Object

The root type of the language. All values are instances of Object.

Factories

cholesky(const RealMatrix A) -> Object

Computes the Cholesky decomposition of a RealMatrix A.. By default, the standard algorithm is used; to use the robust algorithm instead, provide the option 'algorithm' with value 'robust'.

Parameters

• A: The RealMatrix.

cholesky(const ComplexMatrix A) -> Object

Computes the Cholesky decomposition of a ComplexMatrix A.. By default, the standard algorithm is used; to use the robust algorithm instead, provide the option 'algorithm' with value 'robust'.

Parameters

• A: The ComplexMatrix.

cholesky(const RealMatrix A, const Map options) -> Object

Computes the Cholesky decomposition of a RealMatrix A.

Parameters

• A: The RealMatrix.
• options: Map of Cholesky options
  • algorithm (string): The Cholesky algorithm to use. Possible values are 'standard' (default) and 'robust' (Robust Cholesky).

cholesky(const ComplexMatrix A, const Map options) -> Object

Computes the Cholesky decomposition of a ComplexMatrix A.

Parameters

• A: The ComplexMatrix.
• options: Map of Cholesky options
  • algorithm (string): The Cholesky algorithm to use. Possible values are 'standard' (default) and 'robust' (Robust Cholesky).

eigensolver(const ComplexMatrix mat) -> Object

Computes the eigenvalues and eigenvectors of a matrix.

Computes the eigenvalues and eigenvectors of the given matrix. If the matrix is known to be self-adjoint, setting the is_hermitian option to true can improve performance.

Parameters

• mat: The ComplexMatrix to compute the eigendecomposition of.

eigensolver(const RealMatrix mat) -> Object

Computes the eigenvalues and eigenvectors of a matrix.

Computes the eigenvalues and eigenvectors of the given matrix. If the matrix is known to be self-adjoint, setting the is_hermitian option to true can improve performance.

Parameters

• mat: The RealMatrix to compute the eigendecomposition of.

eigensolver(const RealMatrix mat, const Map options) -> Object

Computes the eigenvalues and eigenvectors of a matrix.

Computes the eigenvalues and eigenvectors of the given matrix. If the matrix is known to be self-adjoint, setting the is_hermitian option to true can improve performance.

Parameters

• mat: The RealMatrix to compute the eigendecomposition of.
• options: A map of options for the eigensolver.
  • is_hermitian (bool): Whether the operator is Hermitian (default: false). If true, Hermitian-specific algorithms are used, which can improve performance.

eigensolver(const RealMatrix A, const RealMatrix B) -> Object

Computes the eigenvalues and eigenvectors of a matrix.

Computes the eigenvalues and eigenvectors of the given matrix pencil (AX - BXD). If the matrix is known to be self-adjoint, setting the is_hermitian option to true can improve performance.

Parameters

• A: The RealMatrix A of the matrix pencil (AX - BXD).
• B: The RealMatrix B of the matrix pencil (AX - BXD).

eigensolver(const ComplexMatrix mat, const Map options) -> Object

Computes the eigenvalues and eigenvectors of a matrix.

Computes the eigenvalues and eigenvectors of the given matrix. If the matrix is known to be self-adjoint, setting the is_hermitian option to true can improve performance.

Parameters

• mat: The ComplexMatrix to compute the eigendecomposition of.
• options: A map of options for the eigensolver.
  • is_hermitian (bool): Whether the operator is Hermitian (default: false). If true, Hermitian-specific algorithms are used, which can improve performance.

eigensolver(const ComplexMatrix A, const ComplexMatrix B) -> Object

Computes the eigenvalues and eigenvectors of a matrix.

Computes the eigenvalues and eigenvectors of the given matrix pencil (AX - BXD). If the matrix is known to be self-adjoint, setting the is_hermitian option to true can improve performance.

Parameters

• A: The ComplexMatrix A of the matrix pencil (AX - BXD).
• B: The ComplexMatrix B of the matrix pencil (AX - BXD).

eigensolver(const RealMatrix A, const RealMatrix B, const Map options) -> Object

Computes the eigenvalues and eigenvectors of a matrix.

