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     <title>LON-CAPA Homework System</title>      <title>LON-CAPA Homework System</title>
   </head>    </head>
   
   <body>    <body bgcolor="white">
     <h1>LON-CAPA Homework System</h1>      <h1>LON-CAPA Homework System</h1>
   
     <h2>Tags</h2>      <h2>Tags</h2>
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     <h2>&lt;script&gt; Functions</h2>      <h2>&lt;script&gt; Functions</h2>
     <p>       <p> 
       A list of functions that have been written that are available in         A list of functions that have been written that are available in 
       the Safe space scripting environment inside a problem. The eventual        the Safe space scripting environment inside a problem. 
       goal is to provide all of the functions available in CAPA. Detailed  
       descriptions of each function and comparison with CAPA is given in  
       <a href="homework6.html">CAPA to LON-CAPA Functions</a>.  
     </p>      </p>
     <ul>      <ul>
       <li>sin(x), cos(x), tan(x)</li>        <li>sin(x), cos(x), tan(x)</li>
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       <li>caparesponse_check</li>        <li>caparesponse_check</li>
       <li>caparesponse_check_list</li>        <li>caparesponse_check_list</li>
     </ul>      </ul>
   <!-- Table inserted by H. K. Ng 
       06/01/2001
       06/12/2001
   -->
       <p> 
         Detailed descriptions of each function and comparison with CAPA.
       </p>
   
   <table border=1>    <table border=1>
       <tr>        <tr>
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                  y is real. $x can be a pure number. $m must be an integer and can be a                   y is real. $x can be a pure number. $m must be an integer and can be a
                  pure integer number. $y can be a pure real number</td>                   pure integer number. $y can be a pure real number</td>
              <td valign="top">In CAPA, j0, j1 and jn are contained in one function,               <td valign="top">In CAPA, j0, j1 and jn are contained in one function,
                  jn(m,x) where m takes the value of 0, 1 or 2. jv(y,x) was not implemented</td>                   jn(m,x) where m takes the value of 0, 1 or 2. jv(y,x) is new to LON-CAPA.</td>
     </tr>      </tr>
   
     <tr>      <tr>
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                  yv(y,x), y is real. $x can be a pure number. $m must be an integer and                   yv(y,x), y is real. $x can be a pure number. $m must be an integer and
                  can be a pure integer number. $y can be a pure real number</td>                   can be a pure integer number. $y can be a pure real number</td>
              <td valign="top">In CAPA, y0, y1 and yn are contained in one function,               <td valign="top">In CAPA, y0, y1 and yn are contained in one function,
                  yn(m,x) where m takes the value of 0, 1 or 2. yv(y,x) was not implemented</td>                   yn(m,x) where m takes the value of 0, 1 or 2. yv(y,x) is new to LON-CAPA.</td>
     </tr>      </tr>
   
     <tr>      <tr>
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     </tr>      </tr>
   
     <tr>      <tr>
                <td valign="top">map(seed;a,b,c,d;w,x,y,z)</td>
                <td valign="top">Option 1 - &amp;map($seed,[\$w,\$x,\$y,\$z],[$a,$b,$c,$d]) or <br> 
                     Option 2 - &amp;map($seed,\@mappedArray,[$a,$b,$c,$d]) <br>
                     Option 3 - @mappedArray = &amp;map($seed,[$a,$b,$c,$d]) <br>
                     Option 4 - ($w,$x,$y,$z) = &amp;map($seed,\@a) <br>
                     where $a='A'<br>
                           $b='B'<br>
                           $c='B'<br>
                           $d='B'<br>
                           $w, $x, $y, and $z are variables</td>
                <td valign="top">Assigns to the variables $w, $x, $y and $z the values of the
                     $a, $b, $c and $c (A, B, C and D). The precise value for $w .. depends
                     on the seed. (Option 1 of calling map). 
                     In option 2, the values of $a, $b .. are mapped into the array, @mappedArray. The two
                     options illustrate the different grouping. Options 3 and 4 give a consistent 
                     way (with other functions) of mapping the items. For each option, the group can
                     be passed as an array, for example, [$a,$b,$c,$d] => \@a.</td>
                <td valign="top">In CAPA, the arguments are divided into three groups separated
                     by a semicolon ;. In LON-CAPA, the separation is done by using [] brackets or
                     using an array @a. Note the backslash (\) before the arguments in the
                     second and third groups.</td>
       </tr>
   
