Provided by: gmt-common_5.4.3+dfsg-1_all 
NAME
grdmath - Reverse Polish Notation (RPN) calculator for grids (element by element)
SYNOPSIS
grdmath [ -Amin_area[/min_level/max_level][+ag|i|s |S][+r|l][ppercent] ] [ -Dresolution[+] ] [
-Iincrement ] [ -M ] [ -N ] [ -Rregion ] [ -V[level] ] [ -bibinary ] [ -dinodata ] [ -fflags ] [
-hheaders ] [ -iflags ] [ -nflags ] [ -r ] [ -x[[-]n] ] operand [ operand ] OPERATOR [ operand ] OPERATOR
… = outgrdfile
Note: No space is allowed between the option flag and the associated arguments.
DESCRIPTION
grdmath 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).
Arbitrarily complicated expressions may therefore be evaluated; the final result is written to an output
grid file. Grid operations are element-by-element, not matrix manipulations. 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 -r). The expression = outgrdfile can occur as many times as the depth of the stack allows in
order to save intermediate results. Complicated or frequently occurring expressions may be coded as a
macro for future use or stored and recalled via named memory locations.
REQUIRED ARGUMENTS
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).
OPTIONAL ARGUMENTS
-Amin_area[/min_level/max_level][+ag|i|s|S][+r|l][+ppercent]
Features with an area smaller than min_area in km^2 or of hierarchical level that is lower than
min_level or higher than max_level will not be plotted [Default is 0/0/4 (all features)]. Level 2
(lakes) contains regular lakes and wide river bodies which we normally include as lakes; append +r
to just get river-lakes or +l to just get regular lakes. By default (+ai) we select the ice shelf
boundary as the coastline for Antarctica; append +ag to instead select the ice grounding line as
coastline. For expert users who wish to print their own Antarctica coastline and islands via psxy
you can use +as to skip all GSHHG features below 60S or +aS to instead skip all features north of
60S. Finally, append +ppercent to exclude polygons whose percentage area of the corresponding
full-resolution feature is less than percent. See GSHHG INFORMATION below for more details. (-A is
only relevant to the LDISTG operator)
-Dresolution[+]
Selects the resolution of the data set to use with the operator LDISTG ((f)ull, (h)igh,
(i)ntermediate, (l)ow, and (c)rude). The resolution drops off by 80% between data sets [Default is
l]. Append + to automatically select a lower resolution should the one requested not be available
[abort if not found].
-Ixinc[unit][+e|n][/yinc[unit][+e|n]]
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 s to indicate arc seconds.
If one of the units e, f, k, M, n or u is appended instead, the increment is assumed to be given
in meter, foot, km, Mile, nautical mile or US survey foot, respectively, and will be converted to
the equivalent degrees longitude at the middle latitude of the region (the conversion depends on
PROJ_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 +e 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 +n 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 App-file-formats for details. Note: if -Rgrdfile is used then the 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].
-Rxmin/xmax/ymin/ymax[+r][+uunit] (more …)
Specify the region of interest.
-V[level] (more …)
Select verbosity level [c].
-bi[ncols][t] (more …)
Select native binary input. The binary input option only applies to the data files needed by
operators LDIST, PDIST, and INSIDE.
-dinodata (more …)
Replace input columns that equal nodata with NaN.
-f[i|o]colinfo (more …)
Specify data types of input and/or output columns.
-g[a]x|y|d|X|Y|D|[col]z[+|-]gap[u] (more …)
Determine data gaps and line breaks.
-h[i|o][n][+c][+d][+rremark][+rtitle] (more …)
Skip or produce header record(s).
-icols[+l][+sscale][+ooffset][,…] (more …)
Select input columns and transformations (0 is first column).
-n[b|c|l|n][+a][+bBC][+c][+tthreshold] (more …)
Select interpolation mode for grids.
-r (more …)
Set pixel node registration [gridline]. Only used with -R -I.
