grdmath¶
Reverse Polish Notation (RPN) calculator for grids (element by element)
Synopsis¶
gmt grdmath [ Amin_area[/min_level/max_level][+a[gi][sS]][+lr][+ppercent] ] [ C[cpt] ] [ Dresolution[+f] ] [ Iincrement ] [ M ] [ N ] [ Rregion ] [ S ] [ V[level] ] [ aflags ] [ bibinary ] [ dinodata[+ccol] ] [ eregexp ] [ fflags ] [ ggaps ] [ hheaders ] [ iflags ] [ nflags ] [ rreg ] [ x[[]n] ] [ PAR=value ] operand [ operand ] OPERATOR [ operand ] OPERATOR … = outgrid
Note: No space is allowed between the option flag and the associated arguments.
Description¶
grdmath will perform operations like add, subtract, multiply, and hundreds of other operands on one or more grid files or constants using Reverse Polish Notation (RPN) syntax. Arbitrarily complicated expressions may therefore be evaluated; the final result is written to an output grid file. Grid operations are elementbyelement, 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 rreg). The expression = outgrid 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.
HewlettPackard made lots of calculators (left) using Reverse Polish Notation, which is a postfix system for mathematical notion originally developed by Jan_Łukasiewicz (right). Here, operands are entered first followed by an operator, e.g., “3 5 +” instead of “3 + 5 =” (photo courtesy of John W. Robbins).
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).
 outgrid
The name of a 2D grid file that will hold the final result. (See Grid File Formats).
Optional Arguments¶
 Amin_area[/min_level/max_level][+a[gi][sS]][+lr][+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 riverlakes or +l to just get regular lakes. Append +ppercent to exclude polygons whose percentage area of the corresponding fullresolution feature is less than percent. Use +a to control special aspects of the Antarctica coastline: By default (or add i) we select the ice shelf boundary as the coastline for Antarctica; alternatively, add g to select the ice grounding line instead. For expert users who wish to utilize their own Antarctica (with islands) coastline you can add s to skip all GSHHG features below 60S. In contrast, you can add S to instead skip all features north of 60S. See GSHHG Information below for more details. (A is only relevant to the LDISTG operator)
 C[cpt]
Retain the grid’s default CPT (if it has one), or alternatively replace it with a new default cpt [Default removes any default CPT from the output grid].
 Dresolution[+f]
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 +f to automatically select a lower resolution should the one requested not be available [abort if not found].
 Ix_inc[+en][/y_inc[+en]]
Set the grid spacing as x_inc [and optionally y_inc].
Geographical (degrees) coordinates: Optionally, append an increment unit. Choose among:
m to indicate arc minutes
s to indicate arc seconds
e (meter), f (foot), k (km), M (mile), n (nautical mile) or u (US survey foot), in which case the increment 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 not given or given but set to 0 it will be reset equal to x_inc; otherwise it will be converted to degrees latitude.
All coordinates: The following modifiers are supported:
+e to slightly adjust the max x (east) or y (north) to fit exactly the given increment if needed [Default is to slightly adjust the increment to fit the given domain].
+n to define the number of nodes rather than the increment, in which case the increment is recalculated from the number of nodes, the registration (see GMT File Formats), and the domain. Note: If Rgrdfile is used then the grid spacing and the registration have already been initialized; use I and R to override these 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 \(10^{4}\) times the grid spacing of the domain of the first grid listed].
 Rxmin/xmax/ymin/ymax[+r][+uunit]
Specify the region of interest. (See full description) (See cookbook information).
 S
Reduce (i.e., collapse) the entire stack to a single grid by applying the next operator to all coregistered nodes across the entire stack. You must specify S after listing all of your grids. Note: You can only follow S with a reducing operator, i.e., from the list ADD, AND, MAD, LMSSCL, MAX, MEAN, MEDIAN, MIN, MODE, MUL, RMS, STD, SUB, VAR or XOR.
