grdmath(1) GMT grdmath(1)
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 a| = 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). Arbi-
trarily complicated expressions may therefore be evaluated; the final
result is written to an output grid file. Grid operations are ele-
ment-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 occur-
ring 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 hier-
archical 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 Antarc-
tica; append +ag to instead select the ice grounding line as
coastline. For expert users who wish to print their own Antarc-
tica 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 fea-
ture 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, nau-
tical mile or US survey foot, respectively, and will be con-
verted to the equivalent degrees longitude at the middle lati-
tude 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 coordi-
nates: 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 recalcu-
lated from the number of nodes and the domain. The resulting
increment value depends on whether you have selected a grid-
line-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 a|)
Specify the region of interest.
-V[level] (more a|)
Select verbosity level [c].
-bi[ncols][t] (more a|)
Select native binary input. The binary input option only applies
to the data files needed by operators LDIST, PDIST, and INSIDE.
-dinodata (more a|)
Replace input columns that equal nodata with NaN.
-f[i|o]colinfo (more a|)
Specify data types of input and/or output columns.
-g[a]x|y|d|X|Y|D|[col]z[+|-]gap[u] (more a|)
Determine data gaps and line breaks.
-h[i|o][n][+c][+d][+rremark][+rtitle] (more a|)
Skip or produce header record(s).
-icols[+l][+sscale][+ooffset][,^<i>a|] (more a|)
Select input columns and transformations (0 is first column).
-n[b|c|l|n][+a][+bBC][+c][+tthreshold] (more a|)
Select interpolation mode for grids.
-r (more a|)
Set pixel node registration [gridline]. Only used with -R -I.
-x[[-]n] (more a|)
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 explana-
tion 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. aargsa 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 func- |
| | | tion for p = A, n = |
| | | B, and x = C |
+----------+------+---------------------+
|BPDF | 3 1 | Binomial probabil- |
| | | ity density func- |
| | | tion 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 opera- |
| | | tor) |
+----------+------+---------------------+
|BITNOT | 1 1 | ~A (bitwise NOT |
| | | operator, i.e., |
| | | return twoas com- |
| | | plement) |
+----------+------+---------------------+
|BITOR | 2 1 | A | B (bitwise OR |
| | | operator) |
+----------+------+---------------------+
|BITRIGHT | 2 1 | A >> B (bitwise |
| | | right-shift opera- |
| | | tor) |
+----------+------+---------------------+
|BITTEST | 2 1 | 1 if bit B of A is |
| | | set, else 0 (bit- |
| | | wise 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 criti- |
| | | cal value for alpha |
| | | = A and nu = B |
+----------+------+---------------------+
|CHICDF | 2 1 | Chi-squared cumula- |
| | | tive distribution |
| | | function for chi2 = |
| | | A and nu = B |
+----------+------+---------------------+
|CHIPDF | 2 1 | Chi-squared proba- |
| | | bility 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 coeffi- |
| | | cient r(A, B) |
+----------+------+---------------------+
|COS | 1 1 | cos (A) (A in radi- |
| | | ans) |
+----------+------+---------------------+
|COSD | 1 1 | cos (A) (A in |
| | | degrees) |
+----------+------+---------------------+
|COSH | 1 1 | cosh (A) |
+----------+------+---------------------+
|COT | 1 1 | cot (A) (A in radi- |
| | | ans) |
+----------+------+---------------------+
|COTD | 1 1 | cot (A) (A in |
| | | degrees) |
+----------+------+---------------------+
|CSC | 1 1 | csc (A) (A in radi- |
| | | ans) |
+----------+------+---------------------+
|CSCD | 1 1 | csc (A) (A in |
| | | degrees) |
+----------+------+---------------------+
|CURV | 1 1 | Curvature of A |
| | | (Laplacian) |
+----------+------+---------------------+
|D2DX2 | 1 1 | d^2(A)/dx^2 2nd de- |
| | | rivative |
+----------+------+---------------------+
|D2DY2 | 1 1 | d^2(A)/dy^2 2nd de- |
| | | rivative |
+----------+------+---------------------+
|D2DXY | 1 1 | d^2(A)/dxdy 2nd de- |
| | | rivative |
+----------+------+---------------------+
|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 Kilome- |
| | | ters |
+----------+------+---------------------+
|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 cumula- |
| | | tive distribution |
| | | function for x = A |
| | | and lambda = B |
+----------+------+---------------------+
|ECRIT | 2 1 | Exponential distri- |
| | | bution critical |
| | | value for alpha = A |
| | | and lambda = B |
+----------+------+---------------------+
|EPDF | 2 1 | Exponential proba- |
| | | bility 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 func- |
| | | tion 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 dis- |
| | | tribution 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 col- |
| | | umn |
+----------+------+---------------------+
|FLOOR | 1 1 | floor (A) (greatest |
| | | integer <= A) |
+----------+------+---------------------+
|FMOD | 2 1 | A % B (remainder |
| | | after truncated |
| | | division) |
+----------+------+---------------------+
|FPDF | 3 1 | F probability den- |
| | | sity 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 func- |
| | | tion for z = A |
+----------+------+---------------------+
|LCRIT | 1 1 | Laplace distribu- |
| | | tion 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 oper- |
| | | ates 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 (mini- |