-x[[-]n] (more …)
Limit number of cores used in multi-threaded algorithms (OpenMP required).
-^ or just -
Print a short message about the syntax of the command, then exits (NOTE: on Windows just use -).
-+ or just +
Print an extensive usage (help) message, including the explanation of any module-specific option
(but not the GMT common options), then exits.
-? or no arguments
Print a complete usage (help) message, including the explanation of all options, then exits.
OPERATORS
Choose among the following 209 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 B if A == NaN, else A
───────────────────────────────────────────────────
ARC 2 1 Return arc(A,B) on [0 pi]
───────────────────────────────────────────────────
AREA 0 1 Area of each gridnode cell
(in km^2 if geographic)
───────────────────────────────────────────────────
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)
───────────────────────────────────────────────────
BCDF 3 1 Binomial cumulative
distribution function for p
= A, n = B, and x = C
───────────────────────────────────────────────────
BPDF 3 1 Binomial probability density
function for p = A, n = B,
and x = C
───────────────────────────────────────────────────
BEI 1 1 bei (A)
───────────────────────────────────────────────────
BER 1 1 ber (A)
───────────────────────────────────────────────────
BITAND 2 1 A & B (bitwise AND operator)
───────────────────────────────────────────────────
BITLEFT 2 1 A << B (bitwise left-shift
operator)
───────────────────────────────────────────────────
BITNOT 1 1 ~A (bitwise NOT operator,
i.e., return two’s
complement)
───────────────────────────────────────────────────
BITOR 2 1 A | B (bitwise OR operator)
───────────────────────────────────────────────────
BITRIGHT 2 1 A >> B (bitwise right-shift
operator)
───────────────────────────────────────────────────
BITTEST 2 1 1 if bit B of A is set, else
0 (bitwise TEST operator)
───────────────────────────────────────────────────
BITXOR 2 1 A ^ B (bitwise XOR operator)
───────────────────────────────────────────────────
CAZ 2 1 Cartesian azimuth from grid
nodes to stack x,y (i.e., A,
B)
───────────────────────────────────────────────────
CBAZ 2 1 Cartesian back-azimuth from
grid nodes to stack x,y
(i.e., A, B)
───────────────────────────────────────────────────
CDIST 2 1 Cartesian distance between
grid nodes and stack x,y
(i.e., A, B)
───────────────────────────────────────────────────
CDIST2 2 1 As CDIST but only to nodes
that are != 0
───────────────────────────────────────────────────
CEIL 1 1 ceil (A) (smallest integer
>= A)
───────────────────────────────────────────────────
CHICRIT 2 1 Chi-squared critical value
for alpha = A and nu = B
───────────────────────────────────────────────────
CHICDF 2 1 Chi-squared cumulative
distribution function for
chi2 = A and nu = B
───────────────────────────────────────────────────
CHIPDF 2 1 Chi-squared probability
density function for chi2 =
A and nu = B
───────────────────────────────────────────────────
COMB 2 1 Combinations n_C_r, with n =
A and r = 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)
───────────────────────────────────────────────────
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
───────────────────────────────────────────────────
D2DY2 1 1 d^2(A)/dy^2 2nd derivative
───────────────────────────────────────────────────
D2DXY 1 1 d^2(A)/dxdy 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
───────────────────────────────────────────────────
DENAN 2 1 Replace NaNs in A with
values from B
───────────────────────────────────────────────────
DILOG 1 1 dilog (A)
───────────────────────────────────────────────────
DIV 2 1 A / B
───────────────────────────────────────────────────
DUP 1 2 Places duplicate of A on the
stack
───────────────────────────────────────────────────
ECDF 2 1 Exponential cumulative
distribution function for x
= A and lambda = B
───────────────────────────────────────────────────
ECRIT 2 1 Exponential distribution
critical value for alpha = A
and lambda = B
───────────────────────────────────────────────────
EPDF 2 1 Exponential probability
density function for x = A
and lambda = B
───────────────────────────────────────────────────
