NAME

       gmtmath  -  Reverse  Polish  Notation  calculator for data
       tables


SYNOPSIS

       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 ] OPER­
       ATOR ... = [ outfile ]


DESCRIPTION

       gmtmath will perform operations like add, subtract, multi­
       ply,  and  divide  on one or more table data files or con­
       stants 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.  How­
       ever, 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).

       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 then
              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).
              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 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).
              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).

       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,  while   -Cr
              reverses (toggles) the current choices.

       -H     Input  file(s)  has  Header  record(s).  Number  of
              header records can be changed by editing your .gmt­
              defaults  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 num­
              bered 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 "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)..TP  -bo  Selects
              binary  output.  Append  s  for  single   precision
              [Default is double].


BEWARE

       The  operator PLM calculates the associated Legendre poly­
       nomial 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  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 =`


BUGS

       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 pos­
       itive radius (e.g., log, kei, etc.) are passed  the  abso­
       lute 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),  grd2xyz(l),  grdedit(l),  grdinfo(l), grdmath(l),
       xyz2grd(l)



                            1 Mar 2002                 GMTMATH(l)

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