pyUni10.Matrix¶

class pyUni10.Matrix¶

Proxy of C++ uni10::Matrix class

Class for matrices

pyUni10.Matrix(Rnum, Cnum, [elem, ]diag=False)

pyUni10.Matrix(Ma)

Creates a Real Matrix object

Parameters:	Rnum (int) – number of Rows Cnum (int) – number of Columns diag (bool) – Set True for a diagonal matrix elem (iterable) – Matrix elements Ma (Matrix) – another Matrix object
Returns:	a Matrix object
Return type:	Matrix

pyUni10.CMatrix(Rnum, Cnum, [elem, ]diag=False)¶

Creates a Complex Matrix object

Parameters:	Rnum (int) – number of Rows Cnum (int) – number of Columns diag (bool) – Set True for a diagonal matrix elem (iterable) – Matrix elements Ma (Matrix) – another Matrix object
Returns:	a Complex Matrix object
Return type:	Matrix

Methods

If no datatype flag is specified, the member functions default to Real. To explicitly declare the data type, the class provides constructors and member functions with the following syntax:

func(RTYPE, ...) for Real datatype and func(CTYPE), ...) for Complex datatype.

Matrix.col()¶

Returns the number of columns in Matrix

Returns:	number of columns in Matrix
Return type:	int

Matrix.eigh()¶

Diagonalizes a symmetric/hermitian Matrix and returns a tuple of matrices (\(D, U\)),

where \(D\) is a diagonal matrix of eigenvalues and \(U\) is a matrix of row-vectors of eigenvectors.

return:	\(D\) : diagonal matrix of eigenvalues \(U\) : matrix of eigenvectors
rtype:	tuple of Matrix

Note

This function will not check wether the matrix is symmetric/hermitian.

The operation is a wrapper of Lapack function dsyev() for Real matrix zheev() for Complex matrix.

Matrix.eig()¶

Diagonalizes a general Matrix and returns a tuple of matrices (\(D, U\)), where \(D\) is a diagonal matrix of eigenvalues and \(U\) is a matrix of row-vectors of right eigenvectors.

Returns:	\(D\) : diagonal matrix of eigenvalues \(U\) : matrix of right eigenvectors
Return type:	tuple of Matrix

Note

Only the right eigenvectors will be given. The operation is a wrapper of Lapack function Xsyev().

Matrix.elemNum()¶

Returns the number of elements in Matrix

Returns:	number of elements in Matrix
Return type:	int

Matrix.getElem()¶

Returns the reference to the elements of Matrix

Returns:	reference to the element of Matrix
Return type:	float *

Matrix.identity()¶

Returns an identity matrix

Returns:	an identity matrix
Return type:	Matrix

Matrix.isDiag()¶

Checks whether Matrix is diagonal

Returns:	True or False
Return type:	bool

Matrix.inverse()¶

Returns inverse matrix of Matrix

Returns:	inverse matrix of Matrix
Rtpye:	Matrix

Matrix.load(filename)¶

Loads Matrix from a binary file named filename

Parameters:	filename (str) – input filename

Matrix.norm()¶

Returns \(L^2\) norm of Matrix

Returns:	\(L^2\) norm of Matrix
Return type:	float

Matrix.orthoRand()¶

Generates an orthogonal basis with random elements and assigns it to the elements of Matrix

Returns:	Matrix of orthogonal basis
Return type:	Matrix

Matrix.randomize()¶

Assigns random elements to Matrix

Returns:	Matrix of random elements
Return type:	Matrix

Matrix.resize(Rnum, Cnum)¶

Set the dimensions of Matrix to (Rnum, Cnum)

Returns:	Matrix of size (Rnum, Cnum)
Return type:	Matrix

Matrix.row()¶

Returns the number of rows in Matrix

Returns:	number of rows in Matrix
Return type:	int

Matrix.save(filename)¶

Saves Matrix to a binary file named filename

Parameters:	filename (str) – output filename

Matrix.setElem(elem)¶

Set elements of Matrix to elem

Parameters:	elem (array of floats) – data

Matrix.set_zero()¶

Set elements of Matrix to zero

Parameters:	elem (array of floats) – data

Matrix.sum()¶

Performs the summation of all elements in Matrix

Returns:	sum of all elements in Matrix
Return type:	float

Matrix.svd()¶

Performs SVD of Matrix

Factorizes the \(m \times n\) matrix \(A\) into two unitary matrices \(U\) and \(V^\dagger\), and a diagonal matrix \(\Sigma\) of singular values (real, non-negative) such that

\[A= U \Sigma V^{\dagger}\]

Returns:	\(U\) : a \(m \times n\) row-major matrix \(\Sigma\) : a \(n \times n\) diagonal matrix \(V^{\dagger}\): a \(n \times m\) row-major matrix
Return type:	tuple of Matix

Note

This is a wrapper of the Lapack function Xgesvd()

Matrix.trace()¶

Takes the trace of a square matrix Matrix

Returns:	trace of a square matrix Matrix
Return type:	float
Raise:	RunTimeError if Matrix is not a square matrix

Matrix.transpose()¶

Performs in-place transpose of a Real Matrix. The number of rows and the number of columns are exchanged.

Returns:	Matrix
Return type:	Matrix

Matrix.conj()¶

Performs in-place complex conjugation of elements in Matrix.

Returns:	complex conjugate of Matrix
Return type:	Matrix

Matrix.cTranspose()¶

Performs in-place Hermitian conjugate of a Complex Matrix. The number of rows and the number of columns are exchanged.

Returns:	Matrix
Return type:	Matrix

Matrix.max()¶

Returns the maximum matrix element

Returns:	maximum matrix elements
Return type:	float

Matrix.absMax()¶

Returns the matrix element with the maximum absolute value

Returns:	the matrix element with the maximum absolute value
Return type:	float

Note

This method only works for Real matrix

Matrix.absMaxNorm()¶

Normalizes the Matrix such that the maximum matrix element has absolute value 1

Returns:	normalized Matrix
Return type:	Matrix

Note

This method only works for Real matrix

Matrix.qr()¶

Matrix.rq()¶

Matrix.ql()¶

Matrix.lq()¶

Performs QR, RQ, QL, LQ decompositions of Matrix.

Returns:	A tuple of Matrix of upper(R)/lower(L) triangular matrix and a unitary matrix (Q)
Return type:	tuple of Matrix

Matrix.typeID()¶

Returns datatype of Matrix

Returns:	CTYPE or RTYPE
Return type:	int