--- doc/homework/homework5.html 2001/05/31 20:51:31 1.3 +++ doc/homework/homework5.html 2001/06/13 19:53:03 1.6 @@ -4,7 +4,7 @@ LON-CAPA Homework System - +

LON-CAPA Homework System

Tags

@@ -300,10 +300,7 @@

<script> Functions

A list of functions that have been written that are available in - the Safe space scripting environment inside a problem. The eventual - goal is to provide all of the functions available in CAPA. Detailed - descriptions of each function and comparison with CAPA is given in - CAPA to LON-CAPA Functions. + the Safe space scripting environment inside a problem.

+ +

+ Detailed descriptions of each function and comparison with CAPA. +

+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
CAPA Functions + LON-CAPA + Descriptions + Differences (if any) +
sin(x), cos(x), tan(x)&sin($x), &cos($x), &tan($x)Trigonometric functions where x is in radians. $x + can be a pure number, i.e., you can call &sin(3.1415) 
sin(x), cos(x), tan(x)&sin($x), &cos($x), &tan($x)Trigonometric functions where x is in radians. $x + can be a pure number, i.e., you can call &sin(3.1415) 
asin(x), acos(x), atan(x), atan2(y,x)&asin($x), &acos($x), &atan($x), &atan2($y,$x)Inverse trigonometric functions. Return value is + in radians. For asin and acos the value of x must be between -1 and 1. + The atan2 returns a value between -pi and pi the sign of which is determined + by y. $x and $y can be pure numbers 
log(x), log10(x)&log($x), &log10($x)Natural and base-10 logarithm. $x can be a pure number 
exp(x), pow(x,y), sqrt(x)&exp($x), &pow($x,$y), &sqrt($x)Exponential, power and square root, i.e.,ex, xy and /x. $x and $y can be pure numbers 
abs(x), sgn(x)&abs($x), &sgn($x)Abs takes the absolute value of x while sgn(x) returns + 1, 0 or -1 depending on the value of x. For x>0, sgn(x) = 1, for x=0, sgn(x) + = 0 and for x<0, sgn(x) = -1. $x can be a pure number 
erf(x), erfc(x)&erf($x), &erfc($x)Error function.  erf = 2/sqrt(pi) integral (0,x) et-sq and erfx(x) = 1.0 - erf(x).  $x can be a pure number 
ceil(x), floor(x)&ceil($x), &floor($x)Ceil function returns an integer rounded up whereas + floor function returns and integer rounded down. If x is an integer than + it returns the value of the integer. $x can be a pure number 
min(...), max(...)&min(...), &max(...)Returns the minimum/ maximum value of a list of + arguments if the arguments are numbers. If the arguments are strings then + it returns a string sorted according to the ASCII codes 
factorial(n)&factorial($n)Argument (n) must be an integer else it will round + down. The largest value for n is 170. $n can be a pure number 
N%M$N%$MN and M are integers and returns the remainder (in + integer) of N/M. $N and $M can be pure numbers 
sinh(x), cosh(x), tanh(x)&sinh($x), &cosh($x), &tanh($x)Hyperbolic functions. $x can be a pure number 
asinh(x), acosh(x), atanh(x)&asinh($x), &acosh($x), &atanh($x)Inverse hyperbolic functions. $x can be a pure number 
roundto(x,n)&roundto($x,$n)Rounds a real number to n decimal points. $x and + $n can be pure numbers 
web("a","b","c") or web(a,b,c)&web("a","b","c") or &web($a,$b,$c)Returns either a, b or c depending on the output + medium. a is for plain ASCII, b for tex output and c for html output 
html("a") or html(a)&html("a") or &html($a)Output only if the output mode chosen is in html + format 
jn(m,x)&j0($x), &j1($x), &jn($m,$x), &jv($y,$x)Bessel functions of the first kind with orders 0, + 1 and m respectively. For jn(m,x), m must be an integer whereas for jv(y,x), + y is real. $x can be a pure number. $m must be an integer and can be a + pure integer number. $y can be a pure real numberIn CAPA, j0, j1 and jn are contained in one function, + jn(m,x) where m takes the value of 0, 1 or 2. jv(y,x) is new to LON-CAPA.
yn(m,x)&y0($x), &y1($x), &yn($m,$x), &yv($y,$x)Bessel functions of the second kind with orders + 0, 1 and m respectively. For yn(m,x), m must be an integer whereas for + yv(y,x), y is real. $x can be a pure number. $m must be an integer and + can be a pure integer number. $y can be a pure real numberIn CAPA, y0, y1 and yn are contained in one function, + yn(m,x) where m takes the value of 0, 1 or 2. yv(y,x) is new to LON-CAPA.
random(l,u,d)&random($l,$u,$d)Returns a uniformly distributed random number between + the lower bound, l and upper bound, u in steps of d. $l, $u and $d can + be pure numbersIn CAPA, all the 3 arguments must be of the same + type. However, now you can mix the type
