.. index:: ! gmtmath ******* gmtmath ******* .. only:: not man gmtmath - Reverse Polish Notation (RPN) calculator for data tables Synopsis -------- .. include:: common_SYN_OPTs.rst_ **gmtmath** [ |-A|\ *t_f(t).d*\ [**+e**]\ [**+s**\ \|\ **w**] ] [ |-C|\ *cols* ] [ |-E|\ *eigen* ] [ |-I| ] [ |-N|\ *n\_col*\ [/*t_col*] ] [ |-Q| ] [ |-S|\ [**f**\ \|\ **l**] ] [ |-T|\ *t\_min*/*t_max*/*t_inc*\ [**+n**\ ]\|\ *tfile* ] [ |SYN_OPT-V| ] [ |SYN_OPT-b| ] [ |SYN_OPT-d| ] [ |SYN_OPT-e| ] [ |SYN_OPT-f| ] [ |SYN_OPT-g| ] [ |SYN_OPT-h| ] [ |SYN_OPT-i| ] [ |SYN_OPT-o| ] [ |SYN_OPT-s| ] *operand* [ *operand* ] **OPERATOR** [ *operand* ] **OPERATOR** ... **=** [ *outfile* ] |No-spaces| Description ----------- **gmtmath** will 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]. Data operations are element-by-element, not matrix manipulations (except where noted). Some operators only require one operand (see below). If no data tables are used in the expression then options **-T**, **-N** can be set (and optionally **-bo** to indicate the data type for binary tables). If STDIN is given, the standard input will be read and placed on the stack as if a file with that content had been given on the command line. By default, all columns except the "time" column are operated on, but this can be changed (see **-C**). 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 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). The special argument STDIN means that *stdin* will be read and placed on the stack; STDIN can appear more than once if necessary. *outfile* The name of a table data file that will hold the final result. If not given then the output is sent to stdout. Optional Arguments ------------------ .. _-A: **-A**\ *t_f(t).d*\ [**+e**]\ [**+r**]\ [**+s**\ \|\ **w**] Requires **-N** and will partially initialize a table with values from the given file containing *t* and *f(t)* only. The *t* is placed in column *t\_col* while *f(t)* goes into column *n\_col* - 1 (see **-N**). Append **+r** to only place *f(t)* and leave the left hand side of the matrix equation alone. If used with operators LSQFIT and SVDFIT you can optionally append the modifier **+e** which will instead evaluate the solution and write a data set with four columns: t, f(t), the model solution at t, and the the residuals at t, respectively [Default writes one column with model coefficients]. Append **+w** if *t_f(t).d* has a third column with weights, or append **+s** if *t_f(t).d* has a third column with 1-sigma. In those two cases we find the weighted solution. The weights (or sigmas) will be output as the last column when **+e** is in effect. .. _-C: **-C**\ *cols* Select 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**). **-Ca** selects all columns, including time column, while **-Cr** reverses (toggles) the current choices. When **-C** is in effect it also controls which columns from a file will be placed on the stack. .. _-E: **-E**\ *eigen* Sets the minimum eigenvalue used by operators LSQFIT and SVDFIT [1e-7]. Smaller eigenvalues are set to zero and will not be considered in the solution. .. _-I: **-I** Reverses the output row sequence from ascending time to descending [ascending]. .. _-N: **-N**\ *n_col*\ [/*t_col*] Select the number of columns and optionally the column number that contains the "time" variable [0]. Columns are numbered starting at 0 [2/0]. If input files are specified then **-N** will add any missing columns. .. _-Q: **-Q** Quick mode for scalar calculation. Shorthand for **-Ca** **-N**\ 1/0 **-T**\ 0/0/1. In this mode, constants may have plot units (i.e., c, i, p) and if so the final answer will be reported in the unit set by :ref:`PROJ_LENGTH_UNIT `. .. _-S: **-S**\ [**f**\ \|\ **l**] Only report the first or last 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 identical values. Append **l** to get the last row and **f** to get the first row only [Default]. .. _-T: **-T**\ *t_min*/*t_max*/*t_inc*\ [**+n**\ ]\|\ *tfile* Required 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**). Append **+n** if you are specifying the number of equidistant points instead. If there is no time column (only data columns), give **-T** with no arguments; this also implies **-Ca**. Alternatively, give the name of a file whose first column contains the desired t-coordinates which may be irregular. .. _-V: .. |Add_-V| unicode:: 0x20 .. just an invisible code .. include:: explain_-V.rst_ .. |Add_-bi| unicode:: 0x20 .. just an invisible code .. include:: explain_-bi.rst_ .. |Add_-bo| replace:: [Default is same as input, but see **-o**] .. include:: explain_-bo.rst_ .. |Add_-d| unicode:: 0x20 .. just an invisible code .. include:: explain_-d.rst_ .. |Add_-e| unicode:: 0x20 .. just an invisible code .. include:: explain_-e.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_-ocols.rst_ .. include:: explain_-s.rst_ .. include:: explain_help.rst_ Operators --------- Choose among the following 185 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) | +-----------------+--------+--------------------------------------------------------------------------------------------+ | **ACSC** | 1 1 | acsc (A) | +-----------------+--------+--------------------------------------------------------------------------------------------+ | **ACOT** | 1 1 | acot (A) | +-----------------+--------+--------------------------------------------------------------------------------------------+ | **ADD** | 2 1 | A + B | +-----------------+--------+--------------------------------------------------------------------------------------------+ | **AND** | 2 1 | B if A == NaN, else A | +-----------------+--------+--------------------------------------------------------------------------------------------+ | **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) | +-----------------+--------+--------------------------------------------------------------------------------------------+ | **CEIL** | 1 1 | ceil (A) (smallest integer >= A) | +-----------------+--------+--------------------------------------------------------------------------------------------+ | **CHICRIT** | 2 1 | Chi-squared distribution 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 | +-----------------+--------+--------------------------------------------------------------------------------------------+ | **COL** | 1 1 | Places column A on the stack | +-----------------+--------+--------------------------------------------------------------------------------------------+ | **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) | +-----------------+--------+--------------------------------------------------------------------------------------------+ | **DDT** | 1 1 | d(A)/dt Central 1st derivative | +-----------------+--------+--------------------------------------------------------------------------------------------+ | **D2DT2** | 1 1 | d^2(A)/dt^2 2nd derivative | +-----------------+--------+--------------------------------------------------------------------------------------------+ | **D2R** | 1 1 | Converts Degrees to Radians | +-----------------+--------+--------------------------------------------------------------------------------------------+ | **DENAN** | 2 1 | Replace NaNs in A with values from B | +-----------------+--------+--------------------------------------------------------------------------------------------+ | **DILOG** | 1 1 | dilog (A) | +-----------------+--------+--------------------------------------------------------------------------------------------+ | **DIFF** | 1 1 | Forward difference between adjacent elements of A (A[1]-A[0], A[2]-A[1], ..., NaN) | +-----------------+--------+--------------------------------------------------------------------------------------------+ | **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) | +-----------------+--------+--------------------------------------------------------------------------------------------+ | **ERFINV** | 1 1 | Inverse error function of A | +-----------------+--------+--------------------------------------------------------------------------------------------+ | **EQ** | 2 1 | 1 if A == B, else 0 | +-----------------+--------+--------------------------------------------------------------------------------------------+ | **EXCH** | 2 2 | Exchanges A and B on the stack | +-----------------+--------+--------------------------------------------------------------------------------------------+ | **EXP** | 1 1 | exp (A) | +-----------------+--------+--------------------------------------------------------------------------------------------+ | **FACT** | 1 1 | A! (A factorial) | +-----------------+--------+--------------------------------------------------------------------------------------------+ | **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 | +-----------------+--------+--------------------------------------------------------------------------------------------+ | **FLIPUD** | 1 1 | Reverse order of 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 | +-----------------+--------+--------------------------------------------------------------------------------------------+ | **INT** | 1 1 | Numerically integrate A | +-----------------+--------+--------------------------------------------------------------------------------------------+ | **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) | +-----------------+--------+--------------------------------------------------------------------------------------------+ | **KN** | 2 1 | Modified Bessel function of A (2nd kind, order B) | +-----------------+--------+--------------------------------------------------------------------------------------------+ | **KEI** | 1 1 | kei (A) | +-----------------+--------+--------------------------------------------------------------------------------------------+ | **KER** | 1 1 | ker (A) | +-----------------+--------+--------------------------------------------------------------------------------------------+ | **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 | +-----------------+--------+--------------------------------------------------------------------------------------------+ | **LE** | 2 1 | 1 if A <= B, else 0 | +-----------------+--------+--------------------------------------------------------------------------------------------+ | **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 | +-----------------+--------+--------------------------------------------------------------------------------------------+ | **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) | +-----------------+--------+--------------------------------------------------------------------------------------------+ | **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 | +-----------------+--------+--------------------------------------------------------------------------------------------+ | **LSQFIT** | 1 0 | Let current table be [A \| b] return least squares solution x = A \\ b | +-----------------+--------+--------------------------------------------------------------------------------------------+ | **LT** | 2 1 | 1 if A < B, else 0 | +-----------------+--------+--------------------------------------------------------------------------------------------+ | **MAD** | 1 1 | Median Absolute Deviation (L1 STD) of A | +-----------------+--------+--------------------------------------------------------------------------------------------+ | **MADW** | 2 1 | Weighted Median Absolute Deviation (L1 STD) of A for weights in B | +-----------------+--------+--------------------------------------------------------------------------------------------+ | **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 | +-----------------+--------+--------------------------------------------------------------------------------------------+ | **PERM** | 2 1 | Permutations n_P_r, with n = A and r = B | +-----------------+--------+--------------------------------------------------------------------------------------------+ | **PPDF** | 2 1 | Poisson distribution P(x,lambda), with x = A and lambda = 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) | +-----------------+--------+--------------------------------------------------------------------------------------------+ | **POP** | 1 0 | Delete top element from the stack | +-----------------+--------+--------------------------------------------------------------------------------------------+ | **POW** | 2 1 | A ^ 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 | Weighted 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 | +-----------------+--------+--------------------------------------------------------------------------------------------+ | **ROTT** | 2 1 | Rotate A by the (constant) shift B in the t-direction | +-----------------+--------+--------------------------------------------------------------------------------------------+ | **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) | +-----------------+--------+--------------------------------------------------------------------------------------------+ | **STEPT** | 1 1 | Heaviside step function H(t-A) | +-----------------+--------+--------------------------------------------------------------------------------------------+ | **SUB** | 2 1 | A - B | +-----------------+--------+--------------------------------------------------------------------------------------------+ | **SUM** | 1 1 | Cumulative sum of A | +-----------------+--------+--------------------------------------------------------------------------------------------+ | **TAN** | 1 1 | tan (A) (A in radians) | +-----------------+--------+--------------------------------------------------------------------------------------------+ | **TAND** | 1 1 | tan (A) (A in degrees) | +-----------------+--------+--------------------------------------------------------------------------------------------+ | **TANH** | 1 1 | tanh (A) | +-----------------+--------+--------------------------------------------------------------------------------------------+ | **TAPER** | 1 1 | Unit weights cosine-tapered to zero within A of end margins | +-----------------+--------+--------------------------------------------------------------------------------------------+ | **TN** | 2 1 | Chebyshev polynomial Tn(-1