 V[level]
Select verbosity level [w]. (See full description) (See cookbook information).
 a[[col=]name[,…]] (more …)
Set aspatial column associations col=name.
 birecord[+bl] (more …)
Select native binary format for primary table input. The binary input option only applies to the data files needed by operators LDIST, PDIST, and INSIDE.
 dinodata[+ccol] (more …)
Replace input columns that equal nodata with NaN.
 e[~]“pattern”  e[~]/regexp/[i] (more …)
Only accept data records that match the given pattern.
 f[io]colinfo (more …)
Specify data types of input and/or output columns.
 gxyzdXYDgap[u][+a][+ccol][+np] (more …)
Determine data gaps and line breaks.
 h[io][n][+c][+d][+msegheader][+rremark][+ttitle] (more …)
Skip or produce header record(s).
 icols[+l][+ddivisor][+sscaledk][+ooffset][,…][,t[word]] (more …)
Select input columns and transformations (0 is first column, t is trailing text, append word to read one word only).
 n[bcln][+a][+bBC][+c][+tthreshold] (more …)
Select interpolation mode for grids.
 x[[]n] (more …)
Limit number of cores used in multithreaded algorithms (OpenMP required).
 ^ or just 
Print a short message about the syntax of the command, then exit (Note: on Windows just use ).
 + or just +
Print an extensive usage (help) message, including the explanation of any modulespecific option (but not the GMT common options), then exit.
 ? or no arguments
Print a complete usage (help) message, including the explanation of all options, then exit.
 PAR=value
Temporarily override a GMT default setting; repeatable. See gmt.conf for parameters.
Operators¶
Choose among the following operators. “Args” are the number of input and output arguments.
Operator 
Args 
Returns 
Type of function 

ABS 
1 1 
Absolute value of A 
Arithmetic 
ACOS 
1 1 
Inverse cosine (result in radians) 
Calculus 
ACOSD 
1 1 
Inverse cosine (result in degrees) 
Calculus 
ACOSH 
1 1 
Inverse hyperbolic cosine 
Calculus 
ACOT 
1 1 
Inverse of cotangent (result in radians) 
Calculus 
ACOTD 
1 1 
Inverse of cotangent (result in degrees) 
Calculus 
ACSC 
1 1 
Inverse of cosecant (result in radians) 
Calculus 
ACSCD 
1 1 
Inverse of cosecant (result in degrees) 
Calculus 
ADD 
2 1 
A + B (addition) 
Arithmetic 
AND 
2 1 
B if A equals NaN, else A 
Logic 
ARC 
2 1 
Return arc (A,B) on [0 pi] 
Arithmetic 
AREA 
0 1 
Area of each gridnode cell (in km^2 if geographic) 
Special Operators 
ASEC 
1 1 
Inverse of secant (result in radians) 
Calculus 
ASECD 
1 1 
Inverse of secant (result in degrees) 
Calculus 
ASIN 
1 1 
Inverse of sine (result in radians) 
Calculus 
ASIND 
1 1 
Inverse of sine (result in degrees) 
Calculus 
ASINH 
1 1 
Inverse of hyperbolic sine 
Calculus 
ATAN 
1 1 
Inverse of tangent (result in radians) 
Calculus 
ATAND 
1 1 
Inverse of tangent (result in degrees) 
Calculus 
ATAN2 
2 1 
Inverse of tangent of A/B (result in radians) 
Calculus 
ATAN2D 
2 1 
Inverse of tangent of A/B (result in degrees) 
Calculus 
ATANH 
1 1 
Inverse of hyperbolic tangent 
Calculus 
BCDF 
3 1 
Binomial cumulative distribution function for p = A, n = B, and x = C 
Probability 
BPDF 
3 1 
Binomial probability density function for p = A, n = B, and x = C 
Probability 
BEI 
1 1 
Kelvin function bei (A) 
Special Functions 
BER 
1 1 
Kelvin function ber (A) 
Special Functions 
BITAND 
2 1 
