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<title>GRDMATH</title>
</head>
<body bgcolor="#ffffff">
<h1 align=center>GRDMATH</h1>
<a href="#NAME">NAME</a><br>
<a href="#SYNOPSIS">SYNOPSIS</a><br>
<a href="#DESCRIPTION">DESCRIPTION</a><br>
<a href="#OPTIONS">OPTIONS</a><br>
<a href="#NOTES ON OPERATORS">NOTES ON OPERATORS</a><br>
<a href="#GRID VALUES PRECISION">GRID VALUES PRECISION</a><br>
<a href="#GRID FILE FORMATS">GRID FILE FORMATS</a><br>
<a href="#GEOGRAPHICAL AND TIME COORDINATES">GEOGRAPHICAL AND TIME COORDINATES</a><br>
<a href="#EXAMPLES">EXAMPLES</a><br>
<a href="#REFERENCES">REFERENCES</a><br>
<a href="#SEE ALSO">SEE ALSO</a><br>
<hr>
<a name="NAME"></a>
<h2>NAME</h2>
<p style="margin-left:11%; margin-top: 1em">grdmath −
Reverse Polish Notation calculator for grid files</p>
<a name="SYNOPSIS"></a>
<h2>SYNOPSIS</h2>
<p style="margin-left:11%; margin-top: 1em"><b>grdmath</b>
[ <b>−F</b> ] [
<b>−I</b><i>xinc</i>[<i>unit</i>][<b>=</b>|<b>+</b>][/<i>yinc</i>[<i>unit</i>][<b>=</b>|<b>+</b>]]
] [ <b>−M</b> ] [ <b>−N</b> ] [
<b>−R</b><i>west</i>/<i>east</i>/<i>south</i>/<i>north</i>[<b>r</b>]
] [ <b>−V</b> ] [
<b>−bi</b>[<b>s</b>|<b>S</b>|<b>d</b>|<b>D</b>[<i>ncol</i>]|<b>c</b>[<i>var1</i><b>/</b><i>...</i>]]
] [ <b>−f</b><i>colinfo</i> ] <i>operand</i> [
<i>operand</i> ] <b>OPERATOR</b> [ <i>operand</i> ]
<b>OPERATOR</b> ... <b>=</b> <i>outgrdfile</i></p>
<a name="DESCRIPTION"></a>
<h2>DESCRIPTION</h2>
<p style="margin-left:11%; margin-top: 1em"><b>grdmath</b>
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 <b>−R</b>, <b>−I</b> must be set
(and optionally <b>−F</b>). The expression <b>=</b>
<i>outgrdfile</i> can occur as many times as the depth of
the stack allows. <i><br>
operand</i></p>
<p style="margin-left:22%;">If <i>operand</i> 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).</p>
<p style="margin-left:11%;"><i>outgrdfile</i></p>
<p style="margin-left:22%;">The name of a 2-D grid file
that will hold the final result. (See GRID FILE FORMATS
below).</p>
<p style="margin-left:11%;"><b>OPERATORS</b></p>
<p style="margin-left:22%;">Choose among the following 145
operators. "args" are the number of input and
output arguments.</p>
<table width="100%" border=0 rules="none" frame="void"
cellspacing="0" cellpadding="0">
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top">Operator</p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">args</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">Returns</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>ABS</b></p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">1 1</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">abs (A).</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>ACOS</b></p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">1 1</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">acos (A).</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>ACOSH</b></p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">1 1</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">acosh (A).</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>ACOT</b></p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">1 1</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">acot (A).</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>ACSC</b></p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">1 1</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">acsc (A).</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>ADD</b></p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">2 1</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">A + B.</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>AND</b></p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">2 1</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">NaN if A and B == NaN, B if A == NaN, else
A.</p> </td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>ASEC</b></p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">1 1</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">asec (A).</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>ASIN</b></p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">1 1</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">asin (A).</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>ASINH</b></p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">1 1</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">asinh (A).</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>ATAN</b></p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">1 1</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">atan (A).</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>ATAN2</b></p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">2 1</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">atan2 (A, B).</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>ATANH</b></p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">1 1</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">atanh (A).</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>BEI</b></p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">1 1</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">bei (A).</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>BER</b></p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">1 1</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">ber (A).</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>CAZ</b></p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">2 1</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">Cartesian azimuth from grid nodes to stack
x,y.</p> </td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>CBAZ</b></p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">2 1</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">Cartesian backazimuth from grid nodes to
stack x,y.</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>CDIST</b></p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">2 1</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">Cartesian distance between grid nodes and
stack x,y.</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>CEIL</b></p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">1 1</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">ceil (A) (smallest integer >= A).</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>CHICRIT</b></p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">2 1</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">Critical value for
chi-squared-distribution, with alpha = A and n = B.</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>CHIDIST</b></p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">2 1</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">chi-squared-distribution P(chi2,n), with
chi2 = A and n = B.</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>CORRCOEFF</b></p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">2 1</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">Correlation coefficient r(A, B).</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>COS</b></p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">1 1</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">cos (A) (A in radians).</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>COSD</b></p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">1 1</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">cos (A) (A in degrees).</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>COSH</b></p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">1 1</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">cosh (A).</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>COT</b></p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">1 1</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">cot (A) (A in radians).</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>COTD</b></p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">1 1</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">cot (A) (A in degrees).</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>CPOISS</b></p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">2 1</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">Cumulative Poisson distribution
