pygsti.tools.matrixtools

Matrix related utility functions

Functions

approximate_matrix_log(m, target_logm[, ...])	Construct an approximate logarithm of superoperator matrix m that is real and near the target_logm.
assert_hermitian(mat, tol)
assert_projector(mx[, tol])	Raise a ValueError if mx is not an orthogonal projector, per is_projector().
column_basis_vector(i, dim)	Returns the ith standard basis vector in dimension dim.
column_norms(m[, ord])	Compute the norms of the columns of a matrix.
columns_are_orthogonal(m[, tol])	Checks whether a matrix contains orthogonal columns.
columns_are_orthonormal(m[, tol])	Checks whether a matrix contains orthogonal columns.
complex_compare(a, b)	Comparison function for complex numbers that compares real part, then imaginary part.
compute_kite(eigenvalues)	Computes the "kite" corresponding to a list of eigenvalues.
csr_sum(data, coeffs, csr_mxs, csr_sum_indices)	Accelerated summation of several CSR-format sparse matrices.
csr_sum_flat(data, coeffs, ...)	Computation of the summation of several CSR-format sparse matrices.
csr_sum_flat_indices(csr_matrices)	Precomputes quantities allowing fast computation of linear combinations of CSR sparse matrices.
csr_sum_indices(csr_matrices)	Precomputes the indices needed to sum a set of CSR sparse matrices.
eigendecomposition(m, *[, assume_hermitian])
eigenvalues(m, *[, assume_hermitian, ...])
expm_multiply_fast(prep_a, v[, tol])	Multiplies v by an exponentiated matrix.
expm_multiply_prep(a[, tol])	Computes "prepared" meta-info about matrix a, to be used in expm_multiply_fast.
expop_multiply_prep(op[, a_1_norm, tol])	Returns "prepared" meta-info about operation op, which is assumed to be traceless (so no shift is needed).
find_zero_communtant_connection(u, u_inv, ...)	Find a matrix R such that u_inv R u0 is diagonal AND log(R) has no projection onto the commutant of G0.
gram_matrix(m[, adjoint])	If adjoint=False, then return m.T.conj() @ m, computed in a more efficient way.
independent_columns(m[, ...])	Computes the indices of the linearly-independent columns in a matrix.
induced_projector(mx[, tol, require_real])	Return the orthogonal projector onto range(mx), for mx proportional to a projector.
int64_parity(x)	Compute the partity of x.
intersection_space(space1, space2[, tol, ...])	TODO: docstring
is_hermitian(mx[, tol])	Test whether mx is a hermitian matrix.
is_pos_def(mx[, tol, attempt_cholesky])	Test whether mx is a positive-definite matrix.
is_projector(mx[, tol])	Test whether mx is an orthogonal projector, i.e. Hermitian and idempotent.
is_valid_density_mx(mx[, tol])	Test whether mx is a valid density matrix (hermitian, positive-definite, and unit trace).
jamiolkowski_angle(hamiltonian_mx)	TODO: docstring
matrix_sign(m)	Compute the matrix s = sign(m).
minweight_match(a, b[, metricfn, ...])	Matches the elements of two vectors, a and b by minimizing the weight between them.
minweight_match_realmxeigs(a, b[, metricfn, ...])	Matches the elements of a and b, whose elements are assumed to either real or one-half of a conjugate pair.
mx_to_string(m[, width, prec, withbrackets])	Generate a "pretty-format" string for a matrix.
mx_to_string_complex(m[, real_width, ...])	Generate a "pretty-format" string for a complex-valued matrix.
ndarray_base(a[, verbosity])	Get the base memory object for numpy array a.
near_identity_matrix_log(m[, tol])	Construct the logarithm of superoperator matrix m that is near the identity.
nice_nullspace(m[, tol, orthogonalize])	Computes the nullspace of a matrix, and tries to return a "nice" basis for it.
norm1(m)	Returns the Schatten 1-norm of a matrix
norm1to1(operator[, num_samples, mx_basis])	The Hermitian 1-to-1 norm of a superoperator represented in the standard basis.
normalize_columns(m[, return_norms, ord])	Normalizes the columns of a matrix.
nullspace(m[, tol])	Compute the nullspace of a matrix.
nullspace_qr(m[, tol])	Compute the nullspace of a matrix using the QR decomposition.
pinv_of_matrix_with_orthogonal_columns(m)	Return the matrix "pinv_m" so m @ pinvm and pinv_m @ m are orthogonal projectors onto subspaces of dimension rank(m).
pivot_indices_after_deflation(m_fixed, m)	m_fixed and m have the same number of rows.
prime_factors(n)	GCD algorithm to produce prime factors of n
print_mx(mx[, width, prec, withbrackets])	Print matrix in pretty format.
project_onto_antikite(mx, kite)	Project mx onto the complement of kite, so mx is zero everywhere on the kite.
project_onto_kite(mx, kite)	Project mx onto kite, so mx is zero everywhere except on the kite.
random_hermitian(dim)	Generates a random Hermitian matrix
real_matrix_log(m[, action_if_imaginary, tol])	Construct a real logarithm of real matrix m.
safe_norm(a[, part])	Get the frobenius norm of a matrix or vector, a, when it is either a dense array or a sparse matrix.
safe_onenorm(a)	Computes the 1-norm of the dense or sparse matrix a.
scale_columns(m, scale_values)	Scale each column of a matrix by a given value.
sign_fix_qr(q, r[, tol])	Change the signs of the columns of Q and rows of R to follow a convention.
sorted_eig(mx)	Similar to numpy.eig, but returns sorted output.
sparse_equal(a, b[, atol])	Checks whether two Scipy sparse matrices are (almost) equal.
sparse_onenorm(a)	Computes the 1-norm of the scipy sparse matrix a.
to_operatorlike(obj)
to_unitary(scaled_unitary)	Compute the scaling factor required to turn a scalar multiple of a unitary matrix to a unitary matrix.
union_space(space1, space2[, tol])	TODO: docstring
unitary_superoperator_matrix_log(m, mx_basis)	Construct the logarithm of superoperator matrix m.
vec(matrix_in)	Stacks the columns of a matrix to return a vector
zvals_int64_to_dense(zvals_int, nqubits[, ...])	Fills a dense array with the super-ket representation of a computational basis state.
zvals_to_dense(self, zvals[, superket])	Construct the dense operator or superoperator representation of a computational basis state.

Classes

IdentityOperator()	A representation of the identity operator on any and all vector spaces.
OperatorLike(*args, **kwargs)