A & B (bitwise AND operator) 
Logic 
BITLEFT 
2 1 
A << B (bitwise leftshift operator) 
Arithmetic 
BITNOT 
1 1 
~A (bitwise NOT operator, i.e., return two’s complement) 
Logic 
BITOR 
2 1 
A  B (bitwise OR operator) 
Logic 
BITRIGHT 
2 1 
A >> B (bitwise rightshift operator) 
Arithmetic 
BITTEST 
2 1 
1 if bit B of A is set, else 0 (bitwise TEST operator) 
Logic 
BITXOR 
2 1 
A ^ B (bitwise XOR operator) 
Logic 
BLEND 
3 1 
Blend A and B using weights in C (01 range) as A*C + B*(1C) 
Special Operators 
CAZ 
2 1 
Cartesian azimuth from grid nodes to stack x,y (i.e., A, B) 
Special Operators 
CBAZ 
2 1 
Cartesian backazimuth from grid nodes to stack x,y (i.e., A, B) 
Special Operators 
CDIST 
2 1 
Cartesian distance between grid nodes and stack x,y (i.e., A, B) 
Special Operators 
CDIST2 
2 1 
As CDIST but only to nodes that are != 0 
Special Operators 
CEIL 
1 1 
ceil (A) (smallest integer >= A) 
Logic 
CHICRIT 
2 1 
Chisquared distribution critical value for alpha = A and nu = B 
Probability 
CHICDF 
2 1 
Chisquared cumulative distribution function for chi2 = A and nu = B 
Probability 
CHIPDF 
2 1 
Chisquared probability density function for chi2 = A and nu = B 
Probability 
COMB 
2 1 
Combinations n_C_r, with n = A and r = B 
Probability 
CORRCOEFF 
2 1 
Correlation coefficient r(A, B) 
Probability 
COS 
1 1 
Inverse cosine (result in radians) 
Calculus 
COSD 
1 1 
Inverse cosine (result in degrees) 
Calculus 
COSH 
1 1 
Inverse hyperbolic cosine 
Calculus 
COT 
1 1 
Inverse of cotangent (result in radians) 
Calculus 
COTD 
1 1 
Inverse of cotangent (result in degrees) 
Calculus 
CSC 
1 1 
Inverse of cosecant (result in radians) 
Calculus 
CSCD 
1 1 
Inverse of cosecant (result in degrees) 
Calculus 
CUMSUM 
2 1 
Cumulative sum per row (B=±13) or column (B=±24) in A. Sign of B sets summation direction 
Arithmetic 
CURV 
1 1 
Curvature of A (Laplacian) 
Calculus 
D2DX2 
1 1 
d^2(A)/dx^2 2nd derivative 
Calculus 
D2DY2 
1 1 
d^2(A)/dy^2 2nd derivative 
Calculus 
D2DXY 
1 1 
d^2(A)/dxdy 2nd derivative 
Calculus 
D2R 
1 1 
Converts degrees to radians 
Special Operators 
DDX 
1 1 
d(A)/dx Central 1st derivative 
Calculus 
DAYNIGHT 
3 1 
1 where sun at (A, B) shines and 0 elsewhere, with C transition width 
Special Operators 
DDY 
1 1 
d(A)/dy Central 1st derivative 
Calculus 
DEG2KM 
1 1 
Converts spherical degrees to kilometers 
Special Operators 
DENAN 
2 1 
Replace NaNs in A with values from B 
Logic 
DILOG 
1 1 
Dilogarithm (Spence’s) function 
Special Functions 
DIV 
2 1 
A / B (division) 
Arithmetic 
DOT 
2 1 
2D (Cartesian) or 3D (geographic) dot products between nodes and stack (A, B) unit vector(s) 
Special Operators 
DUP 
1 2 
Places duplicate of A on the stack 
Special Operators 
ECDF 
2 1 
Exponential cumulative distribution function for x = A and lambda = B 
Probability 
ECRIT 
2 1 
Exponential distribution critical value for alpha = A and lambda = B 
Probability 
EPDF 
2 1 
Exponential probability density function for x = A and lambda = B 
Probability 
ERF 
1 1 
Error function erf (A) 
Probability 
ERFC 
1 1 
Complementary Error function erfc (A) 
Probability 
EQ 
2 1 
1 if A equals B, else 0 
Logic 
ERFINV 
1 1 
Inverse error function of A 
Probability 
EXCH 
2 2 
Exchanges A and B on the stack 
Special Operators 
EXP 
1 1 
E raised to a power. 
