LON-CAPA Homework System

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<script> Functions

A list of functions that have been written that are available in 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 $N%$M N 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. $y can be a pure real number In CAPA, j0, j1 and jn are contained in one function, jn(m,x) where m takes the value of 0, 1 or 2. jv(y,x) is new to LON-CAPA.
yn(m,x) &y0($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. $y can be a pure real number In CAPA, y0, y1 and yn are contained in one function, yn(m,x) where m takes the value of 0, 1 or 2. yv(y,x) is new to LON-CAPA.
random(l,u,d) &random($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 $d can be pure numbers In CAPA, all the 3 arguments must be of the same type. However, now you can mix the type
choose(i,...) &choose($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. $i can be a pure integer  
tex(a,b), tex("a","b") &tex($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,$y) If x is an integer, returns a string. If x is real than the output is a string with format given by y. For example, if x = 12.3456, &to_string(x,".3F") = 12.345 and &to_string(x,".3E") = 1.234E+01.  
capa_id(), class(), section(), set(), problem() &class(), &section() Returns null string, class descriptive name, section number, set number and null string. capa_id(), set() and problem() are no longer used. Currently, they return a null value.
name(), student_number() &name(), &student_number() Return the full name in the following format: lastname, firstname initial. Student_number returns the student 9-alphanumeric string. If undefined, the functions return null.  
open_date(), due_date(), answer_date() &open_date(), &due_date(), &answer_date() Problem open date, due date and answer date. The time is also included in 24-hr format. Output format for time is changed slightly. If pass noon, it displays ..pm else it displays ..am. So 23:59 is displayed as 11:59 pm.
get_seed(), set_seed() Not implemented Get and set the random seed.  
sub_string(a,b,c) &sub_string($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 $n+1 element since the array count starts from 0
"xx" can be a variable or a calculation. In LON-CAPA, an array is defined by @arrayname. It is not necessary to specify the dimension of the array. 
array_moments(B,A) @B=&array_moments(@A) Evaluates the moments of an array A and place the result in array B[i] where i = 0 to 4. The contents of B are as follows: B[0] = number of elements, B[1] = mean, B[2] = variance, B[3] = skewness and B[4] = kurtosis. In CAPA, the moments are passed as an array in the first argument whereas in LON-CAPA, the array containing the moments are set equal to the function.
array_max(Name), array_min(Name) &min(@Name), &max(@Name) In LON-CAPA to find the maximum value of an array, use &max(@arrayname)  and to find the minimum value of an array, use &min(@arrayname) Combined with the min and max functions defined earlier.
init_array(Name) undef @name To destroy the contents of an array, use Use perl intrinsic undef function.
random_normal (return_array,item_cnt,seed,av,std_dev) @return_array=&random_normal ($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 $seed In CAPA the results are passed as the first argument whereas in LON-CAPA the results are set equal to the function.
random_beta (return_array,item_cnt,seed,aa,bb) @return_array=&random_beta ($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


Guy Albertelli
Last modified: Tue June 12 15:25 EDT 2001