[ Basic Info | References | User Guide ]
Basic Information on maths
Task: maths
Purpose: Mathematical operations on images and image data
Categories: utility, map combination, map manipulation
MATHS is a MIRIAD task which performs arithmetic expressions on a
number of images. The expression to be performed is given in a
FORTRAN-like syntax, and can consist of operators, real constants
and FORTRAN functions. Normal FORTRAN precedence applies.
Operators can be +, -, * and /, and all logical and relational
operators (e.g. .and. .or. .not. .gt. .ge. etc). In MATHS convention,
a positive value is considered TRUE, and a negative or zero value
is considered FALSE. Functions
appear only in the generic, rather than specific forms. For example
use ``log10'' rather than ``alog10'', and ``max'' rather than
``amax1''. Integers and double precision constants are converted to
reals. File names take the place of variables, and the expression
is evaluated on each pixel of the image. When there is more than
one file name in the input expression, the expression is evaluated
at corresponding pixels of the input images. For example to average
image ``fred'' with image ``bill'', use:
exp=(fred+bill)/2
When a file name starts with a numeric character, or contains a
character which might be confused with an operator the file name
should be bracketed by angular ( < and > ). For example:
exp=(<2ndtry>+bill.dat)/2
mask=<bmap.fft>.gt.0.5
Files cannot take the name ``x,'' ``y'' or ``z''. MATHS interprets
these as being the 3 independent variables of an image, which
vary linearly between the limits set by the XRANGE, YRANGE and
ZRANGE parameters. The user chooses the meaning of these units.
For example, to create one cycle of a two dimensional sine wave
along the x and y coordinate axes use:
exp=sin(x)*sin(y) xrange=-3.14,3.14 yrange=-3.14,3.14
In addition to the expression, MATHS also allows the user to specify
a "mask expression". MATHS main expression is only evaluated at
pixels where the "mask expression" is TRUE or positive valued. MATHS
does not check for divide by zero, logs of a negative number
or any similar problem. It will probably crash if this is attempted.
Consequently, when performing potentially dangerous operations, it
is best to guard the main expression by masking out dangerous
situations. The mask expression can also be used to prevent the
calculation where doing so would be undesirable for other reasons
(e.g. where the signal is too weak to get meaningful results).
For example:
exp=sqrt(fred) mask=fred.gt.0
Key: exp
The expression to be evaluated.
Key: mask
The mask expression. The expression given by "exp" is evaluated
only at those pixels where the mask expression is TRUE or
positive valued. Pixels, which fail this test, are marked as blank
in the output image.
Key: region
The region of interest in the input images. Full region
specifications are supported, however the output map will contain
only the bounding box. (see also mask=)
Default: full map.
Key: out
The name of the output image.
Key: imsize
The output image size. This is used only if there is no input
images (i.e. the expression consists of a function of ``x'' and
``y'' only). No default.
Key: xrange
When ``x'' is present in the input expression, then the x variable
is varied linearly between the two limits set by XRANGE. The default
is -0.5,0.5.
Key: yrange
When ``y'' is present in the input expression, then the y variable
is varied linearly between the two limits set by YRANGE. The default
is -0.5,0.5
Key: zrange
When ``z'' is present in the input expression, then the z variable
is varied linearly between the two limits set br ZRANGE. The default
is 0,1.
Key: options
Extra processing options. Several can be given, separated by
commas. Minimum match is used. Currently there is but one option:
grow Allow inputs to ``grow'' extra axes, if needed, through
replication. For example, if the expression subtracts
a single-plane image from a cube, options=grow allows
the operation to proceed by first growing the image into
a cube through replication the plane. Normally (i.e.
without this option), MATHS insists that the inputs must
be identical in size.
unmask Treat all pixels as if they were valid.