choose(i,...)&choose($i,...)Choose the ith item from the argument list. i must + be an integer greater than 0 and the value of i should not exceed the number + of items. $i can be a pure integer 
map(seed;a,b,c,d;w,x,y,z)Option 1 - &map($seed,[\$w,\$x,\$y,\$z],\@a) or
+ Option 2 - &map($seed,\@a,[$w,$x,$y,$z])
+ where @a=('A','B','C','D')
+ $w='W'
+ $x='X'
+ $y='Y'
+ $z='Z'
Assigns to the variables $w, $x, $y and $z the values of the + variables A, B, C and D depending on the seed. (Option 1 of calling map). + In option 2, the values of $w, $x .. are mapped into the array @a. The two + options illustrate the different grouping.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.
rmap(seed;a,b,c,d;w,x,y,z)&rmap($seed,[\$w,\$x,\$y,\$z],\@a) or
+ &rmap($seed,\@a,[$w,$x,$y,$z])
+ where @a=('A','B','C','D')
+ $w='W'
+ $x='X'
+ $y='Y'
+ $z='Z'
The rmap functions does the reverse action of map if the same seed + is used in calling map and rmap. 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.
tex(a,b), tex("a","b")&tex($a,$b), &tex("a","b")Returns a if the output mode is in tex otherwise + returns b 
var_in_tex(a)&var_in_tex($a)Equivalent to tex("a","") 
to_string(x), to_string(x,y)&to_string($x), &to_string($x,$y)If x is an integer, returns a string. If x is real + than the output is a string with format given by y. For example, if x = + 12.3456, &to_string(x,".3F") = 12.345 and &to_string(x,".3E") = + 1.234E+01. 
capa_id(), class(), section(), set(), problem()&class(), &section()Returns null string, class descriptive name, section + number, set number and null string.capa_id(), set() and problem() are no longer used. + Currently, they return a null value.
name(), student_number()&name(), &student_number()Return the full name in the following format: lastname, + firstname initial. Student_number returns the student 9-alphanumeric string. + If undefined, the functions return null. 
open_date(), due_date(), answer_date()&open_date(), &due_date(), &answer_date()Problem open date, due date and answer date. The + time is also included in 24-hr format.Output format for time is changed slightly. If pass + noon, it displays ..pm else it displays ..am. So 23:59 is displayed as + 11:59 pm.
get_seed(), set_seed()Not implementedGet and set the random seed. 
sub_string(a,b,c)&sub_string($a,$b,$c)
perl  substr function. + However, note the differences
Retrieve a portion of string a starting from b and + length c. For example,  $a = "Welcome to LON-CAPA"; + $result=&sub_string($a,4,4); then $result is "come"Perl intrinsic function, substr(string,b,c) starts + counting from 0 (as opposed to 1). In the example to the left, substr($a,4,4) + returns "ome ".
array[xx]@arrayname
Array is intrinsic in perl. + To access a specific element use $arrayname[$n] where $n + is the $n+1 element since the array count starts from 0
"xx" can be a variable or a calculation.In LON-CAPA, an array is defined by @arrayname. + It is not necessary to specify the dimension of the array. 
array_moments(B,A)@B=&array_moments(@A)Evaluates the moments of an array A and place the + result in array B[i] where i = 0 to 4. The contents of B are as follows: + B[0] = number of elements, B[1] = mean, B[2] = variance, B[3] = skewness + and B[4] = kurtosis.In CAPA, the moments are passed as an array in the first argument whereas + in LON-CAPA, the array containing the moments are set equal to the function.
array_max(Name), array_min(Name)&min(@Name), &max(@Name)In LON-CAPA to find the maximum value of an array, use + &max(@arrayname)  and to find the minimum value of an array, use + &min(@arrayname)Combined with the min and max functions defined + earlier.
init_array(Name)undef @nameTo destroy the contents of an array, useUse perl intrinsic undef function.
random_normal (return_array,item_cnt,seed,av,std_dev)@return_array=&random_normal ($item_cnt,$seed,$av,$std_dev)Generate $item_cnt deviates of normal distribution of average $av and + standard deviation $std_dev. The distribution is generated from seed $seedIn CAPA the results are passed as the first argument whereas in LON-CAPA + the results are set equal to the function.
random_beta (return_array,item_cnt,seed,aa,bb)@return_array=&random_beta ($item_cnt,$seed,$aa,$bb)
+ NOTE: Both $aa and $bb MUST be greater than 1.0E-37.