   
       <tr>
                <td valign="top">rmap(seed;a,b,c,d;w,x,y,z)</td>
                <td valign="top">Option 1 - &amp;rmap($seed,[\$w,\$x,\$y,\$z],[$a,$b,$c,$d]) or <br> 
                     Option 2 - &amp;rmap($seed,\@rmappedArray,[$a,$b,$c,$d]) <br>
                     Option 3 - @rmapped_array = &amp;rmap($seed,[$a,$b,$c,$d]) <br>
                     Option 4 - ($w,$x,$y,$z) = &amp;rmap($seed,\@a) <br>
                     where $a='A'<br>
                           $b='B'<br>
                           $c='B'<br>
                           $d='B'<br>
                           $w, $x, $y, and $z are variables</td>
                <td valign="top">The rmap functions does the reverse action of map if the same seed
                     is used in calling map and rmap. </td>
                <td valign="top">In CAPA, the arguments are divided into three groups separated
                     by a semicolon ;. In LON-CAPA, the separation is done by using [] brackets or
                     using an array @a. Note the backslash (\) before the arguments in the
                     second and third groups.</td>
       </tr>
   
       <tr>
              <td valign="top">tex(a,b), tex("a","b")</td>               <td valign="top">tex(a,b), tex("a","b")</td>
              <td valign="top">&amp;tex($a,$b), &amp;tex("a","b")</td>               <td valign="top">&amp;tex($a,$b), &amp;tex("a","b")</td>
              <td valign="top">Returns a if the output mode is in tex otherwise               <td valign="top">Returns a if the output mode is in tex otherwise
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                   result in array B[i] where i = 0 to 4. The contents of B are as follows:                    result in array B[i] where i = 0 to 4. The contents of B are as follows:
                   B[0] = number of elements, B[1] = mean, B[2] = variance, B[3] = skewness                    B[0] = number of elements, B[1] = mean, B[2] = variance, B[3] = skewness
                   and B[4] = kurtosis.</td>                    and B[4] = kurtosis.</td>
              <td valign="top">&nbsp;</td>               <td valign="top">In CAPA, the moments are passed as an array in the first argument whereas
                     in LON-CAPA, the array containing the moments are set equal to the function.</td>
     </tr>      </tr>
   