Arithmetic 
FACT 
1 1 
A! (A factorial) 
Arithmetic 
EXTREMA 
1 1 
Local extrema: 1 is a (local) minimum, +1 a (local) maximum, and 0 elsewhere 
Calculus 
FCDF 
3 1 
F cumulative distribution function for F = A, nu1 = B, and nu2 = C 
Probability 
FCRIT 
3 1 
F distribution critical value for alpha = A, nu1 = B, and nu2 = C 
Probability 
FISHER 
3 1 
Fisher probability density function at nodes for center lon = A, lat = B, with kappa = C 
Probability 
FLIPLR 
1 1 
Reverse order of values in each row 
Special Operators 
FLIPUD 
1 1 
Reverse order of each column 
Special Operators 
FLOOR 
1 1 
greatest integer less than or equal to A 
Logic 
FMOD 
2 1 
A % B (remainder after truncated division) 
Arithmetic 
FPDF 
3 1 
F probability density function for F = A, nu1 = B, and nu2 = C 
Probability 
GE 
2 1 
1 if A >= (greater or equal than) B, else 0 
Logic 
GT 
2 1 
1 if A > (greater than) B, else 0 
Logic 
HSV2LAB 
3 3 
Convert h,s,v triplets to l,a,b triplets, with h = A (0360), s = B and v = C (01) 
Special Operators 
HSV2RGB 
3 3 
Convert h,s,v triplets to r,g,b triplets, with h = A (0360), s = B and v = C (01) 
Special Operators 
HSV2XYZ 
3 3 
Convert h,s,v triplets to x,t,z triplets, with h = A (0360), s = B and v = C (01) 
Special Operators 
HYPOT 
2 1 
Hypotenuse of a right triangle of sides A and B (= sqrt (A^2 + B^2)) 
Calculus 
I0 
1 1 
Modified Bessel function of A (1st kind, order 0) 
Special Functions 
I1 
1 1 
Modified Bessel function of A (1st kind, order 1) 
Special Functions 
IFELSE 
3 1 
B if A is not equal to 0, else C 
Logic 
IN 
2 1 
Modified Bessel function of A (1st kind, order B) 
Special Functions 
INRANGE 
3 1 
1 if B <= A <= C, else 0 
Logic 
INSIDE 
1 1 
1 when inside or on polygon(s) in A, else 0 
Special Operators 
INV 
1 1 
Inverse error function of A 
Probability 
ISFINITE 
1 1 
1 if A is finite, else 0 
Logic 
ISNAN 
1 1 
1 if A equals NaN, else 0 
Logic 
J0 
1 1 
Bessel function of A (1st kind, order 0) 
Special Functions 
J1 
1 1 
Bessel function of A (1st kind, order 1) 
Special Functions 
JN 
2 1 
Bessel function of A (1st kind, order B) 
Special Functions 
K0 
1 1 
Modified Kelvin function of A (2nd kind, order 0) 
Special Functions 
K1 
1 1 
Modified Bessel function of A (2nd kind, order 1) 
Special Functions 
KEI 
1 1 
Kelvin function kei (A) 
Special Functions 
KER 
1 1 
Kelvin function ker (A) 
Special Functions 
KM2DEG 
1 1 
Converts kilometers to spherical degrees 
Special Operators 
KN 
2 1 
Modified Bessel function of A (2nd kind, order B) 
Special Functions 
KURT 
1 1 
Kurtosis of A 
Probability 
LAB2HSV 
3 3 
Convert l,a,b triplets to h,s,v triplets 
Special Operators 
LAB2RGB 
3 3 
Convert l,a,b triplets to r,g,b triplets 
Special Operators 
LAB2XYZ 
3 3 
Convert l,a,b triplets to x,y,z triplets 
Special Operators 
LCDF 
1 1 
Laplace cumulative distribution function for z = A 
Probability 
LCRIT 
1 1 
Laplace distribution critical value for alpha = A 
Probability 
LDIST 
1 1 
Compute minimum distance (in km if fg) from lines in multisegment ASCII file A 
Special Operators 
LDIST2 
2 1 
As LDIST, from lines in ASCII file B but only to nodes where A != 0 
Special Operators 
LDISTG 
0 1 
As LDIST, but operates on the GSHHG dataset (see A, D for options). 
