GRDMATH(1) Generic Mapping Tools GRDMATH(1)NAMEgrdmath - Reverse Polish Notation calculator for grid files
SYNOPSISgrdmath [ -F ] [ -Ixinc[unit][=|+][/yinc[unit][=|+]] ] [ -M ] [ -N ] [
-Rwest/east/south/north[r] ] [ -V ] [ -bi[s|S|d|D[ncol]|c[var1/...]] ]
[ -fcolinfo ] operand [ operand ] OPERATOR [ operand ] OPERATOR ... =
outgrdfile
DESCRIPTIONgrdmath will perform operations like add, subtract, multiply, and
divide on one or more grid files or constants using Reverse Polish
Notation (RPN) syntax (e.g., Hewlett-Packard calculator-style). Arbi‐
trarily complicated expressions may therefore be evaluated; the final
result is written to an output grid file. When two grids 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 grid files are used in the expression then options -R,
-I must be set (and optionally -F). The expression = outgrdfile can
occur as many times as the depth of the stack allows.
operand
If operand can be opened as a file it will be read as a grid
file. If not a file, it is interpreted as a numerical constant
or a special symbol (see below).
outgrdfile
The name of a 2-D grid file that will hold the final result.
(See GRID FILE FORMATS below).
OPERATORS
Choose among the following 147 operators. "args" are the number
of input and output arguments.
Operator args Returns
ABS 1 1 abs (A).
ACOS 1 1 acos (A).
ACOSH 1 1 acosh (A).
ACOT 1 1 acot (A).
ACSC 1 1 acsc (A).
ADD 2 1 A + B.
AND 2 1 NaN if A and B == NaN, B if A == NaN, else A.
ASEC 1 1 asec (A).
ASIN 1 1 asin (A).
ASINH 1 1 asinh (A).
ATAN 1 1 atan (A).
ATAN2 2 1 atan2 (A, B).
ATANH 1 1 atanh (A).
BEI 1 1 bei (A).
BER 1 1 ber (A).
CAZ 2 1 Cartesian azimuth from grid nodes to stack x,y.
CBAZ 2 1 Cartesian backazimuth from grid nodes to stack
x,y.
CDIST 2 1 Cartesian distance between grid nodes and stack
x,y.
CEIL 1 1 ceil (A) (smallest integer >= A).
CHICRIT 2 1 Critical value for chi-squared-distribution, with
alpha = A and n = B.
CHIDIST 2 1 chi-squared-distribution P(chi2,n), with chi2 = A
and n = B.
CORRCOEFF 2 1 Correlation coefficient r(A, B).
COS 1 1 cos (A) (A in radians).
COSD 1 1 cos (A) (A in degrees).
COSH 1 1 cosh (A).
COT 1 1 cot (A) (A in radians).
COTD 1 1 cot (A) (A in degrees).
CPOISS 2 1 Cumulative Poisson distribution F(x,lambda), with
x = A and lambda = B.
CSC 1 1 csc (A) (A in radians).
CSCD 1 1 csc (A) (A in degrees).
CURV 1 1 Curvature of A (Laplacian).
D2DX2 1 1 d^2(A)/dx^2 2nd derivative.
D2DXY 1 1 d^2(A)/dxdy 2nd derivative.
D2DY2 1 1 d^2(A)/dy^2 2nd derivative.
D2R 1 1 Converts Degrees to Radians.
DDX 1 1 d(A)/dx Central 1st derivative.
DDY 1 1 d(A)/dy Central 1st derivative.
DEG2KM 1 1 Converts Spherical Degrees to Kilometers.
DILOG 1 1 dilog (A).
DIV 2 1 A / B.
DUP 1 2 Places duplicate of A on the stack.
EQ 2 1 1 if A == B, else 0.
ERF 1 1 Error function erf (A).
ERFC 1 1 Complementary Error function erfc (A).
ERFINV 1 1 Inverse error function of A.
EXCH 2 2 Exchanges A and B on the stack.
EXP 1 1 exp (A).
EXTREMA 1 1 Local Extrema: +2/-2 is max/min, +1/-1 is saddle
with max/min in x, 0 elsewhere.
