help mata rpnfcn()
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Title

rpnfcn() -- A generic function evaluator based on Reverse Polish Notation (RPN)

Syntax

numeric matrix rpnfcn(pointer matrix A)

Description

mf_rpnfcn(A) returns the result of sequentially evaluating the commands given in the rows of matrix A.

The fundamental commands allowed in A falls in the following categories

Stack manipulation Commands that enters matrices into the stack, copies and interchange stack elements.

Binary operators The four basic arithmetic operations of addition, subtraction, multiplication, and division.

Single element functions Distribution functions which are executed on the current top element of the stack and replace it with the result.

Numerical integration Functions used for numerical integration based on Monte Carlo with stratified, antithetic sampling.

Remarks

Each row of A should consist of two elements, first a pointer to a function, and second either a pointer to an appropriate argument matrix or a null pointer. Upon completion of evaluation of all rows in A, only one matrix should be present in the internal stack set up by rpnfcn(), which is then returned as the result of the evaluation.

Note, that it is the users responsibility that matrices are conformable, as most procedures internally use the Mata colon operators, see Mata colon operators. The lack of check on matrix dimensions is considered a feature, as it for example allows specifying a (1 x 2) matrix as parameter vector for a function which then uses this pair of parameter values for evaluating all elements of a (n x m) matrix in the stack. Equally well, a (n x 2) parameter matrix can be supplied to the same function, now with the implication that the pair of values in each row of the parameter matrix is applied to all elements of the corresponding row in the (n x m) matrix in the stack.

Example

Consider the density for the minimum of two Weibull distributed random variables at x with the two parameter vectors theta1 and theta2. The following code defines and evaluates the algorithm matrix corresponding to this.

. mata ------------------------------------------------- mata (type end to exit) ----- : x = (NULL)

: theta1 = (NULL)

: theta2 = (NULL)

: fweimin = (&tostack(), &x \ > &enter(), NULL \ > &enter(), NULL \ > &fwei(), &theta1 \ > &swapst(), NULL \ > &Swei(), &theta2 \ > &product(), NULL \ > &rotst(), NULL \ > &enter(), NULL \ > &Swei(), &theta1 \ > &swapst(), NULL \ > &fwei(), &theta2 \ > &product(), NULL \ > &add(), NULL > )

: x = (0, 2, 8 \ > .7, 1, 6)

: theta1 = (-2, 2)

: theta2 = (0, .3)

: rpnfcn(fweimin) 1 2 3 +-------------------------------------------+ 1 | 0 .1344860648 4.74373e-08 | 2 | .6423218484 .4965861523 .0000298698 | +-------------------------------------------+

: end -------------------------------------------------------------------------------

Source code

rpnfcn.mata

Author

Henrik StÝvring, Research Unit of General Practice, University of Southern Denmark. Please email hstovring@health.sdu.dk if you have comments, questions or observe any problems.

Also see

Manual: [M] Mata Reference Manual

Online: help for [M-0] mata, RPN stack manipulation functions, RPN binary operators, RPN distribution functions, RPN functions for integration