Computes the Cholesky decomposition of a hermitian, positive definite matrix.
Returns a map containing two matrices with the keys [:L :L*] such that

Such that:
  M = L.L*

Where
  - M must be a hermitian, positive definite matrix
  - L is a lower triangular matrix
  - L* is the conjugate transpose of L

If :return parameter is specified in options map, it returns only specified keys.

Intended usage: (let [{:keys [L L*]} (cholesky M)] ....)
                (let [{:keys [L*]} (cholesky M {:return [:L*]})] ....)

Computes the Eigen decomposition of a diagonalisable matrix.
Returns a map containing matrices for each of the the keys [:Q :A] such that:

   M l= Q.A.Q<sup>-1</sup>

Where:
  - Q is a matrix where each column is the ith normalised eigenvector of M
  - A is a diagonal matrix whose diagonal elements are the eigenvalues.
  - Q<sup>-1</sup> is the inverse of Q

If :return parameter is specified in options map, it returns only specified keys.

Intended usage: (let [{:keys [Q A]} (eigen M)] ....)
                (let [{:keys [A]} (eigen M {:return [:A]})] ....)

Computes least-squares solution to a linear matrix equation.

Intended usage: (let [X (least-squares A B)] ....)

Computes the LU(P) decomposition of a matrix with partial row pivoting.
Returns a map containing the keys [:L :U :P], such that:
  P.A = L.U

Where
  - L is a lower triangular matrix
  - U is an upper triangular matrix
  - P is a permutation matrix

If :return parameter is specified in options map, it returns only specified keys.

Intended usage: (let [{:keys [L U P]} (lu A)] ....)
                (let [{:keys [L U]} (lu M {:return [:L :U]})] ....)

Computes the norm of a matrix or vector.

By default calculates 2-norm for vectors and Frobenius 2-norm for matrices. The optional p argument specifies use of the p-norm instead.

Special cases of p argument:
Double/POSITIVE_INFINITY - Infinity norm

Intended usage: (let [n (norm v 1)] ....)
                (let [n (norm v Double/POSITIVE_INFINITY)] ....)
                (let [n (norm v)] ....)

Computes QR decomposition of a full rank matrix.
Returns a map containing matrices of an input matrix type with the keys [:Q :R] such that:
     M = Q.R

Where:
 - Q is an orthogonal matrix
 - R is an upper triangular matrix (= right triangular matrix)
If :return parameter is specified in options map, it returns only specified keys.
If :compact parameter is specified in options map, compact versions of matrices are returned.

Returns nil if decomposition is impossible.

Intended usage: (let [{:keys [Q R]} (qr M)] ....)
                (let [{:keys [R]} (qr M {:return [:R]})] ....)

Computes the rank of a matrix, i.e. the number of linearly independent rows.

Intended usage: (let [r (rank m)] ....)

Solves a linear matrix equation, or system of linear scalar equations, i.e. finds the
value X such that:

  A.X = B

Where:
  - A is a square matrix containing the coefficients of the linear system
  - B is a vector containing the right-hand side of the linear system.
If B is missing, it is taken as an identity matrix and returns inverse of A

Intended usage: (let [X (solve A B)] ....)

Computes the Singular Value decomposition of a matrix.
Returns a map containing the keys [:U :S :V*] such that:
  M = U.S.V*

Where
  - U is an unitary matrix
  - S is a diagonal matrix whose elements are the singular values of the original matrix
  - V* is an unitary matrix

If :return parameter is specified in options map, it returns only specified keys.

Intended usage: (let [{:keys [U S V*]} (svd M)] ....)
                (let [{:keys [S]} (svd M {:return [:S]})] ....)