Sparse matrix utilities (structsolve.sparseutils)

Utilities for sparse matrices

Removal of the null rows and columns of the system matrices, assembly of symmetric and skew-symmetric matrices from their upper triangle, and a check of symmetry.

structsolve.sparseutils.finalize_symmetric_matrix(M)

Check for nan and inf values and make a matrix symmetric

The stored values of M are checked with assert statements, which are skipped when Python runs with optimizations (-O), and the matrix is completed with make_symmetric() and converted to CSR format.

Parameters:

Msparse matrix

A square matrix with the upper triangle defined, see make_symmetric().

Returns:

M_symcsr_matrix

The symmetric sparse matrix.

Raises:

AssertionError

When M contains nan or inf values.

structsolve.sparseutils.is_symmetric(m)

Check if a sparse matrix is symmetric

The off-diagonal non-zero entries below the diagonal are compared with their transposed entries above it with numpy.allclose(), i.e. with its default tolerances. False is returned without comparing the values when the numbers of stored entries below and above the diagonal differ.

Parameters:

marray or sparse matrix

A square matrix.

Returns:

checkbool

The check result.

Raises:

ValueError

When m is not square.

See also

structsolve.linear_buckling.is_symmetric

check with a relative norm.

structsolve.sparseutils.make_skew_symmetric(m)

Returns a new coo_matrix which is skew-symmetric

Convenient function to populate a sparse matrix skew-symmetricaly, where the off-diagonal elements below the diagonal are negative when compared to the terms above the diagonal. Only the upper triagle of matrix m has to be defined.

The rows, cols and values are evaluated such that where rows > cols the values will be ignored and recreated from the region where cols > rows, with the opposite sign, in order to obtain a skew-symmetric matrix. The diagonal of m is kept as given.

Parameters:

marray or sparse matrix

A square matrix with the upper triangle defined.

Returns:

m_skewcoo_matrix

The skew-symmetric sparse matrix, of the shape and dtype of m.

Raises:

ValueError

When m is not square.

See also

make_symmetric

structsolve.sparseutils.make_symmetric(m)

Returns a new coo_matrix which is symmetric

Convenient function to populate a sparse matrix symmetricaly. Only the upper triagle of matrix m has to be defined.

The rows, cols and values are evaluated such that where rows > cols the values will be ignored and recreated from the region where cols > rows, in order to obtain a symmetric matrix.

Parameters:

marray or sparse matrix

A square matrix with the upper triangle defined.

Returns:

m_symcoo_matrix

The symmetric sparse matrix, of the shape and dtype of m.

Raises:

ValueError

When m is not square.

See also

make_skew_symmetric, finalize_symmetric_matrix

structsolve.sparseutils.remove_null_cols(*args, **kwargs)

Remove null rows and cols of a square sparse matrix.

A degree of freedom is removed when both its row and its column of the first matrix are null, such that an unsymmetric matrix, e.g. with the load stiffness of a follower load, never loses an equation whose row is not null. For a matrix with a symmetric pattern of null rows and columns this is the same as removing the null columns.

Parameters:

argslist of sparse matrices

The first matrix in this list will be used to extract the rows and columns to be removed from all the other matrices. Use csr_matrix to obtain a better performance.

silentbool, optional

Keyword argument telling whether the log messages should be printed. Default False.

kwargskeyword arguments, optional

Only silent is read; other keyword arguments are ignored.

Returns:

outlist of sparse matrices and used columns

A list with the reduced matrices, in CSR format and in the same order of args, plus an array containing the indices of the columns that were kept at the last position.

See also

structsolve.static.solve

uses it before solving.