ERF 1 1 Error function erf (A)
───────────────────────────────────────────────────
ERFC 1 1 Complementary Error function
erfc (A)
───────────────────────────────────────────────────
EQ 2 1 1 if A == B, else 0
───────────────────────────────────────────────────
ERFINV 1 1 Inverse error function of A
───────────────────────────────────────────────────
EXCH 2 2 Exchanges A and B on the
stack
───────────────────────────────────────────────────
EXP 1 1 exp (A)
───────────────────────────────────────────────────
FACT 1 1 A! (A factorial)
───────────────────────────────────────────────────
EXTREMA 1 1 Local Extrema: +2/-2 is
max/min, +1/-1 is saddle
with max/min in x, 0
elsewhere
───────────────────────────────────────────────────
FCDF 3 1 F cumulative distribution
function for F = A, nu1 = B,
and nu2 = C
───────────────────────────────────────────────────
FCRIT 3 1 F distribution critical
value for alpha = A, nu1 =
B, and nu2 = 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)
───────────────────────────────────────────────────
FPDF 3 1 F probability density
function for F = A, nu1 = B,
and nu2 = C
───────────────────────────────────────────────────
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)
───────────────────────────────────────────────────
IFELSE 3 1 B if A != 0, else C
───────────────────────────────────────────────────
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
───────────────────────────────────────────────────
ISFINITE 1 1 1 if A is finite, else 0
───────────────────────────────────────────────────
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
───────────────────────────────────────────────────
LCDF 1 1 Laplace cumulative
distribution function for z
= A
───────────────────────────────────────────────────
LCRIT 1 1 Laplace distribution
critical value for alpha = A
───────────────────────────────────────────────────
LDIST 1 1 Compute minimum distance (in
km if -fg) from lines in
multi-segment ASCII file A
───────────────────────────────────────────────────
LDIST2 2 1 As LDIST, from lines in
ASCII file B but only to
nodes where A != 0
───────────────────────────────────────────────────
LDISTG 0 1 As LDIST, but operates on
the GSHHG dataset (see -A,
-D for options).
───────────────────────────────────────────────────
LE 2 1 1 if A <= B, else 0
───────────────────────────────────────────────────
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)
───────────────────────────────────────────────────
LMSSCL 1 1 LMS scale estimate (LMS STD)
of A
───────────────────────────────────────────────────
LMSSCLW 2 1 Weighted LMS scale estimate
(LMS STD) of A for weights
in B
───────────────────────────────────────────────────
LOWER 1 1 The lowest (minimum) value
of A
───────────────────────────────────────────────────
LPDF 1 1 Laplace probability density
function for z = A
───────────────────────────────────────────────────
LRAND 2 1 Laplace random noise with
mean A and std. deviation 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
───────────────────────────────────────────────────
MEANW 2 1 Weighted mean value of A for
weights in B
───────────────────────────────────────────────────
MEDIAN 1 1 Median value of A
───────────────────────────────────────────────────
MEDIANW 2 1 Weighted median value of A
for weights in B
───────────────────────────────────────────────────
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
───────────────────────────────────────────────────
MODEW 2 1 Weighted mode value (Least
Median of Squares) of A for
weights in B
───────────────────────────────────────────────────
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
───────────────────────────────────────────────────
NORM 1 1 Normalize (A) so
max(A)-min(A) = 1
───────────────────────────────────────────────────
NOT 1 1 NaN if A == NaN, 1 if A ==
0, else 0
───────────────────────────────────────────────────
NRAND 2 1 Normal, random values with
mean A and std. deviation B
───────────────────────────────────────────────────
OR 2 1 NaN if B == NaN, else A
───────────────────────────────────────────────────
PCDF 2 1 Poisson cumulative
distribution function for x
= A and lambda = B
