NAME
grdmath - Reverse Polish Notation calculator for grd files
SYNOPSIS
grdmath [ -Ixinc[m|c][/yinc[m|c]] -Rwest/east/south/north
-V] operand [ operand ] OPERATOR [ operand ] OPERATOR ... =
outgrdfile
DESCRIPTION
grdmath will perform operations like add, subtract, multi-
ply, and divide on one or more grd 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 grd file. When two grd files 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 grdfiles are used in the expression then
options -R, -I must be set (and optionally -F).
operand
If operand can be opened as a file it will be read as a
grd file. If not a file, it is interpreted as a numer-
ical constant or a special symbol (see below).
outgrdfile is a 2-
D grd file that will hold the final result.
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).
CDIST 2 Cartesian distance between grid
nodes and stack x,y.
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).
CURV 1 Curvature of A (Laplacian).
D2DX2 1 d^2(A)/dx^2 2nd derivative.
D2DY2 1 d^2(A)/dy^2 2nd derivative.
D2R 1 Converts Degrees to Radians.
DDX 1 d(A)/dx 1st derivative.
DDY 1 d(A)/dy 1st derivative.
DILOG 1 Dilog (A).
DIV(/) 2 A / B.
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.
EXCH 2 Exchanges A and B on the stack.
EXP 1 exp (A).
FLOOR 1 floor (A) (greatest integer <= A).
FMOD 2 A % B (remainder).
GDIST 2 Great distance (in degrees) between
grid nodes and stack lon,lat.
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.
STEPX 1 Heaviside step function in x: H(x-
A).
STEPY 1 Heaviside step function in y: H(y-
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).
YLM 2 Re and Im normalized surface harmonics
(degree A, order B).
YN 2 Bessel function of A (2nd kind, order
B).
SYMBOLS
The following symbols have special meaning:
PI 3.1415926...
E 2.7182818...
X Grid with x-coordinates
Y Grid with y-coordinates
OPTIONS
-I x_inc [and optionally y_inc] is the grid spacing.
Append m to indicate minutes or c to indicate seconds.
-R west, east, south, and north specify the Region of
interest. To specify boundaries in degrees and minutes
[and seconds], use the dd:mm[:ss] format. Append r if
lower left and upper right map coordinates are given
instead of wesn.
-F Select pixel registration. [Default is grid registra-
tion].
-V Selects verbose mode, which will send progress reports
to stderr [Default runs "silently"].
BEWARE
The operator GDIST calculates spherical distances bewteen
the (lon, lat) point on the stack and all node positions in
the grid. The grid domain and the (lon, lat) point are
expected to be in degrees. The operator YLM calculates the
fully normalized spherical harmonics for degree L and order
M for all positions in the grid, which is assumed to be in
degrees. YLM returns two grids, the Real (cosine) and Ima-
ginary (sine) component of the complex spherical harmonic.
Use the POP operator (and EXCH) to get rid of one of them.
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. Unlike
YLM, PLM is not normalized.
All the derivatives are based on central finite differences,
with natural boundary conditions.
EXAMPLES
To take log10 of the average of 2 files, use
grdmath file1.grd file2.grd ADD 0.5 MUL LOG10 =
file3.grd
Given the file ages.grd, which holds seafloor ages in m.y.,
use the relation depth(in m) = 2500 + 350 * sqrt (age) to
estimate normal seafloor depths:
grdmath ages.grd SQRT 350 MUL 2500 ADD = depths.grd
To find the angle a (in degrees) of the largest principal
stress from the stress tensor given by the three files
s_xx.grd s_yy.grd, and s_xy.grd from the relation tan (2*a)
= 2 * s_xy / (s_xx - s_yy), try
grdmath 2 s_xy.grd MUL s_xx.grd s_yy.grd SUB DIV ATAN2
2 DIV = direction.grd
To calculate the fully normalized spherical harmonic of
degree 8 and order 4 on a 1 by 1 degree world map, using the
real amplitude 0.4 and the imaginary amplitude 1.1, try
grdmath -R0/360/-90/90 -I1 8 4 YML 1.1 MUL EXCH 0.4 MUL
ADD = harm.grd
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. 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(l), gmtmath(l), grd2xyz(l), grdedit(l), grdinfo(l),
xyz2grd(l)