## 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). 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).
                  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)

    GMT3.4.6                          1 Jan 2005                        GRDMATH(l)