## NAME

           grdmath - Reverse Polish Notation calculator for grd files

## SYNOPSIS

           grdmath  [  -F  ] [ -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 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). The expression =  outgrdfile  can  occur  as  many
           times as the depth of the stack allows.

           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).
                  CAZ 2 Cartesian azimuth from grid nodes to stack x,y
                  CDIST 2 Cartesian distance between grid nodes and stack x,y.
                  CEIL 1 ceil (A) (smallest integer >= A).
                  CHICRIT  2  Critical  value  for  chi-squared-distribution, with
                  alpha = A and n = B.
                  CHIDIST 2 chi-squared-distribution P(chi2,nn), with chi2 = A and
                  n = 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 erf (A).
                  ERFC 1 Complementary Error function erfc (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.
                  FCRIT 3 Critical value for F-distribution, with alpha = A, n1  =
                  B, and n2 = C.
                  FDIST  3 F-distribution Q(F,n1,n2), with F = A, n1 = B, and n2 =
                  C.
                  FLIPLR 1 Reverse order of values in each row
                  FLIPUD 1 Reverse order of values in each column
                  FLOOR 1 floor (A) (greatest integer <= A).
                  FMOD 2 A % B (remainder).
                  GE 2 1 if A >= B, else 0.
                  GT 2 1 if A > B, else 0.
                  HYPOT 2 hypot (A, B) = sqrt (A*A + B*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).
                  INRANGE 3 1 if B <= A <= C, else 0
                  INSIDE 1 1 when inside polygon(s) in A, else 0
                  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).
                  LDIST 1 Compute distance from lines in multi-segment ASCII  file
                  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) (base 10).
                  LOG1P 1 log (1+A) (accurate for small A).
                  LOG2 1 log2 (A) (base 2).
                  LOWER 1 The lowest (minimum) value of A.
                  LRAND 2 Laplace random noise with mean A and std. deviation B.
                  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 (Least Median of Squares) of A.
                  MUL(x) 2 A * B.
                  NAN 2 NaN if A == B, else A.
                  NEG 1 -A.
                  NEQ 2 1 if A != B, else 0.
                  NRAND  2 Normal, random values with mean A and std. deviation B.
                  OR 2 NaN if A or B == NaN, else A.
                  PDIST 1 Compute distance from points in ASCII file 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).
                  ROTX 2 Rotate A by the (constant) shift B in x-direction
                  ROTY 2 Rotate A by the (constant) shift B in y-direction
                  SAZ 2 Sperhical azimuth from grid nodes to stack x,y
                  SDIST  2  Spherical (Great circle) distance (in degrees) between
                  grid nodes and stack lon,lat (A, B).
                  SIGN 1 sign (+1 or -1) of A.
                  SIN 1 sin (A) (A in radians).
                  SINC 1 sinc (A) (sin (pi*A)/(pi*A)).
                  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).
                  TCRIT 2 Critical value for Student’s t-distribution, with  alpha
                  = A and n = B.
                  TDIST  2 Student’s t-distribution A(t,n), with t = A, and n = 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).
                  ZCRIT 1 Critical value for the normal-distribution, with alpha =
                  A.

           SYMBOLS
                  The following symbols have special meaning:

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

## OPTIONS

           -F     Select pixel registration (used with -R, -I). [Default  is  grid
                  registration].

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

           -R     xmin, xmax, ymin, and ymax specify the Region of  interest.  For
                  geographic  regions,  these  limits  correspond  to  west, east,
                  south, and north and you may specify them in decimal degrees  or
                  in  [+-]dd:mm[:ss.xxx][W|E|S|N]  format.  Append r if lower left
                  and upper right map coordinates are given instead of  wesn.  The
                  two  shorthands  -Rg  -Rd  stand  for  global  domain  (0/360 or
                  -180/+180 in longitude respectively, with -90/+90 in  latitude).
                  For  calendar time coordinates you may either give relative time
                  (relative  to  the  selected  TIME_EPOCH  and  in  the  selected
                  TIME_UNIT;  append  t  to  -JX|x),  or absolute time of the form
                  [date]T[clock] (append T to -JX|x). At least  one  of  date  and
                  clock must be present; the T is always required. The date string
                  must be of the form [-]yyyy[-mm[-dd]]  (Gregorian  calendar)  or
                  yyyy[-Www[-d]]  (ISO week calendar), while the clock string must
                  be of the form hh:mm:ss[.xxx]. The use of delimiters  and  their
                  type  and  positions must be as indicated (however, input/output
                  and plotting formats are flexible).

           -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, of save both  by  giving  two
           consequtive  = file.grd calls.  The operator PLM calculates the associ-
           ated 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), use

           grdmath  2  s_xy.grd MUL s_xx.grd s_yy.grd SUB DIV ATAN2 2 DIV = direc-
           tion.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:

           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:

           grdmath faa.grd DUP EXTREMA 2 EQ MUL DUP 100 GT MUL 0 NAN = 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)

    GMT4.0                            1 Oct 2004                        GRDMATH(l)