F(x,lambda), with x = A and lambda = B.</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>CSC</b></p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">1 1</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">csc (A) (A in radians).</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>CSCD</b></p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">1 1</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">csc (A) (A in degrees).</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>CURV</b></p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">1 1</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">Curvature of A (Laplacian).</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>D2DX2</b></p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">1 1</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">d^2(A)/dx^2 2nd derivative.</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>D2DXY</b></p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">1 1</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">d^2(A)/dxdy 2nd derivative.</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>D2DY2</b></p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">1 1</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">d^2(A)/dy^2 2nd derivative.</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>D2R</b></p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">1 1</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">Converts Degrees to Radians.</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>DDX</b></p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">1 1</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">d(A)/dx Central 1st derivative.</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>DDY</b></p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">1 1</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">d(A)/dy Central 1st derivative.</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>DILOG</b></p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">1 1</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">dilog (A).</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>DIV</b></p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">2 1</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">A / B.</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>DUP</b></p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">1 2</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">Places duplicate of A on the stack.</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>EQ</b></p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">2 1</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">1 if A == B, else 0.</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>ERF</b></p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">1 1</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">Error function erf (A).</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>ERFC</b></p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">1 1</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">Complementary Error function erfc (A).</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>ERFINV</b></p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">1 1</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">Inverse error function of A.</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>EXCH</b></p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">2 2</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">Exchanges A and B on the stack.</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>EXP</b></p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">1 1</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">exp (A).</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>EXTREMA</b></p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">1 1</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">Local Extrema: +2/-2 is max/min, +1/-1 is
saddle with max/min in x, 0 elsewhere.</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>FACT</b></p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">1 1</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">A! (A factorial).</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>FCRIT</b></p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">3 1</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">Critical value for F-distribution, with
alpha = A, n1 = B, and n2 = C.</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>FDIST</b></p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">3 1</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">F-distribution Q(F,n1,n2), with F = A, n1 =
B, and n2 = C.</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>FLIPLR</b></p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">1 1</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">Reverse order of values in each row.</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>FLIPUD</b></p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">1 1</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">Reverse order of values in each column.</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>FLOOR</b></p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">1 1</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">floor (A) (greatest integer <= A).</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>FMOD</b></p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">2 1</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">A % B (remainder after truncated
division).</p> </td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>GE</b></p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">2 1</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">1 if A >= B, else 0.</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>GT</b></p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">2 1</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">1 if A > B, else 0.</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>HYPOT</b></p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">2 1</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">hypot (A, B) = sqrt (A*A + B*B).</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>I0</b></p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">1 1</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">Modified Bessel function of A (1st kind,
order 0).</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>I1</b></p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">1 1</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">Modified Bessel function of A (1st kind,
order 1).</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>IN</b></p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">2 1</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">Modified Bessel function of A (1st kind,
