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Diff for /capa/capa51/pProj/Changes between versions 1.2 and 1.3

version 1.2, 2000/02/09 22:10:24 version 1.3, 2000/08/30 15:02:30
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   New functions
   
   
   array_min(array_name)
   array_max(array_name)
   
   will calculate the min or max value from the 
   array given by array_name. All elements in 
   array array_name should be of numerical type, 
   if there is one element assigned a string value, 
   then array_min() and array_max() will give an
   error, indicating that it could not calculate 
   the min or max value for strings.
   
   /LET arr[123]=123
   /LET arr[456]=456
   /LET arr[1]=1
   /LET arr[34]=34
   /LET arr[56]=56
   /LET arr[78]=78
   /LET arr[12]=12
   /LET arr[4]=4
   /LET arr["124"]=124
   /LET arr[1.2]=1.01234567
   /LET max = array_max(arr)
   /LET min = array_min(arr)
   
   The results of max will be 456 and min will be 1.
   
   
   array_moments(result_array, input_array)
   
   
   /LET elements = array_moments(result_array, data_array)
   
   The input array is data_array and the calculated results will be placed in a newly
   created array named result_array. This resulting array contains exactly five elements, 
   result_array[0]  = number of elements in input array
   result_array[1]  = mean value of elements in input array
   result_array[2]  = variance of elements in input array
   result_array[3]  = skewness of elements in input array
   result_array[4]  = Kurtosis value of elements in input array
   
   Suppose all values in array data_array is denoted by $X$, 
   the $i$-th element in the array is denoted by $x_i$, and 
   the number of elements in the array is denoted by $n$.
   The formula of mean value is given by $\Sigma_{i=0}^{n-1} x_i / n$.
   Let $\mu$ represents the mean value of the array. 
   The variance is defined as  $\frac{\Sigma_{i=0}^{n-1}(x_i - \mu)^2}{n-1}$. 
   The standard deviation of the array can be calculated by taking the square root
   of variance. Let $\sigma$ denotes the standard deviation of the array. 
   Skewness is calculated from $\frac{\Sigma_{x=0}^{n-1}((x_i - \mu)/\sigma)^3}{n}$
   The Kurtosis value is from the formula 
   \frac{\Sigma_{i=0}^{n-1}(x_i - \mu)/\sigma)^4}{n} - 3$
   The constant $3$ is used to make the normal distribution appear to have a zero Kurtosis.
   
   
   Formula answer
   
   As of CAPA 5.1, a new type of answer can be used by the instructor. 
   A formula as an answer to a problem. That is, the instructor defines a string of 
   formula and ask the students to enter the formula, as long as the entered formula
   is equivalent to the answer formula, the CAPA system will check and 
   issue correctness or incorrectness based on their equivalence. 
   The underlying mechanism behind this type of answer is that besides the formula string, 
   two additional pieces of informations have to be provided 
   by the instructor, (1) the list of variables used in the answer string and 
   (2) the values of these variables to be used in evaluating formula equivalence.
   Those two pieces of information are given within a pair of angle brackets appearing
   as the right hand side of the keywork "eval =". 
   
   The list of variables is entered as a string or a variable containing a 
   string value. Within that string, each variable is separated by a comma. 
   The symbol '@' then follows. 
   Two forms of variable values can be used. A string with comma separated numerical values
   or two comma separated numerical values divided by a ':' symbol and followed by
   a '#' symbol and an integer indicating the number of values to be 
   interpolated within the two values given previously. Both form can be replaced by
   a variable containing the proper string value. 
   
   Tolerence can be given to allow the instructor fine tune the results
   of acceptable values when checking the equivalence of two formulae. 
   
   
   /LET f="x^2+y*y^(2)"
   /LET vlist = "x,y"
   /LET pts = "1,4:4,5#5"
   
   /ANS(f,str=FML ,eval = <"x,y" @ "-1.0,-1.0":"1,1"#4, pts, "0.0,0.0"> ,tol=1e-9) 
   
   --
 Fixed rad != 1/s  in capaUnit.c  Fixed rad != 1/s  in capaUnit.c
 add   init_array() function to the user  add   init_array() function to the user
   
Removed from v.1.2  
changed lines
  Added in v.1.3

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