"equal" .eq. .EQ. == "not equal" .ne. .NE. !=
"less than" .lt. .LT. < "less than/equal" .le. .LE. <= =<
"greater than" .gt. .GT. > "greater than/equal" .ge. .GE. >= =>
"or" .or. .OR. || "and" .and. .AND. &&
"negation" .not. .NOT. ! "approx. equal(1e-7)" ~
Note that the exclamation point, '!', is a special UNIX character, so
if it is used on the command line rather than entered at a task
prompt, it must be preceded by a backslash to force the UNIX shell to
ignore it.
"addition" + "subtraction" -
"multiplication" * "division" /
"negation" - "exponentiation" ** ^
"absolute value" abs(x) "cosine" cos(x)
"sine" sin(x) "tangent" tan(x)
"arc cosine" arccos(x) "arc sine" arcsin(x)
"arc tangent" arctan(x) "arc tangent" arctan2(y,x)
"hyperbolic cos" cosh(x) "hyperbolic sin" sinh(x)
"hyperbolic tan" tanh(x) "round to nearest int" round(x)
"round down to int" floor(x) "round up to int" ceil(x)
"exponential" exp(x) "square root" sqrt(x)
"natural log" log(x) "common log" log10(x)
"error function" erf(x) "complement of erf" erfc(x)
"gamma function" gamma(x)
"modulus" x % y
"bitwise AND" x & y "bitwise OR" x | y
"bitwise XOR" x ^^ y (bitwise operators are 32-bit int only)
"random # [0.0,1.0)" random()
"random Gausian" randomn() "random Poisson" randomp(x)
"minimum" min(x,y) "maximum" max(x,y)
"cumulative sum" accum(x) "sequential difference" seqdiff(x)
"if-then-else" b?x:y
"angular separation" angsep(ra1,dec1,ra2,de2) (all in degrees)
"substring" strmid(s,p,n) "string search" strstr(s,r)
The bitwise operators for AND, OR and XOR operate upon 32-bit integer
expressions only.
Three different random number functions are provided: random(), with no arguments, produces a uniform random deviate between 0 and 1; randomn(), also with no arguments, produces a normal (Gaussian) random deviate with zero mean and unit standard deviation; randomp(x) produces a Poisson random deviate whose expected number of counts is X. X may be any positive real number of expected counts, including fractional values, but the return value is an integer.
When the random functions are used in a vector expression, by default the same random value will be used when evaluating each element of the vector. If different random numbers are desired, then the name of a vector column should be supplied as the single argument to the random function (e.g., "flux + 0.1 * random(flux)", where "flux" is the name of a vector column). This will create a vector of random numbers that will be used in sequence when evaluating each element of the vector expression.
An alternate syntax for the min and max functions has only a single argument which should be a vector value (see below). The result will be the minimum/maximum element contained within the vector.
The accum(x) function forms the cumulative sum of x, element by element. Vector columns are supported simply by performing the summation process through all the values. Null values are treated as 0. The seqdiff(x) function forms the sequential difference of x, element by element. The first value of seqdiff is the first value of x. A single null value in x causes a pair of nulls in the output. The seqdiff and accum functions are functional inverses, i.e., seqdiff(accum(x)) == x as long as no null values are present.
In the if-then-else expression, "b?x:y", b is an explicit boolean value or expression. There is no automatic type conversion from numeric to boolean values, so one needs to use "iVal!=0" instead of merely "iVal" as the boolean argument. x and y can be any scalar data type (including string).
The angsep function computes the angular separation in degrees between 2 celestial positions, where the first 2 parameters give the RA-like and Dec-like coordinates (in decimal degrees) of the first position, and the 3rd and 4th parameters give the coordinates of the second position.
The substring function strmid(S,P,N) extracts a substring from S, starting at string position P, with a substring length N. The first character position in S is labeled as 1. If P is 0, or refers to a position beyond the end of S, then the extracted substring will be NULL. S, P, and N may be functions of other columns.