Computes the eigenvalues and eigenvectors of the given matrix pencil (AX - BXD). If the matrix is known to be self-adjoint, setting the is_hermitian option to true can improve performance.

Parameters

• A: The RealMatrix A of the matrix pencil (AX - BXD).
• B: The RealMatrix B of the matrix pencil (AX - BXD).
• options: A map of options for the eigensolver.
  • is_hermitian (bool): Whether the operator is Hermitian (default: false). If true, Hermitian-specific algorithms are used, which can improve performance.

eigensolver(const ComplexMatrix A, const ComplexMatrix B, const Map options) -> Object

Computes the eigenvalues and eigenvectors of a matrix.

Computes the eigenvalues and eigenvectors of the given matrix pencil (AX - BXD). If the matrix is known to be self-adjoint, setting the is_hermitian option to true can improve performance.

Parameters

• A: The ComplexMatrix A of the matrix pencil (AX - BXD).
• B: The ComplexMatrix B of the matrix pencil (AX - BXD).
• options: A map of options for the eigensolver.
  • is_hermitian (bool): Whether the operator is Hermitian (default: false). If true, Hermitian-specific algorithms are used, which can improve performance.

lu(const ComplexMatrix A) -> Object

Computes the LU decomposition of a ComplexMatrix A.. By default, partial pivoting is used and the resulting factorization is PA = LU, where P is a permutation matrix, L is lower triangular with unit diagonal elements, and U is upper triangular. To use full pivoting instead, provide the option 'pivoting' with value 'full'. The resulting factorization is PAQ = LU, where P and Q are permutation matrices.

Parameters

• A: The ComplexMatrix.

lu(const RealMatrix A) -> Object

Computes the LU decomposition of a RealMatrix A.. By default, partial pivoting is used and the resulting factorization is PA = LU, where P is a permutation matrix, L is lower triangular with unit diagonal elements, and U is upper triangular. To use full pivoting instead, provide the option 'pivoting' with value 'full'. The resulting factorization is PAQ = LU, where P and Q are permutation matrices.

Parameters

• A: The RealMatrix.

lu(const ComplexMatrix A, const Map options) -> Object

Computes the LU decomposition of a ComplexMatrix A.

Parameters

• A: The ComplexMatrix.
• options: Map of LU options
  • pivoting (string): The LU pivoting to use. Possible values are 'partial' (default) and 'full'.

lu(const RealMatrix A, const Map options) -> Object

Computes the LU decomposition of a RealMatrix A.

Parameters

• A: The RealMatrix.
• options: Map of LU options
  • pivoting (string): The LU pivoting to use. Possible values are 'partial' (default) and 'full'.

matrix(const Operator matrix, const StateInfo options) -> Object

Constructs the matrix representation of the provided operator according to the specified options. If a specialized matrix construction method is found, returns the corresponding matrix, otherwise returns the result of calling to_matrix on the provided operator.

Parameters

• matrix: The input operator from which the matrix is built.
• options: A set of options used to deduce the output matrix type.

matrix(const Operator matrix, as_complex options) -> Object

Constructs the matrix representation of the provided operator according to the specified options. If a specialized matrix construction method is found, returns the corresponding matrix, otherwise returns the result of calling to_matrix on the provided operator.

Parameters

• matrix: The input operator from which the matrix is built.
• options: A set of options used to deduce the output matrix type.

matrix(const Operator matrix, as_real options) -> Object

Constructs the matrix representation of the provided operator according to the specified options. If a specialized matrix construction method is found, returns the corresponding matrix, otherwise returns the result of calling to_matrix on the provided operator.

Parameters

• matrix: The input operator from which the matrix is built.
• options: A set of options used to deduce the output matrix type.

operator_function(const ComplexMatrix matrix, const ComplexFunctionWithDeriv fun) -> Object

Approximates a matrix function using the Krylov subspace method.

This function is accepts non-Hermitian matrices. The scalar function signature should be (complex, integer) -> complex. Options are provided as a map of option names to their values.

