Description Usage Arguments Details Value See also Examples
SDP_rnk_pred
produces the (estimated) probability vector for the
rank of the solution of a random semidefinite program.
1 | SDP_rnk_pred(n, m, beta = 1, C = 0.2)
|
n |
size of matrix |
m |
number of constraints |
beta |
Dyson index specifying the underlying (skew-) field:
|
C |
estimated constant in the variance of index normalized curvature measures |
The semidefinite program is assumed to be of the form
min_(X in S^n) (C,X)_(S^n)
subject to (A_k,X)_(S^n)=b_k , k=1,...,m
X>=0.
Generically, if a solution to this program exists, then it is unique, and its
rank satisfies some inequalities, known as Pataki Inequalities. In the natural
random model the rank probabilities can be expressed in terms of curvature
measures, which is what this function estimates. See the vignette accompanying
the symconivol
package for more details and
references.
The output of SDP_rnk_pred
is a is a list of three elements:
P
: the estimated probability vector (in form of a tibble
to avoid confusion about the index),
bnds
: the Pataki bounds,
plot
: a histogram plot (ggplot2) of the probability vector
(the vertical lines indicate the Pataki bounds).
Package: symconivol
1 2 3 4 5 6 |
Add the following code to your website.
For more information on customizing the embed code, read Embedding Snippets.