order B).</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>INRANGE</b></p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">3 1</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">1 if B <= A <= C, else 0.</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>INSIDE</b></p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">1 1</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">1 when inside or on polygon(s) in A, else
0.</p> </td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>INV</b></p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">1 1</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">1 / A.</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>ISNAN</b></p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">1 1</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">1 if A == NaN, else 0.</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>J0</b></p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">1 1</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">Bessel function of A (1st kind, order
0).</p> </td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>J1</b></p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">1 1</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">Bessel function of A (1st kind, order
1).</p> </td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>JN</b></p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">2 1</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">Bessel function of A (1st kind, order
B).</p> </td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>K0</b></p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">1 1</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">Modified Kelvin function of A (2nd kind,
order 0).</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>K1</b></p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">1 1</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">Modified Bessel function of A (2nd kind,
order 1).</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>KEI</b></p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">1 1</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">kei (A).</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>KER</b></p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">1 1</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">ker (A).</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>KN</b></p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">2 1</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">Modified Bessel function of A (2nd kind,
order B).</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>KURT</b></p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">1 1</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">Kurtosis of A.</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>LDIST</b></p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">1 1</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">Compute distance from lines in
multi-segment ASCII file A.</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>LE</b></p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">2 1</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">1 if A <= B, else 0.</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>LMSSCL</b></p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">1 1</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">LMS scale estimate (LMS STD) of A.</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>LOG</b></p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">1 1</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">log (A) (natural log).</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>LOG10</b></p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">1 1</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">log10 (A) (base 10).</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>LOG1P</b></p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">1 1</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">log (1+A) (accurate for small A).</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>LOG2</b></p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">1 1</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">log2 (A) (base 2).</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>LOWER</b></p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">1 1</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">The lowest (minimum) value of A.</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>LRAND</b></p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">2 1</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">Laplace random noise with mean A and std.
deviation B.</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>LT</b></p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">2 1</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">1 if A < B, else 0.</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>MAD</b></p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">1 1</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">Median Absolute Deviation (L1 STD) of
A.</p> </td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>MAX</b></p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">2 1</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">Maximum of A and B.</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>MEAN</b></p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">1 1</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">Mean value of A.</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>MED</b></p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">1 1</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">Median value of A.</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>MIN</b></p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">2 1</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">Minimum of A and B.</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>MOD</b></p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">2 1</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">A mod B (remainder after floored
division).</p> </td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>MODE</b></p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">1 1</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">Mode value (Least Median of Squares) of
A.</p> </td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>MUL</b></p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">2 1</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">A * B.</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>NAN</b></p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">2 1</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">NaN if A == B, else A.</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>NEG</b></p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">1 1</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">-A.</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>NEQ</b></p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">2 1</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">1 if A != B, else 0.</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>NOT</b></p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">1 1</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">NaN if A == NaN, 1 if A == 0, else 0.</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>NRAND</b></p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">2 1</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">Normal, random values with mean A and std.
