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**NAME**

gmtmath - Reverse Polish Notation calculator for data tables

**SYNOPSIS**

gmtmath[-Ccols] [-Hnrec] [-Nn_col/t_col] [-Q] [-S][-Tt_min/t_max/t_inc] [-V] [-bi[s][n] ] [-bo[s][n] ]operand[operand]OPERATOR[operand]OPERATOR...=[outfile]

**DESCRIPTION**

gmtmathwill perform operations like add, subtract, multiply, and divide on one or more table data 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 file [or standard output]. When two data tables 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 data tables are used in the expression then options-T,-Nmust be set (and optionally-b). By default, all columns except the "time" column are operated on, but this can be changed (see-C).operandIfoperandcan be opened as a file it will be read as an ASCII (or binary, see-bi) table data file. If not a file, it is interpreted as a numerical constant or a special symbol (see below).outfileis a table data file that will hold the final result. If not given then the output is sent to stdout.OPERATORSChoose among the following operators: Operator n_args ReturnsABS1 abs (A).ACOS1 acos (A).ACOSH1 acosh (A).ADD(+)2 A + B.AND2 NaN if A and B == NaN, B if A == NaN, else A.ASIN1 asin (A).ASINH1 asinh (A).ATAN1 atan (A).ATAN22 atan2 (A, B).ATANH1 atanh (A).BEI1 bei (A).BER1 ber (A).CEIL1 ceil (A) (smallest integer >= A).CHIDIST2 Chi-squared-distribution P(chi2,nu), with chi2 = A and nu = B.COS1 cos (A) (A in radians).COSD1 cos (A) (A in degrees).COSH1 cosh (A).D2DT21 d^2(A)/dt^2 2nd derivative.D2R1 Converts Degrees to Radians.DILOG1 Dilog (A).DIV(/)2 A / B.DDT1 d(A)/dt 1st derivative.DUP1 Places duplicate of A on the stack.ERF1 Error function of A.ERFC1 Complementory Error function of A.ERFINV1 Inverse error function of A.EQ2 1 if A == B, else 0.EXCH2 Exchanges A and B on the stack.EXP1 exp (A).FDIST4 F-dist Q(var1,var2,nu1,nu2), with var1 = A, var2 = B, nu1 = C, and nu2 = D.FLOOR1 floor (A) (greatest integer <= A).FMOD2 A % B (remainder).GE2 1 if A >= B, else 0.GT2 1 if A > B, else 0.HYPOT2 hypot (A, B).I01 Modified Bessel function of A (1st kind, order 0).I11 Modified Bessel function of A (1st kind, order 1).IN2 Modified Bessel function of A (1st kind, order B).INT1 Numerically integrate A.INV1 1 / A.ISNAN1 1 if A == NaN, else 0.J01 Bessel function of A (1st kind, order 0).J11 Bessel function of A (1st kind, order 1).JN2 Bessel function of A (1st kind, order B).K01 Modified Kelvin function of A (2nd kind, order 0).K11 Modified Bessel function of A (2nd kind, order 1).KN2 Modified Bessel function of A (2nd kind, order B).KEI1 kei (A).KER1 ker (A).LE2 1 if A <= B, else 0.LMSSCL1 LMS scale estimate (LMS STD) of A.LOG1 log (A) (natural log).LOG101 log10 (A).LOG1P1 log (1+A) (accurate for small A).LOWER1 The lowest (minimum) value of A.LT2 1 if A < B, else 0.MAD1 Median Absolute Deviation (L1 STD) of A.MAX2 Maximum of A and B.MEAN1 Mean value of A.MED1 Median value of A.MIN2 Minimum of A and B.MODE1 Mode value (LMS) of A.MUL(x)2 A * B.NAN2 NaN if A == B, else A.NEG1 -A.NRAND2 Normal, random values with mean A and std. deviation B.OR2 NaN if A or B == NaN, else A.PLM3 Associated Legendre polynomial P(-1<A<+1) degree B order C.POP1 Delete top element from the stack.POW(^)2 A ^ B.R22 R2 = A^2 + B^2.R2D1 Convert Radians to Degrees.RAND2 Uniform random values between A and B.RINT1 rint (A) (nearest integer).SIGN1 sign (+1 or -1) of A.SIN1 sin (A) (A in radians).SIND1 sin (A) (A in degrees).SINH1 sinh (A).SQRT1 sqrt (A).STD1 Standard deviation of A.STEP1 Heaviside step function H(A).STEPT1 Heaviside step function H(t-A).SUB(-)2 A - B.SUM1 Cumulative sum of ATAN1 tan (A) (A in radians).TAND1 tan (A) (A in degrees).TANH1 tanh (A).TDIST2 Student's t-distribution A(t,nu) = 1 - 2p, with t = A, and nu = B.'UPPER1 The highest (maximum) value of A.XOR2 B if A == NaN, else A.Y01 Bessel function of A (2nd kind, order 0).Y11 Bessel function of A (2nd kind, order 1).YN2 Bessel function of A (2nd kind, order B).SYMBOLSThe following symbols have special meaning:PI3.1415926...E2.7182818...TTable with t-coordinates

