NAME

       grdmath - Reverse Polish Notation calculator for grd files


SYNOPSIS

       grdmath  [ -F ] [ -Ixinc[m|c][/yinc[m|c]] -Rwest/east/south/north -V] [
       -f[i|o]colinfo ] 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 Nota-
       tion  (RPN) syntax (e.g., Hewlett-Packard calculator-style).  Arbitrar-
       ily 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).
              CHIDIST        2    Chi-squared-distribution  P(chi2,nu),   with
              chi2 = A and nu = B.
              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    Complementory Error function of A.
              ERFINV         1    Inverse error function of A.
              EQ        2    1 if A == B, else 0.
              EXCH      2    Exchanges A and B on the stack.
              EXP       1    exp (A).
              EXTREMA        1    Local  Extrema:  +2/-2  is max/min, +1/-1 is
              saddle with max/min in x, 0 elsewhere.
              FDIST          4    F-dist Q(var1,var2,nu1,nu2), with var1 =  A,
              var2 = B, nu1 = C, and nu2 = D.
              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.
              GE        2    1 if A >= B, else 0.
              GT        2    1 if A > B, else 0.
              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.
              ISNAN          1    1 if A == NaN, else 0.
              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).
              LE        2    1 if A <= B, else 0.
              LMSSCL         1    LMS scale estimate (LMS STD) of A.
              LOG       1    log (A) (natural log).
              LOG10          1    log10 (A).
              LOG1P          1    log (1+A) (accurate for small A).
              LOWER          1    The lowest (minimum) value of A.
              LT        2    1 if A < B, else 0.
              MAD       1    Median Absolute Deviation (L1 STD) of 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.
              MODE      1    Mode value (LMS) of A.
              MUL(x)         2    A * B.
              NAN       2    NaN if A == B, else A.
              NEG       1    -A.
              NRAND          2    Normal, random values with mean A  and  std.
              deviation B.
              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.
              RAND      2    Uniform random values between A and B.
              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.
              STEP      1    Heaviside step function: H(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).
              TDIST          2    Student's t-distribution A(t,nu) = 1  -  2p,
              with t = A, and nu = B.
              UPPER          1    The highest (maximum) value of A.
              XOR       2    B if A == NaN, else 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 (used with -R, -I).  [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 opera-
       tor  (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 natu-
       ral 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

       To  extract  the  locations of local maxima that exceed 100 mGal in the
       file faa.grd, try
            grdmath faa.grd DUP EXTREMA 2 EQ MUL DUP 100 GT NAN MUL = z.grd
            grd2xyz z.grd -S > max.xyz


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.
       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  Func-
       tions, 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(l), gmtmath(l), grd2xyz(l), grdedit(l), grdinfo(l), xyz2grd(l)



VERSION                              DATE                           GRDMATH(l)

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