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sd.hpp
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1 #ifndef STAN_MATH_REV_MAT_FUN_SD_HPP
2 #define STAN_MATH_REV_MAT_FUN_SD_HPP
3
4 #include <stan/math/prim/arr/err/check_nonzero_size.hpp>
5 #include <stan/math/prim/mat/fun/Eigen.hpp>
6 #include <stan/math/prim/mat/fun/mean.hpp>
7 #include <stan/math/rev/core.hpp>
8 #include <boost/math/tools/promotion.hpp>
9 #include <cmath>
10 #include <vector>
11
12 namespace stan {
13 namespace math {
14
15 namespace { // anonymous
16
17 // if x.size() = N, and x[i] = x[j] =
18 // then lim sd(x) -> 0 [ d/dx[n] sd(x) ] = sqrt(N) / N
19
20 var calc_sd(size_t size,
21 const var* dtrs) {
22 using std::sqrt;
23 vari** varis
24 = reinterpret_cast<vari**>(ChainableStack::memalloc_
25 .alloc(size * sizeof(vari*)));
26 for (size_t i = 0; i < size; ++i)
27 varis[i] = dtrs[i].vi_;
28 double sum = 0.0;
29 for (size_t i = 0; i < size; ++i)
30 sum += dtrs[i].vi_->val_;
31 double mean = sum / size;
32 double sum_of_squares = 0;
33 for (size_t i = 0; i < size; ++i) {
34 double diff = dtrs[i].vi_->val_ - mean;
35 sum_of_squares += diff * diff;
36 }
37 double variance = sum_of_squares / (size - 1);
38 double sd = sqrt(variance);
39 double* partials
40 = reinterpret_cast<double*>(ChainableStack::memalloc_
41 .alloc(size * sizeof(double)));
42 if (sum_of_squares < 1e-20) {
43 double grad_limit = 1 / std::sqrt(static_cast<double>(size));
44 for (size_t i = 0; i < size; ++i)
45 partials[i] = grad_limit;
46 } else {
47 double multiplier = 1 / (sd * (size - 1));
48 for (size_t i = 0; i < size; ++i)
49 partials[i] = multiplier * (dtrs[i].vi_->val_ - mean);
50 }
51 return var(new stored_gradient_vari(sd, size,
52 varis, partials));
53 }
54
55 }
56
64 inline var sd(const std::vector<var>& v) {
65 check_nonzero_size("sd", "v", v);
66 if (v.size() == 1) return 0;
67 return calc_sd(v.size(), &v[0]);
68 }
69
70 /*
71 * Return the sample standard deviation of the specified vector,
72 * row vector, or matrix. Raise domain error if size is not
73 * greater than zero.
74 *
75 * @tparam R number of rows
76 * @tparam C number of columns
77 * @param[in] m input matrix
78 * @return sample standard deviation of specified matrix
79 */
80 template <int R, int C>
81 var sd(const Eigen::Matrix<var, R, C>& m) {
82 check_nonzero_size("sd", "m", m);
83 if (m.size() == 1) return 0;
84 return calc_sd(m.size(), &m(0));
85 }
86
87 }
88 }
89 #endif
stan::math::sum
fvar< T > sum(const std::vector< fvar< T > > &m)
Return the sum of the entries of the specified standard vector.
Definition: sum.hpp:20
core.hpp
stan::math::sqrt
fvar< T > sqrt(const fvar< T > &x)
Definition: sqrt.hpp:14
stan
Definition: log_sum_exp.hpp:8
stan::math::AutodiffStackStorage::memalloc_
static stack_alloc memalloc_
Definition: autodiffstackstorage.hpp:16
stan::math::var
Independent (input) and dependent (output) variables for gradients.
Definition: var.hpp:30
stan::math::check_nonzero_size
bool check_nonzero_size(const char *function, const char *name, const T_y &y)
Return true if the specified matrix/vector is of non-zero size.
Definition: check_nonzero_size.hpp:29
stan::math::sd
boost::math::tools::promote_args< T >::type sd(const std::vector< T > &v)
Returns the unbiased sample standard deviation of the coefficients in the specified column vector...
Definition: sd.hpp:22
stan::math::variance
boost::math::tools::promote_args< T >::type variance(const std::vector< T > &v)
Returns the sample variance (divide by length - 1) of the coefficients in the specified standard vect...
Definition: variance.hpp:24
mean.hpp
stan::math::mean
boost::math::tools::promote_args< T >::type mean(const std::vector< T > &v)
Returns the sample mean (i.e., average) of the coefficients in the specified standard vector...
Definition: mean.hpp:23
Eigen.hpp
stan::math::e
double e()
Return the base of the natural logarithm.
Definition: constants.hpp:94
stan::math::size
int size(const std::vector< T > &x)
Return the size of the specified standard vector.
Definition: size.hpp:17
check_nonzero_size.hpp
stan::math::stack_alloc::alloc
void * alloc(size_t len)
Return a newly allocated block of memory of the appropriate size managed by the stack allocator...
Definition: stack_alloc.hpp:162

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