.TH GRDMATH 1gmt "Feb 27 2014" "GMT 4.5.13 (SVN)" "Generic Mapping Tools"
.SH NAME
grdmath \- Reverse Polish Notation calculator for grid files
.SH SYNOPSIS
\fBgrdmath\fP [ \fB\-F\fP ] [ \fB\-I\fP\fIxinc\fP[\fIunit\fP][\fB=\fP|\fB+\fP][/\fIyinc\fP[\fIunit\fP][\fB=\fP|\fB+\fP]] ] [ \fB\-M\fP ] [ \fB\-N\fP ] [ \fB\-R\fP\fIwest\fP/\fIeast\fP/\fIsouth\fP/\fInorth\fP[\fBr\fP] ] [ \fB\-V\fP ] [ \fB\-bi\fP[\fBs\fP|\fBS\fP|\fBd\fP|\fBD\fP[\fIncol\fP]|\fBc\fP[\fIvar1\fP\fB/\fP\fI...\fP]] ] [ \fB\-f\fP\fIcolinfo\fP ] 
\fIoperand\fP [ \fIoperand\fP ] \fBOPERATOR\fP [ \fIoperand\fP ] \fBOPERATOR\fP ... \fB=\fP \fIoutgrdfile\fP
.SH DESCRIPTION
\fBgrdmath\fP 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.
When two grids are on the stack, each element in file A is modified by the corresponding element in file B.
However, some operators only require one operand (see below).  If no grid files are used in the
expression then options \fB\-R\fP, \fB\-I\fP must be set (and optionally \fB\-F\fP).  The expression
\fB=\fP \fIoutgrdfile\fP can occur as many times as the depth of the stack allows.
.TP
\fIoperand\fP
If \fIoperand\fP 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).
.TP
\fIoutgrdfile\fP
The name of a 2-D grid file that will hold the final result.
(See GRID FILE FORMATS below).
.TP
.B OPERATORS
Choose among the following 147 operators. "args" are the number of input and output arguments.
.br
.sp
Operator	args	Returns
.br
.sp
\fBABS      \fP	1 1	abs (A).
.br
\fBACOS     \fP	1 1	acos (A).
.br
\fBACOSH    \fP	1 1	acosh (A).
.br
\fBACOT     \fP	1 1	acot (A).
.br
\fBACSC     \fP	1 1	acsc (A).
.br
\fBADD      \fP	2 1	A + B.
.br
\fBAND      \fP	2 1	NaN if A and B == NaN, B if A == NaN, else A.
.br
\fBASEC     \fP	1 1	asec (A).
.br
\fBASIN     \fP	1 1	asin (A).
.br
\fBASINH    \fP	1 1	asinh (A).
.br
\fBATAN     \fP	1 1	atan (A).
.br
\fBATAN2    \fP	2 1	atan2 (A, B).
.br
\fBATANH    \fP	1 1	atanh (A).
.br
\fBBEI      \fP	1 1	bei (A).
.br
\fBBER      \fP	1 1	ber (A).
.br
\fBCAZ      \fP	2 1	Cartesian azimuth from grid nodes to stack x,y.
.br
\fBCBAZ     \fP	2 1	Cartesian backazimuth from grid nodes to stack x,y.
.br
\fBCDIST    \fP	2 1	Cartesian distance between grid nodes and stack x,y.
.br
\fBCEIL     \fP	1 1	ceil (A) (smallest integer >= A).
.br
\fBCHICRIT  \fP	2 1	Critical value for chi-squared-distribution, with alpha = A and n = B.
.br
\fBCHIDIST  \fP	2 1	chi-squared-distribution P(chi2,n), with chi2 = A and n = B.
.br
\fBCORRCOEFF\fP	2 1	Correlation coefficient r(A, B).
.br
\fBCOS      \fP	1 1	cos (A) (A in radians).
.br
\fBCOSD     \fP	1 1	cos (A) (A in degrees).
