.TH GRDMATH l "1 Jan 2004"
.SH NAME
grdmath \- Reverse Polish Notation calculator for grd files
.SH SYNOPSIS
\fBgrdmath\fP [ \fB\-F\fP ] [ \fB\-I\fP\fIxinc\fP[\fBm|c\fP][/\fIyinc\fP[\fBm|c\fP]] \fB\-R\fP\fIwest/east/south/north\fP \fB\-V\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 grd 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 grd file. When two grd files 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 grdfiles are used in the
expression then options \fB\-R, \-I\fP must be set (and optionally \fB\-F\fP).
.TP
\fIoperand\fP
If \fIoperand\fP can be opened as a file it will be read as a grd file. If not a file, it is interpreted
as a numerical constant or a special symbol (see below).
.TP
\fIoutgrdfile\fP is a 2-D grd file that will hold the final result.
.TP
.B OPERATORS
Choose among the following operators:
.br
Operator n_args Returns
.br
.sp
\fBABS\fP 1 abs (A).
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\fBACOS\fP 1 acos (A).
.br
\fBACOSH\fP 1 acosh (A).
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\fBADD(+)\fP 2 A + B.
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\fBAND\fP 2 NaN if A and B == NaN, B if A == NaN, else A.
.br
\fBASIN\fP 1 asin (A).
.br
\fBASINH\fP 1 asinh (A).
.br
\fBATAN\fP 1 atan (A).
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\fBATAN2\fP 2 atan2 (A, B).
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\fBATANH\fP 1 atanh (A).
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\fBBEI\fP 1 bei (A).
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\fBBER\fP 1 ber (A).
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\fBCDIST\fP 2 Cartesian distance between grid nodes and stack x,y.
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\fBCEIL\fP 1 ceil (A) (smallest integer >= A).
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\fBCHIDIST\fP 2 Chi-squared-distribution P(chi2,nu), with chi2 = A and nu = B.
.br
\fBCOS\fP 1 cos (A) (A in radians).
.br
\fBCOSD\fP 1 cos (A) (A in degrees).
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\fBCOSH\fP 1 cosh (A).
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\fBCURV\fP 1 Curvature of A (Laplacian).
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\fBD2DX2\fP 1 d^2(A)/dx^2 2nd derivative.
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\fBD2DY2\fP 1 d^2(A)/dy^2 2nd derivative.
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\fBD2R\fP 1 Converts Degrees to Radians.
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\fBDDX\fP 1 d(A)/dx 1st derivative.
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\fBDDY\fP 1 d(A)/dy 1st derivative.
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\fBDILOG\fP 1 Dilog (A).
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\fBDIV(/)\fP 2 A / B.
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\fBDUP\fP 1 Places duplicate of A on the stack.
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\fBERF\fP 1 Error function of A.
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\fBERFC\fP 1 Complementory Error function of A.
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\fBERFINV\fP 1 Inverse error function of A.
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\fBEQ\fP 2 1 if A == B, else 0.
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\fBEXCH\fP 2 Exchanges A and B on the stack.
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\fBEXP\fP 1 exp (A).
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\fBEXTREMA\fP 1 Local Extrema: +2/-2 is max/min, +1/-1 is saddle with max/min in x, 0 elsewhere.
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\fBFDIST\fP 4 F-dist Q(var1,var2,nu1,nu2), with var1 = A, var2 = B, nu1 = C, and nu2 = D.
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\fBFLOOR\fP 1 floor (A) (greatest integer <= A).
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\fBFMOD\fP 2 A % B (remainder).
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\fBGDIST\fP 2 Great distance (in degrees) between grid nodes and stack lon,lat.
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\fBGE\fP 2 1 if A >= B, else 0.
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\fBGT\fP 2 1 if A > B, else 0.
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\fBHYPOT\fP 2 hypot (A, B).
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\fBI0\fP 1 Modified Bessel function of A (1st kind, order 0).
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\fBI1\fP 1 Modified Bessel function of A (1st kind, order 1).
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\fBIN\fP 2 Modified Bessel function of A (1st kind, order B).
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\fBINV\fP 1 1 / A.
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\fBISNAN\fP 1 1 if A == NaN, else 0.
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\fBJ0\fP 1 Bessel function of A (1st kind, order 0).
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\fBJ1\fP 1 Bessel function of A (1st kind, order 1).
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\fBJN\fP 2 Bessel function of A (1st kind, order B).
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\fBK0\fP 1 Modified Kelvin function of A (2nd kind, order 0).
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\fBK1\fP 1 Modified Bessel function of A (2nd kind, order 1).
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\fBKN\fP 2 Modified Bessel function of A (2nd kind, order B).
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\fBKEI\fP 1 kei (A).
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\fBKER\fP 1 ker (A).
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\fBLE\fP 2 1 if A <= B, else 0.
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\fBLMSSCL\fP 1 LMS scale estimate (LMS STD) of A.
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\fBLOG\fP 1 log (A) (natural log).
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\fBLOG10\fP 1 log10 (A).
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\fBLOG1P\fP 1 log (1+A) (accurate for small A).
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\fBLOWER\fP 1 The lowest (minimum) value of A.
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\fBLT\fP 2 1 if A < B, else 0.
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\fBMAD\fP 1 Median Absolute Deviation (L1 STD) of A.
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\fBMAX\fP 2 Maximum of A and B.
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\fBMEAN\fP 1 Mean value of A.