Special Operators 
LE 
2 1 
1 if A <= (equal or smaller than) B, else 0 
Logic 
LOG 
1 1 
Dilogarithm (Spence’s) function 
Special Functions 
LOG10 
1 1 
\(\log_{10}\) (A) (logarithm base 10) 
Arithmetic 
LOG1P 
1 1 
log (1+A) (natural logarithm, accurate for small A) 
Arithmetic 
LOG2 
1 1 
\(\log_2\) (A) (logarithm base 2) 
Arithmetic 
LMSSCL 
1 1 
LMS (Least Median of Squares) scale estimate (LMS STD) of A 
Probability 
LMSSCLW 
2 1 
Weighted LMS scale estimate (LMS STD) of A for weights in B 
Probability 
LOWER 
1 1 
The lowest (minimum) value of A 
Arithmetic 
LPDF 
1 1 
Laplace probability density function for z = A 
Probability 
LRAND 
2 1 
Laplace random noise with mean A and std. deviation B 
Probability 
LT 
2 1 
1 if A < (smaller than) B, else 0 
Logic 
MAD 
1 1 
Median Absolute Deviation (L1 STD) of A 
Probability 
MAX 
2 1 
Maximum of A and B 
Probability 
MEAN 
1 1 
Mean value of A 
Probability 
MEANW 
2 1 
Weighted mean value of A for weights in B 
Probability 
MEDIAN 
1 1 
Median value of A 
Probability 
MEDIANW 
2 1 
Weighted median value of A for weights in B 
Probability 
MIN 
2 1 
Minimum of A and B 
Probability 
MOD 
2 1 
A % B (remainder after truncated division) 
Arithmetic 
MODE 
1 1 
Mode value (Least Median of Squares) of A 
Probability 
MODEW 
2 1 
Weighted mode value (Least Median of Squares) of A for weights in B 
Probability 
MUL 
2 1 
A x B (multiplication) 
Arithmetic 
NAN 
2 1 
NaN if A == B, else A Logic 

NEG 
1 1 
Negative (A) 
Arithmetic 
NEQ 
2 1 
1 If A is not equal to B, else 0 
Logic 
NORM 
1 1 
Normalize (A) so min(A) = 0 and max(A) = 1 
Probability 
NOT 
1 1 
~A (bitwise NOT operator, i.e., return two’s complement) 
Logic 
NRAND 
2 1 
Normal, random values with mean A and std. deviation B 
Probability 
OR 
2 1 
NaN if B equals NaN, else A 
Logic 
PCDF 
2 1 
Poisson cumulative distribution function for x = A and lambda = B 
Probability 
PDIST 
1 1 
Compute minimum distance (in km if fg) from points in ASCII file A 
Special Operators 
PDIST2 
2 1 
As PDIST, from points in ASCII file B but only to nodes where A != 0 
Special Operators 
PERM 
2 1 
Permutations n_P_r, with n = A and r = B 
Probability 
PLM 
3 1 
Associated Legendre polynomial P(A) degree B order C 
Special Functions 
PLMg 
3 1 
Normalized associated Legendre polynomial P(A) degree B order C (geophysical convention) 
Special Functions 
POINT 
1 2 
Compute mean x and y from ASCII file A and place them on the stack 
Special Operators 
POP 
1 0 
Delete top element from the stack 
Special Operators 
POW 
2 1 
A to the power of B 
Arithmetic 
PPDF 
2 1 
Poisson distribution P(x,lambda), with x = A and lambda = B 
Probability 
PQUANT 
2 1 
The B’th quantile (0100%) of A 
Probability 
PQUANTW 
3 1 
The C’th weighted quantile (0100%) of A for weights in B 
Probability 
PSI 
1 1 
Psi (or Digamma) of A 
Special Functions 
PV 
3 1 
Legendre function Pv(A) of degree v = real(B) + imag(C) 
Special Functions 
QV 
3 1 
Legendre function Qv(A) of degree v = real(B) + imag(C) 
Special Functions 
R2 
2 1 
Hypotenuse squared (= A^2 + B^2) 
Calculus 
R2D 
1 1 
Convert radians to degrees 
Special Operators 
RAND 
2 1 
Laplace random noise with mean A and std. deviation B 
Probability 
RCDF 
1 1 
Rayleigh cumulative distribution function for z = A 
Probability 
RCRIT 
1 1 
Rayleigh distribution critical value for alpha = A 
Probability 
RGB2HSV 
3 3 
Convert r,g,b triplets to h,s,v triplets, with r = A, g = B, and b = C (in 0255 range) 
Special Operators 
RGB2LAB 
3 3 
Convert r,g,b triplets to l,a,b triplets, with r = A, g = B, and b = C (in 0255 range) 
Special Operators 
RGB2XYZ 
3 3 
Convert r,g,b triplets to x,y,x triplets, with r = A, g = B, and b = C (in 0255 range) 
Special Operators 
RINT 
1 1 
rint (A) (round to integral value nearest to A) 