.br
\fBCOSH     \fP	1 1	cosh (A).
.br
\fBCOT      \fP	1 1	cot (A) (A in radians).
.br
\fBCOTD     \fP	1 1	cot (A) (A in degrees).
.br
\fBCPOISS   \fP	2 1	Cumulative Poisson distribution F(x,lambda), with x = A and lambda = B.
.br
\fBCSC      \fP	1 1	csc (A) (A in radians).
.br
\fBCSCD     \fP	1 1	csc (A) (A in degrees).
.br
\fBCURV     \fP	1 1	Curvature of A (Laplacian).
.br
\fBD2DX2    \fP	1 1	d^2(A)/dx^2 2nd derivative.
.br
\fBD2DXY    \fP	1 1	d^2(A)/dxdy 2nd derivative.
.br
\fBD2DY2    \fP	1 1	d^2(A)/dy^2 2nd derivative.
.br
\fBD2R      \fP	1 1	Converts Degrees to Radians.
.br
\fBDDX      \fP	1 1	d(A)/dx Central 1st derivative.
.br
\fBDDY      \fP	1 1	d(A)/dy Central 1st derivative.
.br
\fBDEG2KM   \fP	1 1	Converts Spherical Degrees to Kilometers.
.br
\fBDILOG    \fP	1 1	dilog (A).
.br
\fBDIV      \fP	2 1	A / B.
.br
\fBDUP      \fP	1 2	Places duplicate of A on the stack.
.br
\fBEQ       \fP	2 1	1 if A == B, else 0.
.br
\fBERF      \fP	1 1	Error function erf (A).
.br
\fBERFC     \fP	1 1	Complementary Error function erfc (A).
.br
\fBERFINV   \fP	1 1	Inverse error function of A.
.br
\fBEXCH     \fP	2 2	Exchanges A and B on the stack.
.br
\fBEXP      \fP	1 1	exp (A).
.br
\fBEXTREMA  \fP	1 1	Local Extrema: +2/-2 is max/min, +1/-1 is saddle with max/min in x, 0 elsewhere.
.br
\fBFACT     \fP	1 1	A! (A factorial).
.br
\fBFCRIT    \fP	3 1	Critical value for F-distribution, with alpha = A, n1 = B, and n2 = C.
.br
\fBFDIST    \fP	3 1	F-distribution Q(F,n1,n2), with F = A, n1 = B, and n2 = C.
.br
\fBFLIPLR   \fP	1 1	Reverse order of values in each row.
.br
\fBFLIPUD   \fP	1 1	Reverse order of values in each column.
.br
\fBFLOOR    \fP	1 1	floor (A) (greatest integer <= A).
.br
\fBFMOD     \fP	2 1	A % B (remainder after truncated division).
.br
\fBGE       \fP	2 1	1 if A >= B, else 0.
.br
\fBGT       \fP	2 1	1 if A > B, else 0.
.br
\fBHYPOT    \fP	2 1	hypot (A, B) = sqrt (A*A + B*B).
.br
\fBI0       \fP	1 1	Modified Bessel function of A (1st kind, order 0).
.br
\fBI1       \fP	1 1	Modified Bessel function of A (1st kind, order 1).
.br
\fBIN       \fP	2 1	Modified Bessel function of A (1st kind, order B).
.br
\fBINRANGE  \fP	3 1	1 if B <= A <= C, else 0.
.br
\fBINSIDE   \fP	1 1	1 when inside or on polygon(s) in A, else 0.
.br
\fBINV      \fP	1 1	1 / A.
.br
\fBISNAN    \fP	1 1	1 if A == NaN, else 0.
.br
\fBJ0       \fP	1 1	Bessel function of A (1st kind, order 0).
.br
\fBJ1       \fP	1 1	Bessel function of A (1st kind, order 1).
.br
\fBJN       \fP	2 1	Bessel function of A (1st kind, order B).
.br
\fBK0       \fP	1 1	Modified Kelvin function of A (2nd kind, order 0).