     <tr>      <tr>
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              <td valign="top">To destroy the contents of an array, use</td>               <td valign="top">To destroy the contents of an array, use</td>
              <td valign="top">Use perl intrinsic undef function.</td>               <td valign="top">Use perl intrinsic undef function.</td>
     </tr>      </tr>
        <tr>
     <tr>               <td valign="top">random_normal (return_array,item_cnt,seed,av,std_dev)</td>
              <td valign="top">random_norma(...), random_beta(...), random_gamma(...),               <td valign="top">@return_array=&random_normal ($item_cnt,$seed,$av,$std_dev)</td>
                random_exponential(...), random_poisson(...), random_chi(...), random_noncentral(...)</td>               <td valign="top">Generate $item_cnt deviates of normal distribution of average $av and
              <td valign="top">Not yet implemented.</td>                          standard deviation $std_dev. The distribution is generated from seed $seed</td>
              <td valign="top">&nbsp;</td>               <td valign="top">In CAPA the results are passed as the first argument whereas in LON-CAPA 
              <td valign="top">&nbsp;</td>                          the results are set equal to the function.</td>
     </tr>      </tr>
   </table>       <tr>
                <td valign="top">random_beta (return_array,item_cnt,seed,aa,bb)</td>
                <td valign="top">@return_array=&random_beta ($item_cnt,$seed,$aa,$bb) <br>
                           NOTE: Both $aa and $bb MUST be greater than 1.0E-37.</td>
                <td valign="top">Generate $item_cnt deviates of beta distribution. 
                           The density of beta is:
                           X^($aa-1) *(1-X)^($bb-1) /B($aa,$bb) for 0&lt;X&lt;1.</td>
                <td valign="top">In CAPA the results are passed as the first argument whereas in LON-CAPA 
                           the results are set equal to the function.</td>
       </tr>
        <tr>
                <td valign="top">random_gamma (return_array,item_cnt,seed,a,r)</td>
                <td valign="top">@return_array=&random_gamma ($item_cnt,$seed,$a,$r) <br>
                           NOTE: Both $a and $r MUST be positive.</td>
                <td valign="top">Generate $item_cnt deviates of gamma distribution. 
                           The density of gamma is:
                           ($a**$r)/gamma($r) * X**($r-1) * exp(-$a*X).</td>
                <td valign="top">In CAPA the results are passed as the first argument whereas in LON-CAPA 
                           the results are set equal to the function.</td>
       </tr>
        <tr>
                <td valign="top">random_exponential (return_array,item_cnt,seed,av)</td>
                <td valign="top">@return_array=&random_exponential ($item_cnt,$seed,$av) <br>
                           NOTE: $av MUST be non-negative.</td>
                <td valign="top">Generate $item_cnt deviates of exponential distribution. </td>
                <td valign="top">In CAPA the results are passed as the first argument whereas in LON-CAPA 
                           the results are set equal to the function.</td>
       </tr>
        <tr>
                <td valign="top">random_poisson (return_array,item_cnt,seed,mu)</td>
                <td valign="top">@return_array=&random_poisson ($item_cnt,$seed,$mu) <br>
                           NOTE: $mu MUST be non-negative.</td>
                <td valign="top">Generate $item_cnt deviates of poisson distribution. </td>
                <td valign="top">In CAPA the results are passed as the first argument whereas in LON-CAPA 
                           the results are set equal to the function.</td>
       </tr>
        <tr>
                <td valign="top">random_chi (return_array,item_cnt,seed,df)</td>
                <td valign="top">@return_array=&random_chi ($item_cnt,$seed,$df) <br>
                           NOTE: $df MUST be positive.</td>
                <td valign="top">Generate $item_cnt deviates of chi_square distribution with $df 
                           degrees of freedom. </td>
                <td valign="top">In CAPA the results are passed as the first argument whereas in LON-CAPA 
                           the results are set equal to the function.</td>
       </tr>
        <tr>
                <td valign="top">random_noncentral_chi (return_array,item_cnt,seed,df,nonc)</td>
                <td valign="top">@return_array=&random_noncentral_chi ($item_cnt,$seed,$df,$nonc) <br>
                           NOTE: $df MUST be at least 1 and $nonc MUST be non-negative.</td>
                <td valign="top">Generate $item_cnt deviates of noncentral_chi_square 
                           distribution with $df 
                           degrees of freedom and noncentrality parameter $nonc. </td>
                <td valign="top">In CAPA the results are passed as the first argument whereas in LON-CAPA 
                           the results are set equal to the function.</td>
       </tr>
        <tr>
                <td valign="top">NOT IMPLEMENTED IN CAPA</td>
                <td valign="top">@return_array=&random_f ($item_cnt,$seed,$dfn,$dfd) <br>
                           NOTE: Both $dfn and $dfd MUST be positive.</td>
                <td valign="top">Generate $item_cnt deviates of F (variance ratio) distribution with  
                           degrees of freedom $dfn (numerator) and $dfd (denominator). </td>
                <td valign="top">New to LON-CAPA</td>
