matlab superiorfloat,mvncdf 函数

function [y,err] = mvncdf(varargin)

%MVNCDF Multivariate normal cumulative distribution function (cdf).

%   Y = MVNCDF(X) returns the cumulative probability of the multivariate

%   normal distribution with zero mean and identity covariance matrix,

%   evaluated at each row of X.  Rows of the N-by-D matrix X correspond to

%   observations or points, and columns correspond to variables or

%   coordinates.  Y is an N-by-1 vector.

%

%   Y = MVNCDF(X,MU,SIGMA) returns the cumulative probability of the

%   multivariate normal distribution with mean MU and covariance SIGMA,

%   evaluated at each row of X.  MU is a 1-by-D vector, and SIGMA is a

%   D-by-D symmetric, positive definite matrix.  MU can also be a scalar

%   value, which MVNCDF replicates to match the size of X.  If the

%   covariance matrix is diagonal, containing variances along the diagonal

%   and zero covariances off the diagonal, SIGMA may also be specified as a

%   1-by-D matrix containing just the diagonal. Pass in the empty

%   matrix for MU to use its default value when you want to only specify

%   SIGMA.

%

%   The multivariate normal cumulative probability at X is defined as the

%   probability that a random vector V, distributed as multivariate normal,

%   will fall within the semi-infinite rectangle with upper limits defined by

%   X, i.e., Pr{V(1)<=X(1), V(2)<=X(2), ... V(D)<=X(D)}.

%

%   Y = MVNCDF(XL,XU,MU,SIGMA) returns the multivariate normal cumulative

%   probability evaluated over the rectangle (hyper-rectangle for D>2)

%   with lower and upper limits defined by XL and XU, respectively.

%

%   [Y,ERR] = MVNCDF(...) returns an estimate of the error in Y.  For

%   bivariate and trivariate distributions, MVNCDF uses adaptive quadrature on

%   a transformation of the t density, based on methods developed by Drezner

%   and Wesolowsky, and by Genz, as described in the references.  The default

%   absolute error tolerance for these cases is 1e-8.  For four or more

%   dimensions, MVNCDF uses a quasi-Monte Carlo integration algorithm based on

%   methods developed by Genz and Bretz, as described in the references.  The

%   default absolute error tolerance for these cases is 1e-4.  For

%   univariate distributions and when SIGMA is specified as a diagonal,

%   numerical integration is not used and ERR returns NaN.

%

%   [...] = MVNCDF(...,OPTIONS) speci