**OPTIONS**

-CSelect the columns that will be operated on until next occurrence of-C. List columns separated by commas; ranges like 1,3-5,7 are allowed. [-C(no arguments) resets the default action of using all columns except time column (see-N].-Caselects all columns, inluding time column, while-Crreverses (toggles) the current choices.-HInput file(s) has Header record(s). Number of header records can be changed by editing your .gmtdefaults file. If used,GMTdefault is 1 header record.-NSelect the number of columns and the column number that contains the "time" variable. Columns are numbered starting at 0 [2/0].-QQuick mode for scalar calculation. Shorthand for-Ca-N1/0-T0/0/1.-SOnly report the first row of the results [Default is all rows]. This is useful if you have computed a statistic (say the MODE) and only want to report a single number instead of numerous records with idendical values.-TRequired when no input files are given. Sets the t-coordinates of the first and last point and the equidistant sampling interval for the "time" column (see-N). If there is no time column (only data columns), give-Twith no arguments; this also implies-Ca.-VSelects verbose mode, which will send progress reports to stderr [Default runs "silently"].-biSelects binary input. Appendsfor single precision [Default is double]. Appendnfor the number of columns in the binary file(s).-boSelects binary output. Appendsfor single precision [Default is double].

**BEWARE**

The operatorPLMcalculates the associated Legendre polynomial of degree L and order M, and its argument is the cosine of the colatitude which must satisfy -1 <= x <= +1.PLMis not normalized. All derivatives are based on central finite differences, with natural boundary conditions.

**EXAMPLES**

To take log10 of the average of 2 data files, use gmtmath file1.d file2.dADD0.5MULLOG10=file3.d Given the file samples.d, which holds seafloor ages in m.y. and seafloor depth in m, use the relation depth(in m) = 2500 + 350 * sqrt (age) to print the depth anomalies: gmtmath samples.d TSQRT350MUL2500ADDSUB=| lpr To take the average of columns 1 and 4-6 in the three data sets sizes.1, sizes.2, and sizes.3, use gmtmath-C1,4-6 sizes.1 sizes.2ADDsizes.3ADD3DIV=ave.d To take the 1-column data set ages.d and calculate the modal value and assign it to a variable, try set mode_age = `gmtmath-S-Tages.dMODE=` To use gmtmath as a RPN Hewlett-Packard calculator on scalars (i.e., no input files) and calculate arbitrary expressions, use the-Qoption. As an example, we will calculate the value of Kei (((1 + 1.75)/2.2) + cos (60)) and store the result in the shell variable z: set z = `gmtmath-Q1 1.75ADD2.2DIV60COSDADDKEI=`

**BUGS**

Files that have the same name as some operators, e.g., ADD, SIGN, =, etc. cannot be read and must not be present in the current directory. Piping of files is not allowed on input, but the output can be sent to stdout. The stack limit is hard-wired to 50. All functions expecting a positive radius (e.g., log, kei, etc.) are passed the absolute value of their argument.

**REFERENCES**

Abramowitz, M., and I. A. Stegun, 1964,HandbookofMathematicalFunctions, Applied Mathematics Series, vol. 55, Dover, New York. Press, W. H., S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, 1992,NumericalRecipes, 2nd edition, Cambridge Univ., New York.

**SEE** **ALSO**

gmt(1gmt),grd2xyz(1gmt),grdedit(1gmt),grdinfo(1gmt),grdmath(1gmt),xyz2grd(1gmt) 1 Jan 2004 GMTMATH(l)