## NAME

          grdmath - Reverse Polish Notation calculator for grd files

## SYNOPSIS

          grdmath [ -Ixinc[m|c][/yinc[m|c]] -Rwest/east/south/north -V] operand [
          operand ] OPERATOR [ operand ] OPERATOR ... = outgrdfile

## DESCRIPTION

          grdmath will perform operations like add, subtract, multiply, and
          divide on one or more grd files or constants using Reverse Polish
          Notation (RPN) syntax (e.g., Hewlett-Packard calculator-style).
          Arbitrarily complicated expressions may therefore be evaluated; the
          final result is written to an output grd file. When two grd files are
          on the stack, each element in file A is modified by the corresponding
          element in file B.  However, some operators only require one operand
          (see below).  If no grdfiles are used in the expression then options
          -R, -I must be set (and optionally -F).

          operand
               If operand can be opened as a file it will be read as a grd file.
               If not a file, it is interpreted as a numerical constant or a
               special symbol (see below).

          outgrdfile is a 2-D grd file that will hold the final result.

          OPERATORS
               Choose among the following operators:
               Operator       n_args    Returns

               ABS       1    abs (A).
               ACOS      1    acos (A).
               ACOSH          1    acosh (A).
               ADD(+)         2    A + B.
               AND       2    NaN if A and B == NaN, B if A == NaN, else A.
               ASIN      1    asin (A).
               ASINH          1    asinh (A).
               ATAN      1    atan (A).
               ATAN2          2    atan2 (A, B).
               ATANH     1    atanh (A).
               BEI       1    bei (A).
               BER       1    ber (A).
               CDIST          2    Cartesian distance between grid nodes and
               stack x,y.
               CEIL      1    ceil (A) (smallest integer >= A).
               COS       1    cos (A) (A in radians).
               COSD      1    cos (A) (A in degrees).
               COSH      1    cosh (A).
               CURV      1    Curvature of A (Laplacian).
               D2DX2          1    d^2(A)/dx^2 2nd derivative.
               D2DY2          1    d^2(A)/dy^2 2nd derivative.
               D2R       1    Converts Degrees to Radians.
               DDX       1    d(A)/dx 1st derivative.
               DDY       1    d(A)/dy 1st derivative.
               DILOG          1    Dilog (A).
               DIV(/)         2    A / B.
               DUP       1    Places duplicate of A on the stack.
               ERF       1    Error function of A.
               ERFC      1    Complimentory Error function of A.
               EXCH      2    Exchanges A and B on the stack.
               EXP       1    exp (A).
               FLOOR          1    floor (A) (greatest integer <= A).
               FMOD      2    A % B (remainder).
               GDIST          2    Great distance (in degrees) between grid
               nodes and stack lon,lat.
               HYPOT          2    hypot (A, B).
               I0        1    Modified Bessel function of A (1st kind, order 0).
               I1        1    Modified Bessel function of A (1st kind, order 1).
               IN        2    Modified Bessel function of A (1st kind, order B).
               INV       1    1 / A.
               J0        1    Bessel function of A (1st kind, order 0).
               J1        1    Bessel function of A (1st kind, order 1).
               JN        2    Bessel function of A (1st kind, order B).
               K0        1    Modified Kelvin function of A (2nd kind, order 0).
               K1        1    Modified Bessel function of A (2nd kind, order 1).
               KN        2    Modified Bessel function of A (2nd kind, order B).
               KEI       1    kei (A).
               KER       1    ker (A).
               LOG       1    log (A) (natural log).
               LOG10          1    log10 (A).
               LOG1P          1    log (1+A) (accurate for small A).
               MAX       2    Maximum of A and B.
               MEAN      1    Mean value of A.
               MED       1    Median value of A.
               MIN       2    Minimum of A and B.
               MUL(x)         2    A * B.
               NEG       1    -A.
               OR        2    NaN if A or B == NaN, else A.
               PLM       3    Associated Legendre polynomial P(-1<A<+1) degree B
               order C.
               POP       1    Delete top element from the stack.
               POW(^)         2    A ^ B.
               R2        2    R2 = A^2 + B^2.
               R2D       1    Convert Radians to Degrees.
               RINT      1    rint (A) (nearest integer).
               SIGN      1    sign (+1 or -1) of A.
               SIN       1    sin (A) (A in radians).
               SIND      1    sin (A) (A in degrees).
               SINH      1    sinh (A).
               SQRT      1    sqrt (A).
               STD       1    Standard deviation of A.
               STEPX          1    Heaviside step function in x: H(x-A).
               STEPY          1    Heaviside step function in y: H(y-A).
               SUB(-)         2    A - B.
               TAN       1    tan (A) (A in radians).
               TAND      1    tan (A) (A in degrees).
               TANH      1    tanh (A).
               Y0        1    Bessel function of A (2nd kind, order 0).
               Y1        1    Bessel function of A (2nd kind, order 1).
               YLM       2    Re and Im normalized surface harmonics (degree A,
               order B).
               YN        2    Bessel function of A (2nd kind, order B).

