@@ -50,7 +50,8 @@ $$ 1.0 / 2.0 = 0.5 $$
5050
5151* Replacement* : Use the integer division operator ` operator%/% ` instead.
5252
53- ## integrate_ode_rk45, integrate_ode_adams, integrate_ode_bdf ODE integrators {#functions-old-ode-solver}
53+
54+ ## integrate_ode_rk45, integrate_ode_adams, integrate_ode_bdf ODE Integrators {#functions-old-ode-solver}
5455
5556These ODE integrator functions have been replaced by those described in:
5657
@@ -201,7 +202,7 @@ with values consisting of solutions at the specified times.
201202The sizes must match, and in particular, the following groups are of
202203the same size:
203204
204- * state variables passed into the system function, derivatives
205+ * state variables passed into the system function, derivatives
205206returned by the system function, initial state passed into the
206207solver, and rows of the return value of the solver,
207208
@@ -210,3 +211,65 @@ solver,
210211
211212* parameters, real data and integer data passed to the solver will
212213be passed to the system function
214+
215+
216+ ## Exponentiated quadratic covariance functions {#cov_exp_quad}
217+
218+ These covariance functions have been replaced by those described in:
219+
220+ ``` {r results='asis', echo=FALSE}
221+ if (knitr::is_html_output()) {
222+ cat(' * <a href="gaussian-process-covariance-functions.html">Gaussian Process Covariance Functions</a>\n')
223+ }
224+ ```
225+
226+ With magnitude $\alpha$ and length scale $l$, the exponentiated quadratic kernel is:
227+
228+ $$
229+ k(x_i, x_j) = \alpha^2 \exp \left(-\dfrac{1}{2\rho^2} \sum_{d=1}^D (x_{i,d} - x_{j,d})^2 \right)
230+ $$
231+
232+ <!-- matrix; cov_exp_quad; (row_vectors x, real alpha, real rho); -->
233+ \index{{\tt \bfseries cov\_ exp\_ quad }!{\tt (row\_ vectors x, real alpha, real rho): matrix}|hyperpage}
234+
235+ ` matrix ` ** ` cov_exp_quad ` ** ` (row_vectors x, real alpha, real rho) ` <br >\newline
236+ The covariance matrix with an exponentiated quadratic kernel of x.
237+ ` r since("2.16, deprecated since 2.20, scheduled for removal in 2.32") `
238+
239+ <!-- matrix; cov_exp_quad; (vectors x, real alpha, real rho); -->
240+ \index{{\tt \bfseries cov\_ exp\_ quad }!{\tt (vectors x, real alpha, real rho): matrix}|hyperpage}
241+
242+ ` matrix ` ** ` cov_exp_quad ` ** ` (vectors x, real alpha, real rho) ` <br >\newline
243+ The covariance matrix with an exponentiated quadratic kernel of x.
244+ ` r since("2.16, deprecated since 2.20, scheduled for removal in 2.32") `
245+
246+ <!-- matrix; cov_exp_quad; (array[] real x, real alpha, real rho); -->
247+ \index{{\tt \bfseries cov\_ exp\_ quad }!{\tt (array[ ] real x, real alpha, real rho): matrix}|hyperpage}
248+
249+ ` matrix ` ** ` cov_exp_quad ` ** ` (array[] real x, real alpha, real rho) ` <br >\newline
250+ The covariance matrix with an exponentiated quadratic kernel of x.
251+ ` r since("2.16, deprecated since 2.20, scheduled for removal in 2.32") `
252+
253+ <!-- matrix; cov_exp_quad; (row_vectors x1, row_vectors x2, real alpha, real rho); -->
254+ \index{{\tt \bfseries cov\_ exp\_ quad }!{\tt (row\_ vectors x1, row\_ vectors x2, real alpha, real rho): matrix}|hyperpage}
255+
256+ ` matrix ` ** ` cov_exp_quad ` ** ` (row_vectors x1, row_vectors x2, real alpha, real rho) ` <br >\newline
257+ The covariance matrix with an exponentiated quadratic kernel of x1 and
258+ x2.
259+ ` r since("2.18, deprecated since 2.20, scheduled for removal in 2.32") `
260+
261+ <!-- matrix; cov_exp_quad; (vectors x1, vectors x2, real alpha, real rho); -->
262+ \index{{\tt \bfseries cov\_ exp\_ quad }!{\tt (vectors x1, vectors x2, real alpha, real rho): matrix}|hyperpage}
263+
264+ ` matrix ` ** ` cov_exp_quad ` ** ` (vectors x1, vectors x2, real alpha, real rho) ` <br >\newline
265+ The covariance matrix with an exponentiated quadratic kernel of x1 and
266+ x2.
267+ ` r since("2.18, deprecated since 2.20, scheduled for removal in 2.32") `
268+
269+ <!-- matrix; cov_exp_quad; (array[] real x1, array[] real x2, real alpha, real rho); -->
270+ \index{{\tt \bfseries cov\_ exp\_ quad }!{\tt (array[ ] real x1, array[ ] real x2, real alpha, real rho): matrix}|hyperpage}
271+
272+ ` matrix ` ** ` cov_exp_quad ` ** ` (array[] real x1, array[] real x2, real alpha, real rho) ` <br >\newline
273+ The covariance matrix with an exponentiated quadratic kernel of x1 and
274+ x2.
275+ ` r since("2.18, deprecated since 2.20, scheduled for removal in 2.32") `
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