linalg.stencil#

Functions#

`compute_diag_len`(pads, shifts_domain, ...[, ...])	Compute the diagonal length and the padding of the stencil matrix for each direction, using the shifts of the domain and the codomain.
`flip_axis`(index, n)

Classes#

Inheritance diagram of psydac.linalg.stencil

`StencilDiagonalMatrix`(V, W, data)	Linear operator which operates between stencil vector spaces, and which can be represented by a matrix with non-zero entries only on its main diagonal.
`StencilInterfaceMatrix`(V, W, s_d, s_c, ...)	Matrix in n-dimensional stencil format for an interface.
`StencilMatrix`(V, W[, pads, backend])	Matrix in n-dimensional stencil format.
`StencilVector`(V)	Vector in n-dimensional stencil format.
`StencilVectorSpace`(cart[, dtype])	Vector space for n-dimensional stencil format.

Details#

class StencilVectorSpace(cart, dtype=<class 'float'>)[source]#

Bases: VectorSpace

Vector space for n-dimensional stencil format. Two different initializations are possible:

serial : StencilVectorSpace(npts, pads, periods, shifts=None, starts=None, ends=None, dtype=float)
parallel: StencilVectorSpace(cart, dtype=float)

Parameters:

nptstuple-like (int): Number of entries along each direction (= global dimensions of vector space).
padstuple-like (int): Padding p along each direction needed for the ghost regions.
periodstuple-like (bool): Periodicity along each direction.
shiftstuple-like (int): shift m of the coefficients in each direction.
startstuple-like (int): Index of the first coefficient local to the space in each direction.
endstuple-like (int): Index of the last coefficient local to the space in each direction.
dtypetype: Type of scalar entries.
cartpsydac.ddm.cart.CartDecomposition: Tensor-product grid decomposition according to MPI Cartesian topology.

property dimension#: The dimension of a vector space V is the cardinality (i.e. the number of vectors) of a basis of V over its base field.

property dtype#: The data type of the field over which the space is built.

zeros()[source]#

Get a copy of the null element of the StencilVectorSpace V.

Returns:

nullStencilVector: A new vector object with all components equal to zero.

axpy(a, x, y)[source]#

Increment the vector y with the a-scaled vector x, i.e. y = a * x + y, provided that x and y belong to the same vector space V (self). The scalar value a may be real or complex, depending on the field of V.

Parameters:

ascalar: The scaling coefficient needed for the operation.
xStencilVector: The vector which is not modified by this function.
yStencilVector: The vector modified by this function (incremented by a * x).

property mpi_type#

property shape#

property parallel#

property cart#

property npts#

property starts#

property ends#

property parent_starts#

property parent_ends#

property pads#

property periods#

property shifts#

property ndim#

property interfaces#

set_interface(axis, ext, cart)[source]#

Set the interface space along a given axis and extremity.

Parameters:

axisint: The axis of the new Interface space.
ext: {-1, 1}: The extremity of the new Interface space.
cart: CartDecomposition: The cart of the new space.

class StencilVector(V)[source]#

Bases: Vector

Vector in n-dimensional stencil format.

Parameters:

Vpsydac.linalg.stencil.StencilVectorSpace: Space to which the new vector belongs.

property space#: Vector space to which this vector belongs.

property dtype#: The data type of the vector field V this vector belongs to.

dot(v)[source]#

Return the inner vector product between self and v.

If the values are real, it returns the classical scalar product. If the values are complex, it returns the classical sesquilinear product with linearity on the vector v.

Parameters:

vStencilVector: Vector of the same space than self needed for the scalar product.

Returns:

null: self._space.dtype: Scalar containing scalar product of v and self.

conjugate(out=None)[source]#

Compute the complex conjugate vector.

If the field is real (i.e. self.dtype in (np.float32, np.float64)) this method is equivalent to copy. If the field is complex (i.e. self.dtype in (np.complex64, np.complex128)) this method returns the complex conjugate of self, element-wise.

The behavior of this function is similar to numpy.conjugate(self, out=None).

copy(out=None)[source]#: Ensure x.copy(out=x) returns x and not a new object.

property starts#

property ends#

property pads#

toarray(*, order='C', with_pads=False)[source]#

Return a numpy 1D array corresponding to the given StencilVector, with or without pads.

Parameters:

with_padsbool: If True, include pads in output array.
order: {‘C’,’F’}: Memory representation of the data ‘C’ for row-major ordering (C-style), ‘F’ column-major ordering (Fortran-style).

Returns:

arraynumpy.ndarray: A copy of the data array collapsed into one dimension.

toarray_local(*, order='C')[source]#: return the local array without the padding

topetsc()[source]#: Convert to petsc data structure.

property ghost_regions_in_sync#

update_ghost_regions()[source]#

Update ghost regions before performing non-local access to vector elements (e.g. in matrix-vector product).