deviation B.</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>OR</b></p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">2 1</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">NaN if A or B == NaN, else A.</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>PDIST</b></p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">1 1</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">Compute distance from points in ASCII file
A.</p> </td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>PLM</b></p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">3 1</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">Associated Legendre polynomial P(A) degree
B order C.</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>PLMg</b></p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">3 1</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">Normalized associated Legendre polynomial
P(A) degree B order C (geophysical convention).</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>POP</b></p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">1 0</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">Delete top element from the stack.</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>POW</b></p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">2 1</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">A ^ B.</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>PQUANT</b></p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">2 1</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">The B’th Quantile (0-100%) of A.</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>PSI</b></p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">1 1</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">Psi (or Digamma) of A.</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>PV</b></p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">3 1</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">Legendre function Pv(A) of degree v =
real(B) + imag(C).</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>QV</b></p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">3 1</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">Legendre function Qv(A) of degree v =
real(B) + imag(C).</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>R2</b></p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">2 1</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">R2 = A^2 + B^2.</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>R2D</b></p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">1 1</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">Convert Radians to Degrees.</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>RAND</b></p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">2 1</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">Uniform random values between A and B.</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>RINT</b></p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">1 1</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">rint (A) (nearest integer).</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>ROTX</b></p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">2 1</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">Rotate A by the (constant) shift B in
x-direction.</p> </td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>ROTY</b></p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">2 1</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">Rotate A by the (constant) shift B in
y-direction.</p> </td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>SAZ</b></p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">2 1</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">Spherical azimuth from grid nodes to stack
x,y.</p> </td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>SBAZ</b></p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">2 1</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">Spherical backazimuth from grid nodes to
stack x,y.</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>SDIST</b></p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">2 1</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">Spherical (Great circle) distance (in
degrees) between grid nodes and stack lon,lat (A, B).</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>SEC</b></p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">1 1</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">sec (A) (A in radians).</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>SECD</b></p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">1 1</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">sec (A) (A in degrees).</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>SIGN</b></p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">1 1</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">sign (+1 or -1) of A.</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>SIN</b></p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">1 1</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">sin (A) (A in radians).</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>SINC</b></p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">1 1</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">sinc (A) (sin (pi*A)/(pi*A)).</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>SIND</b></p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">1 1</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">sin (A) (A in degrees).</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>SINH</b></p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">1 1</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">sinh (A).</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>SKEW</b></p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">1 1</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">Skewness of A.</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>SQR</b></p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">1 1</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">A^2.