The string search function strstr(S,R) searches for the first occurrence of the substring R in S. The result is an integer, indicating the character position of the first match (where 1 is the first character position of S). If no match is found, then strstr() returns a NULL value.
"real to integer" (int) x (INT) x
"integer to real" (float) i (FLOAT) i
#pi 3.1415... #e 2.7182...
#deg #pi/180 #row current row number
#null undefined value #snull undefined string
A string constant must be enclosed in quotes as in 'Crab'. The
"null" constants are useful for conditionally setting table values
to a NULL, or undefined, value (eg., "col1==-99 ? #NULL : col1").
Integer constants may be specified using the following notation,
13245 decimal integer
0x12f3 hexidecimal integer
0o1373 octal integer
0b01001 binary integer
Note that integer constants are only allowed to be 32-bit, i.e.
between -2\string^(31) and +2\string^(31). Integer constants may be used in any
arithmetic expression where an integer would be appropriate. Thus,
they are distinct from bitmasks (which may be of arbitrary length,
allow the "wildcard" bit, and may only be used in logical
expressions; see below).
near(value_1, value_2, tolerance)
ISNULL(x)
DEFNULL(x,y)
SETNULL(x,y)
ISNULL(x)
returns a boolean value of TRUE if the argument x is NULL. DEFNULL(x,y)
"defines" a value to be substituted for NULL values; it
returns the value of x if x is not NULL, otherwise it returns the
value of y. SETNULL(x,y) allows NULL values to be inserted into
a variable; if x==y, a NULL value is returned; otherwise y is returned
(x and y must be numerical, and x must be a scalar).
binary: b0110xx1010000101xxxx0001
octal: o720x1 -> (b111010000xxx001)
hex: h0FxD -> (b00001111xxxx1101)
In all the representations, an x or X is allowed in the mask as a
wild card. Note that the x represents a different number of wild
card bits in each representation. All representations are case
insensitive. Although bitmasks may be of arbitrary length and contain
a wildcard, they may only be used in logical expressions, unlike
integer constants (see above) which may be used in any arithmetic
expression.
To construct the boolean expression using the mask as the boolean equal operator described above on a bit table column. For example, if you had a 7 bit column named flags in a FITS table and wanted all rows having the bit pattern 0010011, the selection expression would be:
flags == b0010011
or
flags .eq. b10011
It is also possible to test if a range of bits is less than, less
than equal, greater than and greater than equal to a particular
boolean value:
flags <= bxxx010xx
flags .gt. bxxx100xx
flags .le. b1xxxxxxx
Notice the use of the x bit value to limit the range of bits being
compared.
It is not necessary to specify the leading (most significant) zero (0) bits in the mask, as shown in the second expression above.
Bit wise AND, OR and NOT operations are also possible on two or more bit fields using the '&'(AND), '|'(OR), and the '!'(NOT) operators. All of these operators result in a bit field which can then be used with the equal operator. For example:
(!flags) == b1101100
(flags & b1000001) == bx000001
Bit fields can be appended as well using the '+' operator. Strings
can be concatenated this way, too.
Arithmetic and logical operations are all performed on an element by element basis. Comparing two vector columns, eg "COL1 == COL2", thus results in another vector of boolean values indicating which elements of the two vectors are equal.
Several functions are available that operate on a vector. All but the last two return a scalar result:
"minimum" MIN(V) "maximum" MAX(V)
"average" AVERAGE(V) "median" MEDIAN(V)
"sumation" SUM(V) "standard deviation" STDDEV(V)
"# of values" NELEM(V) "# of non-null values" NVALID(V)
"# axes" NAXIS(V) "axis dimension" NAXES(V,n)
"axis pos'n" AXISELEM(V,n) "vector element pos'n" ELEMENTNUM(V)
"promote to array" ARRAY(X,d)
where V represents the name of a vector column or a manually
constructed vector using curly brackets as described below. The
first 6 of these functions ignore any null values in the vector when
computing the result. The STDDEV() function computes the sample
standard deviation, i.e. it is proportional to 1/SQRT(N-1) instead
of 1/SQRT(N), where N is NVALID(V).
