matrix¶

The matrix module defines an abstract Matrix object and several implementations. Matrix objects support basic addition and subtraction operations and provide a consistent insterface for solving linear systems. Matrices can be converted into other forms suitable for external processing via the export method.

exception nutils.matrix.MatrixError¶

Bases: Exception

General error message for matrix-related failure.

__weakref__¶: list of weak references to the object (if defined)

exception nutils.matrix.BackendNotAvailable¶

Bases: nutils.matrix.MatrixError

Error message reporting that the selected matrix backend is not available on the system.

exception nutils.matrix.ToleranceNotReached(best)¶

Bases: nutils.matrix.MatrixError

Error message reporting that the configured linear solver tolerance was not reached. The .best attribute carries the non-conforming solution.

class nutils.matrix.Backend¶

Bases: object

backend base class

abstract assemble(self, data, index, shape)¶: Assemble a (sparse) matrix based on index-value pairs.

Note

This function is abstract.

__weakref__¶: list of weak references to the object (if defined)

class nutils.matrix.Matrix(shape)¶

Bases: object

matrix base class

abstract __add__(self, other)¶: add two matrices

abstract __mul__(self, other)¶: multiply matrix with a scalar

abstract __matmul__(self, other)¶: multiply matrix with a dense tensor

abstract __neg__(self)¶: negate matrix

abstract property T¶: transpose matrix

rowsupp(self, tol=0)¶: return row indices with nonzero/non-small entries

solve(self, rhs=None, *, lhs0=None, constrain=None, rconstrain=None, solver='direct', atol=0.0, rtol=0.0, **solverargs)¶

Solve system given right hand side vector and/or constraints.

Parameters

rhs (float vector or None) – Right hand side vector. None implies all zeros.
lhs0 (class:float vector or None) – Initial values. None implies all zeros.
constrain (float or bool array, or None) – Column constraints. For float values, a number signifies a constraint, NaN signifies a free dof. For boolean, a True value signifies a constraint to the value in lhs0, a False value signifies a free dof. None implies no constraints.
rconstrain (bool array or None) – Row constrains. A True value signifies a constrains, a False value a free dof. None implies that the constraints follow those defined in constrain (by implication the matrix must be square).
solver (str) – Name of the solver algorithm. The set of available solvers depends on the type of the matrix (i.e. the active backend), although all matrices should implement at least the ‘direct’ solver.
**kwargs – All remaining arguments are passed on to the selected solver method.

Returns

Left hand side vector.

Return type

numpy.ndarray

solve_leniently(self, *args, **kwargs)¶: Identical to nutils.matrix.Matrix.solve(), but emit a warning in case tolerances are not met rather than an exception, while returning the obtained solution vector.