       </tr>
        <tr>
                <td valign="top">NOT IMPLEMENTED IN CAPA</td>
                <td valign="top">@return_array=&random_noncentral_f ($item_cnt,$seed,$dfn,$dfd,$nonc) <br>
                           NOTE: $dfn must be at least 1, $dfd MUST be positive, and $nonc must
                           be non-negative.</td>
                <td valign="top">Generate $item_cnt deviates of noncentral F (variance ratio) 
                           distribution with degrees of freedom $dfn (numerator) and $dfd (denominator).
                           $nonc is the noncentrality parameter. </td>
                <td valign="top">New to LON-CAPA</td>
       </tr>
        <tr>
                <td valign="top">NOT IMPLEMENTED IN CAPA</td>
                <td valign="top">@return_array=&random_multivariate_normal ($item_cnt,$seed,@mean,@covar) <br>
                           NOTE: @mean should be a length p array of real numbers. @covar should be a length
                           p array of references to length p arrays or real numbers (i.e. a p by p matrix.</td>
                <td valign="top">Generate $item_cnt deviates of multivariate_normal distribution with  
                           mean vector @mean and variance-covariance matrix. </td>
                <td valign="top">New to LON-CAPA</td>
       </tr>
        <tr>
                <td valign="top">NOT IMPLEMENTED IN CAPA</td>
                <td valign="top">@return_array=&random_multinomial ($item_cnt,$seed,@p) <br>
                           NOTE: $item_cnt is rounded with int() and the result must be non-negative. 
                           The number of elements in @p must be at least 2.</td>
                <td valign="top">Returns single observation from multinomial distribution with  
                           $item_cnt events classified into as many categories as the length of @p.
                           The probability of an event being classified into category i is given by 
                           ith element of @p. The observation is an array with length equal to @p, so
                           when called in a scalar context it returns the length of @p. The sum of the
                           elements of the obervation is equal to $item_cnt.</td>
                <td valign="top">New to LON-CAPA</td>
       </tr>
        <tr>
                <td valign="top">NOT IMPLEMENTED IN CAPA</td>
                <td valign="top">@return_array=&random_permutation ($item_cnt,@array) </td>
                <td valign="top">Returns @array randomly permuted.</td>
                <td valign="top">New to LON-CAPA</td>
       </tr>
        <tr>
                <td valign="top">NOT IMPLEMENTED IN CAPA</td>
                <td valign="top">@return_array=&random_uniform ($item_cnt,$seed,$low,$high) <br>
                           NOTE: $low must be less than or equal to $high.</td>
                <td valign="top">Generate $item_cnt deviates from a uniform distribution. </td>
                <td valign="top">New to LON-CAPA</td>
       </tr>
        <tr>
                <td valign="top">NOT IMPLEMENTED IN CAPA</td>
                <td valign="top">@return_array=&random_uniform_integer ($item_cnt,$seed,$low,$high) <br>
                           NOTE: $low and $high are both passed through int().
                                 $low must be less than or equal to $high.</td>
                <td valign="top">Generate $item_cnt deviates from a uniform distribution in integers. </td>
                <td valign="top">New to LON-CAPA</td>
       </tr>
        <tr>
                <td valign="top">NOT IMPLEMENTED IN CAPA</td>
                <td valign="top">@return_array=&random_binomial ($item_cnt,$seed,$nt,$p) <br>
                           NOTE: $nt is rounded using int() and the result must be non-negative. 
                                 $p must be between 0 and 1 inclusive.</td>
                <td valign="top">Generate $item_cnt deviates from the binomial distribution with
                           $nt trials and the probabilty of an event in each trial is $p. </td>
                <td valign="top">New to LON-CAPA</td>
       </tr>
        <tr>
                <td valign="top">NOT IMPLEMENTED IN CAPA</td>
                <td valign="top">@return_array=&random_negative_binomial ($item_cnt,$seed,$ne,$p) <br>
                           NOTE: $ne is rounded using int() and the result must be positive. 
                                 $p must be between 0 and 1 exclusive.</td>
                <td valign="top">Generate an array of $item_cnt outcomes generated from 
                           negative binomial distribution with
                           $ne events and the probabilty of an event in each trial is $p. </td>
                <td valign="top">New to LON-CAPA</td>
       </tr>
    </table>
   <!-- insertion ends -->
   
     <h2>&lt;script&gt; Variables</h2>      <h2>&lt;script&gt; Variables</h2>
     <ul>      <ul>
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     <address><a href="mailto:albertel@marvin.lite.msu.edu">Guy Albertelli</a></address>      <address><a href="mailto:albertel@marvin.lite.msu.edu">Guy Albertelli</a></address>
 <!-- Created: Thu May 17 15:05:35 EDT 2001 -->  <!-- Created: Thu May 17 15:05:35 EDT 2001 -->
 <!-- hhmts start -->  <!-- hhmts start -->
 Last modified: Fri May 18 21:29:39 EDT 2001  Last modified: Tue June 12 15:25 EDT 2001
 <!-- hhmts end -->  <!-- hhmts end -->
   </body>    </body>
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