FACT 1 1 A! (A factorial).
FCRIT 3 1 Critical value for F-distribution, with alpha =
A, n1 = B, and n2 = C.
FDIST 3 1 F-distribution Q(F,n1,n2), with F = A, n1 = B,
and n2 = C.
FLIPLR 1 1 Reverse order of values in each row.
FLIPUD 1 1 Reverse order of values in each column.
FLOOR 1 1 floor (A) (greatest integer <= A).
FMOD 2 1 A % B (remainder after truncated division).
GE 2 1 1 if A >= B, else 0.
GT 2 1 1 if A > B, else 0.
HYPOT 2 1 hypot (A, B) = sqrt (A*A + B*B).
I0 1 1 Modified Bessel function of A (1st kind, order
0).
I1 1 1 Modified Bessel function of A (1st kind, order
1).
IN 2 1 Modified Bessel function of A (1st kind, order
B).
INRANGE 3 1 1 if B <= A <= C, else 0.
INSIDE 1 1 1 when inside or on polygon(s) in A, else 0.
INV 1 1 1 / A.
ISNAN 1 1 1 if A == NaN, else 0.
J0 1 1 Bessel function of A (1st kind, order 0).
J1 1 1 Bessel function of A (1st kind, order 1).
JN 2 1 Bessel function of A (1st kind, order B).
K0 1 1 Modified Kelvin function of A (2nd kind, order
0).
K1 1 1 Modified Bessel function of A (2nd kind, order
1).
KEI 1 1 kei (A).
KER 1 1 ker (A).
KM2DEG 1 1 Converts Kilometers to Spherical Degrees.
KN 2 1 Modified Bessel function of A (2nd kind, order
B).
KURT 1 1 Kurtosis of A.
LDIST 1 1 Compute distance from lines in multi-segment
ASCII file A.
LE 2 1 1 if A <= B, else 0.
LMSSCL 1 1 LMS scale estimate (LMS STD) of A.
LOG 1 1 log (A) (natural log).
LOG10 1 1 log10 (A) (base 10).
LOG1P 1 1 log (1+A) (accurate for small A).
LOG2 1 1 log2 (A) (base 2).
LOWER 1 1 The lowest (minimum) value of A.
LRAND 2 1 Laplace random noise with mean A and std. devia‐
tion B.
LT 2 1 1 if A < B, else 0.
MAD 1 1 Median Absolute Deviation (L1 STD) of A.
MAX 2 1 Maximum of A and B.
MEAN 1 1 Mean value of A.
MED 1 1 Median value of A.
MIN 2 1 Minimum of A and B.
MOD 2 1 A mod B (remainder after floored division).
MODE 1 1 Mode value (Least Median of Squares) of A.
MUL 2 1 A * B.
NAN 2 1 NaN if A == B, else A.
NEG 1 1 -A.
NEQ 2 1 1 if A != B, else 0.
NOT 1 1 NaN if A == NaN, 1 if A == 0, else 0.
NRAND 2 1 Normal, random values with mean A and std. devia‐
tion B.
OR 2 1 NaN if A or B == NaN, else A.
PDIST 1 1 Compute distance from points in ASCII file A.
PLM 3 1 Associated Legendre polynomial P(A) degree B
order C.
PLMg 3 1 Normalized associated Legendre polynomial P(A)
degree B order C (geophysical convention).
POP 1 0 Delete top element from the stack.
POW 2 1 A ^ B.
PQUANT 2 1 The B'th Quantile (0-100%) of A.
PSI 1 1 Psi (or Digamma) of A.
PV 3 1 Legendre function Pv(A) of degree v = real(B) +
imag(C).
QV 3 1 Legendre function Qv(A) of degree v = real(B) +
imag(C).
R2 2 1 R2 = A^2 + B^2.
R2D 1 1 Convert Radians to Degrees.
RAND 2 1 Uniform random values between A and B.
RINT 1 1 rint (A) (nearest integer).
ROTX 2 1 Rotate A by the (constant) shift B in x-direc‐
tion.
ROTY 2 1 Rotate A by the (constant) shift B in y-direc‐
tion.