───────────────────────────────────────────────────
PDIST 1 1 Compute minimum distance (in
km if -fg) from points in
ASCII file A
───────────────────────────────────────────────────
PDIST2 2 1 As PDIST, from points in
ASCII file B but only to
nodes where A != 0
───────────────────────────────────────────────────
PERM 2 1 Permutations n_P_r, with n =
A and r = B
───────────────────────────────────────────────────
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)
───────────────────────────────────────────────────
POINT 1 2 Compute mean x and y from
ASCII file A and place them
on the stack
───────────────────────────────────────────────────
POP 1 0 Delete top element from the
stack
───────────────────────────────────────────────────
POW 2 1 A ^ B
───────────────────────────────────────────────────
PPDF 2 1 Poisson distribution
P(x,lambda), with x = A and
lambda = B
───────────────────────────────────────────────────
PQUANT 2 1 The B’th Quantile (0-100%)
of A
───────────────────────────────────────────────────
PQUANTW 3 1 The C’th weighted quantile
(0-100%) of A for weights in
B
───────────────────────────────────────────────────
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
───────────────────────────────────────────────────
RCDF 1 1 Rayleigh cumulative
distribution function for z
= A
───────────────────────────────────────────────────
RCRIT 1 1 Rayleigh distribution
critical value for alpha = A
───────────────────────────────────────────────────
RINT 1 1 rint (A) (round to integral
value nearest to A)
───────────────────────────────────────────────────
RMS 1 1 Root-mean-square of A
───────────────────────────────────────────────────
RMSW 1 1 Root-mean-square of A for
weights in B
───────────────────────────────────────────────────
RPDF 1 1 Rayleigh probability density
function for z = A
───────────────────────────────────────────────────
ROLL 2 0 Cyclicly shifts the top A
stack items by an amount B
───────────────────────────────────────────────────
ROTX 2 1 Rotate A by the (constant)
shift B in x-direction
───────────────────────────────────────────────────
ROTY 2 1 Rotate A by the (constant)
shift B in y-direction
───────────────────────────────────────────────────
SDIST 2 1 Spherical (Great
circle|geodesic) distance
(in km) between nodes and
stack (A, B)
───────────────────────────────────────────────────
SDIST2 2 1 As SDIST but only to nodes
that are != 0
───────────────────────────────────────────────────
SAZ 2 1 Spherical azimuth from grid
nodes to stack lon, lat
(i.e., A, B)
───────────────────────────────────────────────────
SBAZ 2 1 Spherical back-azimuth from
grid nodes to stack lon, lat
(i.e., 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
───────────────────────────────────────────────────
STDW 2 1 Weighted standard deviation
of A for weights in B
───────────────────────────────────────────────────
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
───────────────────────────────────────────────────
SUM 1 1 Sum of all values in A
───────────────────────────────────────────────────
TAN 1 1 tan (A) (A in radians)
───────────────────────────────────────────────────
TAND 1 1 tan (A) (A in degrees)
───────────────────────────────────────────────────
TANH 1 1 tanh (A)
───────────────────────────────────────────────────
TAPER 2 1 Unit weights cosine-tapered
to zero within A and B of x
and y grid margins
───────────────────────────────────────────────────
TCDF 2 1 Student’s t cumulative
distribution function for t
= A, and nu = B
───────────────────────────────────────────────────
TCRIT 2 1 Student’s t distribution
critical value for alpha = A
and nu = B
───────────────────────────────────────────────────
TN 2 1 Chebyshev polynomial
Tn(-1<t<+1,n), with t = A,
and n = B
───────────────────────────────────────────────────
TPDF 2 1 Student’s t probability
density function for t = A,
and nu = B
───────────────────────────────────────────────────
TRIM 3 1 Alpha-trim C to NaN if
values fall in tails A and B
(in percentage)
───────────────────────────────────────────────────
UPPER 1 1 The highest (maximum) value
of A
───────────────────────────────────────────────────
VAR 1 1 Variance of A