Arithmetic 
RMS 
1 1 
Rootmeansquare of A 
Arithmetic 
RMSW 
1 1 
Weighted rootmeansquare of A for weights in B 
Arithmetic 
RPDF 
1 1 
Rayleigh probability density function for z = A 
Probability 
ROLL 
2 0 
Cyclically shifts the top A stack items by an amount B 
Special Operators 
ROTX 
2 1 
Rotate A by the (constant) shift B in xdirection 
Arithmetic 
ROTY 
2 1 
Rotate A by the (constant) shift B in ydirection 
Arithmetic 
SADDLE 
1 1 
Saddle point (±), with (local) minimum (1) or maximum (+1) in xdirection, 0 elsewhere 
Calculus 
SDIST 
2 1 
Spherical (Great circlegeodesic) distance (in km) between nodes and stack (A, B) Example 
Special Operators 
SDIST2 
2 1 
As SDIST but only to nodes that are != 0 
Special Operators 
SAZ 
2 1 
Spherical azimuth from grid nodes to stack lon, lat (i.e., A, B) 
Special Operators 
SBAZ 
2 1 
Spherical backazimuth from grid nodes to stack lon, lat (i.e., A, B) 
Special Operators 
SEC 
1 1 
Inverse of secant (result in radians) 
Calculus 
SECD 
1 1 
Inverse of secant (result in degrees) 
Calculus 
SIGN 
1 1 
Sign (+1 or 1) of A 
Logic 
SIN 
1 1 
Inverse of sine (result in radians) 
Calculus 
SINC 
1 1 
Normalized sinc function. 
Special Functions 
SIND 
1 1 
Inverse of sine (result in degrees) 
Calculus 
SINH 
1 1 
Inverse of hyperbolic sine 
Calculus 
SKEW 
1 1 
Skewness of A 
Probability 
SQR 
1 1 
Square (to the power of 2) 
Arithmetic 
SQRT 
1 1 
Square root 
Arithmetic 
STD 
1 1 
Standard deviation of A 
Probability 
STDW 
2 1 
Weighted standard deviation of A for weights in B 
Probability 
STEP 
1 1 
Heaviside step function H(A) 
Special Functions 
STEPX 
1 1 
Heaviside step function in x: H(xA) 
Special Functions 
STEPY 
1 1 
Heaviside step function in y: H(yA) 
Special Functions 
SUB 
2 1 
A  B (subtraction) 
Arithmetic 
SUM 
1 1 
Cumulative sum of A 
Arithmetic 
TAN 
1 1 
Inverse of tangent (result in radians) 
Calculus 
TAND 
1 1 
Inverse of tangent (result in degrees) 
Calculus 
TANH 
1 1 
Inverse of hyperbolic tangent 
Calculus 
TAPER 
2 1 
Unit weights cosinetapered to zero within A of end margins 
Special Operators 
TCDF 
2 1 
Student’s t cumulative distribution function for t = A, and nu = B 
Probability 
TCRIT 
2 1 
Student’s t distribution critical value for alpha = A and nu = B 
Probability 
TN 
2 1 
~A (bitwise NOT operator, i.e., return two’s complement) 
Logic 
TPDF 
2 1 
Student’s t probability density function for t = A, and nu = B 
Probability 
TRIM 
3 1 
Alphatrim C to NaN if values fall in tails A and B (in percentage) 
Special Operators 
UPPER 
1 1 
The highest (maximum) value of A 
Arithmetic 
VAR 
1 1 
Variance of A 
Probability 
VARW 
2 1 
Weighted variance of A for weights in B 
Probability 
VPDF 
3 1 
Von Mises density distribution V(x,mu,kappa), with angles = A, mu = B, and kappa = C 
Probability 
WCDF 
3 1 
Weibull cumulative distribution function for x = A, scale = B, and shape = C 
Probability 
WCRIT 
3 1 
Weibull distribution critical value for alpha = A, scale = B, and shape = C 
Probability 
WPDF 
3 1 
Weibull density distribution P(x,scale,shape), with x = A, scale = B, and shape = C 
Probability 
WRAP 
1 1 
wrap A in radians onto [pi,pi] 
Special Operators 
XOR 
2 1 
A ^ B (bitwise XOR operator) 
Logic 
XYZ2HSV 
3 3 
Convert x,y,z triplets to h,s,v triplets 
Special Operators 
XYZ2LAB 
3 3 
Convert x,y,z triplets to l,a,b triplets 
Special Operators 
XYZ2RGB 
3 3 
Convert x,y,z triplets to r,g,b triplets 
Special Operators 
Y0 
1 1 
Bessel function of A (2nd kind, order 0) 
Special Functions 
Y1 
1 1 
Bessel function of A (2nd kind, order 1) 
Special Functions 
YLM 
2 2 
Real and Imaginary orthonormalized spherical harmonics degree A order B 
Special Functions 
YLMg 
2 2 
Cos and Sin normalized spherical harmonics degree A order B (geophysical convention) 