</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>SQRT</b></p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">1 1</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">sqrt (A).</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>STD</b></p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">1 1</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">Standard deviation of A.</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>STEP</b></p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">1 1</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">Heaviside step function: H(A).</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>STEPX</b></p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">1 1</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">Heaviside step function in x: H(x-A).</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>STEPY</b></p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">1 1</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">Heaviside step function in y: H(y-A).</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>SUB</b></p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">2 1</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">A - B.</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>TAN</b></p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">1 1</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">tan (A) (A in radians).</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>TAND</b></p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">1 1</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">tan (A) (A in degrees).</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>TANH</b></p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">1 1</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">tanh (A).</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>TCRIT</b></p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">2 1</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">Critical value for Student’s
t-distribution, with alpha = A and n = B.</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>TDIST</b></p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">2 1</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">Student’s t-distribution A(t,n), with
t = A, and n = B.</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>TN</b></p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">2 1</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">Chebyshev polynomial Tn(-1<t<+1,n),
with t = A, and n = B.</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>UPPER</b></p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">1 1</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">The highest (maximum) value of A.</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>XOR</b></p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">2 1</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">B if A == NaN, else A.</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>Y0</b></p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">1 1</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">Bessel function of A (2nd kind, order
0).</p> </td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>Y1</b></p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">1 1</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">Bessel function of A (2nd kind, order
1).</p> </td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>YLM</b></p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">2 2</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">Re and Im orthonormalized spherical
harmonics degree A order B.</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>YLMg</b></p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">2 2</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">Cos and Sin normalized spherical harmonics
degree A order B (geophysical convention).</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>YN</b></p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">2 1</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">Bessel function of A (2nd kind, order
B).</p> </td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>ZCRIT</b></p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">1 1</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">Critical value for the normal-distribution,
with alpha = A.</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>ZDIST</b></p></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">1 1</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%"></td>
<td width="8%"></td>
<td width="69%">
<p valign="top">Cumulative normal-distribution C(x), with x
= A.</p></td>
</table>
<p style="margin-left:11%;"><b>SYMBOLS</b></p>
<p style="margin-left:22%;">The following symbols have
special meaning:</p>
<table width="100%" border=0 rules="none" frame="void"
cellspacing="0" cellpadding="0">
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>PI</b></p></td>
<td width="77%">
<p valign="top">3.1415926...</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>E</b></p></td>
<td width="77%">
<p valign="top">2.7182818...</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>EULER</b></p></td>
<td width="77%">
<p valign="top">0.5772156...</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>XMIN</b></p></td>
<td width="77%">
<p valign="top">Minimum x value</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>XMAX</b></p></td>
<td width="77%">
<p valign="top">Maximum x value</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>XINC</b></p></td>
<td width="77%">
<p valign="top">x increment</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>NX</b></p></td>
<td width="77%">
<p valign="top">The number of x nodes</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>YMIN</b></p></td>
<td width="77%">
<p valign="top">Minimum y value</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>YMAX</b></p></td>
<td width="77%">
<p valign="top">Maximum y value</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>YINC</b></p></td>
<td width="77%">
<p valign="top">y increment</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>NY</b></p></td>
