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 + 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. $i can be a pure integer | ++ |
| map(seed;a,b,c,d;w,x,y,z) | +Option 1 - &map($seed,[\$w,\$x,\$y,\$z],[$a,$b,$c,$d]) or + Option 2 - &map($seed,\@mappedArray,[$a,$b,$c,$d]) + Option 3 - @mappedArray = &map($seed,[$a,$b,$c,$d]) + Option 4 - ($w,$x,$y,$z) = &map($seed,\@a) + where $a='A' + $b='B' + $c='B' + $d='B' + $w, $x, $y, and $z are variables |
+ 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. | +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) | +Option 1 - &rmap($seed,[\$w,\$x,\$y,\$z],[$a,$b,$c,$d]) or + Option 2 - &rmap($seed,\@rmappedArray,[$a,$b,$c,$d]) + Option 3 - @rmapped_array = &rmap($seed,[$a,$b,$c,$d]) + Option 4 - ($w,$x,$y,$z) = &rmap($seed,\@a) + where $a='A' + $b='B' + $c='B' + $d='B' + $w, $x, $y, and $z are variables |
+ 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(), §ion() | +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 | +