.br
\fBK1       \fP	1 1	Modified Bessel function of A (2nd kind, order 1).
.br
\fBKEI      \fP	1 1	kei (A).
.br
\fBKER      \fP	1 1	ker (A).
.br
\fBKM2DEG   \fP	1 1	Converts Kilometers to Spherical Degrees.
.br
\fBKN       \fP	2 1	Modified Bessel function of A (2nd kind, order B).
.br
\fBKURT     \fP	1 1	Kurtosis of A.
.br
\fBLDIST    \fP	1 1	Compute distance from lines in multi-segment ASCII file A.
.br
\fBLE       \fP	2 1	1 if A <= B, else 0.
.br
\fBLMSSCL   \fP	1 1	LMS scale estimate (LMS STD) of A.
.br
\fBLOG      \fP	1 1	log (A) (natural log).
.br
\fBLOG10    \fP	1 1	log10 (A) (base 10).
.br
\fBLOG1P    \fP	1 1	log (1+A) (accurate for small A).
.br
\fBLOG2     \fP	1 1	log2 (A) (base 2).
.br
\fBLOWER    \fP	1 1	The lowest (minimum) value of A.
.br
\fBLRAND    \fP	2 1	Laplace random noise with mean A and std. deviation B.
.br
\fBLT       \fP	2 1	1 if A < B, else 0.
.br
\fBMAD      \fP	1 1	Median Absolute Deviation (L1 STD) of A.
.br
\fBMAX      \fP	2 1	Maximum of A and B.
.br
\fBMEAN     \fP	1 1	Mean value of A.
.br
\fBMED      \fP	1 1	Median value of A.
.br
\fBMIN      \fP	2 1	Minimum of A and B.
.br
\fBMOD      \fP	2 1	A mod B (remainder after floored division).
.br
\fBMODE     \fP	1 1	Mode value (Least Median of Squares) of A.
.br
\fBMUL      \fP	2 1	A * B.
.br
\fBNAN      \fP	2 1	NaN if A == B, else A.
.br
\fBNEG      \fP	1 1	-A.
.br
\fBNEQ      \fP	2 1	1 if A != B, else 0.
.br
\fBNOT      \fP	1 1	NaN if A == NaN, 1 if A == 0, else 0.
.br
\fBNRAND    \fP	2 1	Normal, random values with mean A and std. deviation B.
.br
\fBOR       \fP	2 1	NaN if A or B == NaN, else A.
.br
\fBPDIST    \fP	1 1	Compute distance from points in ASCII file A.
.br
\fBPLM      \fP	3 1	Associated Legendre polynomial P(A) degree B order C.
.br
\fBPLMg     \fP	3 1	Normalized associated Legendre polynomial P(A) degree B order C (geophysical convention).
.br
\fBPOP      \fP	1 0	Delete top element from the stack.
.br
\fBPOW      \fP	2 1	A ^ B.
.br
\fBPQUANT   \fP	2 1	The B'th Quantile (0-100%) of A.\"'
.br
\fBPSI      \fP	1 1	Psi (or Digamma) of A.
.br
\fBPV       \fP	3 1	Legendre function Pv(A) of degree v = real(B) + imag(C).
.br
\fBQV       \fP	3 1	Legendre function Qv(A) of degree v = real(B) + imag(C).
.br
\fBR2       \fP	2 1	R2 = A^2 + B^2.
.br
\fBR2D      \fP	1 1	Convert Radians to Degrees.
.br
\fBRAND     \fP	2 1	Uniform random values between A and B.
.br
\fBRINT     \fP	1 1	rint (A) (nearest integer).
.br
\fBROTX     \fP	2 1	Rotate A by the (constant) shift B in x-direction.
.br
\fBROTY     \fP	2 1	Rotate A by the (constant) shift B in y-direction.
.br
\fBSAZ      \fP	2 1	Spherical azimuth from grid nodes to stack x,y.