Generate $item_cnt deviates of beta distribution. + The density of beta is: + X^($aa-1) *(1-X)^($bb-1) /B($aa,$bb) for 0<X<1.In CAPA the results are passed as the first argument whereas in LON-CAPA + the results are set equal to the function.
random_gamma (return_array,item_cnt,seed,a,r)@return_array=&random_gamma ($item_cnt,$seed,$a,$r)
+ NOTE: Both $a and $r MUST be positive.
Generate $item_cnt deviates of gamma distribution. + The density of gamma is: + ($a**$r)/gamma($r) * X**($r-1) * exp(-$a*X).In CAPA the results are passed as the first argument whereas in LON-CAPA + the results are set equal to the function.
random_exponential (return_array,item_cnt,seed,av)@return_array=&random_exponential ($item_cnt,$seed,$av)
+ NOTE: $av MUST be non-negative.
Generate $item_cnt deviates of exponential distribution. In CAPA the results are passed as the first argument whereas in LON-CAPA + the results are set equal to the function.
random_poisson (return_array,item_cnt,seed,mu)@return_array=&random_poisson ($item_cnt,$seed,$mu)
+ NOTE: $mu MUST be non-negative.
Generate $item_cnt deviates of poisson distribution. In CAPA the results are passed as the first argument whereas in LON-CAPA + the results are set equal to the function.
random_chi (return_array,item_cnt,seed,df)@return_array=&random_chi ($item_cnt,$seed,$df)
+ NOTE: $df MUST be positive.
Generate $item_cnt deviates of chi_square distribution with $df + degrees of freedom. In CAPA the results are passed as the first argument whereas in LON-CAPA + the results are set equal to the function.
random_noncentral_chi (return_array,item_cnt,seed,df,nonc)@return_array=&random_noncentral_chi ($item_cnt,$seed,$df,$nonc)
+ NOTE: $df MUST be at least 1 and $nonc MUST be non-negative.
Generate $item_cnt deviates of noncentral_chi_square + distribution with $df + degrees of freedom and noncentrality parameter $nonc. In CAPA the results are passed as the first argument whereas in LON-CAPA + the results are set equal to the function.
NOT IMPLEMENTED IN CAPA@return_array=&random_f ($item_cnt,$seed,$dfn,$dfd)
+ NOTE: Both $dfn and $dfd MUST be positive.
Generate $item_cnt deviates of F (variance ratio) distribution with + degrees of freedom $dfn (numerator) and $dfd (denominator). New to LON-CAPA
NOT IMPLEMENTED IN CAPA@return_array=&random_noncentral_f ($item_cnt,$seed,$dfn,$dfd,$nonc)
+ NOTE: $dfn must be at least 1, $dfd MUST be positive, and $nonc must + be non-negative.
Generate $item_cnt deviates of noncentral F (variance ratio) + distribution with degrees of freedom $dfn (numerator) and $dfd (denominator). + $nonc is the noncentrality parameter. New to LON-CAPA
NOT IMPLEMENTED IN CAPA@return_array=&random_multivariate_normal ($item_cnt,$seed,@mean,@covar)
+ 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.
Generate $item_cnt deviates of multivariate_normal distribution with + mean vector @mean and variance-covariance matrix. New to LON-CAPA
NOT IMPLEMENTED IN CAPA@return_array=&random_multinomial ($item_cnt,$seed,@p)
+ 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.
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 $item_cnt.New to LON-CAPA
NOT IMPLEMENTED IN CAPA@return_array=&random_permutation ($item_cnt,@array) Returns @array randomly permuted.New to LON-CAPA
NOT IMPLEMENTED IN CAPA@return_array=&random_uniform ($item_cnt,$seed,$low,$high)
+ NOTE: $low must be less than or equal to $high.
Generate $item_cnt deviates from a uniform distribution. New to LON-CAPA
NOT IMPLEMENTED IN CAPA@return_array=&random_uniform_integer ($item_cnt,$seed,$low,$high)
+ NOTE: $low and $high are both passed through int(). + $low must be less than or equal to $high.
Generate $item_cnt deviates from a uniform distribution in integers. New to LON-CAPA
NOT IMPLEMENTED IN CAPA@return_array=&random_binomial ($item_cnt,$seed,$nt,$p)
+ NOTE: $nt is rounded using int() and the result must be non-negative. + $p must be between 0 and 1 inclusive.
Generate $item_cnt deviates from the binomial distribution with + $nt trials and the probabilty of an event in each trial is $p. New to LON-CAPA
NOT IMPLEMENTED IN CAPA@return_array=&random_negative_binomial ($item_cnt,$seed,$ne,$p)
+ NOTE: $ne is rounded using int() and the result must be positive. + $p must be between 0 and 1 exclusive.
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. New to LON-CAPA
+ +

<script> Variables