Annotation of loncom/html/adm/help/tex/Problem_LON-CAPA_Functions.tex, revision 1.2
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:
25: \&erf(\$x), \&erfc(\$x) & Error function. erf = 2/sqrt(pi) integral (0,x) et-sq and \emph{ erfx(x)}
26: = 1.0 - \emph{erf(x)}
27: . \$x can be a pure number \\
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:
48: \&format(\$x,''nn'') & Display or format \$x as nn where nn is nF or nE and n is an integer. Also supports the first character being a \$, it thjen will format the result with a call to \&dollarformat() described below. \\
49: \hline
50:
51: \&prettyprint(\$x,''nn'') & Display or format \$x as nn where nn is nF or nE 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. In E mode it will attempt to generate a pretty x10\^{}3 rather than a E3 following the number \\
52: \hline
53:
54: \&dollarformat(\$x & Reformats \$x to have a \$ (or $\backslash$\$ if in tex mode) and to have , grouping thousands. \\
55: \hline
56:
57: \&roundto(\$x,\$n) & Rounds a real number to n decimal points. \$x and \$n can be pure numbers \\
58: \hline
59:
60: \&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 \\
61: \hline
62:
63: \&html(``a'') or \&html(\$a) & Output only if the output mode chosen is in html format \\
64: \hline
65:
66: \&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 \\
67: \hline
68:
69: \&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 \\
70: \hline
71:
72: \&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 \\
73: \hline
74:
75: \&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 \\
76: \hline
77:
78: \parbox{6.49cm}{
1.2 ! bowersj2 79: Option 1 - \&map(\$seed,[$\backslash$\$w,$\backslash$\$x,$\backslash$\$y,$\backslash$\$z],[\$a,\$b,\$c,\$d]) or \\
! 80: Option 2 - \&map(\$seed,$\backslash$@mappedArray,[\$a,\$b,\$c,\$d]) \\
! 81: Option 3 - @mappedArray = \&map(\$seed,[\$a,\$b,\$c,\$d]) \\
! 82: Option 4 - (\$w,\$x,\$y,\$z) = \&map(\$seed,$\backslash$@a) \\
! 83: where \$a='A'\\
! 84: \$b='B'\\
! 85: \$c='B'\\
! 86: \$d='B'\\
1.1 bowersj2 87: \$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. \\
88: \hline
89:
1.2 ! bowersj2 90: \parbox{6.49cm}{Option 1 - \&rmap(\$seed,[$\backslash$\$w,$\backslash$\$x,$\backslash$\$y,$\backslash$\$z],[\$a,\$b,\$c,\$d]) or \\
! 91: Option 2 - \&rmap(\$seed,$\backslash$@rmappedArray,[\$a,\$b,\$c,\$d]) \\
! 92: Option 3 - @rmapped\_array = \&rmap(\$seed,[\$a,\$b,\$c,\$d]) \\
! 93: Option 4 - (\$w,\$x,\$y,\$z) = \&rmap(\$seed,$\backslash$@a) \\
! 94: where \$a='A'\\
! 95: \$b='B'\\
! 96: \$c='B'\\
! 97: \$d='B'\\
1.1 bowersj2 98: \$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. \\
99: \hline
100:
101: \$a=\&xmlparse(\$string) & Runs the internal parser over the argument parsing for display. \textbf{Warning}
102: This will result in different strings in different targets. Don't use the results of this function as an answer. \\
103: \hline
104:
105: \&tex(\$a,\$b), \&tex(``a'',''b'') & Returns a if the output mode is in tex otherwise returns b \\
106: \hline
107:
108: \&var\_in\_tex(\$a) & Equivalent to tex(``a'',''``) \\
109: \hline
110:
111: \&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. \\
112: \hline
113:
114: \&class(), \§ion() & Returns null string, class descriptive name, section number, set number and null string. \\
115: \hline
116:
117: \&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. \\
118: \hline
119:
120: \&open\_date(), \&due\_date(), \&answer\_date() & Problem open date, due date and answer date. The time is also included in 24-hr format. \\
121: \hline
122:
123: Not implemented & Get and set the random seed. \\
124: \hline
125:
126: \&sub\_string(\$a,\$b,\$c)
127: 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'' \\
128: \hline
129:
130: @arrayname
131: 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. \\
132: \hline
133:
134: @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. \\
135: \hline
136:
137: \&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) \\
138: \hline
139:
140: undef @name & To destroy the contents of an array, use \\
141: \hline
142:
143: @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 \\
144: \hline
145:
146: @return\_array=\&random\_beta (\$item\_cnt,\$seed,\$aa,\$bb)
147: 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$<$1. \\
148: \hline
149:
150: @return\_array=\&random\_gamma (\$item\_cnt,\$seed,\$a,\$r)
151: NOTE: Both \$a and \$r MUST be positive. & Generate \$item\_cnt deviates of gamma distribution. The density of gamma is: (\$a**\$r)/gamma(\$r) * X**(\$r-1) * exp(-\$a*X). \\
152: \hline
153:
154: @return\_array=\&random\_exponential (\$item\_cnt,\$seed,\$av)
155: NOTE: \$av MUST be non-negative. & Generate \$item\_cnt deviates of exponential distribution. \\
156: \hline
157:
158: @return\_array=\&random\_poisson (\$item\_cnt,\$seed,\$mu)
159: NOTE: \$mu MUST be non-negative. & Generate \$item\_cnt deviates of poisson distribution. \\
160: \hline
161:
162: @return\_array=\&random\_chi (\$item\_cnt,\$seed,\$df)
163: NOTE: \$df MUST be positive. & Generate \$item\_cnt deviates of chi\_square distribution with \$df degrees of freedom. \\
164: \hline
165:
166: @return\_array=\&random\_noncentral\_chi (\$item\_cnt,\$seed,\$df,\$nonc)
167: NOTE: \$df MUST be at least 1 and \$nonc MUST be non-negative. & Generate \$item\_cnt deviates of noncentral\_chi\_square distribution with \$df degrees of freedom and noncentrality parameter \$nonc. \\
168: \hline
169:
170: @return\_array=\&random\_f (\$item\_cnt,\$seed,\$dfn,\$dfd)
171: NOTE: Both \$dfn and \$dfd MUST be positive. & Generate \$item\_cnt deviates of F (variance ratio) distribution with degrees of freedom \$dfn (numerator) and \$dfd (denominator). \\
172: \hline
173:
174: @return\_array=\&random\_noncentral\_f (\$item\_cnt,\$seed,\$dfn,\$dfd,\$nonc)
175: NOTE: \$dfn must be at least 1, \$dfd MUST be positive, and \$nonc must be non-negative. & Generate \$item\_cnt deviates of noncentral F (variance ratio) distribution with degrees of freedom \$dfn (numerator) and \$dfd (denominator). \$nonc is the noncentrality parameter. \\
176: \hline
177:
178: @return\_array=\&random\_multivariate\_normal (\$item\_cnt,\$seed,$\backslash$@mean,$\backslash$@covar)
179: 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. \\
180: \hline
181:
182: @return\_array=\&random\_multinomial (\$item\_cnt,\$seed,@p)
183: 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. \\
184: \hline
185:
186: @return\_array=\&random\_permutation (\$seed,@array) & Returns @array randomly permuted. \\
187: \hline
188:
189: @return\_array=\&random\_uniform (\$item\_cnt,\$seed,\$low,\$high)
190: NOTE: \$low must be less than or equal to \$high. & Generate \$item\_cnt deviates from a uniform distribution. \\
191: \hline
192:
193: @return\_array=\&random\_uniform\_integer (\$item\_cnt,\$seed,\$low,\$high)
194: 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. \\
195: \hline
196:
197: @return\_array=\&random\_binomial (\$item\_cnt,\$seed,\$nt,\$p)
198: 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. \\
199: \hline
200:
201: @return\_array=\&random\_negative\_binomial (\$item\_cnt,\$seed,\$ne,\$p)
202: 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. \\
203: \hline
204: \end{longtable}
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