NAME
gmtmath - Reverse Polish Notation calculator for data tables
SYNOPSIS
gmtmath [ -At_f(t).d ] [ -Ccols ] [ -Hnrec ] [ -Nn_col/t_col ] [ -Q ]
[ -S[f|l] ][ -Tt_min/t_max/t_inc|tfile ] [ -V ] [ -bi[s][n] ] [
-bo[s][n] ] 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 Pol-
ish 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).
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).
CHICRIT 2 Critical value for chi-squared-distribution, with
alpha = A and n = B.
CHIDIST 2 chi-squared-distribution P(chi2,n), with chi2 = A and
n = B.
COL 1 Places column A on the stack.
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 erf (A).
ERFC 1 Complementary Error function erfc (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).
FCRIT 3 Critical value for F-distribution, with alpha = A, n1 =
B, and n2 = C.
FDIST 3 F-distribution Q(F,n1,n2), with F = A, n1 = B, and n2 =
C.
FLIPUD 1 Reverse order of each column
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) = sqrt (A*A + B*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) (base 10).
LOG1P 1 log (1+A) (accurate for small A).
LOG2 1 log2 (A) (base 2).
LOWER 1 The lowest (minimum) value of A.
LRAND 2 Laplace random noise with mean A and std. deviation B.
LSQFIT 1 Let current table be [A | b]; return least squares
solution x = A \ b.
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 (Least Median of Squares) of A.
MUL(x) 2 A * B.
NAN 2 NaN if A == B, else A.
NEG 1 -A.
NEQ 2 1 if A != B, else 0.
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).
ROOTS 2 Treats col A as f(t) = 0 and returns its roots
ROTT 2 Rotate A by the (constant) shift B in the t-direction.
SIGN 1 sign (+1 or -1) of A.
SIN 1 sin (A) (A in radians).
SINC 1 sinc (A) (sin (pi*A)/(pi*A)).
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).
TCRIT 2 Critical value for Student’s t-distribution, with alpha
= A and n = B.
TDIST 2 Student’s t-distribution A(t,n), with t = A, and n = 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).
ZCRIT 1 Critical value for the normal-distribution, with alpha =
A.
SYMBOLS
The following symbols have special meaning:
PI 3.1415926...
E 2.7182818...
T Table with t-coordinates
OPTIONS
-A Requires -N and will partially initialize a table with values
from the given file containing t and f(t) only. The t is placed
in column t_col while f(t) goes into column n_col - 1 (see -N).
-C Select the columns that will be operated on until next occur-
rence 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, including 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 .gmtdefaults4 file. If used, GMT
default is 1 header record. Use -Hi if only input data should
have header records [Default will write out header records if
the input data have them].
-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 or last 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 numer-
ous records with identical values. Append l to get the last row
and f to get the first row only [Default].
-T Required when no input files are given. Sets the t-coordinates
of the first and last point and the equidistant sampling inter-
val for the "time" column (see -N). If there is no time column
(only data columns), give -T with no arguments; this also
implies -Ca. Alternatively, give the name of a file whose first
column contains the desired t-coordinates which may be
irregular.
-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]. Append n for the number of columns in the binary
file(s).
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
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 evaluate the dilog(x) function for coordinates given in the file
t.d:
gmtmath -Tt.d T DILOG = dilog.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 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 =‘
To use gmtmath as a general least squares equation solver, imagine that
the current table is the augmented matrix [ A | b ] and you want the
least squares solution x to the matrix equation A * x = b. The opera-
tor LSQFIT does this; it is your job to populate the matrix correctly
first. The -A option will facilitate this. Suppose you have a 2-column
file ty.d with t and b(t) and you would like to fit a the model y(t) =
a + b*t + c*H(t-t0), where H is the Heaviside step function for a given
t0 = 1.55. Then, you need a 4-column augmented table loaded with t in
column 0 and your observed y(t) in column 3. The calculation becomes
gmtmath -N4/1 -Aty.d -C0 1 ADD -C2 1.55 STEPT ADD -Ca LSQFIT = solu-
tion.d
Note we use the -C option to select which columns we are working on,
then make active all the columns we need (here all of them, with -Ca)
before calling LSQFIT. The second and fourth columns are preloaded with
t and y(t), respectively, the other columns are zero. If you already
have a precalculated table with the augmented matrix [ A | b ] in a
file (say lsqsys.d), the least squares solution is simply
gmtmath -T lsqsys.d LSQFIT = solution.d
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 positive radius (e.g., LOG, KEI, etc.) are passed the absolute value
of their argument. The DDT and D2DT2 functions only work on regularly
spaced data. ROOTS must be the last operator on the stack, only fol-
lowed by =.
REFERENCES
Abramowitz, M., and I. A. Stegun, 1964, Handbook of Mathematical Func-
tions, 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)
GMT4.0 1 Oct 2004 GMTMATH(l)
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