.br
\fBSBAZ     \fP	2 1	Spherical backazimuth from grid nodes to stack x,y.
.br
\fBSDIST    \fP	2 1	Spherical (Great circle|geodesic) distance (in km) between grid nodes and stack lon,lat (A, B).
.br
\fBSEC      \fP	1 1	sec (A) (A in radians).
.br
\fBSECD     \fP	1 1	sec (A) (A in degrees).
.br
\fBSIGN     \fP	1 1	sign (+1 or -1) of A.
.br
\fBSIN      \fP	1 1	sin (A) (A in radians).
.br
\fBSINC     \fP	1 1	sinc (A) (sin (pi*A)/(pi*A)).
.br
\fBSIND     \fP	1 1	sin (A) (A in degrees).
.br
\fBSINH     \fP	1 1	sinh (A).
.br
\fBSKEW     \fP	1 1	Skewness of A.
.br
\fBSQR      \fP	1 1	A^2.
.br
\fBSQRT     \fP	1 1	sqrt (A).
.br
\fBSTD      \fP	1 1	Standard deviation of A.
.br
\fBSTEP     \fP	1 1	Heaviside step function: H(A).
.br
\fBSTEPX    \fP	1 1	Heaviside step function in x: H(x-A).
.br
\fBSTEPY    \fP	1 1	Heaviside step function in y: H(y-A).
.br
\fBSUB      \fP	2 1	A - B.
.br
\fBTAN      \fP	1 1	tan (A) (A in radians).
.br
\fBTAND     \fP	1 1	tan (A) (A in degrees).
.br
\fBTANH     \fP	1 1	tanh (A).
.br
\fBTCRIT    \fP	2 1	Critical value for Student's t-distribution, with alpha = A and n = B.\"'
.br
\fBTDIST    \fP	2 1	Student's t-distribution A(t,n), with t = A, and n = B.\"'
.br
\fBTN       \fP	2 1	Chebyshev polynomial Tn(-1<t<+1,n), with t = A, and n = B.
.br
\fBUPPER    \fP	1 1	The highest (maximum) value of A.
.br
\fBXOR      \fP	2 1	0 if A == NaN and B == NaN, NaN if B == NaN, else A.
.br
\fBY0       \fP	1 1	Bessel function of A (2nd kind, order 0).
.br
\fBY1       \fP	1 1	Bessel function of A (2nd kind, order 1).
.br
\fBYLM      \fP	2 2	Re and Im orthonormalized spherical harmonics degree A order B.
.br
\fBYLMg     \fP	2 2	Cos and Sin normalized spherical harmonics degree A order B (geophysical convention).
.br
\fBYN       \fP	2 1	Bessel function of A (2nd kind, order B).
.br
\fBZCRIT    \fP	1 1	Critical value for the normal-distribution, with alpha = A.
.br
\fBZDIST    \fP	1 1	Cumulative normal-distribution C(x), with x = A.
.br
.TP
.B SYMBOLS
The following symbols have special meaning:
.br
.sp
\fBPI\fP	3.1415926...
.br
\fBE \fP	2.7182818...
.br
\fBEULER \fP	0.5772156...
.br
\fBXMIN \fP	Minimum x value
.br
\fBXMAX \fP	Maximum x value
.br
\fBXINC \fP	x increment
.br
\fBNX \fP	The number of x nodes
.br
\fBYMIN \fP	Minimum y value
.br
\fBYMAX \fP	Maximum y value
.br
\fBYINC \fP	y increment
.br
\fBNY \fP	The number of y nodes
.br
\fBX \fP	Grid with x-coordinates
.br
\fBY \fP	Grid with y-coordinates
.br
\fBXn \fP	Grid with normalized [-1 to +1] x-coordinates
.br
\fBYn \fP	Grid with normalized [-1 to +1] y-coordinates
.SH OPTIONS
.TP
\fB\-F\fP
Force pixel node registration [Default is gridline registration].
(Node registrations are defined in \fBGMT\fP Cookbook Appendix B on grid file formats.)
