cupy.random.multivariate_normal(mean, cov, size=None, check_valid='ignore', tol=1e-08, method='cholesky', dtype=<class 'float'>)[source]

Multivariate normal distribution.

Returns an array of samples drawn from the multivariate normal distribution. Its probability density function is defined as

\[f(x) = \frac{1}{(2\pi|\Sigma|)^(n/2)} \exp\left(-\frac{1}{2} (x-\mu)^{\top}\Sigma^{-1}(x-\mu)\right).\]
  • mean (1-D array_like, of length N) – Mean of the multivariate normal distribution \(\mu\).

  • cov (2-D array_like, of shape (N, N)) – Covariance matrix \(\Sigma\) of the multivariate normal distribution. It must be symmetric and positive-semidefinite for proper sampling.

  • size (int or tuple of ints) – The shape of the array. If None, a zero-dimensional array is generated.

  • check_valid ('warn', 'raise', 'ignore') – Behavior when the covariance matrix is not positive semidefinite.

  • tol (float) – Tolerance when checking the singular values in covariance matrix.

  • method – { ‘cholesky’, ‘eigh’, ‘svd’}, optional The cov input is used to compute a factor matrix A such that A @ A.T = cov. This argument is used to select the method used to compute the factor matrix A. The default method ‘cholesky’ is the fastest, while ‘svd’ is the slowest but more robust than the fastest method. The method eigh uses eigen decomposition to compute A and is faster than svd but slower than cholesky.

  • dtype – Data type specifier. Only numpy.float32 and numpy.float64 types are allowed.


Samples drawn from the multivariate normal distribution.

Return type



Default method is set to fastest, ‘cholesky’, unlike numpy which defaults to ‘svd’. Cholesky decomposition in CuPy will fail silently if the input covariance matrix is not positive definite and give invalid results, unlike in numpy, where an invalid covariance matrix will raise an exception. Setting check_valid to ‘raise’ will replicate numpy behavior by checking the input, but will also force device synchronization. If validity of input is unknown, setting method to ‘einh’ or ‘svd’ and check_valid to ‘warn’ will use cholesky decomposition for positive definite matrices, and fallback to the specified method for other matrices (i.e., not positive semi-definite), and will warn if decomposition is suspect.

See also