(cholesky-decomposition A)Compute Cholesky decomposition of a complex Hermitian positive definite matrix A. Returns a map with lower triangular matrix L in SoA form.
Compute Cholesky decomposition of a complex Hermitian positive definite matrix A. Returns a map with lower triangular matrix L in SoA form.
(condition-number A)Compute condition number of a complex matrix A. Returns a positive real number or Double/POSITIVE_INFINITY if A is singular.
Compute condition number of a complex matrix A. Returns a positive real number or Double/POSITIVE_INFINITY if A is singular.
(density-matrix psi)Compute the density matrix from a pure state vector psi. Returns a density matrix in SoA form.
Compute the density matrix from a pure state vector psi. Returns a density matrix in SoA form.
(eigen-general A)(eigen-general A eps)Compute eigen-decomposition of a complex square matrix A. Returns a map with eigenvalues and eigenvectors in SoA form. Optionally accepts a tolerance for numerical stability.
Compute eigen-decomposition of a complex square matrix A. Returns a map with eigenvalues and eigenvectors in SoA form. Optionally accepts a tolerance for numerical stability.
(eigen-hermitian A)(eigen-hermitian A eps)Compute eigen-decomposition of a complex Hermitian matrix A. Returns a map with eigenvalues and eigenvectors in SoA form. Optionally accepts a tolerance for numerical stability.
Compute eigen-decomposition of a complex Hermitian matrix A. Returns a map with eigenvalues and eigenvectors in SoA form. Optionally accepts a tolerance for numerical stability.
(inverse A)Inverse of complex matrix via Gauss-Jordan.
Inverse of complex matrix via Gauss-Jordan.
(lu-decomposition A)(lu-decomposition A eps)Compute LU decomposition of a complex matrix A with partial pivoting. Returns a map with permutation vector P, lower triangular L and upper triangular U matrices in SoA form.
Compute LU decomposition of a complex matrix A with partial pivoting. Returns a map with permutation vector P, lower triangular L and upper triangular U matrices in SoA form.
(matrix-exp A)Compute matrix exponential of a complex matrix A. Returns a complex matrix in SoA form.
Compute matrix exponential of a complex matrix A. Returns a complex matrix in SoA form.
(matrix-log A)Compute matrix logarithm of a complex matrix A. Returns a complex matrix in SoA form.
Compute matrix logarithm of a complex matrix A. Returns a complex matrix in SoA form.
(matrix-sqrt A)Compute matrix square root of a complex matrix A. Returns a complex matrix in SoA form.
Compute matrix square root of a complex matrix A. Returns a complex matrix in SoA form.
(norm2 x)Compute L2 norm of complex vector x (SoA form). Returns a non-negative real number.
Compute L2 norm of complex vector x (SoA form). Returns a non-negative real number.
(outer-product x y)Compute outer product of complex vectors x and y. Returns a complex matrix in SoA form.
Compute outer product of complex vectors x and y. Returns a complex matrix in SoA form.
(positive-semidefinite? A)(positive-semidefinite? A eps)Check if complex matrix A is positive semidefinite. Returns true if A is PSD, false otherwise. Optionally accepts a tolerance for numerical stability.
Check if complex matrix A is positive semidefinite. Returns true if A is PSD, false otherwise. Optionally accepts a tolerance for numerical stability.
(projector-from-state psi)Compute the projector |psi><psi| from a quantum state vector psi. Returns a density matrix in SoA form.
Compute the projector |psi><psi| from a quantum state vector psi. Returns a density matrix in SoA form.
(qr-decomposition A)Compute QR decomposition of a complex matrix A. Returns a map with orthogonal matrix Q and upper triangular matrix R in SoA form.
Compute QR decomposition of a complex matrix A. Returns a map with orthogonal matrix Q and upper triangular matrix R in SoA form.
(solve-linear A b)Solve complex linear system A x = b and return complex vector representation.
Solve complex linear system A x = b and return complex vector representation.
(spectral-norm A)Compute spectral norm of complex matrix A via power iteration on A^H A with Rayleigh quotient convergence.
Compute spectral norm of complex matrix A via power iteration on A^H A with Rayleigh quotient convergence.
(state-normalize state)Normalize a quantum state vector psi. Returns a new state vector with unit norm.
Normalize a quantum state vector psi. Returns a new state vector with unit norm.
(svd A)(svd A eps)Compute singular value decomposition of a complex matrix A. Returns a map with singular values and left/right singular vectors in SoA form. Optionally accepts a tolerance for numerical stability.
Compute singular value decomposition of a complex matrix A. Returns a map with singular values and left/right singular vectors in SoA form. Optionally accepts a tolerance for numerical stability.
(trace A)Compute trace of complex matrix A (SoA form). Returns a complex scalar.
Compute trace of complex matrix A (SoA form). Returns a complex scalar.
(trace-one? rho)(trace-one? rho eps)Check if a density matrix rho has trace one. Optionally accepts a tolerance for numerical stability.
Check if a density matrix rho has trace one. Optionally accepts a tolerance for numerical stability.
(unitary? U)(unitary? U eps)Check if complex matrix U is unitary (U^H U = I). Returns true if unitary, false otherwise. Optionally accepts a tolerance for numerical stability.
Check if complex matrix U is unitary (U^H U = I). Returns true if unitary, false otherwise. Optionally accepts a tolerance for numerical stability.
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