degrees that the region is rotated with respect to
(xCenter,yCenter) except for rectangles which are rotated with re-
spect to the lower left corner (xLoLeft,yLoLeft) - elliptical annuli have
two angles for the inner and outer ellipse respectively (rotationInner,
rotationOuter)
(Xcolumn,Ycolumn) : the coordinates of the point to test - usually given as column names
Please note:
 Although this is usually the case, the above lter functions do not have to be necessarily
applied in the spatial domain. (Xcolumn,Ycolumn) can indeed be the names of any columns
in the table, i.e., selections in any two-dimensional data space are possible.
 In the case of the polygon lter the result of the inclusion test for points that lie exactly on
a boundary or coincide with a vertex is uncertain. If this behavior is unacceptable please
avail the polygon2 lter whose inclusion test results for those points is always positive. This
comes at the price of a worse run time eфciency.
2.11 Three-dimensional lter functions
The following functions evaluate to true if a vector lies inside or on the border of the specied three
dimensional gure:
 cone(vcen, alpha, vtest)
where
vcen : vector dening symmetry axis of gure
alpha : half opening angle of cone in rad
vtest : vector for inclusion test
Please note: For the sake of readability and clarity it is recommended to avail these lters in conjunction
with the In operator (see Sect. 2.13).
2.12 File-based lters
There are three special le-based lters which perform ltering with Good Time Intervals, spatial image
masks, and region tables. The syntax is:
gti(blockspec,Tcolumn)
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mask(blockspec,Xoffset,Yoffset,Xcolumn,Ycolumn)
region(blockspec,Xcolumn,Ycolumn) or region(blockspec)
with
Tcolumn : the time value to be checked; usually a column name
Xoffset,Yoffset : a vector by which the image mask is to be shifted
Xcolumn,Ycolumn : coordinates of point to test - usually given as column names
blockspec is a block specier which must point to a GTI table, a mask image, or a region table re-
spectively. It must be in either of the four forms setname, setname+blockid, setname[blockid], or
setname:blockid where setname must be the name of an existing data set and blockid an identier of
a block in that data set. If the rst form, setname, is used, the lter data are sought in the rst block
of the named data set. For the latter three forms, the data set name is optional. If omitted, it refers
to the data set of the currently processed table. blockid can either be an identier starting with a letter
which must then be the name of a block in the specied data set or a simple number which is directly
interpreted as a block sequence number (starting from 1). 1
2.12.1 gti-lter
The expression gti(x.gti,t) evaluates to true if the time t lies within at least one GTI contained in
the table x.gti. GTI tables must adhere to the OGIP standard [2].
2.12.2 mask-lter
mask(x.msk,x0,y0,x,y) is true if the value of the mask image shifted by (x0; y0) in the data set x.msk
at the location (x; y) is not equal to zero.
If the specied mask image contains the World-Coordinate-System (WCS)[1] attributes CRPIXx, CRVALx,
CDELTx with x being either 1 or 2, image coordinate values are computed from the respective integer pixel
numbers n as
r i
(n) = (n CRPIX i
)  CDELT i
+ CRVAL i ; i = 1; 2 (1)
This eectively denes the pixel size in the mask image as CDELT1CDELT2. If symbolic names have been
specied in the mask lter command as x and y and the corresponding columns in the processed table
have associated WCS-attributes TCRPXx, TCRVLx, and TCDLTx respectively the actual coordinate values
are calculated as above. This eectively denes the table pixel size as TCDLTx  TCDLTy. The mask lter
expression then evaluates to true for each \table pixel" if it has no overlap with any image mask pixel.
Mask images are ordinary rectangular arrays of any integral type supported by the dal.
2.12.3 region-lter
region(reg.fits,x,y) is true if the point (x; y) is contained in any of the regions specied in the region
le reg.fits.
If the second form of the region lter region(reg.fits) is used the coordinates of the test points come
from columns with names taken from the MFORM1 attribute in the specied block.
1 Examples for valid block speciers: gti.fits, gti.fits+3, gti.fits[GTI23], [98], +GTI10, gti.fits:GTI129
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For more informations on this and a formal denition of the region le format see Ref. [3].
2.13 In-operator
The in-operator is available in three distinct forms
1. arith IN intervals
This tests whether the value to which the arithmetic expression arith evaluates lies within
at least one among a list of intervals with numeric boundaries. The interval list is either
a single interval or a comma separated list of interval specications. The following table
provides an overview of the available intervals types (x stands for the value of arith above):
interval specication alternative expression meaning
: or (:] or [:) or (:) true 1 < x < +1
val or [val] val == x x = val
val: or [val:] or [val:) val <= x val <= x < +1
(val:] or (val:) val < x val < x < +1
:val or [:val] or (:val] val >= x 1 < x <= val
[:val) or (:val) val > x 1 < x < val
lo:hi or [lo:hi] lo <= x && hi >= x lo <= x <= hi
(lo:hi] lo < x && hi >= x lo < x <= hi
[lo:hi) lo <= x && hi > x lo <= x < hi
(lo:hi) lo < x && hi > x lo < x < hi
An example of a valid value-in-interval expression which yields true is:
3.1415 in :-10,[1:3),3.1,[3.14:3.19),[4:]
2. arith in gti(gtitable)
This is equivalent to the expression
gti(gtitable, arith)
3. (arith1, arith2) in filter(...)
where filter is either region or mask (see Sect. 2.12) or any of the region selection functions
(see Sect. 2.10). The form is equivalent to
filter(..., arith1, arith2)
for instance
(RAWX, RAWY) in circle(100, 120, 10) == circle(100, 120, 10, RAWX, RAWY)
always evaluates to true.