| | | mum) 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 divi- |
| | | sion) |
+----------+------+---------------------+
|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 val- |
| | | ues with mean A and |
| | | std. deviation B |
+----------+------+---------------------+
|OR | 2 1 | NaN if B == NaN, |
| | | else A |
+----------+------+---------------------+
|PCDF | 2 1 | Poisson cumulative |
| | | distribution func- |
| | | tion 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 associ- |
| | | ated Legendre poly- |
| | | nomial P(A) degree |
| | | B order C (geophys- |
| | | ical 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 distribu- |
| | | tion P(x,lambda), |
| | | with x = A and |
| | | lambda = B |
+----------+------+---------------------+
|PQUANT | 2 1 | The Bath Quantile |
| | | (0-100%) of A |
+----------+------+---------------------+
|PQUANTW | 3 1 | The Cath 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 val- |
| | | ues between A and B |
+----------+------+---------------------+
|RCDF | 1 1 | Rayleigh cumulative |
| | | distribution func- |
| | | tion for z = A |
+----------+------+---------------------+
|RCRIT | 1 1 | Rayleigh distribu- |
| | | tion 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 probabil- |
| | | ity density func- |
| | | tion 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 radi- |
| | | ans) |
+----------+------+---------------------+
|SECD | 1 1 | sec (A) (A in |
| | | degrees) |
+----------+------+---------------------+
|SIGN | 1 1 | sign (+1 or -1) of |
| | | A |
+----------+------+---------------------+
|SIN | 1 1 | sin (A) (A in radi- |
| | | ans) |
+----------+------+---------------------+
|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 radi- |
| | | ans) |
+----------+------+---------------------+
|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 | Studentas t cumula- |
| | | tive distribution |
| | | function for t = A, |
| | | and nu = B |
+----------+------+---------------------+
|TCRIT | 2 1 | Studentas t distri- |
| | | bution critical |
| | | value for alpha = A |
| | | and nu = B |
+----------+------+---------------------+
|TN | 2 1 | Chebyshev polyno- |
| | | mial Tn(-1<t<+1,n), |
| | | with t = A, and n = |
| | | B |
+----------+------+---------------------+
|TPDF | 2 1 | Studentas t proba- |
| | | bility 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 (maxi- |
| | | mum) 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 func- |
| | | tion for x = A, |
| | | scale = B, and |
| | | shape = C |
+----------+------+---------------------+
|WCRIT | 3 1 | Weibull distribu- |
| | | tion 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 orthonor- |
| | | malized spherical |
| | | harmonics degree A |
| | | order B |
+----------+------+---------------------+
|YLMg | 2 2 | Cos and Sin normal- |
| | | ized spherical har- |
| | | monics degree A |
| | | order B (geophysi- |
| | | cal convention) |
+----------+------+---------------------+
|YN | 2 1 | Bessel function of |
| | | A (2nd kind, order |
| | | B) |
+----------+------+---------------------+
|ZCDF | 1 1 | Normal cumulative |
| | | distribution func- |
| | | tion 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 | 3.1415926a| |
+-------+----------------------------+
|E | 2.7182818a| |
+-------+----------------------------+
|EULER | 0.5772156a| |
+-------+----------------------------+
|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, a|, NX-1 |
+-------+----------------------------+
|YROW | Grid with row numbers 0, |
| | 1, a|, NY-1 |
+-------+----------------------------+
|NODE | Grid with node numbers 0, |
| | 1, a|, (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 geo-
graphic 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 calcula-
tions 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-Short-
ley phase (-1)^M. PLMg is normalized in the way that is most com-
monly 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 com-
plex 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 Con-
don-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 gridas 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 preci-
sion once GMT operates on the grid or writes out new grids. To limit
loss of precision when processing data you should always consider nor-
malizing 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 apackinga of grids, writing out floating point
data as 1- or 2-byte integers. (more a|)
GEOGRAPHICAL AND TIME COORDINATES
When the output grid type is netCDF, the coordinates will be labeled
alongitudea, alatitudea, or atimea 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 cor-
recting 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 data-
base using the Douglas-Peucker line-simplification algorithm. The clas-
sification 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 a|
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 Func-
tions, Applied Mathematics Series, vol. 55, Dover, New York.
Holmes, S. A., and W. E. Featherstone, 2002, A unified approach to the
Clenshaw summation and the recursive computation of very high degree
and order normalised associated Legendre functions. Journal of Geodesy,
76, 279-299.
Press, W. H., S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery,
1992, Numerical Recipes, 2nd edition, Cambridge Univ., New York.
Spanier, J., and K. B. Oldman, 1987, An Atlas of Functions, Hemisphere
Publishing Corp.
SEE ALSO
gmt(1), gmtmath(1), grd2xyz(1), grdedit(1), grdinfo(1), xyz2grd(1)
COPYRIGHT
2017, P. Wessel, W. H. F. Smith, R. Scharroo, J. Luis, and F. Wobbe
5.4.2 Jun 24, 2017 grdmath(1)
gmt5 5.4.2 - Generated Thu Jun 29 07:39:24 CDT 2017