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
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