Special Functions 
YN 
2 1 
Bessel function of A (2nd kind, order B) 
Special Functions 
ZCDF 
1 1 
Normal cumulative distribution function for z = A 
Probability 
ZCRIT 
1 1 
Normal distribution critical value for alpha = A 
Probability 
ZPDF 
1 1 
Normal probability density function for z = A 
Probability 
Symbols¶
The following symbols have special meaning:
PI 
3.1415926… 
E 
2.7182818… 
EULER 
0.5772156… 
PHI 
1.6180339… (golden ratio) 
EPS_F 
1.192092896e07 (single precision epsilon 
XMIN 
Minimum x value 
XMAX 
Maximum x value 
XRANGE 
Range of x values 
XINC 
The x increment 
NX 
The number of x nodes 
YMIN 
Minimum y value 
YMAX 
Maximum y value 
YRANGE 
Range of y values 
YINC 
The y increment 
NY 
The number of y nodes 
X 
Grid with xcoordinates 
Y 
Grid with ycoordinates 
XNORM 
Grid with normalized [1 to +1] xcoordinates 
YNORM 
Grid with normalized [1 to +1] ycoordinates 
XCOL 
Grid with column numbers 0, 1, …, NX1 
YROW 
Grid with row numbers 0, 1, …, NY1 
NODE 
Grid with node numbers 0, 1, …, (NX*NY)1 
NODEP 
Grid with node numbers in presence of pad 
Notes On Operators¶
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.
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 backazimuths 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.
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 3D vector to determine the mean location.
The operator PLM calculates the associated Legendre polynomial of degree L and order M (\(0 \leq M \leq L)\), and its argument is the sine of the latitude. PLM is not normalized and includes the CondonShortley phase \((1)^M\). PLMg is normalized in the way that is most commonly used in geophysics. The CondonShortley 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).
The operators YLM and YLMg calculate normalized spherical harmonics for degree L and order M (\(0 \leq M \leq L)\) 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 CondonShortley phase \((1)^M\) is not included in YLM or YLMg, but it can be added by using M as argument.
All the derivatives are based on central finite differences, with natural boundary conditions, and are Cartesian derivatives.
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).
Piping of files is not allowed.
The stack depth limit is hardwired to 100.
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 32bit 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 bitsettings <= 0.
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.
Operators DEG2KM and KM2DEG are only exact when a spherical Earth is selected with PROJ_ELLIPSOID.
Operator DOT normalizes 2D vectors before the dotproduct takes place. For 3D vector they are all unit vectors to begin with.
The colortriplet conversion functions (RGB2HSV, etc.) includes not only r,g,b and h,s,v triplet conversions, but also l,a,b (CIE L a b ) and sRGB (x,y,z) conversions between all four color spaces.
The DAYNIGHT operator returns a grid with ones on the side facing the given sun location at (A,B). If the transition width (C) is zero then we get either 1 or 0, but if C is nonzero then we approximate the step function using an atanapproximation instead. Thus, the values are never exactly 0 or 1, but close, and the smaller C the closer we get.
The VPDF operator expects angles in degrees.
The CUMSUM operator normally resets the accumulated sums at the end of a row or column. Use ±3 or ±4 to have the accumulated sums continue with the start of the next row or column.
Grid Values Precision¶
Regardless of the precision of the input data, GMT programs that create grid files will internally hold the grids in 4byte floating point arrays. This is done to conserve memory and furthermore most if not all real data can be stored using 4byte 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.