The NAXIS(V) function returns the number of axes of the vector, for example a 2D array would be NAXIS(V) == 2. The NAXES(V,n) function returns the dimension of axis n, for example a 4x2 array would have NAXES(V,1) == 4. The ELEMENTNUM(V) and AXISELEM(V,n) functions return vectors of the same size as the input vector V. ELEMENTNUM(V) returns the vector element position for each element in the vector, starting from 1 in each row. The AXISELEM(V,n) function is similar but returns the element position of axis n only.
The SUM function literally sums all the elements in x, returning a scalar value. If V is a boolean vector, SUM returns the number of TRUE elements. The NELEM function returns the number of elements in vector V whereas NVALID return the number of non-null elements in the vector. (NELEM also operates on bit and string columns, returning their column widths.) As an example, to test whether all elements of two vectors satisfy a given logical comparison, one can use the expression
SUM( COL1 > COL2 ) == NELEM( COL1 )
which will return TRUE if all elements of COL1 are greater than
their corresponding elements in COL2.
The ARRAY(X,d) function promotes scalar value X to a vector (or array) table element. X may be any scalar-valued item, including a column, an expression, or a constant value. The resulting vector or array will have the same scalar value replicated into each element position. This may be a useful way to construct large arrays without using the cumbersome {vector} notation. The dimensions of the new array are given by the second argument, d. d can either be a single constant integer value, or a vector of up to five dimensions of the form {Nx,Ny,...}. Thus, ARRAY(TIME,4) would promote TIME to be a 4-vector, and ARRAY(0, {2,3,1}) would construct an array of all 0's with dimensions 2x3x1.
A second form of ARRAY(X,d) can be used where X is a vector or array, and the dimensions d merely change the dimensions of X without changing the total number of vector elements. This is a way to re-dimension an existing array. For example, ARRAY({1,2,3,4},{2,2}) would transform the 4-vector into a 2x2 array.
To specify a single element of a vector, give the column name followed by a comma-separated list of coordinates enclosed in square brackets. For example, if a vector column named PHAS exists in the table as a one dimensional, 256 component list of numbers from which you wanted to select the 57th component for use in the expression, then PHAS[57] would do the trick. Higher dimensional arrays of data may appear in a column. But in order to interpret them, the TDIMn keyword must appear in the header. Assuming that a (4,4,4,4) array is packed into each row of a column named ARRAY4D, the (1,2,3,4) component element of each row is accessed by ARRAY4D[1,2,3,4]. Arrays up to dimension 5 are currently supported. Each vector index can itself be an expression, although it must evaluate to an integer value within the bounds of the vector. Vector columns which contain spaces or arithmetic operators must have their names enclosed in "$" characters as with $ARRAY-4D$[1,2,3,4].
A more C-like syntax for specifying vector indices is also available. The element used in the preceding example alternatively could be specified with the syntax ARRAY4D[4][3][2][1]. Note the reverse order of indices (as in C), as well as the fact that the values are still ones-based (as in Fortran -- adopted to avoid ambiguity for 1D vectors). With this syntax, one does not need to specify all of the indices. To extract a 3D slice of this 4D array, use ARRAY4D[4].
Variable-length vector columns are not supported.
Vectors can be manually constructed within the expression using a comma-separated list of elements surrounded by curly braces ('{}'). For example, '{1,3,6,1}' is a 4-element vector containing the values 1, 3, 6, and 1. The vector can contain only boolean, integer, and real values (or expressions). The elements will be promoted to the highest datatype present. Any elements which are themselves vectors, will be expanded out with each of its elements becoming an element in the constructed vector.