SAZ 2 1 Spherical azimuth from grid nodes to stack x,y.
SBAZ 2 1 Spherical backazimuth from grid nodes to stack
x,y.
SDIST 2 1 Spherical (Great circle|geodesic) distance (in
km) between grid nodes and stack lon,lat (A, B).
SEC 1 1 sec (A) (A in radians).
SECD 1 1 sec (A) (A in degrees).
SIGN 1 1 sign (+1 or -1) of A.
SIN 1 1 sin (A) (A in radians).
SINC 1 1 sinc (A) (sin (pi*A)/(pi*A)).
SIND 1 1 sin (A) (A in degrees).
SINH 1 1 sinh (A).
SKEW 1 1 Skewness of A.
SQR 1 1 A^2.
SQRT 1 1 sqrt (A).
STD 1 1 Standard deviation of A.
STEP 1 1 Heaviside step function: H(A).
STEPX 1 1 Heaviside step function in x: H(x-A).
STEPY 1 1 Heaviside step function in y: H(y-A).
SUB 2 1 A - B.
TAN 1 1 tan (A) (A in radians).
TAND 1 1 tan (A) (A in degrees).
TANH 1 1 tanh (A).
TCRIT 2 1 Critical value for Student's t-distribution, with
alpha = A and n = B.
TDIST 2 1 Student's t-distribution A(t,n), with t = A, and
n = B.
TN 2 1 Chebyshev polynomial Tn(-1<t<+1,n), with t = A,
and n = B.
UPPER 1 1 The highest (maximum) value of A.
XOR 2 1 0 if A == NaN and B == NaN, NaN if B == NaN, else
A.
Y0 1 1 Bessel function of A (2nd kind, order 0).
Y1 1 1 Bessel function of A (2nd kind, order 1).
YLM 2 2 Re and Im orthonormalized spherical harmonics
degree A order B.
YLMg 2 2 Cos and Sin normalized spherical harmonics degree
A order B (geophysical convention).
YN 2 1 Bessel function of A (2nd kind, order B).
ZCRIT 1 1 Critical value for the normal-distribution, with
alpha = A.
ZDIST 1 1 Cumulative normal-distribution C(x), with x = A.
SYMBOLS
The following symbols have special meaning:
PI 3.1415926...
E 2.7182818...
EULER 0.5772156...
XMIN Minimum x value
XMAX Maximum x value
XINC x increment
NX The number of x nodes
YMIN Minimum y value
YMAX Maximum y value
YINC y increment
NY The number of y nodes
X Grid with x-coordinates
Y Grid with y-coordinates
Xn Grid with normalized [-1 to +1] x-coordinates
Yn Grid with normalized [-1 to +1] y-coordinates
OPTIONS-F Force pixel node registration [Default is gridline registra‐
tion]. (Node registrations are defined in GMT Cookbook Appendix
B on grid file formats.) Only used with -R -I.
-I x_inc [and optionally y_inc] is the grid spacing. Optionally,
append a suffix modifier. Geographical (degrees) coordinates:
Append m to indicate arc minutes or c to indicate arc seconds.
If one of the units e, k, i, or n is appended instead, the
increment is assumed to be given in meter, km, miles, or nauti‐
cal miles, respectively, and will be converted to the equivalent
degrees longitude at the middle latitude of the region (the con‐
version depends on ELLIPSOID). If /y_inc is given but set to 0
it will be reset equal to x_inc; otherwise it will be converted
to degrees latitude. All coordinates: If = is appended then the
corresponding max x (east) or y (north) may be slightly adjusted
to fit exactly the given increment [by default the increment may
be adjusted slightly to fit the given domain]. Finally, instead
of giving an increment you may specify the number of nodes
desired by appending + to the supplied integer argument; the
increment is then recalculated from the number of nodes and the
domain. The resulting increment value depends on whether you
have selected a gridline-registered or pixel-registered grid;
see Appendix B for details. Note: if -Rgrdfile is used then
grid spacing has already been initialized; use -I to override
the values.
-M By default any derivatives calculated are in z_units/ x(or
y)_units. However, the user may choose this option to convert
dx,dy in degrees of longitude,latitude into meters using a flat
Earth approximation, so that gradients are in z_units/meter.
