@@ -30,28 +30,33 @@ namespace OpenSim {
3030
3131/* *
3232 * A class for generating Latin hypercube designs.
33+ *
34+ * # Latin hypercube design
3335 *
3436 * A Latin hypercube is an m-by-n matrix, where 'm' is the number of design
3537 * samples and 'n' is the number of variables in the design. Each sample point
3638 * (i.e., each row in the design) is the only sample point in its row and column
3739 * in the hypercube defined by the number of variables.
38- *
40+ *
41+ * \cond
3942 * For example, consider a design with 5 samples and 2 variables:
4043 *
41- * grid matrix
42- * __ __ __ __ __ __ __
43- * | x | | 0.6 0.2 |
44- * | x | | 1.0 0.4 |
45- * q2 | x | q = | 0.2 0.6 |
46- * | x | | 0.8 0.8 |
47- * | x | | 0.4 1.0 |
48- * ‾‾ ‾‾ ‾‾ ‾‾ ‾‾ ‾‾ ‾‾
44+ * grid matrix
45+ * __ __ __ __ __ __ __
46+ * | x | | 0.6 0.2 |
47+ * | x | | 1.0 0.4 |
48+ * q2 | x | q = | 0.2 0.6 |
49+ * | x | | 0.8 0.8 |
50+ * | x | | 0.4 1.0 |
51+ * ‾‾ ‾‾ ‾‾ ‾‾ ‾‾ ‾‾ ‾‾
4952 * q1
50- *
53+ *
5154 * On the left is the 5-by-5 square grid (i.e., 2-D hypercube) that is produced
5255 * if the samples are plotted in the variable space defined by q1 and q2. On the
5356 * right is the 5-by-2 design matrix that contains the 5 samples.
54- *
57+ * \endcond
58+ *
59+ *
5560 * Latin hypercube designs are useful for sampling large, multivariate parameter
5661 * spaces. Optimal Latin hypercube designs are those that maximize the minimum
5762 * distance between samples in the design. This class provides methods for
@@ -60,8 +65,7 @@ namespace OpenSim {
6065 * algorithm from Viana et al. (2009) and the enhanced stochastic evolutionary
6166 * algorithm from Jin et al. (2005).
6267 *
63- * How to create a Latin hypercube design
64- * --------------------------------------
68+ * # How to create a Latin hypercube design
6569 * To create a Latin hypercube design, you must first specify the number of
6670 * variables and samples in the design, and, optionally, the distance criterion
6771 * used to evaluate each design. The distance criterion can be either "maximin"
@@ -103,8 +107,7 @@ namespace OpenSim {
103107 * minimization criterion. While both criteria aim to achieve a similar goal,
104108 * the values returned by each are not directly comparable.
105109 *
106- * Recommendations for different sized designs
107- * -------------------------------------------
110+ * # Recommendations for different sized designs
108111 * To rapidly create a random Latin hypercube design of any size,
109112 * generateRandomDesign() is recommended. This method is fast, but does not
110113 * guarantee that the design is optimal.
@@ -124,8 +127,7 @@ namespace OpenSim {
124127 * it is recommended to use the "phi_p" distance criterion, which approximates
125128 * "maximin", but is much faster.
126129 *
127- * References
128- * ----------
130+ * # References
129131 * - [1] Viana, F.A.C., Venter, G. and Balabanov, V. (2010), An algorithm for
130132 * fast optimal Latin hypercube design of experiments. Int. J. Numer. Meth.
131133 * Engng., 82: 135-156. https://doi.org/10.1002/nme.2750
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