# random_matrix

Functions

 COE(size) Circular orthogonal ensemble (COE). CRE(size) Circular real ensemble (CRE). CUE(size) Circular unitary ensemble (CUE). GOE(size) Gaussian orthogonal ensemble (GOE). GUE(size) Gaussian unitary ensemble (GUE). O_close_1(size[, a]) return an random orthogonal matrix 'close' to the Identity. U_close_1(size[, a]) return an random orthogonal matrix 'close' to the identity. box(size[, W]) return random number uniform in (-W, W]. return (R + 1.j*I) for independent R and I from np.random.standard_normal.

Module description

Provide some random matrix ensembles for numpy.

The implemented ensembles are:

ensemble

matrix class drawn from

measure

invariant under

beta

GOE

real, symmetric

~ exp(-n/4 tr(H^2))

orthogonal O

1

GUE

hermitian

~ exp(-n/2 tr(H^2))

unitary U

2

CRE

O(n)

Haar

orthogonal O

/

COE

U in U(n) with U = U^T

Haar

orthogonal O

1

CUE

U(n)

Haar

unitary U

2

O_close_1

O(n)

?

/

/

U_close_1

U(n)

?

/

/

All functions in this module take a tuple (n, n) as first argument, such that we can use the function from_func() to generate a block diagonal Array with the block from the corresponding ensemble, for example:

npc.Array.from_func_square(GOE, [leg, leg.conj()])