-N Turn off strict domain match checking when multiple grids are
manipulated [Default will insist that each grid domain is within
1e-4 * grid_spacing of the domain of the first grid listed].
-R xmin, xmax, ymin, and ymax specify the Region of interest. For
geographic regions, these limits correspond to west, east,
south, and north and you may specify them in decimal degrees or
in [+-]dd:mm[:ss.xxx][W|E|S|N] format. Append r if lower left
and upper right map coordinates are given instead of w/e/s/n.
The two shorthands -Rg and -Rd stand for global domain (0/360
and -180/+180 in longitude respectively, with -90/+90 in lati‐
tude). Alternatively, specify the name of an existing grid file
and the -R settings (and grid spacing, if applicable) are copied
from the grid. For calendar time coordinates you may either
give (a) relative time (relative to the selected TIME_EPOCH and
in the selected TIME_UNIT; append t to -JX|x), or (b) absolute
time of the form [date]T[clock] (append T to -JX|x). At least
one of date and clock must be present; the T is always required.
The date string must be of the form [-]yyyy[-mm[-dd]] (Gregorian
calendar) or yyyy[-Www[-d]] (ISO week calendar), while the clock
string must be of the form hh:mm:ss[.xxx]. The use of delim‐
iters and their type and positions must be exactly as indicated
(however, input, output and plot formats are customizable; see
gmtdefaults).
-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
d (double)]. Uppercase S or D will force byte-swapping.
Optionally, append ncol, the number of columns in your binary
input file if it exceeds the columns needed by the program. Or
append c if the input file is netCDF. Optionally, append
var1/var2/... to specify the variables to be read. The binary
input option only applies to the data files needed by operators
LDIST, PDIST, and INSIDE.
-f Special formatting of input and/or output columns (time or geo‐
graphical data). Specify i or o to make this apply only to
input or output [Default applies to both]. Give one or more
columns (or column ranges) separated by commas. Append T (abso‐
lute calendar time), t (relative time in chosen TIME_UNIT since
TIME_EPOCH), x (longitude), y (latitude), or f (floating point)
to each column or column range item. Shorthand -f[i|o]g means
-f[i|o]0x,1y (geographic coordinates).
NOTES ON OPERATORS
(1) The operator SDIST calculates spherical distances in km between 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.
Similarly, the SAZ and SBAZ operators calculate spherical azimuth and
back-azimuths in degrees, respectively. A few operators (PDIST, LDIST,
and INSIDE) expects their argument to be a single file with points,
lines, or polygons, respectively. These distances will be in km (for
geographical data, i.e, -fg and Cartesian otherwise. Be aware that
LDIST in particular can be slow for large grids and numerous line seg‐
ments. Note: If the current ELLIPSOID is not spherical then geodesics
are used in the calculations.
(2) The operator PLM calculates the associated Legendre polynomial of
degree L and order M (0 <= M <= L), and its argument is the sine of the
latitude. PLM is not normalized and includes the Condon-Shortley phase
(-1)^M. PLMg is normalized in the way that is most commonly used in
geophysics. The C-S phase can be added by using -M as argument. PLM
will overflow at higher degrees, whereas PLMg is stable until ultra
high degrees (at least 3000).
(3) The operators YLM and YLMg calculate normalized spherical harmonics
for degree L and order M (0 <= M <= L) for all positions in the grid,
which is assumed to be in degrees. YLM and YLMg return two grids, the
real (cosine) and imaginary (sine) component of the complex spherical
harmonic. Use the POP operator (and EXCH) to get rid of one of them,
or save both by giving two consecutive = file.grd calls.
The orthonormalized complex harmonics YLM are most commonly used in
physics and seismology. The square of YLM integrates to 1 over a
sphere. In geophysics, YLMg is normalized to produce unit power when
averaging the cosine and sine terms (separately!) over a sphere (i.e.,
their squares each integrate to 4 pi). The Condon-Shortley phase
(-1)^M is not included in YLM or YLMg, but it can be added by using -M
as argument.
(4) All the derivatives are based on central finite differences, with
natural boundary conditions.
