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       gmtmath - Reverse Polish Notation calculator for data tables


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


       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 are operated on, but this can be changed (see -C).

              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 then
              the output is sent to stdout.

              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).
              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).
              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.
              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).
              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).
              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).
              INT 1 Numerically integrate A.
              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).
              STEPT 1 Heaviside step function H(t-A).
              SUB(-) 2 A - B.
              SUM 1 Cumulative sum of A
              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).
              YN 2 Bessel function of A (2nd kind, order B).

              The following symbols have special meaning:

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


       -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, while -Cr reverses (toggles) the current

       -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.

       -S     Only  report  the first row of the results [Default is all rows]. This is useful if
              you have computed a statistic (say the MODE) and  only  want  to  report  a  single
              number instead of numerous records with idendical values.

       -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).
              If  there  is  no  time column (only data columns), give -T with no arguments; this
              also implies -Ca.

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

       -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].


       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.


       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 take the 1-column data set ages.d and calculate the modal value  and  assign  it  to  a
       variable, try
               set mode_age = `gmtmath -S -T ages.d MODE =`

       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 =`


       Files  that  have 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 is not allowed on input,
       but the output can be sent to stdout.  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


       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.


       gmt(1gmt), grd2xyz(1gmt), grdedit(1gmt), grdinfo(1gmt), grdmath(1gmt), xyz2grd(1gmt)

                                            1 Jan 2004                                 GMTMATH(l)