Only used with \fB\-R\fP \fB\-I\fP.
.TP
\fB\-I\fP
\fIx_inc\fP [and optionally \fIy_inc\fP] is the grid spacing. Optionally, append a suffix
modifier.  \fBGeographical (degrees) coordinates\fP: Append \fBm\fP to
indicate arc minutes or \fBc\fP to indicate arc seconds.  If one of the units \fBe\fP, \fBk\fP, \fBi\fP,
or \fBn\fP is appended instead, the increment is assumed to be given in meter, km, miles, or
nautical miles, respectively, and will be converted to the equivalent degrees longitude at
the middle latitude of the region (the conversion depends on \fBELLIPSOID\fP).  If /\fIy_inc\fP is given but set to 0 it will be reset equal to
\fIx_inc\fP; otherwise it will be converted to degrees latitude.  
\fBAll coordinates\fP: If \fB=\fP is appended then
the corresponding max \fIx\fP (\fIeast\fP) or \fIy\fP (\fInorth\fP) 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 \fInumber of nodes\fP desired by appending \fB+\fP to
the supplied integer argument; the increment is then recalculated from the number of nodes and the domain.
The resulting increment value depends on whether you have selected a gridline-registered
or pixel-registered grid; see Appendix B for details.  Note: if \fB\-R\fP\fIgrdfile\fP is used then
grid spacing has already been initialized; use \fB\-I\fP to override the values.
.TP
\fB\-M\fP
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.
.TP
\fB\-N\fP
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].
.TP
\fB\-R\fP
\fIxmin\fP, \fIxmax\fP, \fIymin\fP, and \fIymax\fP specify the Region of interest.  For geographic
regions, these limits correspond to \fIwest, east, south,\fP and \fInorth\fP and you may specify them
in decimal degrees or in [+-]dd:mm[:ss.xxx][W|E|S|N] format.  Append \fBr\fP if lower left and upper right
map coordinates are given instead of w/e/s/n.  The two shorthands \fB\-Rg\fP and \fB\-Rd\fP stand for global domain
(0/360 and -180/+180 in longitude respectively, with -90/+90 in latitude).  Alternatively, specify the name
of an existing grid file and the \fB\-R\fP settings (and grid spacing, if applicable) are copied from the grid.
For calendar time coordinates you may either give (a) relative
time (relative to the selected \fBTIME_EPOCH\fP and in the selected \fBTIME_UNIT\fP; append \fBt\fP to
\fB\-JX\fP|\fBx\fP), or (b) absolute time of the form [\fIdate\fP]\fBT\fP[\fIclock\fP]
(append \fBT\fP to \fB\-JX\fP|\fBx\fP).  At least one of \fIdate\fP and \fIclock\fP
must be present; the \fBT\fP is always required.  The \fIdate\fP string must be of the form [-]yyyy[-mm[-dd]]
(Gregorian calendar) or yyyy[-Www[-d]] (ISO week calendar), while the \fIclock\fP string must be of
the form hh:mm:ss[.xxx].  The use of delimiters and their type and positions must be exactly as indicated
(however, input, output and plot formats are customizable; see \fBgmtdefaults\fP). 
.TP
\fB\-V\fP
Selects verbose mode, which will send progress reports to stderr [Default runs "silently"].
.TP
\fB\-bi\fP
Selects binary input.
Append \fBs\fP for single precision [Default is \fBd\fP (double)].
Uppercase \fBS\fP or \fBD\fP will force byte-swapping.
Optionally, append \fIncol\fP, the number of columns in your binary input file
if it exceeds the columns needed by the program.
Or append \fBc\fP if the input file is netCDF. Optionally, append \fIvar1\fP\fB/\fP\fIvar2\fP\fB/\fP\fI...\fP to
specify the variables to be read.
The binary input option only applies to the data files needed by operators \fBLDIST\fP, \fPPDIST\fP,
and \fBINSIDE\fP.