Parameters:

directionint: Single direction along which to operate (if not specified, all of them).

exchange_assembly_data()[source]#: Exchange assembly data.

class StencilMatrix(V, W, pads=None, backend=None)[source]#

Bases: LinearOperator

Matrix in n-dimensional stencil format.

This is a linear operator that maps elements of stencil vector space V to elements of stencil vector space W.

For now we only accept V==W.

Parameters:

Vpsydac.linalg.stencil.StencilVectorSpace: Domain of the new linear operator.
Wpsydac.linalg.stencil.StencilVectorSpace: Codomain of the new linear operator.

property domain#: The domain of the linear operator - an element of Vectorspace

property codomain#: The codomain of the linear operator - an element of Vectorspace

property dtype#

dot(v, out=None)[source]#

Return the matrix/vector product between self and v. This function optimized this product.

Parameters:

vStencilVector: Vector of the domain of self needed for the Matrix/Vector product.
outStencilVector: Vector of the codomain of self.

Returns:

outStencilVector: Vector of the codomain of self, contain the result of the product.

vdot(v, out=None)[source]#

Return the matrix/vector product between the conjugate of self and v. This function optimized this product.

Parameters:

vStencilVector: Vector of the domain of self needed for the Matrix/Vector product
outStencilVector: Vector of the codomain of self

Returns:

outStencilVector: Vector of the codomain of self, contain the result of the product

transpose(conjugate=False, out=None)[source]#

” Return the transposed StencilMatrix, or the Hermitian Transpose if conjugate==True

Parameters:

conjugateBool(optional): True to get the Hermitian adjoint.
outStencilMatrix(optional): Optional out for the transpose to avoid temporaries

toarray(**kwargs)[source]#: Convert to Numpy 2D array.

tosparse(**kwargs)[source]#: Convert to any Scipy sparse matrix format.

conjugate(out=None)[source]#

conj(out=None)[source]#

property pads#

property backend#

max()[source]#

copy(out=None)[source]#

Create a copy of self, that can potentially be stored in a given StencilMatrix.

Parameters:

outStencilMatrix(optional): The existing StencilMatrix in which we want to copy self.

remove_spurious_entries()[source]#: If any dimension is NOT periodic, make sure that the corresponding periodic corners are set to zero.

update_ghost_regions()[source]#: Update ghost regions before performing non-local access to matrix elements (e.g. in matrix transposition).

exchange_assembly_data()[source]#: Exchange assembly data.

diagonal(*, inverse=False, sqrt=False, out=None)[source]#

Get the coefficients on the main diagonal as a StencilDiagonalMatrix object.

Parameters:

inversebool: If True, get the inverse of the diagonal. (Default: False). Can be combined with sqrt to get the inverse square root.
sqrtbool: If True, get the square root of the diagonal. (Default: False). Can be combined with inverse to get the inverse square root.
outStencilDiagonalMatrix: If provided, write the diagonal entries into this matrix. (Default: None).

Returns:

StencilDiagonalMatrix: The matrix which contains the main diagonal of self (or its inverse).

topetsc()[source]#: Convert to PETSc data structure.

tocoo_local(order='C')[source]#

property ghost_regions_in_sync#

set_backend(backend)[source]#

class StencilInterfaceMatrix(V, W, s_d, s_c, d_axis, c_axis, d_ext, c_ext, *, flip=None, pads=None, backend=None)[source]#

Bases: LinearOperator

Matrix in n-dimensional stencil format for an interface.

This is a linear operator that maps elements of stencil vector space V to elements of stencil vector space W.

Parameters:

Vpsydac.linalg.stencil.StencilVectorSpace: Domain of the new linear operator.
Wpsydac.linalg.stencil.StencilVectorSpace: Codomain of the new linear operator.
s_dint: The starting index of the domain.
s_cint: The starting index of the codomain.
d_axisint: The axis of the Interface of the domain.
c_axisint: The axis of the Interface of the codomain.
d_extint: The extremity of the domain Interface space. the values must be 1 or -1.
c_extint: The extremity of the codomain Interface space. the values must be 1 or -1.
dimint: The axis of the interface.
pads: <list|tuple>: Padding of the linear operator.

property domain#: The domain of the linear operator - an element of Vectorspace

property codomain#: The codomain of the linear operator - an element of Vectorspace

property dtype#

dot(v, out=None)[source]#: Apply linear operator to Vector v. Result is written to Vector out, if provided.

transpose(conjugate=False, out=None)[source]#: Create new StencilInterfaceMatrix Mt, where domain and codomain are swapped with respect to original matrix M, and Mt_{ij} = M_{ji}.

toarray(**kwargs)[source]#: Convert to Numpy 2D array.

tosparse(**kwargs)[source]#

copy()[source]#

property domain_axis#

property codomain_axis#

property domain_ext#

property codomain_ext#

property domain_start#

property codomain_start#

property dim#

property flip#

property permutation#

property pads#

max()[source]#

property backend#

property ghost_regions_in_sync#

exchange_assembly_data()[source]#: Exchange assembly data.

set_backend(backend)[source]#