(5) Files that have the same names as some operators, e.g., ADD, SIGN,
=, etc. should be identified by prepending the current directory (i.e.,
./LOG).
(6) Piping of files is not allowed.
(7) The stack depth limit is hard-wired to 100.
(8) All functions expecting a positive radius (e.g., LOG, KEI, etc.)
are passed the absolute value of their argument.
GRID VALUES PRECISION
Regardless of the precision of the input data, GMT programs that create
grid files will internally hold the grids in 4-byte floating point
arrays. This is done to conserve memory and furthermore most if not
all real data can be stored using 4-byte floating point values. Data
with higher precision (i.e., double precision values) will lose that
precision once GMT operates on the grid or writes out new grids. To
limit loss of precision when processing data you should always consider
normalizing the data prior to processing.
GRID FILE FORMATS
By default GMT writes out grid as single precision floats in a COARDS-
complaint netCDF file format. However, GMT is able to produce grid
files in many other commonly used grid file formats and also facili‐
tates so called "packing" of grids, writing out floating point data as
2- or 4-byte integers. To specify the precision, scale and offset, the
user should add the suffix =id[/scale/offset[/nan]], where id is a two-
letter identifier of the grid type and precision, and scale and offset
are optional scale factor and offset to be applied to all grid values,
and nan is the value used to indicate missing data. When reading
grids, the format is generally automatically recognized. If not, the
same suffix can be added to input grid file names. See grdreformat(1)
and Section 4.17 of the GMT Technical Reference and Cookbook for more
information.
When reading a netCDF file that contains multiple grids, GMT will read,
by default, the first 2-dimensional grid that can find in that file. To
coax GMT into reading another multi-dimensional variable in the grid
file, append ?varname to the file name, where varname is the name of
the variable. Note that you may need to escape the special meaning of ?
in your shell program by putting a backslash in front of it, or by
placing the filename and suffix between quotes or double quotes. The
?varname suffix can also be used for output grids to specify a variable
name different from the default: "z". See grdreformat(1) and Section
4.18 of the GMT Technical Reference and Cookbook for more information,
particularly on how to read splices of 3-, 4-, or 5-dimensional grids.
GEOGRAPHICAL AND TIME COORDINATES
When the output grid type is netCDF, the coordinates will be labeled
"longitude", "latitude", or "time" based on the attributes of the input
data or grid (if any) or on the -f or -R options. For example, both
-f0x-f1t and -R 90w/90e/0t/3t will result in a longitude/time grid.
When the x, y, or z coordinate is time, it will be stored in the grid
as relative time since epoch as specified by TIME_UNIT and TIME_EPOCH
in the .gmtdefaults file or on the command line. In addition, the unit
attribute of the time variable will indicate both this unit and epoch.
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), use
grdmath 2 s_xy.grd MUL s_xx.grd s_yy.grd SUB DIV ATAN 2 DIV = direc‐
tion.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:
grdmath-R 0/360/-90/90 -I 1 8 4 YML 1.1 MUL EXCH 0.4 MUL ADD =
harm.grd
To extract the locations of local maxima that exceed 100 mGal in the
file faa.grd:
grdmath faa.grd DUP EXTREMA 2 EQ MUL DUP 100 GT MUL 0 NAN = z.grd
grd2xyz z.grd -S > max.xyz
REFERENCES
Abramowitz, M., and I. A. Stegun, 1964, Handbook of Mathematical Func‐
tions, Applied Mathematics Series, vol. 55, Dover, New York.
Holmes, S. A., and W. E. Featherstone, 2002, A unified approach to the
Clenshaw summation and the recursive computation of very high degree
and order normalised associated Legendre functions. Journal of
Geodesy, 76, 279-299.
Press, W. H., S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery,
1992, Numerical Recipes, 2nd edition, Cambridge Univ., New York.
Spanier, J., and K. B. Oldman, 1987, An Atlas of Functions, Hemisphere
Publishing Corp.
SEE ALSOGMT(1), gmtmath(1), grd2xyz(1), grdedit(1), grdinfo(1), xyz2grd(1)GMT 4.5.14 1 Nov 2015 GRDMATH(1)