<td width="77%">
<p valign="top">The number of y nodes</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>X</b></p></td>
<td width="77%">
<p valign="top">Grid with x-coordinates</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>Y</b></p></td>
<td width="77%">
<p valign="top">Grid with y-coordinates</p></td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>Xn</b></p></td>
<td width="77%">
<p valign="top">Grid with normalized [-1 to +1]
x-coordinates</p> </td>
<tr valign="top" align="left">
<td width="22%"></td>
<td width="-14%"></td>
<td width="7%"></td>
<td width="8%">
<p valign="top"><b>Yn</b></p></td>
<td width="77%">
<p valign="top">Grid with normalized [-1 to +1]
y-coordinates</p> </td>
</table>
<a name="OPTIONS"></a>
<h2>OPTIONS</h2>
<table width="100%" border=0 rules="none" frame="void"
cellspacing="0" cellpadding="0">
<tr valign="top" align="left">
<td width="11%"></td>
<td width="4%">
<p style="margin-top: 1em" valign="top"><b>−F</b></p> </td>
<td width="7%"></td>
<td width="78%">
<p style="margin-top: 1em" valign="top">Force pixel node
registration [Default is gridline registration]. (Node
registrations are defined in <b><A HREF="GMT.html">GMT</A></b> Cookbook Appendix B
on grid file formats.) Only used with <b>−R
−I</b>.</p> </td>
<tr valign="top" align="left">
<td width="11%"></td>
<td width="4%">
<p style="margin-top: 1em" valign="top"><b>−I</b></p> </td>
<td width="7%"></td>
<td width="78%">
<p style="margin-top: 1em" valign="top"><i>x_inc</i> [and
optionally <i>y_inc</i>] is the grid spacing. Optionally,
append a suffix modifier. <b>Geographical (degrees)
coordinates</b>: Append <b>m</b> to indicate arc minutes or
<b>c</b> to indicate arc seconds. If one of the units
<b>e</b>, <b>k</b>, <b>i</b>, or <b>n</b> 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
<b><A HREF="gmtdefaults.html#ELLIPSOID">ELLIPSOID</A></b>). If /<i>y_inc</i> is given but set to 0 it
will be reset equal to <i>x_inc</i>; otherwise it will be
converted to degrees latitude. <b>All coordinates</b>: If
<b>=</b> is appended then the corresponding max <i>x</i>
(<i>east</i>) or <i>y</i> (<i>north</i>) 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
<i>number of nodes</i> desired by appending <b>+</b> 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
<b>−R</b><i>grdfile</i> is used then grid spacing has
already been initialized; use <b>−I</b> to override
the values.</p></td>
<tr valign="top" align="left">
<td width="11%"></td>
<td width="4%">
<p style="margin-top: 1em" valign="top"><b>−M</b></p> </td>
<td width="7%"></td>
<td width="78%">
<p style="margin-top: 1em" valign="top">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.</p></td>
<tr valign="top" align="left">
<td width="11%"></td>
<td width="4%">
<p style="margin-top: 1em" valign="top"><b>−N</b></p> </td>
<td width="7%"></td>
<td width="78%">
<p style="margin-top: 1em" valign="top">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].</p></td>
<tr valign="top" align="left">
<td width="11%"></td>
<td width="4%">
<p style="margin-top: 1em" valign="top"><b>−R</b></p> </td>
<td width="7%"></td>
<td width="78%">
<p style="margin-top: 1em" valign="top"><i>xmin</i>,
<i>xmax</i>, <i>ymin</i>, and <i>ymax</i> specify the Region
of interest. For geographic regions, these limits correspond
to <i>west, east, south,</i> and <i>north</i> and you may
specify them in decimal degrees or in
[+-]dd:mm[:ss.xxx][W|E|S|N] format. Append <b>r</b> if lower
left and upper right map coordinates are given instead of
w/e/s/n. The two shorthands <b>−Rg</b> and
<b>−Rd</b> 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 <b>−R</b> 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 <b><A HREF="gmtdefaults.html#TIME_EPOCH">TIME_EPOCH</A></b> and in the
selected <b><A HREF="gmtdefaults.html#TIME_UNIT">TIME_UNIT</A></b>; append <b>t</b> to
<b>−JX</b>|<b>x</b>), or (b) absolute time of the form
[<i>date</i>]<b>T</b>[<i>clock</i>] (append <b>T</b> to
<b>−JX</b>|<b>x</b>). At least one of <i>date</i> and
<i>clock</i> must be present; the <b>T</b> is always
required. The <i>date</i> string must be of the form
[-]yyyy[-mm[-dd]] (Gregorian calendar) or yyyy[-Www[-d]]
(ISO week calendar), while the <i>clock</i> 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
<b><A HREF="gmtdefaults.html">gmtdefaults</A></b>).</p> </td>
<tr valign="top" align="left">
<td width="11%"></td>
<td width="4%">
<p style="margin-top: 1em" valign="top"><b>−V</b></p> </td>
<td width="7%"></td>
<td width="78%">
<p style="margin-top: 1em" valign="top">Selects verbose
mode, which will send progress reports to stderr [Default
runs "silently"].</p></td>
<tr valign="top" align="left">
<td width="11%"></td>
<td width="4%">
<p style="margin-top: 1em" valign="top"><b>−bi</b></p> </td>
<td width="7%"></td>
<td width="78%">
<p style="margin-top: 1em" valign="top">Selects binary
input. Append <b>s</b> for single precision [Default is
<b>d</b> (double)]. Uppercase <b>S</b> or <b>D</b> will
force byte-swapping. Optionally, append <i>ncol</i>, the
number of columns in your binary input file if it exceeds
the columns needed by the program. Or append <b>c</b> if the
input file is netCDF. Optionally, append
<i>var1</i><b>/</b><i>var2</i><b>/</b><i>...</i> to specify
the variables to be read. The binary input option only
applies to the data files needed by operators <b>LDIST</b>,
<b>PDIST</b>, and <b>INSIDE</b>.</p></td>
<tr valign="top" align="left">
<td width="11%"></td>
<td width="4%">
<p style="margin-top: 1em" valign="top"><b>−f</b></p> </td>
<td width="7%"></td>
<td width="78%">
<p style="margin-top: 1em" valign="top">Special formatting
of input and/or output columns (time or geographical data).
Specify <b>i</b> or <b>o</b> 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
<b>T</b> (absolute calendar time), <b>t</b> (relative time
in chosen <b><A HREF="gmtdefaults.html#TIME_UNIT">TIME_UNIT</A></b> since <b><A HREF="gmtdefaults.html#TIME_EPOCH">TIME_EPOCH</A></b>),
<b>x</b> (longitude), <b>y</b> (latitude), or <b>f</b>
(floating point) to each column or column range item.
