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<HTML>
<HEAD>
<TITLE>gmtmath</TITLE>
</HEAD>
<BODY>
<H1>gmtmath</H1>
<HR>
<PRE>
<!-- Manpage converted by man2html 3.0.1 -->
gmtmath - Reverse Polish Notation calculator for data
tables
</PRE>
<H2>SYNOPSIS</H2><PRE>
<B>gmtmath</B> [ <B>-C</B><I>cols</I> ] [ <B>-H</B><I>nrec</I> ] [ <B>-N</B><I>n</I><B>_</B><I>col</I>/<I>t</I><B>_</B><I>col</I> ] [ <B>-Q</B> ]
[ <B>-S</B> ][ <B>-T</B><I>t</I><B>_</B><I>min/t</I><B>_</B><I>max/t</I><B>_</B><I>inc</I> ] [ <B>-V</B> ] [ <B>-bi</B>[<B>s</B>][<I>n</I>] ] [
<B>-bo</B>[<B>s</B>] ] <I>operand</I> [ <I>operand</I> ] <B>OPERATOR</B> [ <I>operand</I> ] <B>OPERATOR</B>
... <B>=</B> [ <I>outfile</I> ]
</PRE>
<H2>DESCRIPTION</H2><PRE>
<B>gmtmath</B> 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
<B>-T,</B> <B>-N</B> must be set (and optionally <B>-b</B>). By default, all
columns except the "time" column are operated on, but this
can be changed (see <B>-C</B>).
<I>operand</I>
If <I>operand</I> can be opened as a file it will be read
as an ASCII (or binary, see <B>-bi</B>) table data file.
If not a file, it is interpreted as a numerical
constant or a special symbol (see below).
<I>outfile</I> is a table data file that will hold the final
result. If not given then
the output is sent to stdout.
<B>OPERATORS</B>
Choose among the following operators:
Operator n_args Returns
<B>ABS</B> 1 abs (A).
<B>ACOS</B> 1 acos (A).
<B>ACOSH</B> 1 acosh (A).
<B>ADD(+)</B> 2 A + B.
<B>AND</B> 2 NaN if A and B == NaN, B if A == NaN, else A.
<B>ASIN</B> 1 asin (A).
<B>ASINH</B> 1 asinh (A).
<B>ATAN</B> 1 atan (A).
<B>ATAN2</B> 2 atan2 (A, B).
<B>ATANH</B> 1 atanh (A).
<B>BEI</B> 1 bei (A).
<B>BER</B> 1 ber (A).
<B>CEIL</B> 1 ceil (A) (smallest integer >= A).
<B>CHIDIST</B> 2 Chi-squared-distribution P(chi2,n), with
<B>COSD</B> 1 cos (A) (A in degrees).
<B>COSH</B> 1 cosh (A).
<B>D2DT2</B> 1 d^2(A)/dt^2 2nd derivative.
<B>D2R</B> 1 Converts Degrees to Radians.
<B>DILOG</B> 1 Dilog (A).
<B>DIV(/)</B> 2 A / B.
<B>DDT</B> 1 d(A)/dt 1st derivative.
<B>DUP</B> 1 Places duplicate of A on the stack.
<B>ERF</B> 1 Error function of A.
<B>ERFC</B> 1 Complimentory Error function of A.
<B>ERFINV</B> 1 Inverse error function of A.
<B>EQ</B> 2 1 if A == B, else 0.
<B>EXCH</B> 2 Exchanges A and B on the stack.
<B>EXP</B> 1 exp (A).
<B>FDIST</B> 4 F-distribution Q(s1,s2,n1,n2), with s1 = A,
s2 = B, n1 = C, and n2 = D.
<B>FLOOR</B> 1 floor (A) (greatest integer <= A).
<B>FMOD</B> 2 A % B (remainder).
<B>GE</B> 2 1 if A >= B, else 0.
<B>GT</B> 2 1 if A > B, else 0.
<B>HYPOT</B> 2 hypot (A, B).
<B>I0</B> 1 Modified Bessel function of A (1st kind, order
0).
<B>I1</B> 1 Modified Bessel function of A (1st kind, order
1).
<B>IN</B> 2 Modified Bessel function of A (1st kind, order
B).
<B>INT</B> 1 Numerically integrate A.
<B>INV</B> 1 1 / A.
<B>ISNAN</B> 1 1 if A == NaN, else 0.
<B>J0</B> 1 Bessel function of A (1st kind, order 0).
<B>J1</B> 1 Bessel function of A (1st kind, order 1).
<B>JN</B> 2 Bessel function of A (1st kind, order B).
<B>K0</B> 1 Modified Kelvin function of A (2nd kind, order
0).
<B>K1</B> 1 Modified Bessel function of A (2nd kind, order
1).
<B>KN</B> 2 Modified Bessel function of A (2nd kind, order
B).
<B>KEI</B> 1 kei (A).
<B>KER</B> 1 ker (A).
<B>LE</B> 2 1 if A <= B, else 0.
<B>LMSSCL</B> 1 LMS scale estimate (LMS STD) of A.
<B>LOG</B> 1 log (A) (natural log).
<B>LOG10</B> 1 log10 (A).
<B>LOG1P</B> 1 log (1+A) (accurate for small A).
<B>LOWER</B> 1 The lowest (minimum) value of A.
<B>LT</B> 2 1 if A < B, else 0.
<B>MAD</B> 1 Median Absolute Deviation (L1 STD) of A.
<B>MAX</B> 2 Maximum of A and B.
<B>MEAN</B> 1 Mean value of A.
<B>MED</B> 1 Median value of A.
<B>MUL(x)</B> 2 A * B.
