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 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
          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, 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.
          limitmem Limit the amount of memory used. This may give
                   a buffer overflow error for complicated expressions.
                   Use for simple expressions with very large images.
 
Revision: 1.7, 2018/11/29 23:34:06 UTC