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# Basic Information on maths

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Purpose: Mathematical operations on images and image data
Categories: utility, map combination, map manipulation

MATHS is a MIRIAD task that 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

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:

Key: exp
The expression to be evaluated.

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
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, 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, 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, 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.
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.

Revision: 1.5, 2011/03/30 05:34:52 UTC
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Generated by miriad@atnf.csiro.au on 21 Jun 2016