Resp: 2 of 2 by wes at kuhub.cc.ukans.edu

Author: [Wes Hubert]

  Date: Thu Apr 04 1991 22:56 

 Lines: 238





 

CMAT is an HP48 program for performing operations on columns of a

matrix. CMAT iterates over each row of the matrix, treating the n

columns of the matrix as if they were variables named C1, C2, ...

Cn, or, optionally, as if they were named with user-specified

names. The operations can be be limited to selected rows of the

matrix by supplying a boolean condition that must be met before

the computation is peformed. If the result column is not in the

original matrix, the matrix will be expanded to include the new

column.

 

Before executing CMAT, you must place on level two of the stack

the matrix object to process, and on level one of the stack either

an algebraic object that specifies the compuation to perform or a

list that specifies a series of variable names, conditions, and

computations.

 

For example, place the matrix

 

[[ 1 5 ]

 [ 2 4 ]

 [ 3 6 ]]

 

on the stack.

 

Next place the algebraic object

 

'C4=C2^2+C1'

 

on the stack. It specifies computing a new column, column four, as

column two squared plus column one. Since column three is not part

of the original matrix, it is filled with zeros.

 

Executing CMAT will replace these objects with the matrix:

 

[[ 1 5 0 26 ]

 [ 2 4 0 18 ]

 [ 3 6 0 39 ]]

 

 

The Evaluation List

 

For computations to complex to specify with a single equation, CMAT

allows an evaluation list instead of an equation.  The list can contain

name assignment lists and conditional expression lists as well as

equations.  Each list begins with a string.  "Names", "If', or "Compute".

The first character is sufficient (e.g. "N" for "Names).  A name list

consists of one or more lists whose first item is a column number and

whose second item is a name for the column.  A conditional list contains

and algebraic object specifying a condition that must be true for a row

in order for the following equation to be processed.  An imperative

list contains an equation, and is equivalent to an equation by itself

not contained in a list (e.g. {"C" 'equation'} and 'equation' are

treated identically.

 

  Name List    {"Names" {2 'Age'} {3 'Income'}}

  Conditional  {"If" 'boolean' 'equation'}

  Imperative   {"Compute" 'equation'}

 

If a column is not explicitly named, it has a default of of Cn where

'n' is the column number, but 'Cn' cannot be used to specify a column

that has been named.  It must be called by its name.

 

An example list:

  { { "N" {4 'Sum'} {5 Mean'}}

    'Sum=C1+C2+C3'

    { "If" 'C1>0' 'Mean=Sum/3' } }

 

 

Immediate Execution Functions

 

Functions that are available only for immediate execution from the

keyboard can be placed into programs by saving them in a program.

For example, RAND cannot be used directly in an algebraic

expression, but

 

<< RAND >> 'RANDOM' STO

 

creates a random number function that can then be used in an

algebraic expression such as

 

'C1=TRNC(10*RANDOM,0)'

 

to create a column of random numbers in the range 0 through 9.

 

 

Missing Value Indicators

 

To handle missing data, filter column variables with functions

such VALID and VALUE in the example below. In this example,

negative values indicate invalid data. The function VALID returns

1 if its argument is in the valid data range, 0 otherwise. The

function VALUE returns the original data value if it is in the

valid data range, 0 otherwise. Using these functions, C4 counts

the number of valid data points, C5 the total of valid data

values, and C6 the mean of the valid data.

 

<< << n | IF 'n>-1' THEN 1 ELSE 0 END >> >> 'VALID' STO

 

<< << n | IF 'n>-1' THEN n ELSE 0 END >> >> 'VALUE' STO

 

{ 'C4=VALID(C1)+VALID(C2)+VALID(C3)'

  'C5=VALUE(C1)+VALUE(C2)+VALUE(C3)'

  {"IF" 'C4>0' 'C6=C5/C4'} }

 

The condition 'C4>0'prevents dividing by zero when evaluating the

expression for C6 if there are no valid values in a row.