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, multi­
       ply,  and  divide  on  one  or more grd files or constants
       using Reverse Polish Notation (RPN) syntax (e.g., Hewlett-
       Packard calculator-style). Arbitrarily complicated expres­
       sions 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  cor­
       responding  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 Complimentory 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  sec­
              onds.

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

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

       -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 argu­
       ment 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 differ­
       ences, 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

       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 Mathe­
       matical 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(l),  gmtmath(l),  grd2xyz(l),  grdedit(l), grdinfo(l),
       xyz2grd(l)



                            1 Mar 2002                 GRDMATH(l)

Man(1) output converted with man2html