Haar¶

The Haar distribution is the uniform distribution over the space of real or complex unitary matrices.

C++ API¶

void Haar(Matrix<F> &A, Int n)¶

void Haar(ElementalMatrix<F> &A, Int n)¶: Draws A from the Haar distribution. The current scheme performs a QR factorization of a Gaussian matrix, but Stewart introduced a well-known scheme which only requires quadratic work for the implicit representation as a product of random Householder reflectors.

void ImplicitHaar(Matrix<F> &A, Matrix<F> &t, Matrix<Base<F>> &d, Int n)¶

void ImplicitHaar(ElementalMatrix<F> &A, ElementalMatrix<F> &t, Elemental<Base<F>> &d, Int n)¶: Sets A to a set of Householder reflectors with the same structure as the result of a QR decomposition. The product of these reflectors is a sample from the Haar distribution.

C API¶

ElError ElHaar_s(ElMatrix_s A, ElInt n)¶

ElError ElHaar_d(ElMatrix_d A, ElInt n)¶

ElError ElHaar_c(ElMatrix_c A, ElInt n)¶

ElError ElHaar_z(ElMatrix_z A, ElInt n)¶

ElError ElHaarDist_s(ElDistMatrix_s A, ElInt n)¶

ElError ElHaarDist_d(ElDistMatrix_d A, ElInt n)¶

ElError ElHaarDist_c(ElDistMatrix_c A, ElInt n)¶

ElError ElHaarDist_z(ElDistMatrix_z A, ElInt n)¶

ElError ElImplicitHaar_s(ElMatrix_s A, ElMatrix_s t, ElMatrix_s d, ElInt n)¶

ElError ElImplicitHaar_d(ElMatrix_d A, ElMatrix_d t, ElMatrix_d d, ElInt n)¶

ElError ElImplicitHaar_c(ElMatrix_c A, ElMatrix_c t, ElMatrix_s d, ElInt n)¶

ElError ElImplicitHaar_z(ElMatrix_z A, ElMatrix_z t, ElMatrix_d d, ElInt n)¶

ElError ElImplicitHaarDist_s(ElDistMatrix_s A, ElDistMatrix_s t, ElDistMatrix_s d, ElInt n)¶

ElError ElImplicitHaarDist_d(ElDistMatrix_d A, ElDistMatrix_d t, ElDistMatrix_d d, ElInt n)¶

ElError ElImplicitHaarDist_c(ElDistMatrix_c A, ElDistMatrix_c t, ElDistMatrix_s d, ElInt n)¶

ElError ElImplicitHaarDist_z(ElDistMatrix_z A, ElDistMatrix_z t, ElDistMatrix_d d, ElInt n)¶

Python API¶

Haar(A, n)¶

ImplicitHaar(A, t, d, n)¶