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
1. For Cartesian grids the operators MEAN, MEDIAN, MODE, LMSSCL, MAD, PQUANT, RMS, STD,
and VAR return the expected value from the given matrix. However, for geographic
grids we perform a spherically weighted calculation where each node value is weighted
by the geographic area represented by that node.
2. 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. The operators LDIST and
PDIST compute spherical distances in km if -fg is set or implied, else they return
Cartesian distances. Note: If the current PROJ_ELLIPSOID is ellipsoidal then geodesics
are used in calculations of distances, which can be slow. You can trade speed with
accuracy by changing the algorithm used to compute the geodesic (see PROJ_GEODESIC).
The operator LDISTG is a version of LDIST that operates on the GSHHG data. Instead of
reading an ASCII file, it directly accesses one of the GSHHG data sets as determined
by the -D and -A options.
3. The operator POINT reads a ASCII table, computes the mean x and mean y values and
places these on the stack. If geographic data then we use the mean 3-D vector to
determine the mean location.
4. 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).
5. 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.nc 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.
6. All the derivatives are based on central finite differences, with natural boundary
conditions, and are Cartesian derivatives.
7. 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).
8. Piping of files is not allowed.
9. The stack depth limit is hard-wired to 100.
10. All functions expecting a positive radius (e.g., LOG, KEI, etc.) are passed the
absolute value of their argument. (9) The bitwise operators (BITAND, BITLEFT, BITNOT,
BITOR, BITRIGHT, BITTEST, and BITXOR) convert a grid’s single precision values to
unsigned 32-bit ints to perform the bitwise operations. Consequently, the largest
whole integer value that can be stored in a float grid is 2^24 or 16,777,216. Any
higher result will be masked to fit in the lower 24 bits. Thus, bit operations are
effectively limited to 24 bit. All bitwise operators return NaN if given NaN
arguments or bit-settings <= 0.
11. When OpenMP support is compiled in, a few operators will take advantage of the ability
to spread the load onto several cores. At present, the list of such operators is:
LDIST, LDIST2, PDIST, PDIST2, SAZ, SBAZ, SDIST, YLM, and grd_YLMg.
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