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 both STO and CLR leave the stack unchanged.
GSHHG Information¶
The coastline database is GSHHG (formerly GSHHS) which is compiled from three sources: World Vector Shorelines (WVS, not including Antarctica), CIA World Data Bank II (WDBII), and Atlas of the Cryosphere (AC, for Antarctica only). Apart from Antarctica, all level1 polygons (oceanland boundary) are derived from the more accurate WVS while all higher level polygons (level 24, representing land/lake, lake/islandinlake, and islandinlake/lakeinislandinlake boundaries) are taken from WDBII. The Antarctica coastlines come in two flavors: icefront 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 lowerresolution databases were derived from the full resolution database using the DouglasPeucker linesimplification algorithm. The classification of rivers and borders follow that of the WDBII. See The Global Selfconsistent, Hierarchical, Highresolution Geography Database (GSHHG) for further details.
Inside/outside Status¶
To determine if a point is inside, outside, or exactly on the boundary of a polygon we need to balance the complexity (and execution time) of the algorithm with the type of data and shape of the polygons. For any Cartesian data we use a nonzero winding algorithm, which is quite fast. For geographic data we will also use this algorithm as long as (1) the polygons do not include a geographic pole, and (2) the longitude extent of the polygons is less than 360. If this is the situation we also carefully adjust the test point longitude for any 360 degree offsets, if appropriate. Otherwise, we employ a full spherical rayshooting method to determine a points status.
Macros¶
Users may save their favorite operator combinations as macros via the file grdmath.macros in their current or user (~/.gmt) 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 nodes that are inside the given Cartesian circle to 1 and those outside to 0:
INCIRCLE = CDIST EXCH DIV 1 LE : usage: r x y INCIRCLE to return 1 inside circle
Marine geophysicist often need to evaluate predicted seafloor depth from an age grid. One such model is the classic Parsons and Sclater [1977] curve. It may be written
A good crossover age for these curves is 26.2682 Myr. A macro for this system is a bit awkward due to the split but can be written
PS77 = STO@T POP 6400 RCL@T 62.8 DIV NEG EXP 3200 MUL SUB RCL@T 26.2682 GT MUL 2500 350 RCL@T SQRT MUL ADD RCL@T 26.2682 LE MUL ADD : usage: age PS77 returns depth
i.e., we evaluate both expressions and multiply them by 1 or 0 depending where they apply, and then add them. With this macro installed you can compute predicted depths in the Pacific northwest via:
gmt grdmath R200/240/40/60 @earth_age_01m_g PS77 = depth_ps77.grd
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¶
Note: Below are some examples of valid syntax for this module.
The examples that use remote files (file names starting with @
)
can be cut and pasted into your terminal for testing.
Other commands requiring input files are just dummy examples of the types
of uses that are common but cannot be run verbatim as written.
To compute all distances to north pole, try:
gmt grdmath Rg I1 0 90 SDIST = dist_to_NP.nc
To take \(\log_{10}\) 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, try:
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, use:
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, use:
gmt grdmath faa.nc DUP EXTREMA 1 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 by:
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 create a dumb file saved as a 32 bits float GeoTiff using GDAL, run:
gmt grdmath Rd I10 X Y MUL = lixo.tiff=gd:GTiff
To compute distances in km from the line trace.txt for the area represented by the geographic grid data.grd, run:
gmt grdmath Rdata.grd trace.txt LDIST = dist_from_line.grd
To demonstrate the stackreducing effect of S, we compute the standard deviation per node of all the grids matching the name model_*.grd using:
gmt grdmath model_*.grd S STD = std_of_models.grd
To create a geotiff with resolution 0.5x0.5 degrees with distances in km from the coast line, use:
gmt grdmath RNO,IS Dc I.5 LDISTG = distance.tif=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 normalized associated Legendre functions. J. of Geodesy, 76, 279299.
B. Parsons and J. G. Sclater, 1977, An analysis of the variation of ocean floor bathymetry and heat flow with age, J. Geophys. Res., 82, 803827.
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.
More on Reverse Polish Notation
Reverse Polish Notation (RPN) or postfix notation is widely used in computer science because of the simplicity of implementing a stackbased computation system. The PostScipt language we used to make GMT graphics is postfix, for instance. To learn more about RPN or postfix, watch this YouTube video explanation: