.. index:: ! grdmath

*******
grdmath
*******

.. only:: not man

    grdmath - Reverse Polish Notation (RPN) calculator for grids (element by element)

Synopsis
--------

.. include:: common_SYN_OPTs.rst_

**grdmath**
[ |SYN_OPT-Area| ]
[ |-D|\ *resolution*\ [**+**] ]
[ |SYN_OPT-I| ]
[ |-M| ] [ |-N| ]
[ |SYN_OPT-R| ] [ |SYN_OPT-V| ]
[ |SYN_OPT-bi| ]
[ |SYN_OPT-di| ]
[ |SYN_OPT-f| ]
[ |SYN_OPT-h| ]
[ |SYN_OPT-i| ]
[ |SYN_OPT-n| ]
[ **-r** ]
[ |SYN_OPT-x| ]
*operand* [ *operand* ] **OPERATOR** [ *operand* ]
**OPERATOR** ... **=** *outgrdfile*

|No-spaces|

Description
-----------

**grdmath** will perform operations like add, subtract, multiply, and
divide on one or more grid files or constants using Reverse Polish
Notation (RPN) syntax (e.g., Hewlett-Packard calculator-style).
Arbitrarily complicated expressions may therefore be evaluated; the
final result is written to an output grid file. Grid operations are
element-by-element, not matrix manipulations. Some operators only
require one operand (see below). If no grid files are used in the
expression then options **-R**, **-I** must be set (and optionally
**-r**). The expression **=** *outgrdfile* can occur as many times as
the depth of the stack allows in order to save intermediate results.
Complicated or frequently occurring expressions may be coded as a macro
for future use or stored and recalled via named memory locations.

Required Arguments
------------------

*operand*
    If *operand* can be opened as a file it will be read as a grid file.
    If not a file, it is interpreted as a numerical constant or a
    special symbol (see below).

*outgrdfile*
    The name of a 2-D grid file that will hold the final result. (See
    GRID FILE FORMATS below).

Optional Arguments
------------------

.. _-A:

.. |Add_-A| replace:: (**-A** is only relevant to the **LDISTG** operator)
.. include:: explain_-A.rst_

.. _-D:

**-D**\ *resolution*\ [**+**]
    Selects the resolution of the data set to use with the operator LDISTG
    ((**f**)ull, (**h**)igh, (**i**)ntermediate, (**l**)ow, and (**c**)rude). The
    resolution drops off by 80% between data sets [Default is **l**].
    Append **+** to automatically select a lower resolution should the one
    requested not be available [abort if not found].

.. _-I:

.. include:: explain_-I.rst_

.. _-M:

**-M**
    By default any derivatives calculated are in z_units/ x(or
    y)\_units. However, the user may choose this option to convert dx,dy
    in degrees of longitude,latitude into meters using a flat Earth
    approximation, so that gradients are in z_units/meter.

.. _-N:

**-N**
    Turn off strict domain match checking when multiple grids are
    manipulated [Default will insist that each grid domain is within
    1e-4 \* grid_spacing of the domain of the first grid listed].

.. _-R:

.. |Add_-R| unicode:: 0x20 .. just an invisible code
.. include:: explain_-R.rst_

.. _-V:

.. |Add_-V| unicode:: 0x20 .. just an invisible code
.. include:: explain_-V.rst_

.. |Add_-bi| replace:: The binary input option
    only applies to the data files needed by operators **LDIST**,
    **PDIST**, and **INSIDE**.
.. include:: explain_-bi.rst_

.. |Add_-di| unicode:: 0x20 .. just an invisible code
.. include:: explain_-di.rst_

.. |Add_-f| unicode:: 0x20 .. just an invisible code
.. include:: explain_-f.rst_

.. |Add_-g| unicode:: 0x20 .. just an invisible code
.. include:: explain_-g.rst_

.. |Add_-h| unicode:: 0x20 .. just an invisible code
.. include:: explain_-h.rst_

.. include:: explain_-icols.rst_

.. include:: explain_-n.rst_

.. |Add_nodereg| replace:: Only used with **-R** **-I**.
.. include:: explain_nodereg.rst_

.. include:: explain_core.rst_

.. include:: explain_help.rst_

Operators
---------

Choose among the following 209 operators. "args" are the number of input
and output arguments.

+---------------+-------+--------------------------------------------------------------------------------------------------------+
| Operator      | args  | Returns                                                                                                |
+---------------+-------+--------------------------------------------------------------------------------------------------------+
| **ABS**       | 1 1   | abs (A)                                                                                                |
+---------------+-------+--------------------------------------------------------------------------------------------------------+
| **ACOS**      | 1 1   | acos (A)                                                                                               |
+---------------+-------+--------------------------------------------------------------------------------------------------------+
| **ACOSH**     | 1 1   | acosh (A)                                                                                              |
+---------------+-------+--------------------------------------------------------------------------------------------------------+
| **ACOT**      | 1 1   | acot (A)                                                                                               |
+---------------+-------+--------------------------------------------------------------------------------------------------------+
| **ACSC**      | 1 1   | acsc (A)                                                                                               |
+---------------+-------+--------------------------------------------------------------------------------------------------------+
| **ADD**       | 2 1   | A + B                                                                                                  |
+---------------+-------+--------------------------------------------------------------------------------------------------------+
| **AND**       | 2 1   | B if A == NaN, else A                                                                                  |
+---------------+-------+--------------------------------------------------------------------------------------------------------+
| **ARC**       | 2 1   | Return arc(A,B) on [0 pi]                                                                              |
+---------------+-------+--------------------------------------------------------------------------------------------------------+
| **AREA**      | 0 1   | Area of each gridnode cell (in km^2 if geographic)                                                     |
+---------------+-------+--------------------------------------------------------------------------------------------------------+
| **ASEC**      | 1 1   | asec (A)                                                                                               |
+---------------+-------+--------------------------------------------------------------------------------------------------------+
| **ASIN**      | 1 1   | asin (A)                                                                                               |
+---------------+-------+--------------------------------------------------------------------------------------------------------+
| **ASINH**     | 1 1   | asinh (A)                                                                                              |
+---------------+-------+--------------------------------------------------------------------------------------------------------+
| **ATAN**      | 1 1   | atan (A)                                                                                               |
+---------------+-------+--------------------------------------------------------------------------------------------------------+
| **ATAN2**     | 2 1   | atan2 (A, B)                                                                                           |
+---------------+-------+--------------------------------------------------------------------------------------------------------+
| **ATANH**     | 1 1   | atanh (A)                                                                                              |
+---------------+-------+--------------------------------------------------------------------------------------------------------+
| **BCDF**      | 3 1   | Binomial cumulative distribution function for p = A, n = B, and x = C                                  |
+---------------+-------+--------------------------------------------------------------------------------------------------------+
| **BPDF**      | 3 1   | Binomial probability density function for p = A, n = B, and x = C                                      |
+---------------+-------+--------------------------------------------------------------------------------------------------------+
| **BEI**       | 1 1   | bei (A)                                                                                                |
+---------------+-------+--------------------------------------------------------------------------------------------------------+
| **BER**       | 1 1   | ber (A)                                                                                                |
+---------------+-------+--------------------------------------------------------------------------------------------------------+
| **BITAND**    | 2 1   | A & B (bitwise AND operator)                                                                           |
+---------------+-------+--------------------------------------------------------------------------------------------------------+
| **BITLEFT**   | 2 1   | A << B (bitwise left-shift operator)                                                                   |
+---------------+-------+--------------------------------------------------------------------------------------------------------+
| **BITNOT**    | 1 1   | ~A (bitwise NOT operator, i.e., return two's complement)                                               |
+---------------+-------+--------------------------------------------------------------------------------------------------------+
| **BITOR**     | 2 1   | A \| B (bitwise OR operator)                                                                           |
+---------------+-------+--------------------------------------------------------------------------------------------------------+
| **BITRIGHT**  | 2 1   | A >> B (bitwise right-shift operator)                                                                  |
+---------------+-------+--------------------------------------------------------------------------------------------------------+
| **BITTEST**   | 2 1   | 1 if bit B of A is set, else 0 (bitwise TEST operator)                                                 |
+---------------+-------+--------------------------------------------------------------------------------------------------------+
| **BITXOR**    | 2 1   | A ^ B (bitwise XOR operator)                                                                           |
+---------------+-------+--------------------------------------------------------------------------------------------------------+
| **CAZ**       | 2 1   | Cartesian azimuth from grid nodes to stack x,y (i.e., A, B)                                            |
+---------------+-------+--------------------------------------------------------------------------------------------------------+
| **CBAZ**      | 2 1   | Cartesian back-azimuth from grid nodes to stack x,y (i.e., A, B)                                       |
+---------------+-------+--------------------------------------------------------------------------------------------------------+
| **CDIST**     | 2 1   | Cartesian distance between grid nodes and stack x,y (i.e., A, B)                                       |
+---------------+-------+--------------------------------------------------------------------------------------------------------+
| **CDIST2**    | 2 1   | As CDIST but only to nodes that are != 0                                                               |
+---------------+-------+--------------------------------------------------------------------------------------------------------+
| **CEIL**      | 1 1   | ceil (A) (smallest integer >= A)                                                                       |
+---------------+-------+--------------------------------------------------------------------------------------------------------+
| **CHICRIT**   | 2 1   | Chi-squared critical value for alpha = A and nu = B                                                    |
+---------------+-------+--------------------------------------------------------------------------------------------------------+
| **CHICDF**    | 2 1   | Chi-squared cumulative distribution function for chi2 = A and nu = B                                   |
+---------------+-------+--------------------------------------------------------------------------------------------------------+
| **CHIPDF**    | 2 1   | Chi-squared probability density function for chi2 = A and nu = B                                       |
+---------------+-------+--------------------------------------------------------------------------------------------------------+
| **COMB**      | 2 1   | Combinations n_C_r, with n = A and r = B                                                               |
+---------------+-------+--------------------------------------------------------------------------------------------------------+
| **CORRCOEFF** | 2 1   | Correlation coefficient r(A, B)                                                                        |
+---------------+-------+--------------------------------------------------------------------------------------------------------+
| **COS**       | 1 1   | cos (A) (A in radians)                                                                                 |
+---------------+-------+--------------------------------------------------------------------------------------------------------+
| **COSD**      | 1 1   | cos (A) (A in degrees)                                                                                 |
+---------------+-------+--------------------------------------------------------------------------------------------------------+
| **COSH**      | 1 1   | cosh (A)                                                                                               |
+---------------+-------+--------------------------------------------------------------------------------------------------------+
| **COT**       | 1 1   | cot (A) (A in radians)                                                                                 |
+---------------+-------+--------------------------------------------------------------------------------------------------------+
| **COTD**      | 1 1   | cot (A) (A in degrees)                                                                                 |
+---------------+-------+--------------------------------------------------------------------------------------------------------+
| **CSC**       | 1 1   | csc (A) (A in radians)                                                                                 |
+---------------+-------+--------------------------------------------------------------------------------------------------------+
| **CSCD**      | 1 1   | csc (A) (A in degrees)                                                                                 |
+---------------+-------+--------------------------------------------------------------------------------------------------------+
| **CURV**      | 1 1   | Curvature of A (Laplacian)                                                                             |
+---------------+-------+--------------------------------------------------------------------------------------------------------+
| **D2DX2**     | 1 1   | d^2(A)/dx^2 2nd derivative                                                                             |
+---------------+-------+--------------------------------------------------------------------------------------------------------+
| **D2DY2**     | 1 1   | d^2(A)/dy^2 2nd derivative                                                                             |
+---------------+-------+--------------------------------------------------------------------------------------------------------+
| **D2DXY**     | 1 1   | d^2(A)/dxdy 2nd derivative                                                                             |
+---------------+-------+--------------------------------------------------------------------------------------------------------+
| **D2R**       | 1 1   | Converts Degrees to Radians                                                                            |
+---------------+-------+--------------------------------------------------------------------------------------------------------+
| **DDX**       | 1 1   | d(A)/dx Central 1st derivative                                                                         |
+---------------+-------+--------------------------------------------------------------------------------------------------------+
| **DDY**       | 1 1   | d(A)/dy Central 1st derivative                                                                         |
+---------------+-------+--------------------------------------------------------------------------------------------------------+
| **DEG2KM**    | 1 1   | Converts Spherical Degrees to Kilometers                                                               |
+---------------+-------+--------------------------------------------------------------------------------------------------------+
| **DENAN**     | 2 1   | Replace NaNs in A with values from B                                                                   |
+---------------+-------+--------------------------------------------------------------------------------------------------------+
| **DILOG**     | 1 1   | dilog (A)                                                                                              |
+---------------+-------+--------------------------------------------------------------------------------------------------------+
| **DIV**       | 2 1   | A / B                                                                                                  |
+---------------+-------+--------------------------------------------------------------------------------------------------------+
| **DUP**       | 1 2   | Places duplicate of A on the stack                                                                     |
+---------------+-------+--------------------------------------------------------------------------------------------------------+
| **ECDF**      | 2 1   | Exponential cumulative distribution function for x = A and lambda = B                                  |
+---------------+-------+--------------------------------------------------------------------------------------------------------+
| **ECRIT**     | 2 1   | Exponential distribution critical value for alpha = A and lambda = B                                   |
+---------------+-------+--------------------------------------------------------------------------------------------------------+
| **EPDF**      | 2 1   | Exponential probability density function for x = A and lambda = B                                      |
+---------------+-------+--------------------------------------------------------------------------------------------------------+
| **ERF**       | 1 1   | Error function erf (A)                                                                                 |
+---------------+-------+--------------------------------------------------------------------------------------------------------+
| **ERFC**      | 1 1   | Complementary Error function erfc (A)                                                                  |
+---------------+-------+--------------------------------------------------------------------------------------------------------+
| **EQ**        | 2 1   | 1 if A == B, else 0                                                                                    |
+---------------+-------+--------------------------------------------------------------------------------------------------------+
| **ERFINV**    | 1 1   | Inverse error function of A                                                                            |
+---------------+-------+--------------------------------------------------------------------------------------------------------+
| **EXCH**      | 2 2   | Exchanges A and B on the stack                                                                         |
+---------------+-------+--------------------------------------------------------------------------------------------------------+
| **EXP**       | 1 1   | exp (A)                                                                                                |
+---------------+-------+--------------------------------------------------------------------------------------------------------+
| **FACT**      | 1 1   | A! (A factorial)                                                                                       |
+---------------+-------+--------------------------------------------------------------------------------------------------------+
| **EXTREMA**   | 1 1   | Local Extrema: +2/-2 is max/min, +1/-1 is saddle with max/min in x, 0 elsewhere                        |
+---------------+-------+--------------------------------------------------------------------------------------------------------+
| **FCDF**      | 3 1   | F cumulative distribution function for F = A, nu1 = B, and nu2 = C                                     |
+---------------+-------+--------------------------------------------------------------------------------------------------------+
| **FCRIT**     | 3 1   | F distribution critical value for alpha = A, nu1 = B, and nu2 = C                                      |
+---------------+-------+--------------------------------------------------------------------------------------------------------+
| **FLIPLR**    | 1 1   | Reverse order of values in each row                                                                    |
+---------------+-------+--------------------------------------------------------------------------------------------------------+
| **FLIPUD**    | 1 1   | Reverse order of values in each column                                                                 |
+---------------+-------+--------------------------------------------------------------------------------------------------------+
| **FLOOR**     | 1 1   | floor (A) (greatest integer <= A)                                                                      |
+---------------+-------+--------------------------------------------------------------------------------------------------------+
| **FMOD**      | 2 1   | A % B (remainder after truncated division)                                                             |
+---------------+-------+--------------------------------------------------------------------------------------------------------+
| **FPDF**      | 3 1   | F probability density function for F = A, nu1 = B, and nu2 = C                                         |
+---------------+-------+--------------------------------------------------------------------------------------------------------+
| **GE**        | 2 1   | 1 if A >= B, else 0                                                                                    |
+---------------+-------+--------------------------------------------------------------------------------------------------------+
| **GT**        | 2 1   | 1 if A > B, else 0                                                                                     |
+---------------+-------+--------------------------------------------------------------------------------------------------------+
| **HYPOT**     | 2 1   | hypot (A, B) = sqrt (A\*A + B\*B)                                                                      |
+---------------+-------+--------------------------------------------------------------------------------------------------------+
| **I0**        | 1 1   | Modified Bessel function of A (1st kind, order 0)                                                      |
+---------------+-------+--------------------------------------------------------------------------------------------------------+
| **I1**        | 1 1   | Modified Bessel function of A (1st kind, order 1)                                                      |
+---------------+-------+--------------------------------------------------------------------------------------------------------+
| **IFELSE**    | 3 1   | B if A != 0, else C                                                                                    |
+---------------+-------+--------------------------------------------------------------------------------------------------------+
| **IN**        | 2 1   | Modified Bessel function of A (1st kind, order B)                                                      |
+---------------+-------+--------------------------------------------------------------------------------------------------------+
| **INRANGE**   | 3 1   | 1 if B <= A <= C, else 0                                                                               |
+---------------+-------+--------------------------------------------------------------------------------------------------------+
| **INSIDE**    | 1 1   | 1 when inside or on polygon(s) in A, else 0                                                            |
+---------------+-------+--------------------------------------------------------------------------------------------------------+
| **INV**       | 1 1   | 1 / A                                                                                                  |
+---------------+-------+--------------------------------------------------------------------------------------------------------+
| **ISFINITE**  | 1 1   | 1 if A is finite, else 0                                                                               |
+---------------+-------+--------------------------------------------------------------------------------------------------------+
| **ISNAN**     | 1 1   | 1 if A == NaN, else 0                                                                                  |
+---------------+-------+--------------------------------------------------------------------------------------------------------+
| **J0**        | 1 1   | Bessel function of A (1st kind, order 0)                                                               |
+---------------+-------+--------------------------------------------------------------------------------------------------------+
| **J1**        | 1 1   | Bessel function of A (1st kind, order 1)                                                               |
+---------------+-------+--------------------------------------------------------------------------------------------------------+
| **JN**        | 2 1   | Bessel function of A (1st kind, order B)                                                               |
+---------------+-------+--------------------------------------------------------------------------------------------------------+
| **K0**        | 1 1   | Modified Kelvin function of A (2nd kind, order 0)                                                      |
+---------------+-------+--------------------------------------------------------------------------------------------------------+
| **K1**        | 1 1   | Modified Bessel function of A (2nd kind, order 1)                                                      |
+---------------+-------+--------------------------------------------------------------------------------------------------------+
| **KEI**       | 1 1   | kei (A)                                                                                                |
+---------------+-------+--------------------------------------------------------------------------------------------------------+
| **KER**       | 1 1   | ker (A)                                                                                                |
+---------------+-------+--------------------------------------------------------------------------------------------------------+
| **KM2DEG**    | 1 1   | Converts Kilometers to Spherical Degrees                                                               |
+---------------+-------+--------------------------------------------------------------------------------------------------------+
| **KN**        | 2 1   | Modified Bessel function of A (2nd kind, order B)                                                      |
+---------------+-------+--------------------------------------------------------------------------------------------------------+
| **KURT**      | 1 1   | Kurtosis of A                                                                                          |
+---------------+-------+--------------------------------------------------------------------------------------------------------+
| **LCDF**      | 1 1   | Laplace cumulative distribution function for z = A                                                     |
+---------------+-------+--------------------------------------------------------------------------------------------------------+
| **LCRIT**     | 1 1   | Laplace distribution critical value for alpha = A                                                      |
+---------------+-------+--------------------------------------------------------------------------------------------------------+
| **LDIST**     | 1 1   | Compute minimum distance (in km if -fg) from lines in multi-segment ASCII file A                       |
+---------------+-------+--------------------------------------------------------------------------------------------------------+
| **LDIST2**    | 2 1   | As LDIST, from lines in ASCII file B but only to nodes where A != 0                                    |
+---------------+-------+--------------------------------------------------------------------------------------------------------+
| **LDISTG**    | 0 1   | As LDIST, but operates on the GSHHG dataset (see -A, -D for options).                                  |
+---------------+-------+--------------------------------------------------------------------------------------------------------+
| **LE**        | 2 1   | 1 if A <= B, else 0                                                                                    |
+---------------+-------+--------------------------------------------------------------------------------------------------------+
| **LOG**       | 1 1   | log (A) (natural log)                                                                                  |
+---------------+-------+--------------------------------------------------------------------------------------------------------+
| **LOG10**     | 1 1   | log10 (A) (base 10)                                                                                    |
+---------------+-------+--------------------------------------------------------------------------------------------------------+
| **LOG1P**     | 1 1   | log (1+A) (accurate for small A)                                                                       |
+---------------+-------+--------------------------------------------------------------------------------------------------------+
| **LOG2**      | 1 1   | log2 (A) (base 2)                                                                                      |
+---------------+-------+--------------------------------------------------------------------------------------------------------+
| **LMSSCL**    | 1 1   | LMS scale estimate (LMS STD) of A                                                                      |
+---------------+-------+--------------------------------------------------------------------------------------------------------+
| **LMSSCLW**   | 2 1   | Weighted LMS scale estimate (LMS STD) of A for weights in B                                            |
+---------------+-------+--------------------------------------------------------------------------------------------------------+
| **LOWER**     | 1 1   | The lowest (minimum) value of A                                                                        |
+---------------+-------+--------------------------------------------------------------------------------------------------------+
| **LPDF**      | 1 1   | Laplace probability density function for z = A                                                         |
+---------------+-------+--------------------------------------------------------------------------------------------------------+
| **LRAND**     | 2 1   | Laplace random noise with mean A and std. deviation B                                                  |
+---------------+-------+--------------------------------------------------------------------------------------------------------+
| **LT**        | 2 1   | 1 if A < B, else 0                                                                                     |
+---------------+-------+--------------------------------------------------------------------------------------------------------+
| **MAD**       | 1 1   | Median Absolute Deviation (L1 STD) of A                                                                |
+---------------+-------+--------------------------------------------------------------------------------------------------------+
| **MAX**       | 2 1   | Maximum of A and B                                                                                     |
+---------------+-------+--------------------------------------------------------------------------------------------------------+
| **MEAN**      | 1 1   | Mean value of A                                                                                        |
+---------------+-------+--------------------------------------------------------------------------------------------------------+
| **MEANW**     | 2 1   | Weighted mean value of A for weights in B                                                              |
+---------------+-------+--------------------------------------------------------------------------------------------------------+
| **MEDIAN**    | 1 1   | Median value of A                                                                                      |
+---------------+-------+--------------------------------------------------------------------------------------------------------+
| **MEDIANW**   | 2 1   | Weighted median value of A for weights in B                                                            |
+---------------+-------+--------------------------------------------------------------------------------------------------------+
| **MIN**       | 2 1   | Minimum of A and B                                                                                     |
+---------------+-------+--------------------------------------------------------------------------------------------------------+
| **MOD**       | 2 1   | A mod B (remainder after floored division)                                                             |
+---------------+-------+--------------------------------------------------------------------------------------------------------+
| **MODE**      | 1 1   | Mode value (Least Median of Squares) of A                                                              |
+---------------+-------+--------------------------------------------------------------------------------------------------------+
| **MODEW**     | 2 1   | Weighted mode value (Least Median of Squares) of A for weights in B                                    |
+---------------+-------+--------------------------------------------------------------------------------------------------------+
| **MUL**       | 2 1   | A \* B                                                                                                 |
+---------------+-------+--------------------------------------------------------------------------------------------------------+
| **NAN**       | 2 1   | NaN if A == B, else A                                                                                  |
+---------------+-------+--------------------------------------------------------------------------------------------------------+
| **NEG**       | 1 1   | -A                                                                                                     |
+---------------+-------+--------------------------------------------------------------------------------------------------------+
| **NEQ**       | 2 1   | 1 if A != B, else 0                                                                                    |
+---------------+-------+--------------------------------------------------------------------------------------------------------+
| **NORM**      | 1 1   | Normalize (A) so max(A)-min(A) = 1                                                                     |
+---------------+-------+--------------------------------------------------------------------------------------------------------+
| **NOT**       | 1 1   | NaN if A == NaN, 1 if A == 0, else 0                                                                   |
+---------------+-------+--------------------------------------------------------------------------------------------------------+
| **NRAND**     | 2 1   | Normal, random values with mean A and std. deviation B                                                 |
+---------------+-------+--------------------------------------------------------------------------------------------------------+
| **OR**        | 2 1   | NaN if B == NaN, else A                                                                                |
+---------------+-------+--------------------------------------------------------------------------------------------------------+
| **PCDF**      | 2 1   | Poisson cumulative distribution function for x = A and lambda = B                                      |
+---------------+-------+--------------------------------------------------------------------------------------------------------+
| **PDIST**     | 1 1   | Compute minimum distance (in km if -fg) from points in ASCII file A                                    |
+---------------+-------+--------------------------------------------------------------------------------------------------------+
| **PDIST2**    | 2 1   | As PDIST, from points in ASCII file B but only to nodes where A != 0                                   |
+---------------+-------+--------------------------------------------------------------------------------------------------------+
| **PERM**      | 2 1   | Permutations n_P_r, with n = A and r = B                                                               |
+---------------+-------+--------------------------------------------------------------------------------------------------------+
| **PLM**       | 3 1   | Associated Legendre polynomial P(A) degree B order C                                                   |
+---------------+-------+--------------------------------------------------------------------------------------------------------+
| **PLMg**      | 3 1   | Normalized associated Legendre polynomial P(A) degree B order C (geophysical convention)               |
+---------------+-------+--------------------------------------------------------------------------------------------------------+
| **POINT**     | 1 2   | Compute mean x and y from ASCII file A and place them on the stack                                     |
+---------------+-------+--------------------------------------------------------------------------------------------------------+
| **POP**       | 1 0   | Delete top element from the stack                                                                      |
+---------------+-------+--------------------------------------------------------------------------------------------------------+
| **POW**       | 2 1   | A ^ B                                                                                                  |
+---------------+-------+--------------------------------------------------------------------------------------------------------+
| **PPDF**      | 2 1   | Poisson distribution P(x,lambda), with x = A and lambda = B                                            |
+---------------+-------+--------------------------------------------------------------------------------------------------------+
| **PQUANT**    | 2 1   | The B'th Quantile (0-100%) of A                                                                        |
+---------------+-------+--------------------------------------------------------------------------------------------------------+
| **PQUANTW**   | 3 1   | The C'th weighted quantile (0-100%) of A for weights in B                                              |
+---------------+-------+--------------------------------------------------------------------------------------------------------+
| **PSI**       | 1 1   | Psi (or Digamma) of A                                                                                  |
+---------------+-------+--------------------------------------------------------------------------------------------------------+
| **PV**        | 3 1   | Legendre function Pv(A) of degree v = real(B) + imag(C)                                                |
+---------------+-------+--------------------------------------------------------------------------------------------------------+
| **QV**        | 3 1   | Legendre function Qv(A) of degree v = real(B) + imag(C)                                                |
+---------------+-------+--------------------------------------------------------------------------------------------------------+
| **R2**        | 2 1   | R2 = A^2 + B^2                                                                                         |
+---------------+-------+--------------------------------------------------------------------------------------------------------+
| **R2D**       | 1 1   | Convert Radians to Degrees                                                                             |
+---------------+-------+--------------------------------------------------------------------------------------------------------+
| **RAND**      | 2 1   | Uniform random values between A and B                                                                  |
+---------------+-------+--------------------------------------------------------------------------------------------------------+
| **RCDF**      | 1 1   | Rayleigh cumulative distribution function for z = A                                                    |
+---------------+-------+--------------------------------------------------------------------------------------------------------+
| **RCRIT**     | 1 1   | Rayleigh distribution critical value for alpha = A                                                     |
+---------------+-------+--------------------------------------------------------------------------------------------------------+
| **RINT**      | 1 1   | rint (A) (round to integral value nearest to A)                                                        |
+---------------+-------+--------------------------------------------------------------------------------------------------------+
| **RMS**       | 1 1   | Root-mean-square of A                                                                                  |
+---------------+-------+--------------------------------------------------------------------------------------------------------+
| **RMSW**      | 1 1   | Root-mean-square of A for weights in B                                                                 |
+---------------+-------+--------------------------------------------------------------------------------------------------------+
| **RPDF**      | 1 1   | Rayleigh probability density function for z = A                                                        |
+---------------+-------+--------------------------------------------------------------------------------------------------------+
| **ROLL**      | 2 0   | Cyclicly shifts the top A stack items by an amount B                                                   |
+---------------+-------+--------------------------------------------------------------------------------------------------------+
| **ROTX**      | 2 1   | Rotate A by the (constant) shift B in x-direction                                                      |
+---------------+-------+--------------------------------------------------------------------------------------------------------+
| **ROTY**      | 2 1   | Rotate A by the (constant) shift B in y-direction                                                      |
+---------------+-------+--------------------------------------------------------------------------------------------------------+
| **SDIST**     | 2 1   | Spherical (Great circle|geodesic) distance (in km) between nodes and stack (A, B) |ex_SDIST|           |
+---------------+-------+--------------------------------------------------------------------------------------------------------+
| **SDIST2**    | 2 1   | As SDIST but only to nodes that are != 0                                                               |
+---------------+-------+--------------------------------------------------------------------------------------------------------+
| **SAZ**       | 2 1   | Spherical azimuth from grid nodes to stack lon, lat (i.e., A, B)                                       |
+---------------+-------+--------------------------------------------------------------------------------------------------------+
| **SBAZ**      | 2 1   | Spherical back-azimuth from grid nodes to stack lon, lat (i.e., A, B)                                  |
+---------------+-------+--------------------------------------------------------------------------------------------------------+
| **SEC**       | 1 1   | sec (A) (A in radians)                                                                                 |
+---------------+-------+--------------------------------------------------------------------------------------------------------+
| **SECD**      | 1 1   | sec (A) (A in degrees)                                                                                 |
+---------------+-------+--------------------------------------------------------------------------------------------------------+
| **SIGN**      | 1 1   | sign (+1 or -1) of A                                                                                   |
+---------------+-------+--------------------------------------------------------------------------------------------------------+
| **SIN**       | 1 1   | sin (A) (A in radians)                                                                                 |
+---------------+-------+--------------------------------------------------------------------------------------------------------+
| **SINC**      | 1 1   | sinc (A) (sin (pi\*A)/(pi\*A))                                                                         |
+---------------+-------+--------------------------------------------------------------------------------------------------------+
| **SIND**      | 1 1   | sin (A) (A in degrees)                                                                                 |
+---------------+-------+--------------------------------------------------------------------------------------------------------+
| **SINH**      | 1 1   | sinh (A)                                                                                               |
+---------------+-------+--------------------------------------------------------------------------------------------------------+
| **SKEW**      | 1 1   | Skewness of A                                                                                          |
+---------------+-------+--------------------------------------------------------------------------------------------------------+
| **SQR**       | 1 1   | A^2                                                                                                    |
+---------------+-------+--------------------------------------------------------------------------------------------------------+
| **SQRT**      | 1 1   | sqrt (A)                                                                                               |
+---------------+-------+--------------------------------------------------------------------------------------------------------+
| **STD**       | 1 1   | Standard deviation of A                                                                                |
+---------------+-------+--------------------------------------------------------------------------------------------------------+
| **STDW**      | 2 1   | Weighted standard deviation of A for weights in B                                                      |
+---------------+-------+--------------------------------------------------------------------------------------------------------+
| **STEP**      | 1 1   | Heaviside step function: H(A)                                                                          |
+---------------+-------+--------------------------------------------------------------------------------------------------------+
| **STEPX**     | 1 1   | Heaviside step function in x: H(x-A)                                                                   |
+---------------+-------+--------------------------------------------------------------------------------------------------------+
| **STEPY**     | 1 1   | Heaviside step function in y: H(y-A)                                                                   |
+---------------+-------+--------------------------------------------------------------------------------------------------------+
| **SUB**       | 2 1   | A - B                                                                                                  |
+---------------+-------+--------------------------------------------------------------------------------------------------------+
| **SUM**       | 1 1   | Sum of all values in A                                                                                 |
+---------------+-------+--------------------------------------------------------------------------------------------------------+
| **TAN**       | 1 1   | tan (A) (A in radians)                                                                                 |
+---------------+-------+--------------------------------------------------------------------------------------------------------+
| **TAND**      | 1 1   | tan (A) (A in degrees)                                                                                 |
+---------------+-------+--------------------------------------------------------------------------------------------------------+
| **TANH**      | 1 1   | tanh (A)                                                                                               |
+---------------+-------+--------------------------------------------------------------------------------------------------------+
| **TAPER**     | 2 1   | Unit weights cosine-tapered to zero within A and B of x and y grid margins                             |
+---------------+-------+--------------------------------------------------------------------------------------------------------+
| **TCDF**      | 2 1   | Student's t cumulative distribution function for t = A, and nu = B                                     |
+---------------+-------+--------------------------------------------------------------------------------------------------------+
| **TCRIT**     | 2 1   | Student's t distribution critical value for alpha = A and nu = B                                       |
+---------------+-------+--------------------------------------------------------------------------------------------------------+
| **TN**        | 2 1   | Chebyshev polynomial Tn(-1<t<+1,n), with t = A, and n = B                                              |
+---------------+-------+--------------------------------------------------------------------------------------------------------+
| **TPDF**      | 2 1   | Student's t probability density function for t = A, and nu = B                                         |
+---------------+-------+--------------------------------------------------------------------------------------------------------+
| **TRIM**      | 3 1   | Alpha-trim C to NaN if values fall in tails A and B (in percentage)                                    |
+---------------+-------+--------------------------------------------------------------------------------------------------------+
| **UPPER**     | 1 1   | The highest (maximum) value of A                                                                       |
+---------------+-------+--------------------------------------------------------------------------------------------------------+
| **VAR**       | 1 1   | Variance of A                                                                                          |
+---------------+-------+--------------------------------------------------------------------------------------------------------+
| **VARW**      | 2 1   | Weighted variance of A for weights in B                                                                |
+---------------+-------+--------------------------------------------------------------------------------------------------------+
| **WCDF**      | 3 1   | Weibull cumulative distribution function for x = A, scale = B, and shape = C                           |
+---------------+-------+--------------------------------------------------------------------------------------------------------+
| **WCRIT**     | 3 1   | Weibull distribution critical value for alpha = A, scale = B, and shape = C                            |
+---------------+-------+--------------------------------------------------------------------------------------------------------+
| **WPDF**      | 3 1   | Weibull density distribution P(x,scale,shape), with x = A, scale = B, and shape = C                    |
+---------------+-------+--------------------------------------------------------------------------------------------------------+
| **WRAP**      | 1 1   | wrap A in radians onto [-pi,pi]                                                                        |
+---------------+-------+--------------------------------------------------------------------------------------------------------+
| **XOR**       | 2 1   | 0 if A == NaN and B == NaN, NaN if B == NaN, else A                                                    |
+---------------+-------+--------------------------------------------------------------------------------------------------------+
| **Y0**        | 1 1   | Bessel function of A (2nd kind, order 0)                                                               |
+---------------+-------+--------------------------------------------------------------------------------------------------------+
| **Y1**        | 1 1   | Bessel function of A (2nd kind, order 1)                                                               |
+---------------+-------+--------------------------------------------------------------------------------------------------------+
| **YLM**       | 2 2   | Re and Im orthonormalized spherical harmonics degree A order B                                         |
+---------------+-------+--------------------------------------------------------------------------------------------------------+
| **YLMg**      | 2 2   | Cos and Sin normalized spherical harmonics degree A order B (geophysical convention)                   |
+---------------+-------+--------------------------------------------------------------------------------------------------------+
| **YN**        | 2 1   | Bessel function of A (2nd kind, order B)                                                               |
+---------------+-------+--------------------------------------------------------------------------------------------------------+
| **ZCDF**      | 1 1   | Normal cumulative distribution function for z = A                                                      |
+---------------+-------+--------------------------------------------------------------------------------------------------------+
| **ZPDF**      | 1 1   | Normal probability density function for z = A                                                          |
+---------------+-------+--------------------------------------------------------------------------------------------------------+
| **ZCRIT**     | 1 1   | Normal distribution critical value for alpha = A                                                       |
+---------------+-------+--------------------------------------------------------------------------------------------------------+

Symbols
-------

The following symbols have special meaning:

+-------------+-------------------------------------------------+
| **PI**      | 3.1415926...                                    |
+-------------+-------------------------------------------------+
| **E**       | 2.7182818...                                    |
+-------------+-------------------------------------------------+
| **EULER**   | 0.5772156...                                    |
+-------------+-------------------------------------------------+
| **EPS_F**   | 1.192092896e-07 (single precision epsilon       |
+-------------+-------------------------------------------------+
| **XMIN**    | Minimum x value                                 |
+-------------+-------------------------------------------------+
| **XMAX**    | Maximum x value                                 |
+-------------+-------------------------------------------------+
| **XRANGE**  | Range of x values                               |
+-------------+-------------------------------------------------+
| **XINC**    | x increment                                     |
+-------------+-------------------------------------------------+
| **NX**      | The number of x nodes                           |
+-------------+-------------------------------------------------+
| **YMIN**    | Minimum y value                                 |
+-------------+-------------------------------------------------+
| **YMAX**    | Maximum y value                                 |
+-------------+-------------------------------------------------+
| **YRANGE**  | Range of y values                               |
+-------------+-------------------------------------------------+
| **YINC**    | y increment                                     |
+-------------+-------------------------------------------------+
| **NY**      | The number of y nodes                           |
+-------------+-------------------------------------------------+
| **X**       | Grid with x-coordinates                         |
+-------------+-------------------------------------------------+
| **Y**       | Grid with y-coordinates                         |
+-------------+-------------------------------------------------+
| **XNORM**   | Grid with normalized [-1 to +1] x-coordinates   |
+-------------+-------------------------------------------------+
| **YNORM**   | Grid with normalized [-1 to +1] y-coordinates   |
+-------------+-------------------------------------------------+
| **XCOL**    | Grid with column numbers 0, 1, ..., NX-1        |
+-------------+-------------------------------------------------+
| **YROW**    | Grid with row numbers 0, 1, ..., NY-1           |
+-------------+-------------------------------------------------+
| **NODE**    | Grid with node numbers 0, 1, ..., (NX*NY)-1     |
+-------------+-------------------------------------------------+

Notes On Operators
------------------

#. For Cartesian grids the operators **MEAN**, **MEDIAN**, **MODE**,
   **LMSSCL**, **MAD**, **PQUANT**, **RMS**, **STD**, and **VAR** return the
   expected value from the given matrix.  However, for geographic grids
   we perform a spherically weighted calculation where each node value
   is weighted by the geographic area represented by that node.

#. The operator **SDIST** calculates spherical distances in km between the
   (lon, lat) point on the stack and all node positions in the grid. The
   grid domain and the (lon, lat) point are expected to be in degrees.
   Similarly, the **SAZ** and **SBAZ** operators calculate spherical
   azimuth and back-azimuths in degrees, respectively. The operators
   **LDIST** and **PDIST** compute spherical distances in km if **-fg** is
   set or implied, else they return Cartesian distances. Note: If the current
   :ref:`PROJ_ELLIPSOID <Projection Parameters>` is ellipsoidal then
   geodesics are used in calculations of distances, which can be slow.
   You can trade speed with accuracy by changing the algorithm used to
   compute the geodesic (see :ref:`PROJ_GEODESIC <Projection Parameters>`).

   The operator **LDISTG** is a version of **LDIST** that operates on the
   GSHHG data. Instead of reading an ASCII file, it directly accesses one of
   the GSHHG data sets as determined by the **-D** and **-A** options.

#. The operator **POINT** reads a ASCII table, computes the mean x and mean
   y values and places these on the stack.  If geographic data then we use
   the mean 3-D vector to determine the mean location.

#. The operator **PLM** calculates the associated Legendre polynomial
   of degree L and order M (0 <= M <= L), and its argument is the sine of
   the latitude. **PLM** is not normalized and includes the Condon-Shortley
   phase (-1)^M. **PLMg** is normalized in the way that is most commonly
   used in geophysics. The C-S phase can be added by using -M as argument.
   **PLM** will overflow at higher degrees, whereas **PLMg** is stable
   until ultra high degrees (at least 3000).

#. The operators **YLM** and **YLMg** calculate normalized spherical
   harmonics for degree L and order M (0 <= M <= L) for all positions in
   the grid, which is assumed to be in degrees. **YLM** and **YLMg** return
   two grids, the real (cosine) and imaginary (sine) component of the
   complex spherical harmonic. Use the **POP** operator (and **EXCH**) to
   get rid of one of them, or save both by giving two consecutive = file.nc calls.

   The orthonormalized complex harmonics **YLM** are most commonly used in
   physics and seismology. The square of **YLM** integrates to 1 over a
   sphere. In geophysics, **YLMg** is normalized to produce unit power when
   averaging the cosine and sine terms (separately!) over a sphere (i.e.,
   their squares each integrate to 4 pi). The Condon-Shortley phase (-1)^M
   is not included in **YLM** or **YLMg**, but it can be added by using -M
   as argument.

#. All the derivatives are based on central finite differences, with
   natural boundary conditions, and are Cartesian derivatives.

#. Files that have the same names as some operators, e.g., **ADD**,
   **SIGN**, **=**, etc. should be identified by prepending the current
   directory (i.e., ./LOG).

#. Piping of files is not allowed.

#. The stack depth limit is hard-wired to 100.

#. All functions expecting a positive radius (e.g., **LOG**, **KEI**,
   etc.) are passed the absolute value of their argument. (9) The bitwise
   operators (**BITAND**, **BITLEFT**, **BITNOT**, **BITOR**, **BITRIGHT**,
   **BITTEST**, and **BITXOR**) convert a grid's single precision values to
   unsigned 32-bit ints to perform the bitwise operations. Consequently,
   the largest whole integer value that can be stored in a float grid is
   2^24 or 16,777,216. Any higher result will be masked to fit in the lower
   24 bits.  Thus, bit operations are effectively limited to 24 bit.  All
   bitwise operators return NaN if given NaN arguments or bit-settings <= 0.

#. When OpenMP support is compiled in, a few operators will take advantage
   of the ability to spread the load onto several cores.  At present, the
   list of such operators is: **LDIST**, **LDIST2**, **PDIST**, **PDIST2**,
   **SAZ**, **SBAZ**, **SDIST**, **YLM**, and **grd_YLMg**.

.. include:: explain_float.rst_

.. include:: explain_grd_inout_short.rst_

.. include:: explain_grd_coord.rst_

.. include:: explain_sto_rcl_clr.rst_

.. include:: explain_gshhs.rst_

Macros
------

Users may save their favorite operator combinations as macros via the
file *grdmath.macros* in their current or user directory. The file may contain
any number of macros (one per record); comment lines starting with # are
skipped. The format for the macros is **name** = **arg1 arg2 ... arg2**
: *comment* where **name** is how the macro will be used. When this
operator appears on the command line we simply replace it with the
listed argument list. No macro may call another macro. As an example,
the following macro expects three arguments (radius x0 y0) and sets the
modes that are inside the given circle to 1 and those outside to 0:

INCIRCLE = CDIST EXCH DIV 1 LE : usage: r x y INCIRCLE to return 1
inside circle

Note: Because geographic or time constants may be present in a macro, it
is required that the optional comment flag (:) must be followed by a space.

Examples
--------

To compute all distances to north pole:

    ::

     gmt grdmath -Rg -I1 0 90 SDIST = dist_to_NP.nc

To take log10 of the average of 2 files, use

   ::

    gmt grdmath file1.nc file2.nc ADD 0.5 MUL LOG10 = file3.nc

Given the file ages.nc, which holds seafloor ages in m.y., use the
relation depth(in m) = 2500 + 350 \* sqrt (age) to estimate normal seafloor depths:

   ::

    gmt grdmath ages.nc SQRT 350 MUL 2500 ADD = depths.nc

To find the angle a (in degrees) of the largest principal stress from
the stress tensor given by the three files s_xx.nc s_yy.nc, and
s_xy.nc from the relation tan (2\*a) = 2 \* s_xy / (s_xx - s_yy), use

   ::

    gmt grdmath 2 s_xy.nc MUL s_xx.nc s_yy.nc SUB DIV ATAN 2 DIV = direction.nc

To calculate the fully normalized spherical harmonic of degree 8 and
order 4 on a 1 by 1 degree world map, using the real amplitude 0.4 and
the imaginary amplitude 1.1:

   ::

    gmt grdmath -R0/360/-90/90 -I1 8 4 YLM 1.1 MUL EXCH 0.4 MUL ADD = harm.nc

To extract the locations of local maxima that exceed 100 mGal in the file faa.nc:

   ::

    gmt grdmath faa.nc DUP EXTREMA 2 EQ MUL DUP 100 GT MUL 0 NAN = z.nc
    gmt grd2xyz z.nc -s > max.xyz

To demonstrate the use of named variables, consider this radial wave
where we store and recall the normalized radial arguments in radians:

   ::

    gmt grdmath -R0/10/0/10 -I0.25 5 5 CDIST 2 MUL PI MUL 5 DIV STO@r COS @r SIN MUL = wave.nc

To creat a dumb file saved as a 32 bits float GeoTiff using GDAL, run

   ::

    gmt grdmath -Rd -I10 X Y MUL = lixo.tiff=gd:GTiff

References
----------

Abramowitz, M., and I. A. Stegun, 1964, *Handbook of Mathematical
Functions*, Applied Mathematics Series, vol. 55, Dover, New York.

Holmes, S. A., and W. E. Featherstone, 2002, A unified approach to the
Clenshaw summation and the recursive computation of very high degree and
order normalised associated Legendre functions. *Journal of Geodesy*,
76, 279-299.

Press, W. H., S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery,
1992, *Numerical Recipes*, 2nd edition, Cambridge Univ., New York.

Spanier, J., and K. B. Oldman, 1987, *An Atlas of Functions*, Hemisphere
Publishing Corp.

See Also
--------

:doc:`gmt`, :doc:`gmtmath`,
:doc:`grd2xyz`, :doc:`grdedit`,
:doc:`grdinfo`, :doc:`xyz2grd`

.. ------------------------------------- Examples per option -------------------

.. |ex_SDIST| raw:: html

   <a href="#openModal">Example</a>
   <div id="openModal" class="modalDialog">
    <div>
        <a href="#close" title="Close" class="close">X</a>
        <h2>To compute all distances to north pole:</h2>
        <p>gmt grdmath -Rg -I1 0 90 SDIST = dist_to_NP.nc</br></p>
    </div>
   </div>