Shorthand <b>−f</b>[<b>i</b>|<b>o</b>]<b>g</b> means
<b>−f</b>[<b>i</b>|<b>o</b>]0<b>x</b>,1<b>y</b>
(geographic coordinates).</p></td>
</table>
<a name="NOTES ON OPERATORS"></a>
<h2>NOTES ON OPERATORS</h2>
<p style="margin-left:11%; margin-top: 1em">(1) The
operator <b>SDIST</b> calculates spherical distances 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 <b>SAZ</b> and
<b>SBAZ</b> operators calculate spherical azimuth and
back-azimuths in degrees, respectively. A few operators
(<b>PDIST</b>, <b>LDIST</b>, and <b>INSIDE</b>) expects
their argument to be a single file with points, lines, or
polygons, respectively. Be aware that <b>LDIST</b> in
particular can be slow for large grids and numerous line
segments. Note: If the current <b><A HREF="gmtdefaults.html#ELLIPSOID">ELLIPSOID</A></b> is not
spherical then geodesics are used in the calculations.</p>
<p style="margin-left:11%; margin-top: 1em">(2) The
operator <b>PLM</b> calculates the associated Legendre
polynomial of degree L and order M (0 <= M <= L), and
its argument is the sine of the latitude. <b>PLM</b> is not
normalized and includes the Condon-Shortley phase (-1)^M.
<b>PLMg</b> is normalized in the way that is most commonly
used in geophysics. The C-S phase can be added by using -M
as argument. <b>PLM</b> will overflow at higher degrees,
whereas <b>PLMg</b> is stable until ultra high degrees (at
least 3000).</p>
<p style="margin-left:11%; margin-top: 1em">(3) The
operators <b>YLM</b> and <b>YLMg</b> 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. <b>YLM</b> and <b>YLMg</b> return two grids,
the real (cosine) and imaginary (sine) component of the
complex spherical harmonic. Use the <b>POP</b> operator (and
<b>EXCH</b>) to get rid of one of them, or save both by
giving two consecutive = file.grd calls. <br>
The orthonormalized complex harmonics <b>YLM</b> are most
commonly used in physics and seismology. The square of
<b>YLM</b> integrates to 1 over a sphere. In geophysics,
<b>YLMg</b> 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 <b>YLM</b>
or <b>YLMg</b>, but it can be added by using -M as
argument.</p>
<p style="margin-left:11%; margin-top: 1em">(4) All the
derivatives are based on central finite differences, with
natural boundary conditions.</p>
<p style="margin-left:11%; margin-top: 1em">(5) Files that
have the same names as some operators, e.g., <b>ADD</b>,
<b>SIGN</b>, <b>=</b>, etc. should be identified by
prepending the current directory (i.e., ./LOG).</p>
<p style="margin-left:11%; margin-top: 1em">(6) Piping of
files is not allowed.</p>
<p style="margin-left:11%; margin-top: 1em">(7) The stack
depth limit is hard-wired to 100.</p>
<p style="margin-left:11%; margin-top: 1em">(8) All
functions expecting a positive radius (e.g., <b>LOG</b>,
<b>KEI</b>, etc.) are passed the absolute value of their
argument.</p>
<a name="GRID VALUES PRECISION"></a>
<h2>GRID VALUES PRECISION</h2>
<p style="margin-left:11%; margin-top: 1em">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.</p>
<a name="GRID FILE FORMATS"></a>
<h2>GRID FILE FORMATS</h2>
<p style="margin-left:11%; margin-top: 1em">By default
<b><A HREF="GMT.html">GMT</A></b> writes out grid as single precision floats in a
COARDS-complaint netCDF file format. However, <b><A HREF="GMT.html">GMT</A></b> 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
<b>=</b><i>id</i>[<b>/</b><i>scale</i><b>/</b><i>offset</i>[<b>/</b><i>nan</i>]],
where <i>id</i> is a two-letter identifier of the grid type
and precision, and <i>scale</i> and <i>offset</i> are
optional scale factor and offset to be applied to all grid
values, and <i>nan</i> 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 <b><A HREF="grdreformat.html">grdreformat</A></b>(1)