───────────────────────────────────────────────────
VARW 2 1 Weighted variance of A for
weights in B
───────────────────────────────────────────────────
WCDF 3 1 Weibull cumulative
distribution function for x
= A, scale = B, and shape =
C
───────────────────────────────────────────────────
WCRIT 3 1 Weibull distribution
critical value for alpha =
A, scale = B, and shape = C
───────────────────────────────────────────────────
WPDF 3 1 Weibull density distribution
P(x,scale,shape), with x =
A, scale = B, and shape = C
───────────────────────────────────────────────────
WRAP 1 1 wrap A in radians onto
[-pi,pi]
───────────────────────────────────────────────────
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) │
├───────────┼──────┼──────────────────────────────┤
│ ZCDF │ 1 1 │ Normal cumulative │
│ │ │ distribution function for z │
│ │ │ = A │
├───────────┼──────┼──────────────────────────────┤
│ ZPDF │ 1 1 │ Normal probability density │
│ │ │ function for z = A │
├───────────┼──────┼──────────────────────────────┤
│ ZCRIT │ 1 1 │ Normal distribution critical │
│ │ │ value for alpha = A │
└───────────┴──────┴──────────────────────────────┘
SYMBOLS
The following symbols have special meaning:
──────────────────────────────────────────────────
PI 3.1415926…
──────────────────────────────────────────────────
E 2.7182818…
──────────────────────────────────────────────────
EULER 0.5772156…
──────────────────────────────────────────────────
EPS_F 1.192092896e-07 (single precision
epsilon
──────────────────────────────────────────────────
XMIN Minimum x value
──────────────────────────────────────────────────
XMAX Maximum x value
──────────────────────────────────────────────────
XRANGE Range of x values
──────────────────────────────────────────────────
XINC x increment
──────────────────────────────────────────────────
NX The number of x nodes
──────────────────────────────────────────────────
YMIN Minimum y value
──────────────────────────────────────────────────
YMAX Maximum y value
──────────────────────────────────────────────────
YRANGE Range of y values
──────────────────────────────────────────────────
YINC y increment
──────────────────────────────────────────────────
NY The number of y nodes
──────────────────────────────────────────────────
X Grid with x-coordinates
──────────────────────────────────────────────────
Y Grid with y-coordinates
──────────────────────────────────────────────────
XNORM Grid with normalized [-1 to +1]
x-coordinates
──────────────────────────────────────────────────
YNORM Grid with normalized [-1 to +1]
y-coordinates
──────────────────────────────────────────────────
XCOL Grid with column numbers 0, 1, …,
NX-1
──────────────────────────────────────────────────
YROW Grid with row numbers 0, 1, …, NY-1
──────────────────────────────────────────────────
NODE Grid with node numbers 0, 1, …,
(NX*NY)-1
┌────────┬───────────────────────────────────────┐
│ │ │
NOTES ON OPERATORS │ │ │
--
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
facilitates so called “packing” of grids, writing out floating point data as 1- or 2-byte integers. (more
…)
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 -R90w/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 gmt.conf file or on the command line. In addition, the unit attribute of the time variable will
indicate both this unit and epoch.
STORE, RECALL AND CLEAR
You may store intermediate calculations to a named variable that you may recall and place on the stack at
a later time. This is useful if you need access to a computed quantity many times in your expression as
it will shorten the overall expression and improve readability. To save a result you use the special
operator STO@label, where label is the name you choose to give the quantity. To recall the stored result
to the stack at a later time, use [RCL]@label, i.e., RCL is optional. To clear memory you may use
CLR@label. Note that STO and CLR leave the stack unchanged.
GSHHS INFORMATION
The coastline database is GSHHG (formerly GSHHS) which is compiled from three sources: World Vector
Shorelines (WVS), CIA World Data Bank II (WDBII), and Atlas of the Cryosphere (AC, for Antarctica only).