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\fBMED\fP 1 Median value of A.
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\fBMIN\fP 2 Minimum of A and B.
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\fBMODE\fP 1 Mode value (LMS) of A.
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\fBMUL(x)\fP 2 A * B.
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\fBNAN\fP 2 NaN if A == B, else A.
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\fBNEG\fP 1 -A.
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\fBNRAND\fP 2 Normal, random values with mean A and std. deviation B.
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\fBOR\fP 2 NaN if A or B == NaN, else A.
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\fBPLM\fP 3 Associated Legendre polynomial P(-1<A<+1) degree B order C.
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\fBPOP\fP 1 Delete top element from the stack.
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\fBPOW(^)\fP 2 A ^ B.
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\fBR2\fP 2 R2 = A^2 + B^2.
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\fBR2D\fP 1 Convert Radians to Degrees.
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\fBRAND\fP 2 Uniform random values between A and B.
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\fBRINT\fP 1 rint (A) (nearest integer).
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\fBSIGN\fP 1 sign (+1 or -1) of A.
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\fBSIN\fP 1 sin (A) (A in radians).
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\fBSIND\fP 1 sin (A) (A in degrees).
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\fBSINH\fP 1 sinh (A).
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\fBSQRT\fP 1 sqrt (A).
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\fBSTD\fP 1 Standard deviation of A.
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\fBSTEP\fP 1 Heaviside step function: H(A).
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\fBSTEPX\fP 1 Heaviside step function in x: H(x-A).
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\fBSTEPY\fP 1 Heaviside step function in y: H(y-A).
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\fBSUB(-)\fP 2 A - B.
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\fBTAN\fP 1 tan (A) (A in radians).
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\fBTAND\fP 1 tan (A) (A in degrees).
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\fBTANH\fP 1 tanh (A).
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\fBTDIST\fP 2 Student's t-distribution A(t,nu) = 1 - 2p, with t = A, and nu = B.'
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\fBUPPER\fP 1 The highest (maximum) value of A.
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\fBXOR\fP 2 B if A == NaN, else A.
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\fBY0\fP 1 Bessel function of A (2nd kind, order 0).
.br
\fBY1\fP 1 Bessel function of A (2nd kind, order 1).
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\fBYLM\fP 2 Re and Im normalized surface harmonics (degree A, order B).
.br
\fBYN\fP 2 Bessel function of A (2nd kind, order B).
.br
.TP
.B SYMBOLS
The following symbols have special meaning:
.br
.sp
\fBPI\fP 3.1415926...
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\fBE \fP 2.7182818...
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\fBX \fP Grid with x-coordinates
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\fBY \fP Grid with y-coordinates
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.SH OPTIONS
.TP
.B \-I
\fIx_inc\fP [and optionally \fIy_inc\fP] is the grid spacing. Append \fBm\fP to indicate minutes or \fBc\fP to indicate seconds.
.TP
.B \-R
\fIwest, east, south,\fP and \fInorth\fP specify the Region of interest. To specify boundaries
in degrees and minutes [and seconds], use the dd:mm[:ss] format. Append \fBr\fP if lower left and upper right
map coordinates are given instead of wesn.
.TP
.B \-F
Select pixel registration (used with \fB\-R, \-I\fP). [Default is grid registration].
.TP
.B \-V
Selects verbose mode, which will send progress reports to stderr [Default runs "silently"].
.SH BEWARE
The operator \fBGDIST\fP calculates spherical distances bewteen 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. The operator
\fBYLM\fP calculates the fully normalized spherical harmonics for degree L and
order M for all positions in the grid, which is assumed to be in degrees.
\fBYLM\fP returns 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. The operator \fBPLM\fP calculates the associated Legendre polynomial
of degree L and order M, and its argument is the cosine of the colatitude
which must satisfy -1 <= x <= +1. Unlike \fBYLM\fP, \fBPLM\fP is not normalized.
.br
All the derivatives are based on central finite differences, with natural
boundary conditions.
.SH EXAMPLES
To take log10 of the average of 2 files, use
.br
        grdmath 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
        grdmath 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), try
.br
        grdmath 2 s_xy.grd \fBMUL\fP s_xx.grd s_yy.grd \fBSUB DIV ATAN2\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, try
.br
        grdmath \fB\-R\fP0/360/-90/90 \fB\-I\fP1 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, try
.br
        grdmath faa.grd \fBDUP EXTREMA\fP 2 \fBEQ MUL DUP\fP 100 \fBGT NAN MUL\fP = z.grd
.br
        grd2xyz z.grd \fB\-S\fP > max.xyz
.SH BUGS
Files that has the same name as some operators, e.g., ADD, SIGN, =, etc. cannot be read
and must not be present in the current directory. Piping of files are not allowed.
The stack limit is hard-wired to 50.
All functions expecting a positive radius (e.g., log, kei, etc.) are passed the
absolute value of their argument.
.SH REFERENCES
Abramowitz, M., and I. A. Stegun, 1964, \fIHandbook of Mathematical
Functions\fP, Applied Mathematics Series, vol. 55, Dover, New York.
.br
Press, W. H., S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, 1992,
\fINumerical Recipes\fP, 2nd edition, Cambridge Univ., New York.
.SH "SEE ALSO"
.IR gmt (1gmt),
.IR gmtmath (1gmt),
.IR grd2xyz (1gmt),
.IR grdedit (1gmt),
.IR grdinfo (1gmt),
.IR xyz2grd (1gmt)