and Section 4.17 of the GMT Technical Reference and Cookbook
for more information.</p>
<p style="margin-left:11%; margin-top: 1em">When reading a
netCDF file that contains multiple grids, <b><A HREF="GMT.html">GMT</A></b> will
read, by default, the first 2-dimensional grid that can find
in that file. To coax <b><A HREF="GMT.html">GMT</A></b> into reading another
multi-dimensional variable in the grid file, append
<b>?</b><i>varname</i> to the file name, where
<i>varname</i> is the name of the variable. Note that you
may need to escape the special meaning of <b>?</b> 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 <b>?</b><i>varname</i> suffix can also be used
for output grids to specify a variable name different from
the default: "z". See <b><A HREF="grdreformat.html">grdreformat</A></b>(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.</p>
<a name="GEOGRAPHICAL AND TIME COORDINATES"></a>
<h2>GEOGRAPHICAL AND TIME COORDINATES</h2>
<p style="margin-left:11%; margin-top: 1em">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 <b>−f</b> or
<b>−R</b> options. For example, both <b>−f0x
−f1t</b> and <b>−R</b>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 <b><A HREF="gmtdefaults.html#TIME_UNIT">TIME_UNIT</A></b> and <b><A HREF="gmtdefaults.html#TIME_EPOCH">TIME_EPOCH</A></b>
in the .gmtdefaults file or on the command line. In
addition, the <b>unit</b> attribute of the time variable
will indicate both this unit and epoch.</p>
<a name="EXAMPLES"></a>
<h2>EXAMPLES</h2>
<p style="margin-left:11%; margin-top: 1em">To take log10
of the average of 2 files, use</p>
<p style="margin-left:11%; margin-top: 1em"><b>grdmath</b>
file1.grd file2.grd <b>ADD</b> 0.5 <b>MUL LOG10 =</b>
file3.grd</p>
<p style="margin-left:11%; margin-top: 1em">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:</p>
<p style="margin-left:11%; margin-top: 1em"><b>grdmath</b>
ages.grd <b>SQRT</b> 350 <b>MUL</b> 2500 <b>ADD =</b>
depths.grd</p>
<p style="margin-left:11%; margin-top: 1em">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</p>
<p style="margin-left:11%; margin-top: 1em"><b>grdmath</b>
2 s_xy.grd <b>MUL</b> s_xx.grd s_yy.grd <b>SUB DIV ATAN2</b>
2 <b>DIV =</b> direction.grd</p>
<p style="margin-left:11%; margin-top: 1em">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:</p>
<p style="margin-left:11%; margin-top: 1em"><b>grdmath
−R</b>0/360/-90/90 <b>−I</b>1 8 4 <b>YML</b> 1.1
<b>MUL EXCH</b> 0.4 <b>MUL ADD</b> = harm.grd</p>
<p style="margin-left:11%; margin-top: 1em">To extract the
locations of local maxima that exceed 100 mGal in the file
faa.grd:</p>
<p style="margin-left:11%; margin-top: 1em"><b>grdmath</b>
faa.grd <b>DUP EXTREMA</b> 2 <b>EQ MUL DUP</b> 100 <b>GT
MUL</b> 0 <b>NAN</b> = z.grd <b><br>
grd2xyz</b> z.grd <b>−S</b> > max.xyz</p>
<a name="REFERENCES"></a>
<h2>REFERENCES</h2>
<p style="margin-left:11%; margin-top: 1em">Abramowitz, M.,
and I. A. Stegun, 1964, <i>Handbook of Mathematical
Functions</i>, 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. <i>Journal of Geodesy</i>,
76, 279-299. <br>
Press, W. H., S. A. Teukolsky, W. T. Vetterling, and B. P.
Flannery, 1992, <i>Numerical Recipes</i>, 2nd edition,
Cambridge Univ., New York. <br>
Spanier, J., and K. B. Oldman, 1987, <i>An Atlas of
Functions</i>, Hemisphere Publishing Corp.</p>
<a name="SEE ALSO"></a>
<h2>SEE ALSO</h2>
<p style="margin-left:11%; margin-top: 1em"><i><A HREF="GMT.html">GMT</A></i>(1),
<i><A HREF="gmtmath.html">gmtmath</A></i>(1), <i><A HREF="grd2xyz.html">grd2xyz</A></i>(1), <i><A HREF="grdedit.html">grdedit</A></i>(1),
<i><A HREF="grdinfo.html">grdinfo</A></i>(1), <i><A HREF="xyz2grd.html">xyz2grd</A></i>(1)</p>
<hr>
</body>
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