## NAME

          gmtmath - Reverse Polish Notation calculator for data tables

## SYNOPSIS

          gmtmath [ -Ccols ] [ -Hnrec ] [ -Nn_col/t_col ] [ -Q ] [
          -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.
               DILOG          1    Dilog (A).
               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.

          -H   Input file(s) has Header record(s).  Number of header records can
               be changed by editing your .gmtdefaults file.  If used, GMT
               default is 1 header record.

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

          -Q   Quick mode for scalar calculation.  Shorthand for -Ca -N1/0
               -T0/0/1.

          -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

          To use gmtmath as a RPN Hewlett-Packard calculator on scalars (i.e.,
          no input files) and calculate arbitrary expressions, use the -Q
          option.  As an example, we will calculate the value of Kei (((1 +
          1.75)/2.2) + cos (60)) and store the result in the shell variable z:

               set z = `gmtmath -Q 1 1.75 ADD 2.2 DIV 60 COSD ADD KEI =`

## 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