COUNT = COUNT{-1} + 1; # BAD - do not use
will not produce an increasing counter. Such recursive
calculations are often not possible with the calculator syntax.
gtifilter( [ "gtifile" [, expr [, "STARTCOL", "STOPCOL" ] ] ] )
or
gtifilter( [ 'gtifile' [, expr [, 'STARTCOL', 'STOPCOL' ] ] ] )
where each "[]" demarks optional parameters. Note that the quotes
around the gtifile and START/STOP column are required. Either single
or double quotes may be used. In cases where this expression is
entered on the Unix command line, enclose the entire expression in
double quotes, and then use single quotes within the expression to
enclose the 'gtifile' and other terms. It is also usually possible
to do the reverse, and enclose the whole expression in single quotes
and then use double quotes within the expression. The gtifile,
if specified, can be blank ("") which will mean to use the first
extension with the name "*GTI*" in the current file, a plain
extension specifier (eg, "+2", "[2]", or "[STDGTI]") which will be
used to select an extension in the current file, or a regular
filename with or without an extension specifier which in the latter
case will mean to use the first extension with an extension name
"*GTI*". Expr can be any arithmetic expression, including simply
the time column name. A vector time expression will produce a
vector boolean result. STARTCOL and STOPCOL are the names of the
START/STOP columns in the GTI extension. If one of them is
specified, they both must be.
In its simplest form, no parameters need to be provided -- default values will be used. The expression "gtifilter()" is equivalent to
gtifilter( "", TIME, "*START*", "*STOP*" )
This will search the current file for a GTI extension, filter the
TIME column in the current table, using START/STOP times taken from
columns in the GTI extension with names containing the strings
"START" and "STOP". The wildcards ('*') allow slight variations in
naming conventions such as "TSTART" or "STARTTIME". The same
default values apply for unspecified parameters when the first one
or two parameters are specified. The function automatically
searches for TIMEZERO/I/F keywords in the current and GTI
extensions, applying a relative time offset, if necessary.
The related function, gtifind(a,b,c,d), is similar to gtifilter() but instead of returning true/false, gtifind() returns the GTI number that brackets the requested time sample. gtifind() returns the row number in the GTI table that matches the time sample, or -1 if the time sample is not within any GTI. gtifind() is particularly useful when entries in a table must be categorized by which GTI the fall within. For example, if events in an event list must be separated by good time interval. The results of gtifind() can be used with histogram binning techniques to bin an event list by which GTI.
gtifind( "gtifile" , expr [, "STARTCOL", "STOPCOL" ] )
The requirements for specifying the gtifile are the same as for
gtifilter() as described above. Like gtifilter(), the expr is
the time-like expression and is optional (defaulting to TIME).
The start and stop columns default to START and STOP.
The function, gtioverlap(a,b,c,d,e), computes the overlap between a user-requested time range and the entries in a GTI. The cases of no overlap, partial overlap, or overlap of many GTIs within the user requested range are handled. gtioverlap() is very useful for calculating exposure times and fractional exposures of individual time bins, say for a light curve. The syntax of gtioverlap() is
gtioverlap( "gtifile" , startExpr, stopExpr [, "STARTCOL", "STOPCOL" ] )
or
gtioverlap( 'gtifile' , startExpr, stopExpr [, 'STARTCOL', 'STOPCOL' ] )
The requirements for specifying the gtifile are the same as for
gtifilter() as described above. Unlike gtifilter(), the startExpr
and stopExpr are not optional. startExpr provides a start of the
user requested time interval. startExpr is typically TIME, but
can be any valid expression. Likewise, stopExpr provides the stop
of the user requested time interval, and can be an expression.
For example, for a light curve with a TIME column and time bin
size of 1.0 seconds, the expression
gtioverlap('gtifile',TIME,TIME+1.0)
would calculate the amount of overlap exposure time between each
one second time bin and the GTI in 'gtifile'. In this case the
time bin is assumed to begin at the time specified by TIME and end
1 second later. Neither startExpr nor stopExpr are required to be
constant, and a light curve is not required to have a constant bin
size. For tables, the overlap is calculated for each entry in the
table.