.TP
\fB\-f\fP
Special formatting of input and/or output columns (time or geographical data).
Specify \fBi\fP or \fBo\fP to make this apply only to input or output [Default applies to both].
Give one or more columns (or column ranges) separated by commas.
Append \fBT\fP (absolute calendar time), \fBt\fP (relative time in chosen \fBTIME_UNIT\fP since \fBTIME_EPOCH\fP),
\fBx\fP (longitude), \fBy\fP (latitude), or \fBf\fP (floating point) to each column
or column range item.  Shorthand \fB\-f\fP[\fBi\fP|\fBo\fP]\fBg\fP means \fB\-f\fP[\fBi\fP|\fBo\fP]0\fBx\fP,1\fBy\fP
(geographic coordinates).
.SH NOTES ON OPERATORS
(1) The operator \fBSDIST\fP 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 \fBSAZ\fP and \fBSBAZ\fP
operators calculate spherical azimuth and back-azimuths in degrees, respectively.
A few operators (\fBPDIST\fP, \fBLDIST\fP, and \fBINSIDE\fP) expects their argument to be
a single file with points, lines, or polygons, respectively. These distances will be in km (for
geographical data, i.e, \fB\-fg\fP and Cartesian otherwise. Be aware that \fBLDIST\fP in particular
can be slow for large grids and numerous line segments.
Note: If the current \fBELLIPSOID\fP is not spherical then geodesics are used in the calculations.
.br
.sp
(2) The operator \fBPLM\fP calculates the associated Legendre polynomial
of degree L and order M (0 <= M <= L), and its argument is the sine of the latitude.
\fBPLM\fP is not normalized and includes the Condon-Shortley phase (-1)^M.
\fBPLMg\fP is normalized in the way that is most commonly used in geophysics.
The C-S phase can be added by using -M as argument.
\fBPLM\fP will overflow at higher degrees, whereas \fBPLMg\fP is stable until ultra high degrees (at
least 3000).
.br
.sp
(3) The operators \fBYLM\fP and \fBYLMg\fP 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.
\fBYLM\fP and \fBYLMg\fP return two grids, the real (cosine) and imaginary (sine) component
of the complex spherical harmonic.  Use the \fBPOP\fP operator (and \fBEXCH\fP) to
get rid of one of them, or save both by giving two consecutive = file.grd calls.
.br
The orthonormalized complex harmonics \fBYLM\fP are most commonly used in physics and seismology.
The square of \fBYLM\fP integrates to 1 over a sphere.
In geophysics, \fBYLMg\fP 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 \fBYLM\fP or \fBYLMg\fP, but it can be added by using -M
as argument.
.br
.sp
(4) All the derivatives are based on central finite differences, with natural boundary conditions.
.br
.sp
(5) Files that have the same names as some operators, e.g., \fBADD\fP, \fBSIGN\fP, \fB=\fP, etc. should be
identified by prepending the current directory (i.e., ./LOG).
.br
.sp
(6) Piping of files is not allowed.
.br
.sp
(7) The stack depth limit is hard-wired to 100.
.br
.sp
(8) All functions expecting a positive radius (e.g., \fBLOG\fP, \fBKEI\fP, etc.) are passed the
absolute value of their argument.
.SH 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.
.SH GRID FILE FORMATS
By default \fBGMT\fP writes out grid as single precision floats in a COARDS-complaint netCDF file format.
However, \fBGMT\fP 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 2- or 4-byte integers. To specify the precision, scale and offset, the user should add the suffix
\fB=\fP\fIid\fP[\fB/\fP\fIscale\fP\fB/\fP\fIoffset\fP[\fB/\fP\fInan\fP]], where \fIid\fP is a two-letter identifier of the grid type and precision, and \fIscale\fP and \fIoffset\fP are optional scale factor
and offset to be applied to all grid values, and \fInan\fP is the value used to indicate missing data.
When reading grids, the format is generally automatically recognized. If not, the same suffix can be added to input grid file names.