Parameters

• matrix: The matrix to wrap.
• fun: A scalar function corresponding to the matrix function.

operator_function(const ComplexMatrix matrix, const Function<complex(complex)> fun) -> Object

Approximates a matrix function using the Krylov subspace method.

This function accepts Hermitian matrices. Options are provided as a map of option names to their values.

Parameters

• matrix: The matrix to wrap.
• fun: A scalar function corresponding to the matrix function.

operator_function(const RealMatrix matrix, const Function<real(real)> fun) -> Object

Approximates a matrix function using the Krylov subspace method.

This function accepts Hermitian matrices. Options are provided as a map of option names to their values.

Parameters

• matrix: The matrix to wrap.
• fun: A scalar function corresponding to the matrix function.

operator_function(const ComplexMatrix matrix, const Function<complex(complex)> fun, const Map opts) -> Object

Approximates a matrix function using the Krylov subspace method.

This function accepts Hermitian matrices. Options are provided as a map of option names to their values.

Parameters

• matrix: The matrix to wrap.
• fun: A scalar function corresponding to the matrix function.
• opts: Options for the operator function.
  • is_real (boolean): Indicates whether the function is real-valued. This option is required to correctly handle real-valued functions.
  • krylov_dimension (integer): The dimension of the Krylov subspace (default: 2 * nev + 2). This parameter must be larger than nev. If convergence issues are encountered, increasing this value may help.

operator_function(const RealMatrix matrix, const Function<real(real)> fun, const Map opts) -> Object

Approximates a matrix function using the Krylov subspace method.

This function accepts Hermitian matrices. Options are provided as a map of option names to their values.

Parameters

• matrix: The matrix to wrap.
• fun: A scalar function corresponding to the matrix function.
• opts: Options for the operator function.
  • is_real (boolean): Indicates whether the function is real-valued. This option is required to correctly handle real-valued functions.
  • krylov_dimension (integer): The dimension of the Krylov subspace (default: 2 * nev + 2). This parameter must be larger than nev. If convergence issues are encountered, increasing this value may help.

operator_function(const ComplexMatrix matrix, const ComplexFunctionWithDeriv fun, const Map opts) -> Object

Approximates a matrix function using the Krylov subspace method.

This function is accepts non-Hermitian matrices. The scalar function signature should be (complex, integer) -> complex. Options are provided as a map of option names to their values.

Parameters

• matrix: The matrix to wrap.
• fun: A scalar function corresponding to the matrix function.
• opts: Options for the operator function.
  • is_real (boolean): Indicates whether the function is real-valued. This option is required to correctly handle real-valued functions.
  • krylov_dimension (integer): The dimension of the Krylov subspace (default: 2 * nev + 2). This parameter must be larger than nev. If convergence issues are encountered, increasing this value may help.

qr(const RealMatrix A) -> Object

Computes the QR decomposition of a RealMatrix A.. By default, no pivoting is used and the resulting factorization is A = QR, where Q is a unitary matrix and R is upper triangular. To use partial (column) pivoting, provide the option 'pivoting' with value 'partial'. The resulting factorization is AP = QR, where P is a permutation matrix. To use full pivoting, provide the option 'pivoting' with value 'full'.

Parameters

• A: The RealMatrix.

qr(const ComplexMatrix A) -> Object

Computes the QR decomposition of a ComplexMatrix A.. By default, no pivoting is used and the resulting factorization is A = QR, where Q is a unitary matrix and R is upper triangular. To use partial (column) pivoting, provide the option 'pivoting' with value 'partial'. The resulting factorization is AP = QR, where P is a permutation matrix. To use full pivoting, provide the option 'pivoting' with value 'full'.

Parameters

• A: The ComplexMatrix.

qr(const ComplexMatrix A, const Map options) -> Object

Computes the QR decomposition of a ComplexMatrix A.

Parameters

• A: The ComplexMatrix.
• options: Map of QR options
  • pivoting (string): The QR pivoting to use. Possible values are 'none' (default), 'partial' and 'full'.

qr(const RealMatrix A, const Map options) -> Object

Computes the QR decomposition of a RealMatrix A.