It is also possible to calculate a single overlap value, which would typically be placed in a keyword. For example, a way to to compute the total overlap exposure of a file whose TIME column is bounded by the keywords TSTART and TSTOP, overlapping with the specified GTI, would be
#EXPOSURE = gtioverlap('gtifile',#TSTART,#TSTOP)
The #EXPOSURE syntax with a leading # ensures that the
requested values are treated as keywords. Otherwise, a column
named EXPOSURE will be created with the (constant) exposure value
in each entry.
regfilter( "regfilename" [ , Xexpr, Yexpr [ , "wcs cols" ] ] )
where each "[]" demarks optional parameters. The region file name
is required and must be enclosed in quotes. The remaining
parameters are optional. The region file is an ASCII text file
which contains a list of one or more geometric shapes (circle,
ellipse, box, etc.) which defines a region on the celestial sphere
or an area within a particular 2D image. The region file is
typically generated using an image display program such as fv/POW
(distribute by the HEASARC), or ds9 (distributed by the Smithsonian
Astrophysical Observatory). Users should refer to the documentation
provided with these programs for more details on the syntax used in
the region files.
In its simpliest form, (e.g., regfilter("region.reg") ) the coordinates in the default 'X' and 'Y' columns will be used to determine if each row is inside or outside the area specified in the region file. Alternate position column names, or expressions, may be entered if needed, as in
regfilter("region.reg", XPOS, YPOS)
Region filtering can be applied most unambiguously if the positions
in the region file and in the table to be filtered are both give in
terms of absolute celestial coordinate units. In this case the
locations and sizes of the geometric shapes in the region file are
specified in angular units on the sky (e.g., positions given in
R.A. and Dec. and sizes in arcseconds or arcminutes). Similarly,
each row of the filtered table will have a celestial coordinate
associated with it. This association is usually implemented using
a set of so-called 'World Coordinate System' (or WCS) FITS keywords
that define the coordinate transformation that must be applied to
the values in the 'X' and 'Y' columns to calculate the coordinate.
Alternatively, one can perform spatial filtering using unitless 'pixel' coordinates for the regions and row positions. In this case the user must be careful to ensure that the positions in the 2 files are self-consistent. A typical problem is that the region file may be generated using a binned image, but the unbinned coordinates are given in the event table. The ROSAT events files, for example, have X and Y pixel coordinates that range from 1 - 15360. These coordinates are typically binned by a factor of 32 to produce a 480x480 pixel image. If one then uses a region file generated from this image (in image pixel units) to filter the ROSAT events file, then the X and Y column values must be converted to corresponding pixel units as in:
regfilter("rosat.reg", X/32.+.5, Y/32.+.5)
Note that this binning conversion is not necessary if the region
file is specified using celestial coordinate units instead of pixel
units because CFITSIO is then able to directly compare the
celestial coordinate of each row in the table with the celestial
coordinates in the region file without having to know anything
about how the image may have been binned.
The last "wcs cols" parameter should rarely be needed. If supplied, this string contains the names of the 2 columns (space or comma separated) which have the associated WCS keywords. If not supplied, the filter will scan the X and Y expressions for column names. If only one is found in each expression, those columns will be used, otherwise an error will be returned.