See \fBgrdreformat\fP(1) and Section 4.17 of the GMT Technical Reference and Cookbook for more information.
.P
When reading a netCDF file that contains multiple grids, \fBGMT\fP will read, by default, the first 2-dimensional grid that can find in that
file. To coax \fBGMT\fP into reading another multi-dimensional variable in the grid file, append \fB?\fP\fIvarname\fP to the file name, where
\fIvarname\fP is the name of the variable. Note that you may need to escape the special meaning of \fB?\fP in your shell program
by putting a backslash in front of it, or by placing the filename and suffix between quotes or double quotes.
The \fB?\fP\fIvarname\fP suffix can also be used for output grids to specify a variable name different from the default: "z".
See \fBgrdreformat\fP(1) and Section 4.18 of the GMT Technical Reference and Cookbook for more information,
particularly on how to read splices of 3-, 4-, or 5-dimensional grids.
.SH 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
\fB\-f\fP or \fB\-R\fP options. For example, both \fB\-f0x\fP \fB\-f1t\fP and \fB\-R\fP 90w/90e/0t/3t will result in a longitude/time
grid. When the x, y, or z coordinate is time, it will be stored in the grid as relative time since epoch as 
specified by \fBTIME_UNIT\fP and \fBTIME_EPOCH\fP in the \.gmtdefaults file or on the command line.
In addition, the \fBunit\fP attribute of the time variable will indicate both this unit and epoch.
.SH EXAMPLES
To take log10 of the average of 2 files, use
.br
.sp
\fBgrdmath\fP file1.grd file2.grd \fBADD\fP 0.5 \fBMUL LOG10 =\fP file3.grd
.br
.sp
Given the file ages.grd, which holds seafloor ages in m.y., use the relation
depth(in m) = 2500 + 350 * sqrt (age) to estimate normal seafloor depths:
.br
.sp
\fBgrdmath\fP ages.grd \fBSQRT\fP 350 \fBMUL \fP2500 \fBADD =\fP depths.grd
.br
.sp
To find the angle a (in degrees) of the largest principal stress from the stress tensor given by the
three files s_xx.grd s_yy.grd, and s_xy.grd from the relation tan (2*a) = 2 * s_xy / (s_xx - s_yy), use
.br
.sp
\fBgrdmath\fP 2 s_xy.grd \fBMUL\fP s_xx.grd s_yy.grd \fBSUB DIV ATAN\fP 2 \fBDIV =\fP direction.grd
.br
.sp
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:
.br
.sp
\fBgrdmath\fP \fB\-R\fP 0/360/-90/90 \fB\-I\fP 1 8 4 \fBYML\fP 1.1 \fBMUL EXCH\fP 0.4 \fBMUL ADD\fP = harm.grd
.br
.sp
To extract the locations of local maxima that exceed 100 mGal in the file faa.grd:
.br
.sp
\fBgrdmath\fP faa.grd \fBDUP EXTREMA\fP 2 \fBEQ MUL DUP\fP 100 \fBGT MUL\fP 0 \fBNAN\fP = z.grd
.br
\fBgrd2xyz\fP z.grd \fB\-S\fP > max.xyz
.SH REFERENCES
Abramowitz, M., and I. A. Stegun, 1964, \fIHandbook of Mathematical
Functions\fP, Applied Mathematics Series, vol. 55, Dover, New York.
.br
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.
\fIJournal of Geodesy\fP, 76, 279-299.
.br
Press, W. H.,  S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, 1992, 
\fINumerical Recipes\fP, 2nd edition, Cambridge Univ., New York.
.br
Spanier, J., and K. B. Oldman, 1987,
\fIAn Atlas of Functions\fP, Hemisphere Publishing Corp.
.SH "SEE ALSO"
.IR GMT (1),
.IR gmtmath (1),
.IR grd2xyz (1),
.IR grdedit (1),
.IR grdinfo (1),
.IR xyz2grd (1)