4. vector in filter(...)
where filter is a three dimensional region selection function (see Sect. 2.11) and vector
is a vector for the inclusion test.
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2.14 Selected-function
The selected function facilitates step-wise ltering of tables. Used as a sub-expression it evaluates to
true for a particular row if that rows has been selected in the selection process preceding the current one.
If the table undergoes selection for the very rst time, selected returns true for all table rows, i.e., has
no eect. As an example, the expression:
SELECTED && PHA >= 10
selects all rows which where selected in the previous selection cycle and with PHA values greater than or
equal to 10.
2.15 Example expressions
The following paragraphs contain lists of sample expressions which should demonstrate how the various
elements described in the above sections can be combined to achieve a desired result:
2.15.1 Table ltering
These sample boolean expressions demonstrate the ltering of an event list table with columns RAWX,
RAWY, PHA, PATTERNID, CCDID, PHASE, TIME, and FLAG:
 RAWX >= 100 && #ROW != 10
select all events with X coordinates greater than or equal to 100; exclude the 10th event
anyway
 RAWX > RAWY
select all events to the right of the line RAWX==RAWY
 CIRCLE(354,383,84,RAWX,RAWY)||ELLIPSE(243,215,27,108,0,RAWX,RAWY)
select events which lie in the circle or the ellipse with the specied parameters
 PATTERNID==4
select all events with PATTERNID equal to 4
 (CCDID==1 && TIME in gti(ccd1.gti))||(CCDID==2 && TIME in gti(ccd2.gti))
select all events from CCD #1 which pass the GTI lters in ccd1.gti plus all events from
CCD #2 which pass the GTI lters in ccd2.gti.
 PHASE>=.3 && PHASE<=.9
select events from the specied phase window
 (PHA>=100 && PHA<=200)||(PHA>=500 && PHA <=600)
select events with PHA values greater than 99 and less than 201 or greater than 499 and
less than 601
 FLAG & b110 != 0
select events which have the second and third bit in an (integral) FLAG column set
 SELECTED && PHA >= 10
select events which have been selected in the previous selection run and have PHA values
greater than or equal to 10
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 PHA in [0:10],(23:40),99,200: && TIME in gti(gti.fits[GTI0])
select events with PHA values in the range 0{10, or 23{40 (excl.), or equal to 99, or greater
than or equal to 200 and arrival times lying within Good-Time-Intervals contained in the
table named GTI0 in the data set gti.fits
 skyvector(RA, DEC) in cone(#RA MED, #DEC MED, 20*#ARCMIN)
select rows for which it is true that the J2000 sky vector constructed from the columns RA
and DEC lies within a cone with an opening angle of 20' and a symmetry axis given through
the sky vector dened by the two attributes #RA MED and #DEC MED
2.15.2 Table column construction
In the following the symbols RAWX, RAWY stand for names of existing columns in the table to be processed:
 sqrt(RAWX**2 + RAWY**2)
Constructs a new table column with radius values (provided RAWX /RAWY contain Cartesian
detection coordinates)
 100. * sin((TIME-#TIMEZERO)/#PERIOD * 360)
Construct a \predicted intensity" column for a very simple time-variable source
 RAWX + 100
Construct a new column which contains the RAWX coordinates shifted by 100 pixels
2.15.3 Array arithmetic
In the following the symbols A1, A2, and A3 stand for arrays with the same dimensionality and equal
extents in each dimension:
 1
Construct a new array and initialize all values to 1.
 A1+A2
Add the two arrays A1 and A2.
 sin(A1+A2)**2 - exp(A3)
Construct an array according to the specied expression involving the existing arrays A1,
A2, and A3.
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2.16 Implementation Status
feature status comment
all functionality described in user section v2.0 implemented in selectlib
v>=3.0
2.17 TODO
feature comment
vector columns support desirable | low priority
matrix algebra support needed for pyramid lter in attfilter task
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References
[1] E. W. Greisen and M. Calabretta. Representation of Celestial Coordinates in FITS. Astron. Astro-
phys., 1996. Found at the URL: ftp://fits.cv.nrao.edu/fits/documents/wcs/wcs.all.ps.
[2] W. Pence L. Angelini and A.F. Tennant. The Proposed Timing FITS File Format for High Energy
Astrophysics Data. Technical Report OGIP/93-003, NASA/GSFC, Nov 1993. Found at the URL:
http://legacy.gsfc.nasa.gov/docs/heasarc/ofwg/docs/summary/ogip 93 003 summary.html.
[3] J. McDowell and A. Rots. FITS REGION Binary Table Design. Technical Re-
port ASC-FITS-REGION-1.0, Chandra Science Center, March 1998. Found at the URL:
http://hea-www.harvard.edu/jcm/asc/docs/asc/region.ps.
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