Parameters

• A: The RealMatrix.
• options: Map of QR options
  • pivoting (string): The QR pivoting to use. Possible values are 'none' (default), 'partial' and 'full'.

state_range(const StateInfo options, integer arguments) -> Object

Creates an iterator for a range of state objects matching the provided option.

The state_range factory provides a way of constructing an iterator of states. The provided options will dispatch the appropriate range method of the state type matching the options.

Parameters

• options: A StateInfo option that specifies the state type produced by the state_range method.
• arguments: Appropriate arguments to build the state range.

Example

state_range(as_basisstate | as_spinhalf,2) //Returns [(1 + 0i)|00>, (1 + 0i)|10>, (1 + 0i)|01>, (1 + 0i)|11>]

svd(const RealMatrix A) -> Object

Computes the singular value decomposition (SVD) of an n-by-p RealMatrix A as a product A=USV^T where U is a n-by-m unitary, V is a p-by-m unitary, $m = min(n,p)$, and S is an m-by-m real positive diagonal matrix; the diagonal entries of S are known as the singular values of A and the columns of U and V are known as the left and right singular vectors of A respectively. Singular values are always sorted in decreasing order.. By default, the Jacobi algorithm is used; to use the block divide and conquer (BDC) algorithm instead, provide the option 'algorithm' with value 'bdc'.

Parameters

• A: The RealMatrix.

svd(const ComplexMatrix A) -> Object

Computes the singular value decomposition (SVD) of an n-by-p ComplexMatrix A as a product A=USV^T where U is a n-by-m unitary, V is a p-by-m unitary, $m = min(n,p)$, and S is an m-by-m real positive diagonal matrix; the diagonal entries of S are known as the singular values of A and the columns of U and V are known as the left and right singular vectors of A respectively. Singular values are always sorted in decreasing order.. By default, the Jacobi algorithm is used; to use the block divide and conquer (BDC) algorithm instead, provide the option 'algorithm' with value 'bdc'.

Parameters

• A: The ComplexMatrix.

svd(const ComplexMatrix A, const Map options) -> Object

Computes the singular value decomposition (SVD) of an n-by-p ComplexMatrix A as a product A=USV^T where U is a n-by-m unitary, V is a p-by-m unitary, $m = min(n,p)$, and S is an m-by-m real positive diagonal matrix; the diagonal entries of S are known as the singular values of A and the columns of U and V are known as the left and right singular vectors of A respectively. Singular values are always sorted in decreasing order.

Parameters

• A: The ComplexMatrix.
• options: Map of SVD options
  • algorithm (string): The SVD algorithm to use. Possible values are 'jacobi' (default) and 'bdc' (Bidiagonal Divide and Conquer).

svd(const RealMatrix A, const Map options) -> Object

Computes the singular value decomposition (SVD) of an n-by-p RealMatrix A as a product A=USV^T where U is a n-by-m unitary, V is a p-by-m unitary, $m = min(n,p)$, and S is an m-by-m real positive diagonal matrix; the diagonal entries of S are known as the singular values of A and the columns of U and V are known as the left and right singular vectors of A respectively. Singular values are always sorted in decreasing order.

Parameters

• A: The RealMatrix.
• options: Map of SVD options
  • algorithm (string): The SVD algorithm to use. Possible values are 'jacobi' (default) and 'bdc' (Bidiagonal Divide and Conquer).

Symbols

Name	Description
=	Assigns a value to an undefined variable.

Members

Name	Description
clone	Creates a deep copy of an object, including its attributes.
get_type_info	Returns the type information of the variable.
is_type	Checks if the variable represents a type.
is_var_const	Checks if the variable is constant.
is_var_null	Checks if the variable is null.
is_var_pointer	Checks if the variable is a pointer.
is_var_reference	Checks if the variable is a reference.
is_var_return_value	Checks if the variable is a return value.
is_var_undef	Checks if the variable is undefined.
type_match	Checks if the variable's type matches the specified type.
type_name	Returns the type name of an object.