NAME

      gmtmath - Reverse Polish Notation calculator for data tables

SYNOPSIS

      gmtmath [ -Ccols ] [ -Nn_col/t_col ] [ -Tt_min/t_max/t_inc ] [ -V ] [
      -bi[s][n] ] [ -bo[s] ] operand [ operand ] OPERATOR [ operand ]
      OPERATOR ... = [ outfile ]

DESCRIPTION

      gmtmath will perform operations like add, subtract, multiply, and
      divide on one or more table data 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 file [or standard output].  When
      two data tables 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 data tables are used in the
      expression then options -T, -N must be set (and optionally -b).  By
      default, all columns except the "time" column is operated on, but this
      can be changed (see -C).

      operand
           If operand can be opened as a file it will be read as an ASCII
           (or binary, see -bi) table data file.  If not a file, it is
           interpreted as a numerical constant or a special symbol (see
           below).

      outfile is a table data file that will hold the final result.  If not given
           the output is sent to stdout.

      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).
           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).
           D2DT2          1    d^2(A)/dt^2 2nd derivative.
           D2R       1    Converts Degrees to Radians.
           DIV(/)         2    A / B.
           DDT       1    d(A)/dt 1st derivative.
           DUP       1    Places duplicate of A on the stack.
           EXCH      2    Exchanges A and B on the stack.
           EXP       1    exp (A).
           ERF       1    Error function of A.
           ERFC      1    Complimentory Error function of A.
           FLOOR          1    floor (A) (greatest integer <= A).
           FMOD      2    A % B (remainder).
           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.
           STEP      1    Heaviside step function H(t-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).
           YN        2    Bessel function of A (2nd kind, order B).

      SYMBOLS
           The following symbols have special meaning:

           PI   3.1415926...
           E    2.7182818...
           T    Table with t-coordinates

OPTIONS

      -C   Select the columns that will be operated on until next occurrence
           of -C.  List columns separated by commas; ranges like 1,3-5,7 are
           allowed.  [-C (no arguments) resets the default action of using
           all columns except time column (see -N].  -Ca selects all
           columns, inluding time column.

      -N   Select the number of columns and the column number that contains
           the "time" variable.  Columns are numbered starting at 0 [2/0].

      -T   Required when no input files are given.  Sets the t-coordinates
           of the first and last point and the equidistant sampling interval
           for the "time" column (see -N).

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

      -bi  Selects binary input.  Append s for single precision [Default is
           double].  Append n for the number of columns in the binary
           file(s).

      -bo  Selects binary output.  Append s for single precision [Default is
           double].

BEWARE

      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. PLM is not normalized.
      All derivatives are based on central finite differences, with natural
      boundary conditions.

EXAMPLES

      To take log10 of the average of 2 data files, use
           gmtmath file1.d file2.d ADD 0.5 MUL LOG10 = file3.d

      Given the file samples.d, which holds seafloor ages in m.y. and
      seafloor depth in m, use the relation depth(in m) = 2500 + 350 * sqrt
      (age) to print the depth anomalies:
           gmtmath samples.d T SQRT 350 MUL 2500 ADD SUB = | lpr

      To take the average of columns 1 and 4-6 in the three data sets
      sizes.1, sizes.2, and sizes.3, use
           gmtmath -C1,4-6 sizes.1 sizes.2 ADD sizes.3 ADD 3 DIV = ave.d

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 on input, but the output can be sent
      to stdout.  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, grd2xyz, grdedit, grdinfo, grdmath, xyz2grd