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.

class nutils.matrix.Backend

Bases: object

backend base class

assemble(self, data, index, shape)

Assemble a (sparse) tensor based on index-value pairs.


This function is abstract.


list of weak references to the object (if defined)

class nutils.matrix.Matrix(shape)

Bases: object

matrix base class

__add__(self, other)

add two matrices

__mul__(self, other)

multiply matrix with a scalar

__neg__(self, other)

negate matrix


transpose matrix

rowsupp(self, tol=0)

return row indices with nonzero/non-small entries

solve(self, rhs=None, *, lhs0=None, constrain=None, rconstrain=None, **solverargs)

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

  • 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).


Left hand side vector.

Return type


submatrix(self, rows, cols)

Create submatrix from selected rows, columns.

  • rows (bool/int array selecting rows for keeping) –

  • cols (bool/int array selecting columns for keeping) –


Matrix instance of reduced dimensions

Return type


export(self, form)

Export matrix data to any of supported forms.


form (str) –

  • “dense” : return matrix as a single dense array

  • ”csr” : return matrix as 3-tuple of (data, indices, indptr)

  • ”coo” : return matrix as 2-tuple of (data, (row, col))


list of weak references to the object (if defined)


Make rhs optional, add lhs0, constrain, rconstrain arguments.

See Matrix.solve.

class nutils.matrix.Numpy

Bases: nutils.matrix.Backend

matrix backend based on numpy array

class nutils.matrix.NumpyMatrix(core)

Bases: nutils.matrix.Matrix

matrix based on numpy array

class nutils.matrix.Scipy

Bases: nutils.matrix.Backend

matrix backend based on scipy’s sparse matrices

class nutils.matrix.ScipyMatrix(core)

Bases: nutils.matrix.Matrix

matrix based on any of scipy’s sparse matrices