These region shapes are supported (names are case insensitive):
Point ( X1, Y1 ) <- One pixel square region
Line ( X1, Y1, X2, Y2 ) <- One pixel wide region
Polygon ( X1, Y1, X2, Y2, ... ) <- Rest are interiors with
Rectangle ( X1, Y1, X2, Y2, A ) | boundaries considered
Box ( Xc, Yc, Wdth, Hght, A ) V within the region
Diamond ( Xc, Yc, Wdth, Hght, A )
Circle ( Xc, Yc, R )
Annulus ( Xc, Yc, Rin, Rout )
Ellipse ( Xc, Yc, Rx, Ry, A )
Elliptannulus ( Xc, Yc, Rinx, Riny, Routx, Routy, Ain, Aout )
Sector ( Xc, Yc, Amin, Amax )
where (Xc,Yc) is the coordinate of the shape's center; (Xn,Yn) are
the coordinates of the shape's edges; Rxxx are the shapes' various
Radii or semimajor/minor axes; and Axxx are the angles of rotation
(or bounding angles for Sector) in degrees. For rotated shapes, the
rotation angle can be left off, indicating no rotation. Common
alternate names for the regions can also be used: rotbox = box;
rotrectangle = rectangle; (rot)rhombus = (rot)diamond; and pie
= sector. When a shape's name is preceded by a minus sign, '-',
the defined region is instead the area *outside* its boundary (ie,
the region is inverted). All the shapes within a single region file
are OR'd together to create the region, and the order is
significant. The overall way of looking at region files is that if
the first region is an excluded region then a dummy included region
of the whole detector is inserted in the front. Then each region
specification as it is processed overrides any selections inside of
that region specified by previous regions. Another way of thinking
about this is that if a previous excluded region is completely
inside of a subsequent included region the excluded region is
ignored.
The positional coordinates may be given either in pixel units, decimal degrees or hh:mm:ss.s, dd:mm:ss.s units. The shape sizes may be given in pixels, degrees, arcminutes, or arcseconds. Look at examples of region file produced by fv/POW or ds9 for further details of the region file format.
"point in a circular region"
circle(xcntr,ycntr,radius,Xcolumn,Ycolumn)
"point in an elliptical region"
ellipse(xcntr,ycntr,xhlf_wdth,yhlf_wdth,rotation,Xcolumn,Ycolumn)
"point in a rectangular region"
box(xcntr,ycntr,xfll_wdth,yfll_wdth,rotation,Xcolumn,Ycolumn)
where
(xcntr,ycntr) are the (x,y) position of the center of the region
(xhlf_wdth,yhlf_wdth) are the (x,y) half widths of the region
(xfll_wdth,yfll_wdth) are the (x,y) full widths of the region
(radius) is half the diameter of the circle
(rotation) is the angle(degrees) that the region is rotated with
respect to (xcntr,ycntr)
(Xcoord,Ycoord) are the (x,y) coordinates to test, usually column
names
NOTE: each parameter can itself be an expression, not merely a
column name or constant.
[ binary && mag <= 5.0] - Extract all binary stars brighter
than fifth magnitude (note that
the initial space is necessary to
prevent it from being treated as a
binning specification)
[#row >= 125 && #row <= 175] - Extract row numbers 125 through 175
[IMAGE[4,5] .gt. 100] - Extract all rows that have the
(4,5) component of the IMAGE column
greater than 100
[abs(sin(theta * #deg)) < 0.5] - Extract all rows having the
absolute value of the sine of theta
less than a half, where the angles
are tabulated in degrees
[SUM( SPEC > 3*BACKGRND )>=1] - Extract all rows containing a
spectrum, held in vector column
SPEC, with at least one value 3
times greater than the background
level held in a keyword, BACKGRND
[VCOL=={1,4,2}] - Extract all rows whose vector column
VCOL contains the 3-elements 1, 4, and
2.
[@rowFilter.txt] - Extract rows using the expression
contained within the text file
rowFilter.txt
[gtifilter()] - Search the current file for a GTI
extension, filter the TIME
column in the current table, using
START/STOP times taken from
columns in the GTI extension
[regfilter("pow.reg")] - Extract rows which have a coordinate
(as given in the X and Y columns)
within the spatial region specified
in the pow.reg region file.
[regfilter("pow.reg", Xs, Ys)] - Same as above, except that the
Xs and Ys columns will be used
to determine the coordinate of each
row in the table.