          SYMBOLS
               The following symbols have special meaning:

               PI   3.1415926...
               E    2.7182818...
               X    Grid with x-coordinates
               Y    Grid with y-coordinates

## OPTIONS

          -I   x_inc [and optionally y_inc] is the grid spacing. Append m to
               indicate minutes or c to indicate seconds.

          -R   west, east, south, and north specify the Region of interest.  To
               specify boundaries in degrees and minutes [and seconds], use the
               dd:mm[:ss] format.  Append r if lower left and upper right map
               coordinates are given instead of wesn.

          -F   Select pixel registration.  [Default is grid registration].

          -V   Selects verbose mode, which will send progress reports to stderr
               [Default runs "silently"].

## BEWARE

          The operator GDIST calculates spherical distances bewteen the (lon,
          lat) point on the stack and all node positions in the grid.  The grid
          domain and the (lon, lat) point are expected to be in degrees.  The
          operator YLM calculates the fully normalized spherical harmonics for
          degree L and order M for all positions in the grid, which is assumed
          to be in degrees.  YLM returns two grids, the Real (cosine) and
          Imaginary (sine) component of the complex spherical harmonic.  Use the
          POP operator (and EXCH) to get rid of one of them.  The operator PLM
          calculates the associated Legendre polynomial of degree L and order M,
          and its argument is the cosine of the colatitude which must satisfy -1
          <= x <= +1. Unlike YLM, PLM is not normalized.
          All the derivatives are based on central finite differences, with
          natural boundary conditions.

## EXAMPLES

          To take log10 of the average of 2 files, use
               grdmath file1.grd file2.grd ADD 0.5 MUL LOG10 = file3.grd

          Given the file ages.grd, which holds seafloor ages in m.y., use the
          relation depth(in m) = 2500 + 350 * sqrt (age) to estimate normal
          seafloor depths:
               grdmath ages.grd SQRT 350 MUL 2500 ADD = depths.grd

          To find the angle a (in degrees) of the largest principal stress from
          the stress tensor given by the three files s_xx.grd s_yy.grd, and
          s_xy.grd from the relation tan (2*a) = 2 * s_xy / (s_xx - s_yy), try
               grdmath 2 s_xy.grd MUL s_xx.grd s_yy.grd SUB DIV ATAN2 2 DIV =
          direction.grd

          To calculate the fully normalized spherical harmonic of degree 8 and
          order 4 on a 1 by 1 degree world map, using the real amplitude 0.4 and
          the imaginary amplitude 1.1, try
               grdmath -R0/360/-90/90 -I1 8 4 YML 1.1 MUL EXCH 0.4 MUL ADD =
          harm.grd

## BUGS

          Files that has the same name as some operators, e.g., ADD, SIGN, =,
          etc. cannot be read and must not be present in the current directory.
          Piping of files are not allowed.  The stack limit is hard-wired to 50.
          Bessel and error functions may not be available on all systems.  The
          Kelvin-Bessel functions (bei, ber, kei, ker) are based on the
          polynomial approximations by Abramowitz and Stegun for r <= 8.  All
          functions expecting a positive radius (e.g., log, kei, etc.) are
          passed the absolute value of their argument.

## REFERENCES

          Abramowitz, M., and I. A. Stegun, 1964, Handbook of Mathematical
          Functions, Applied Mathematics Series, vol. 55, Dover, New York.
          Press, W. H.,  S. A. Teukolsky, W. T. Vetterling, B. P. Flannery,
          1992, Numerical Recipes, 2nd edition, Cambridge Univ., New York.

## SEE ALSO

          gmt, gmtmath, grd2xyz, grdedit, grdinfo, xyz2grd