Annotation of loncom/html/adm/help/tex/Problem_LON-CAPA_Functions.tex, revision 1.11
1.1 bowersj2 1: \label{Problem_LON-CAPA_Functions}
2:
3: \begin{longtable}{|p{8.5cm}|p{8.5cm}|}
4: \hline
5: \textbf{LON-CAPA Function }
6: &\textbf{Description }
7: \endhead
8: \hline
9:
10: \&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) \\
11: \hline
12:
13: \&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 \\
14: \hline
15:
16: \&log(\$x), \&log10(\$x) & Natural and base-10 logarithm. \$x can be a pure number \\
17: \hline
18:
19: \&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 \\
20: \hline
21:
22: \&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 \\
23: \hline
24:
1.6 www 25: \&erf(\$x), \&erfc(\$x) & Error function.
26: erf = 2/sqrt(pi) integral (0,x) et-sq and \emph{ erfx(x)}
27: = 1.0 - \emph{erf(x)}. \$x can be a pure number \\
1.1 bowersj2 28: \hline
29:
30: \&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 \\
31: \hline
32:
33: \&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 \\
34: \hline
35:
36: \&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 \\
37: \hline
38:
39: \$N\%\$M & N and M are integers and returns the remainder (in integer) of N/M. \$N and \$M can be pure numbers \\
40: \hline
41:
42: \&sinh(\$x), \&cosh(\$x), \&tanh(\$x) & Hyperbolic functions. \$x can be a pure number \\
43: \hline
44:
45: \&asinh(\$x), \&acosh(\$x), \&atanh(\$x) & Inverse hyperbolic functions. \$x can be a pure number \\
46: \hline
47:
1.5 albertel 48: \&format(\$x,'nn') & Display or format \$x as nn where nn is nF or nE or nS and n is an integer. \\
1.1 bowersj2 49: \hline
50:
1.7 albertel 51: \&prettyprint(\$x,'nn','optional target') & Note that that tag $<$num$>$ can be used to do the same thing. Display or format \$x as nn where nn is nF or nE or nS and n is an integer. Also supports the first character being a \$, it then will format the result with a a call to \&dollarformat() described below. If the first character is a , it will format it with commas grouping the thousands. In S mode it will fromat the number to the specified number of significant figures and display it in F mode. In E mode it will attempt to generate a pretty x10\^{}3 rather than a E3 following the number, the 'optional target' argument is optional but can be used to force \&prettyprint to generate either 'tex' output, or 'web' output, most people do not need to specify this argument and can leave it blank.\\
1.1 bowersj2 52: \hline
53:
1.6 www 54: \&dollarformat(\$x,'optional target') & Reformats \$x to have a \$ (or $\backslash$\$ if in tex mode) and to have , grouping thousands. The 'optional target' argument is optional but can be used to force \&prettyprint to generate either 'tex' output, or 'web' output, most people do not need to specify this argument and can leave it blank.\\
1.1 bowersj2 55: \hline
1.11 ! albertel 56:
! 57: \parbox{6.49cm}{
! 58: Option 1 - \$best = \&languages() \\
! 59: Option 2 - @all = \&languages() \\
! 60: Option 3 - \$best = \&languages($\backslash$@desired\_languages) \\
! 61: Option 4 - @all = \&languages($\backslash$@desired\_languages) \\
! 62: }& Returns the best language to use, in the first two options returns the languages codes in the preference order of the user. In the second two examples returns the best matches from a list of desired language possibilities. & \\
! 63: \hline
! 64:
1.1 bowersj2 65: \&roundto(\$x,\$n) & Rounds a real number to n decimal points. \$x and \$n can be pure numbers \\
66: \hline
67:
1.10 www 68: \&cas(\$s,\$e)&Evaluates the expression \$e inside the symbolic algebra system \$s. Currently, only the Maxima symbolic math system is implemented. Example: \&cas('maxima','6*7')\\
1.9 albertel 69: \hline
70:
1.1 bowersj2 71: \&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 \\
72: \hline
73:
74: \&html(``a'') or \&html(\$a) & Output only if the output mode chosen is in html format \\
75: \hline
76:
77: \&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 \\
78: \hline
79:
80: \&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 \\
81: \hline
82:
83: \&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 \\
84: \hline
85:
86: \&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 \\
87: \hline
88:
89: \parbox{6.49cm}{
1.2 bowersj2 90: Option 1 - \&map(\$seed,[$\backslash$\$w,$\backslash$\$x,$\backslash$\$y,$\backslash$\$z],[\$a,\$b,\$c,\$d]) or \\
91: Option 2 - \&map(\$seed,$\backslash$@mappedArray,[\$a,\$b,\$c,\$d]) \\
92: Option 3 - @mappedArray = \&map(\$seed,[\$a,\$b,\$c,\$d]) \\
93: Option 4 - (\$w,\$x,\$y,\$z) = \&map(\$seed,$\backslash$@a) \\
1.4 albertel 94: Option 5 - @Z = \&map(\$seed,$\backslash$@a) \\
1.2 bowersj2 95: where \$a='A'\\
96: \$b='B'\\
97: \$c='B'\\
98: \$d='B'\\
1.4 albertel 99: \$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] =$>$ $\backslash$@a. And Option 5 is the same as option 4 the array of results are saved into a signle array rather than an array opf scalar variables.\\
1.1 bowersj2 100: \hline
101:
1.2 bowersj2 102: \parbox{6.49cm}{Option 1 - \&rmap(\$seed,[$\backslash$\$w,$\backslash$\$x,$\backslash$\$y,$\backslash$\$z],[\$a,\$b,\$c,\$d]) or \\
103: Option 2 - \&rmap(\$seed,$\backslash$@rmappedArray,[\$a,\$b,\$c,\$d]) \\
104: Option 3 - @rmapped\_array = \&rmap(\$seed,[\$a,\$b,\$c,\$d]) \\
105: Option 4 - (\$w,\$x,\$y,\$z) = \&rmap(\$seed,$\backslash$@a) \\
1.4 albertel 106: Option 5 - @Z = \&map(\$seed,$\backslash$@a) \\
1.2 bowersj2 107: where \$a='A'\\
108: \$b='B'\\
109: \$c='B'\\
110: \$d='B'\\
1.1 bowersj2 111: \$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. \\
112: \hline
113:
1.7 albertel 114: \$a=\&xmlparse(\$string) & You probably should use the tag $<$parse$>$ instead of this function. Runs the internal parser over the argument parsing for display. \textbf{Warning}
1.1 bowersj2 115: This will result in different strings in different targets. Don't use the results of this function as an answer. \\
116: \hline
117:
118: \&tex(\$a,\$b), \&tex(``a'',''b'') & Returns a if the output mode is in tex otherwise returns b \\
119: \hline
120:
121: \&var\_in\_tex(\$a) & Equivalent to tex(``a'',''``) \\
122: \hline
123:
124: \&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. \\
125: \hline
126:
1.8 www 127: \&class(), \&sec() & Returns null string, class descriptive name, section number, set number and null string. \\
1.1 bowersj2 128: \hline
129:
1.8 www 130: \&name(), \&student\_number(), \&firstname(), \&lastname() & Return the full name in the following format: lastname, firstname initial. Student\_number returns the student 9-alphanumeric string. The functions firstname and lastname return just that part of the name. If undefined, the functions return null. \\
1.1 bowersj2 131: \hline
1.8 www 132: \&check\_status(\$partid) &Returns a number identifing the current status of a part. True values mean that a part is ``done'' (either unanswerable because of tries exhaustion, or correct) or a false value if a part can still be attempted. If \$part is unspecfied, it will check either the current $<$part$>$'s status or if outside of a $<$part$>$, check the status of previous $<$part$>$. The full set of return codes are: 'undef' means it is unattempted, 0 means it is attmpted and wrong but still has tries, 1 means it is marked correct, 2 means they have exceed maximum number of tries, 3 means it after the answer date\\
1.5 albertel 133: \hline
1.1 bowersj2 134: \&open\_date(), \&due\_date(), \&answer\_date() & Problem open date, due date and answer date. The time is also included in 24-hr format. \\
135: \hline
136:
137: Not implemented & Get and set the random seed. \\
138: \hline
139:
140: \&sub\_string(\$a,\$b,\$c)
1.6 www 141: 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'' \\
1.1 bowersj2 142: \hline
143:
144: @arrayname
145: 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. \\
146: \hline
147:
148: @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. \\
149: \hline
150:
1.6 www 151: \&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) \\
1.1 bowersj2 152: \hline
153:
154: undef @name & To destroy the contents of an array, use \\
155: \hline
156:
157: @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 \\
158: \hline
159:
160: @return\_array=\&random\_beta (\$item\_cnt,\$seed,\$aa,\$bb)
161: 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$<$1. \\
162: \hline
163:
164: @return\_array=\&random\_gamma (\$item\_cnt,\$seed,\$a,\$r)
165: NOTE: Both \$a and \$r MUST be positive. & Generate \$item\_cnt deviates of gamma distribution. The density of gamma is: (\$a**\$r)/gamma(\$r) * X**(\$r-1) * exp(-\$a*X). \\
166: \hline
167:
168: @return\_array=\&random\_exponential (\$item\_cnt,\$seed,\$av)
169: NOTE: \$av MUST be non-negative. & Generate \$item\_cnt deviates of exponential distribution. \\
170: \hline
171:
172: @return\_array=\&random\_poisson (\$item\_cnt,\$seed,\$mu)
173: NOTE: \$mu MUST be non-negative. & Generate \$item\_cnt deviates of poisson distribution. \\
174: \hline
175:
176: @return\_array=\&random\_chi (\$item\_cnt,\$seed,\$df)
177: NOTE: \$df MUST be positive. & Generate \$item\_cnt deviates of chi\_square distribution with \$df degrees of freedom. \\
178: \hline
179:
180: @return\_array=\&random\_noncentral\_chi (\$item\_cnt,\$seed,\$df,\$nonc)
181: NOTE: \$df MUST be at least 1 and \$nonc MUST be non-negative. & Generate \$item\_cnt deviates of noncentral\_chi\_square distribution with \$df degrees of freedom and noncentrality parameter \$nonc. \\
182: \hline
183:
184: @return\_array=\&random\_f (\$item\_cnt,\$seed,\$dfn,\$dfd)
185: NOTE: Both \$dfn and \$dfd MUST be positive. & Generate \$item\_cnt deviates of F (variance ratio) distribution with degrees of freedom \$dfn (numerator) and \$dfd (denominator). \\
186: \hline
187:
188: @return\_array=\&random\_noncentral\_f (\$item\_cnt,\$seed,\$dfn,\$dfd,\$nonc)
189: NOTE: \$dfn must be at least 1, \$dfd MUST be positive, and \$nonc must be non-negative. & Generate \$item\_cnt deviates of noncentral F (variance ratio) distribution with degrees of freedom \$dfn (numerator) and \$dfd (denominator). \$nonc is the noncentrality parameter. \\
190: \hline
191:
192: @return\_array=\&random\_multivariate\_normal (\$item\_cnt,\$seed,$\backslash$@mean,$\backslash$@covar)
193: NOTE: @mean should be of length p array of real numbers. @covar should be a length p array of references to length p arrays of 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. \\
194: \hline
195:
196: @return\_array=\&random\_multinomial (\$item\_cnt,\$seed,@p)
197: 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. \\
198: \hline
199:
200: @return\_array=\&random\_permutation (\$seed,@array) & Returns @array randomly permuted. \\
201: \hline
202:
203: @return\_array=\&random\_uniform (\$item\_cnt,\$seed,\$low,\$high)
204: NOTE: \$low must be less than or equal to \$high. & Generate \$item\_cnt deviates from a uniform distribution. \\
205: \hline
206:
207: @return\_array=\&random\_uniform\_integer (\$item\_cnt,\$seed,\$low,\$high)
208: 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. \\
209: \hline
210:
211: @return\_array=\&random\_binomial (\$item\_cnt,\$seed,\$nt,\$p)
212: 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. \\
213: \hline
214:
215: @return\_array=\&random\_negative\_binomial (\$item\_cnt,\$seed,\$ne,\$p)
216: 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. \\
217: \hline
218: \end{longtable}
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