Apart from Antarctica, all level-1 polygons (ocean-land boundary) are derived from the more accurate WVS
while all higher level polygons (level 2-4, representing land/lake, lake/island-in-lake, and
island-in-lake/lake-in-island-in-lake boundaries) are taken from WDBII. The Antarctica coastlines come
in two flavors: ice-front or grounding line, selectable via the -A option. Much processing has taken
place to convert WVS, WDBII, and AC data into usable form for GMT: assembling closed polygons from line
segments, checking for duplicates, and correcting for crossings between polygons. The area of each
polygon has been determined so that the user may choose not to draw features smaller than a minimum area
(see -A); one may also limit the highest hierarchical level of polygons to be included (4 is the
maximum). The 4 lower-resolution databases were derived from the full resolution database using the
Douglas-Peucker line-simplification algorithm. The classification of rivers and borders follow that of
the WDBII. See the GMT Cookbook and Technical Reference Appendix K for further details.
MACROS
Users may save their favorite operator combinations as macros via the file grdmath.macros in their
current or user directory. The file may contain any number of macros (one per record); comment lines
starting with # are skipped. The format for the macros is name = arg1 arg2 … arg2 : comment where name is
how the macro will be used. When this operator appears on the command line we simply replace it with the
listed argument list. No macro may call another macro. As an example, the following macro expects three
arguments (radius x0 y0) and sets the modes that are inside the given circle to 1 and those outside to 0:
INCIRCLE = CDIST EXCH DIV 1 LE : usage: r x y INCIRCLE to return 1 inside circle
Note: Because geographic or time constants may be present in a macro, it is required that the optional
comment flag (:) must be followed by a space.
EXAMPLES
To compute all distances to north pole:
gmt grdmath -Rg -I1 0 90 SDIST = dist_to_NP.nc
To take log10 of the average of 2 files, use
gmt grdmath file1.nc file2.nc ADD 0.5 MUL LOG10 = file3.nc
Given the file ages.nc, which holds seafloor ages in m.y., use the relation depth(in m) = 2500 + 350 *
sqrt (age) to estimate normal seafloor depths:
gmt grdmath ages.nc SQRT 350 MUL 2500 ADD = depths.nc
To find the angle a (in degrees) of the largest principal stress from the stress tensor given by the
three files s_xx.nc s_yy.nc, and s_xy.nc from the relation tan (2*a) = 2 * s_xy / (s_xx - s_yy), use
gmt grdmath 2 s_xy.nc MUL s_xx.nc s_yy.nc SUB DIV ATAN 2 DIV = direction.nc
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:
gmt grdmath -R0/360/-90/90 -I1 8 4 YLM 1.1 MUL EXCH 0.4 MUL ADD = harm.nc
To extract the locations of local maxima that exceed 100 mGal in the file faa.nc:
gmt grdmath faa.nc DUP EXTREMA 2 EQ MUL DUP 100 GT MUL 0 NAN = z.nc
gmt grd2xyz z.nc -s > max.xyz
To demonstrate the use of named variables, consider this radial wave where we store and recall the
normalized radial arguments in radians:
gmt grdmath -R0/10/0/10 -I0.25 5 5 CDIST 2 MUL PI MUL 5 DIV STO@r COS @r SIN MUL = wave.nc
To creat a dumb file saved as a 32 bits float GeoTiff using GDAL, run
gmt grdmath -Rd -I10 X Y MUL = lixo.tiff=gd:GTiff
REFERENCES
Abramowitz, M., and I. A. Stegun, 1964, Handbook of Mathematical Functions, 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 ALSO
gmt, gmtmath, grd2xyz, grdedit, grdinfo, xyz2grd
COPYRIGHT
2018, P. Wessel, W. H. F. Smith, R. Scharroo, J. Luis, and F. Wobbe
5.4.3 Jan 03, 2018 GRDMATH(1gmt)