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, multi-
ply, 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 expres-
sions may therefore be evaluated; the final result is writ-
ten 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).
not given
outfile is a table data file that will hold the final result. If
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). 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.
ERFINV 1 Inverse 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 polyno-
mial 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 cal-
culate 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 func-
tions (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(l), grd2xyz(l), grdedit(l), grdinfo(l), grdmath(l),
xyz2grd(l)