<B>NAN</B> 2 NaN if A == B, else A.
<B>NEG</B> 1 -A.
<B>NRAND</B> 2 Normal, random values with mean A and std.
deviation B.
<B>OR</B> 2 NaN if A or B == NaN, else A.
<B>PLM</B> 3 Associated Legendre polynomial P(-1<A<+1)
degree B order C.
<B>POP</B> 1 Delete top element from the stack.
<B>POW(^)</B> 2 A ^ B.
<B>R2</B> 2 R2 = A^2 + B^2.
<B>R2D</B> 1 Convert Radians to Degrees.
<B>RAND</B> 2 Uniform random values between A and B.
<B>RINT</B> 1 rint (A) (nearest integer).
<B>SIGN</B> 1 sign (+1 or -1) of A.
<B>SIN</B> 1 sin (A) (A in radians).
<B>SIND</B> 1 sin (A) (A in degrees).
<B>SINH</B> 1 sinh (A).
<B>SQRT</B> 1 sqrt (A).
<B>STD</B> 1 Standard deviation of A.
<B>STEP</B> 1 Heaviside step function H(A).
<B>STEPT</B> 1 Heaviside step function H(t-A).
<B>SUB(-)</B> 2 A - B.
<B>SUM</B> 1 Cumulative sum of A
<B>TAN</B> 1 tan (A) (A in radians).
<B>TAND</B> 1 tan (A) (A in degrees).
<B>TANH</B> 1 tanh (A).
<B>TDIST</B> 2 Student's t-distribution A(t,n), with t =
A, and n = B).'
<B>UPPER</B> 1 The highest (maximum) value of A.
<B>XOR</B> 2 B if A == NaN, else A.
<B>Y0</B> 1 Bessel function of A (2nd kind, order 0).
<B>Y1</B> 1 Bessel function of A (2nd kind, order 1).
<B>YN</B> 2 Bessel function of A (2nd kind, order B).
<B>SYMBOLS</B>
The following symbols have special meaning:
<B>PI</B> 3.1415926...
<B>E</B> 2.7182818...
<B>T</B> Table with t-coordinates
</PRE>
<H2>OPTIONS</H2><PRE>
<B>-C</B> Select the columns that will be operated on until
next occurrence of <B>-C</B>. List columns separated by
commas; ranges like 1,3-5,7 are allowed. [<B>-C</B> (no
arguments) resets the default action of using all
columns except time column (see <B>-N</B>]. <B>-Ca</B> selects
all columns, inluding time column, while <B>-Cr</B>
reverses (toggles) the current choices.
<B>-H</B> Input file(s) has Header record(s). Number of
record.
<B>-N</B> Select the number of columns and the column number
that contains the "time" variable. Columns are num
bered starting at 0 [2/0].
<B>-Q</B> Quick mode for scalar calculation. Shorthand for
<B>-Ca</B> <B>-N</B>1/0 <B>-T</B>0/0/1.
<B>-S</B> 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.
<B>-T</B> 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 <B>-N</B>). If there is no time column (only data
columns), give <B>-T</B> with no arguments; this also
implies <B>-Ca</B>.
<B>-V</B> Selects verbose mode, which will send progress
reports to stderr [Default runs "silently"].
<B>-bi</B> Selects binary input. Append <B>s</B> for single precision
[Default is double]. Append <I>n</I> for the number of
columns in the binary file(s).
<B>-bo</B> Selects binary output. Append <B>s</B> for single preci
sion [Default is double].
</PRE>
<H2>BEWARE</H2><PRE>
The operator <B>PLM</B> 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.
<B>PLM</B> is not normalized.
All derivatives are based on central finite differences,
with natural boundary conditions.
</PRE>
<H2>EXAMPLES</H2><PRE>
To take log10 of the average of 2 data files, use
gmtmath file1.d file2.d <B>ADD</B> 0.5 <B>MUL</B> <B>LOG10</B> <B>=</B>
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 <B>SQRT</B> 350 <B>MUL</B> 2500 <B>ADD</B> <B>SUB</B> <B>=</B> |
lpr
To take the average of columns 1 and 4-6 in the three data
<B>DIV</B> <B>=</B> 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 <B>-S</B> <B>-T</B> ages.d <B>MODE</B> <B>=</B>`
To use gmtmath as a RPN Hewlett-Packard calculator on
scalars (i.e., no input files) and calculate arbitrary
expressions, use the <B>-Q</B> 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 <B>-Q</B> 1 1.75 <B>ADD</B> 2.2 <B>DIV</B> 60 <B>COSD</B> <B>ADD</B>
<B>KEI</B> <B>=</B>`
</PRE>
<H2>BUGS</H2><PRE>
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.
</PRE>
<H2>REFERENCES</H2><PRE>
Abramowitz, M., and I. A. Stegun, 1964, <I>Handbook</I> <I>of</I> <I>Mathe</I>
<I>matical</I> <I>Functions</I>, Applied Mathematics Series, vol. 55,
Dover, New York.
Press, W. H., S. A. Teukolsky, W. T. Vetterling, B. P.
Flannery, 1992, <I>Numerical</I> <I>Recipes</I>, 2nd edition, Cambridge
Univ., New York.
</PRE>
<H2>SEE ALSO</H2><PRE>
<I>gmt</I>(l), <I><A HREF="grd2xyz.html">grd2xyz</A></I>(l), <I><A HREF="grdedit.html">grdedit</A></I>(l), <I><A HREF="grdinfo.html">grdinfo</A></I>(l), <I><A HREF="grdmath.html">grdmath</A></I>(l),
<I><A HREF="xyz2grd.html">xyz2grd</A></I>(l)
</PRE>
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